Adaptive Optics (AO) plays a key role in large-aperture ground-based telescopes, which corrected the wavefront distortions of atmospheric turbulence, and a diffraction image can be obtained. The first step for working AO is the phase aberrations sensed by a Wavefront Sensor (WFS) with a bright beacon adjacent to the science object. Unfortunately, the natural beacon is not populated with sufficient number in the sky, while the Rayleigh beacon is generated near 10 km with a significant cone effect. The sodium beacon was generated by the sodium atoms at 90 km excited with a laser tuned to D2 line, which can probe the turbulence along the cylinder path more completely. Thus, the sodium beacon becomes an essential facility for 10 m class telescopes and the next-generation telescopes.The accuracy of the Shack-Harmann WFS is severely affected by the sodium beacon spot profile. The more compact the spot size and the greater the flux of photon return, the better the measurement accuracy. So, it is essential to estimate the sodium beacon spot profile during the AO system's design phase.The spot profile is determined by the power density at the sodium layer and the photon return efficiency of the laser interaction with the sodium atoms. The power density distribution at the sodium layer is spread by many factors, such as the diameters of the Laser Launch Telescope (LLT), the beam quality of the laser, the turbulence along the uplink path, the static aberrations in the laser launch optical path and so forth. Most of the factors can be optimized in the design of the laser launch system. Thus, the turbulence along the uplink path is a critical factor that should be considered.In this paper, the analyzation was based on the second generation LLT at Gaomeigu Lijiang astronomy observatory with a diameter of 300 mm, the laser is a Quasi-continuous Wave (QCW) solid state sodium laser with a power of 20 W, fabricated by the Technical Institute of Physics and Chemistry (TIPC), the atmospheric turbulence (value of Fried parameter r0 at 550 nm) varies from 5 cm to 30 cm.Firstly, the continuous atmosphere was divided into 4 layers, with altitudes of 0 km, 4 km, 8 km and 12 km, the phase disturbance of turbulence was simulated by phase screen theory. The model of sodium laser propagated in the turbulence was established by angular spectrum propagation, the power density at the sodium layer can be obtained, the photon return efficiency was calculated by Monte Carlo method and rate equation, and the spot profile can be obtained.Secondly, a numerical simulation with 250 frames for the sodium beacon spot profile was conducted; the atmospheric turbulence was discrete into 4 layers, and the power density in each layer and sodium layer was affected by the phase aberrations on the previous layer and described by Fresnel diffraction. The spot profile of FWHM (in x and y direction) and photon return for r0 values varies from 5 cm to 30 cm were exhibited. In order to survey the dispersion of the photon return, a box plot was also exhibited.Thirdly, some factors that affected the spot profile were discussed. The first factor is the layers of the continuous atmosphere discrete, including the number of the layers, the height and the relative strength of each layer. The atmosphere divided into 6 layers at Cerro Pachon in Chile was compared. The spot size is nearly the same with the 4 layers, while the photon return is maximized at r0 of 10 cm, which is caused by diffraction of the phase disturbance. The second factor is the pointing direction of the laser beam, that is, the beam wander caused by tip-tilt. The centroids at different values of r0 were obtained by the statistical method, the maximum value of beam wander can reach 60 cm, while the media value is nearly 22~25 cm when r0 is 5 cm. The precision of centroid extraction is also affected by the high-order aberrations, and the number of layers affects the dispersion of the centroid spot. At last, the scintillation caused by the amplitude fluctuation of the atmosphere was discussed. For the 4 layers condition, the scintillation index increased first and then decreased, the maximum value occurs when r0 is 10 cm, the reason is the scintillation saturation. For the 6 layers condition, the scintillation index is decreased with the increase of the r0.We analyzed the spot profile of sodium beacon which was disturbed by turbulence, the FWHM varies from 0.26 m to 0.22 m, the photon return is at the order of 1.3~1.4×107 photons?s-1?m-2. The number of layers was a critical factor that should be considered, and the beam wander and scintillation were also discussed.

The main function of the Visible-light Telescope (VT) in the Sino French cooperative Space Variable Objects Monitor (SVOM) satellite is to perform high-precision observation of the afterglow of a Space Gamma Burst (GRB). VT is a large aperture, long focal length telescope. Due to differences in ground and space environments, the focal plane position needs to be adjusted during orbit. In the design of VT, the focus function is achieved by adjusting the position of the correction mirror using a focusing motor. In the testing of VT, we found that the thermal elastic deformation at the base of the VT outer baffle can pull the secondary mirror supporter, and causing defocusing of the telescope, but the image quality maintains good condition.According to the main structure design of VT, kinetic analysis shows that when one end of the outer frame of the outer baffle is restricted by a constant temperature barrel assembly, and the other end is pulled by the root of the variable temperature outer baffle, the pulled end will contract inward or expand outward, and the four secondary mirror seat ribs will tilt in the same direction along the optical axis under the drive of the outer frame, driving the secondary mirror to move forward or backward in the optical axis direction. If the temperature at the base of the outer baffle is consistent in the circumferential direction, the stress applied to the outer frame of the secondary mirror supporter is circularly symmetrical and points towards the optical axis. The secondary mirror will only move along the optical axis under the driving force of the ribs, without any deviation or translation, and will not change the parallelism and coaxiality of the primary and secondary mirrors, so the system image quality will not be affected. In addition, when one end of the outer frame of the secondary mirror supporter is limited, the outer frame and ribs form an inverted “L” shaped lever structure with the limited end as the fulcrum. The ratio of the displacement of the secondary mirror to the displacement of the outer frame at one end that is pulled is approximately the ratio of the rib length to the width of the outer frame. Considering the amplification effect of the secondary mirror on the focal plane position, slight changes in the position of the secondary mirror will amplify at the focal plane, resulting in a significant defocus on the focal plane. The phenomenon of synchronous changes in the position of the secondary mirror in the optical axis direction caused by changes in the base of the outer baffle can be used as a focusing method with a larger range of travel for telescopes.In order to further analyze the characteristics of this focusing method, a thermodynamic finite element model of the outer baffle, the secondary mirror components, and the barrel assembly was established in Patran2013 software. The analysis results show that when the temperature at the root of the outer baffle changes within the range of 0 ℃~20 ℃, the relationship between the axial displacement of the secondary mirror and the root temperature of the outer baffle is 3.2 μm/℃. Due to the amplification effect of the secondary mirror, the corresponding focal plane displacement is 115 μm/℃. At the same time, simulation analysis results show that when the temperature at the root of the outer baffle is constant, the impact of temperature changes in the non root area of the outer baffle on the telescope can be ignored.In the thermal equilibrium test of VT, the relationship between the temperature at the root of the outer baffle and the defocus of the telescope was tested. Due to the non ideal characteristics of actual products, thermal equilibrium test data shows that when the temperature at the root of the outer baffle is within the range of 5 ℃ to 20 ℃, there is a good linear correspondence between the defocus amount of VT and temperature. The relationship between the defocus amount and the temperature change at the root of the outer baffle is 0.05 mm/℃, and the defocus range reaches 0.75 mm.Finally, data and experimental verification were conducted on the temperature control accuracy that meets the requirements of telescope depth of field. Based on the variation of VT defocus with the temperature at the root of the outer baffle and the optical design depth requirement of ±0.1 mm, the temperature control accuracy at the root of the outer baffle should be ±2 ℃. Assuming that the energy concentration diameter of the VT within the depth of field does not exceed 5% of the design value, the experimental data indicates that the temperature control accuracy should be ±2.1 ℃.

Membrane diffraction imaging has become an important technology for high-quality imaging of large aperture space telescopes due to the advantages of Diffractive Optical Elements (DOE) such as light weight, loose surface tolerance, small size, foldable and unfoldable, and low cost. The main DOEs include Fresnel Zone Plate (FZP), Photon Sieve (PS), Composite Photon Sieve (CPS) and Stitched Zone Plate (SZP). Among them, the FZP has the advantages of ultra-lightness and foldability, and is widely used in optical microscopy, X-ray imaging, astronomical observation, optical communication, optical ranging and aerospace technology. However, due to the multi-level diffraction characteristics of FZP, its non-imaging diffraction order light becomes a strong background noise of the imaging order light, resulting in low contrast of the imaging image; on the other hand, the inevitable processing errors and structural defects in the FZP manufacturing process lead to low diffraction efficiency of FZP, and introduce wavefront distortion of the imaging beam, resulting in a sharp drop in the resolution of the imaging image. In addition, multi-order diffraction is coupled with the beam wavefront aberration, which leads to further degradation of FZP imaging quality. Many factors limit the performance of FZP diffraction imaging, resulting in the fact that its imaging contrast and resolution cannot meet the high requirements of space imaging applications. In this paper, FZP is used as the primary imaging mirror, and the FZP diffraction imaging system is built to study its image degradation process. Starting from the multi-order diffraction characteristics of FZP, the establishment, solution and optimization of its imaging model are carried out. In view of the problem of FZP multi-order diffraction imaging, the equivalent point spread function method is proposed, the numerical solution of the equivalent point spread function is obtained based on the imaging model, and the image restoration study is carried out. In view of the problem of slow algorithm convergence in the process of solving the FZP imaging model, a FZP diffraction efficiency initial value measurement system and measurement method are designed, a measurement experimental platform is built, the initial value of the FZP diffraction efficiency is obtained, and the algorithm convergence speed is accelerated. Specifically, the FZP diffraction efficiency measurement study is carried out. According to the measurement reciprocity principle, synchronous trigger imaging technology is adopted, and micron-level optical path adjustment is achieved by worm and stepper motor. The FZP diffraction efficiency measurement device is established, and the initial value of FZP diffraction efficiency is obtained by averaging multi-frame image data. The parameter solution and image restoration research based on the imaging model are carried out. The equivalent point spread function method is proposed to characterize the interference of many non-imaging diffraction lights of FZP, and the mathematical relationship between the point spread function, equivalent point spread function and diffraction efficiency of the primary and secondary light of FZP is analyzed, and the FZP imaging model is established; then, the equivalent point spread function is solved based on the FZP imaging model and SPGD algorithm by combining numerical simulation and experiment. To avoid the SPGD algorithm from falling into the local optimum during the iterative solution process, the SA algorithm is used for verification. The similar solution results of the two algorithms prove the feasibility of the method; finally, the experimental research of image restoration is carried out based on experimental data. The experimental results show that the restored diffraction image has improvements in contrast, gradient, etc., verifying the feasibility of the parameter solution method of the FZP imaging model proposed in this paper and the model-based diffraction image restoration research.

Microlens arrays have become indispensable core components in advanced micro-optical systems due to their large field of view, low aberrations, and lightweight characteristics. In recent years, as research in micro-optics has deepened, the manufacturing technology for microlens arrays has also been continuously evolving, particularly with significant progress in producing microlens arrays with complex surface profiles. However, to achieve adjustable performance of microlens arrays in areas such as imaging, 3D display, and optical sensing, we need to integrate more functional components into the microlens arrays, which often leads to increased system size and complexity. Therefore, the practical application of adjustable microlens array still faces many challenges. To address this, the use of smart materials such as shape memory polymers, hydrogels, and piezoelectric materials, driven by external stimuli, offers new approaches for the reconfigurability of microlens arrays. The experimental research process is generally divided into three parts: the preparation of the micro-hole array template, the fabrication of the SMP, and the soft lithography process. First, the femtosecond laser parameters are set to create a pit array on quartz glass. Next, the surface is subjected to wet etching with HF, causing the pits to gradually enlarge over time, resulting in the desired micro-hole array template. The preparation of SMP involves mixing epoxy resin and hardener in a 3∶1 ratio, followed by vacuum treatment in an electric vacuum drying oven. Finally, the SMP is evenly coated onto the micro-hole array template, heated at 65 ℃ for three hours, and then peeled off from the quartz template to obtain the SMP-MLA. The MLA obtained through the above process shows clear and smooth edges, and can produce sharp imaging of objects. Initially, the MLA provides a clear image of the letter “T”. At the transition temperature (130 ℃), by mechanically flattening it, the MLA becomes flat, resulting in a sharp decrease in height. Due to the change in the shape of the MLA, clear imaging of objects is no longer possible. However, when the MLA is reheated to the transition temperature, the shape of the MLA quickly returns to its original state, allowing for clear imaging of objects, showcasing the adjustable functionality of the shape memory MLA. We also measured its focal length and resolution. Subsequently, we used the simulation software Zemax to simulate the microlens, obtaining theoretical focal lengths and resolutions. A comparison of the experimental data with the theoretical data indicates that they are consistent. In summary, this paper successfully fabricated a reconfigurable microlens array using smart materials (SMP). Through simulations with Zemax software, the theoretical focal length of the microlens array was determined to be 45 μm, with a theoretical resolution of 5.692 lp/mm. The experimentally measured actual focal length was 45.7 μm, and the resolution measured using a resolution chart was 5.657 lp/mm, indicating that the experimental data aligns well with the theoretical data. The experimental results show that the shape memory MLA possesses unique plasticity and reversibility. By applying mechanical force, the MLA can temporarily deform into a flat state and maintain this shape, allowing for adjustments to its focusing and imaging behavior for controllable modulation. Once the MLA is flattened under mechanical pressure, simply applying heat can trigger its reconfiguration process, restoring its original optical performance. The measured focal length of the recovered microlens array was 45.175 μm, which shows minimal deviation from the initial focal length of 45.7 μm. This experimental result fully validates the adjustable imaging capabilities of this method.

Inspired by the concept of topological insulators from condensed matter physics, the field of photonic crystal research has advanced rapidly in recent years, particularly in the exploration of topologically nontrivial states. Topological characteristics, as global features, are inherently insensitive to local perturbations, which endows topologically protected edge states with remarkable robustness. This robustness implies that light fields or electrons within such states are not susceptible to defects and impurities introduced by manufacturing errors and are resistant to decay due to backscattering during transmission. As a result, photonic crystals exhibit numerous exceptional properties and hold great promise for a wide range of applications, including optical waveguides, optical beam splitters, optical isolators, and resonant cavities. Notably, research into topological lasers based on photonic crystals has attracted considerable attention.This paper first investigates the parameter combinations necessary to achieve topologically nontrivial states in an infinitely large Su-Schrieffer-Heeger model using tight-binding and transfer matrix methods. The study identifies that the coupling strengths between different lattice sites, the gain and loss, and the presence of an imaginary gauge field are key factors contributing to the system's topologically nontrivial characteristics. After determining the parameters capable of inducing topologically nontrivial states, stable edge states and topological supermode protected by topology are observed in a finite-sized microring resonator array. By solving the rate equations for a semiconductor laser with multiple coupled cavities, the study examines the laser output characteristics under topological supermode conditions. It is found that, within a reasonable range of parameters, lasers composed of coupled-resonator optical waveguide arrays can operate under topological supermode, successfully demonstrating stable laser output characterized by supermode.In theoretical research, the tight-binding method is commonly employed to investigate the energy bands of photonic crystals and calculate their topological invariants in order to reveal the topological properties of these materials. However, the photonic crystals that constitute topological lasers are generally finite-sized systems, and the variations in coupling between laser light fields are significant, which limits the applicability of the tight-binding method. It has been shown that the transfer matrix method offers distinct advantages over the traditional tight-binding method when addressing such challenges. This paper utilizes both the tight-binding and transfer matrix methods based on coupled-resonator optical waveguides to examine the band structure and topological characteristics of both infinitely large and finite-sized Su-Schrieffer-Heeger models. The results indicate that in an infinitely large SSH model, topologically nontrivial states can be effectively realized by adjusting the coupling strengths between lattice sites and introducing an imaginary gauge field, while topological changes solely caused by gain and loss are distinctly observed only in a four-site Su-Schrieffer-Heeger model.In the finite-length Su-Schrieffer-Heeger model composed of coupled-resonator optical waveguides, a system containing 33 microrings was constructed, and the transfer matrix method was employed to verify the conditions for the existence and stability of edge states in finite-length coupled-resonator optical waveguides arrays under various parameter combinations. The study found that when specific conditions are met, the imaginary gauge field gives rise to a new zero-energy mode, referred to as the topological supermode, which is globally distributed throughout the system. Although this supermode does not manifest as localized at the edges, it remains topologically protected and exhibits unique stability as a laser output mode.Finally, the laser output behavior under topological supermode conditions was simulated using laser rate equations. These equations describe the variations in light field intensity and carrier density in microrings over time. A set of reasonable parameters was selected for the study, and dimensionless processing was conducted to facilitate the simulation calculations. The simulation results demonstrate that when the imaginary gauge field satisfies specific conditions,lasers in coupled-resonator optical waveguide arrays can operate under topological supermode. Specifically, the laser output intensity stabilizes rapidly at a fixed value after initial relaxation oscillations, forming globally stable laser output throughout the system. Topological supermode not only exhibit stability within individual microrings but also maintain a consistent light field distribution across the entire array. This global stability is crucial for the continuity and consistency of laser output.To further verify the advantages of topological supermode, the study compared laser output under non-topological supermode conditions. The results indicate that when the conditions for topological supermode are not met, the laser output intensity of individual microrings exhibits oscillatory characteristics, however, the intensity fluctuations are significant and challenging to stabilize. This suggests that laser output under non-topological supermode conditions lacks consistency and stability, demonstrating the superiority of topological supermode in stabilizing laser output. Additionally, the study analyzed the trend of instantaneous amplitude changes in laser output, finding that lasers require a longer time to accumulate energy to achieve the first output during the initial stage. Once stable operation is attained, lasers can continuously output stable laser pulses at shorter intervals. Overall, the introduction of topological supermode significantly enhances the operational stability and output consistency of lasers, providing new insights and methods for the research and application of topological lasers. Moreover, we explored the transition of laser output from a globally distributed topological supermode to a localized topological edge state by adjusting the coupling strength and pump current, offering a novel strategy for controlling the output mode of lasers. The performance of topological supermode lasers and topological edge lasers was compared in terms of threshold and linewidth, laying the foundation for future experimental research.

Nanomechanical Resonators (NRs) not only process the motion characteristics of macroscopic mechanical resonators, while also exhibiting an ultra-small small scale and exceptionally high vibration frequency. By coupling NRs with other microstructures such as quantum dots and photonic crystals, many fascinating quantum optical effects will appear in such hybrid nanomechanical systems. The hybrid NR systems are exceptionally sensitive to small forces and can be driven by electric field, light fields, and other modalities, which attract significant research interest. In such hybrid systems, by changing the coupling between the nanomechanical resonator and other micro-structures, the frequencies of the NRs, and the strength of the driving field, the linear optical properties and nonlinear optical properties often change significantly. In this paper, the hybrid nanomechanical resonator system has been proposed. The system consists of two suspended NRs, one of which is embedded with a quantum dot. The NR systems coupled with quantum dots have received extensive attention, but there are few studies on the nonlinear optical properties of such systems. Our work mainly focuses on investigating the nonlinear optical properties of the hybrid system. Deriving the Hamiltonian for each component of the system, and use the Heisenberg equation to obtain the Langevin equation. Through the solution of above equations using semi-classical theory, the dimensionless linear susceptibility and nonlinear optical susceptibility of the system are calculated. The linear and nonlinear absorption and Kerr coefficient of the system under resonance and red detuning are studied by drawing a spectrum diagram based on the relationship between dimensionless linear susceptibility and nonlinear optical susceptibility and detuning. Finally, the optical characteristics of the system are discussed by adjusting the coupling strength, NRs frequency and Rabi frequencies.We studied the dimensionless linear susceptibility, and observed that two peaks appear at the abscissa Δs/ωm1=±1. The frequency of the nanomechanical corresponds exactly to the location two peaks separate. Within a small range along the abscissa, the dispersion and absorption in the spectrum exhibit significant variations. The dimensionless linear susceptibility reveals that the system has phonon-induced transparency and double-Fano resonances phenomenon. Upon activating coupling strength β between quantum dot and NR1, a peak appears in the spectrum, and the amplitude of the peak increases with the increase of the coupling strength β. The vertical vibrations of quantum dot embedded in NR1 interact with the NR1, resulting the appearance of peaks in the spectrum. Next, we study the nonlinear absorption and Kerr coefficient. After the coupling strength λ between NR1 and NR2 is activated, there is a splitting in the spectrum, and the splitting distance increases with the coupling strength of the peak. To further analyze the coupling parameters, after taking points, drawing and fitting, the results show that a functional relationship exists, which is related to the two coupling parameters and the lateral distance and longitudinal height difference of the splitting peak respectively. On this basis, we propose a method to estimate the unknown coupling strength according to the splitting transverse distance and longitudinal height in the spectral line. In the case of red detuning, we analyzed the Kerr coefficient. With the increase of the frequency of the NR2, the two peaks will move to the right and affect the distance between them, and the horizontal coordinate at the peak of the absorption peak remains unchanged. Increasing Rabi frequencies and detuning does not affect the position and distance between the two peaks, while which can cause the horizontal coordinate of the peak of the absorption peak to move to the right. Finally, we plot the dimensionless linear susceptibility, nonlinear absorption and Kerr coefficient on a graph, and analyzed these results collectively. At Δs/ωm1=-1.1 and Δs/ωm1=-0.9, the linear absorption is negative, and the nonlinear absorption and Kerr coefficient are smaller positive values, which means that phonon-induced transparency occurs here. When the Rabi frequencies or coupling strength β get to zero, the Kerr coefficient will change to zero. By adjusting the Rabi frequencies, it is observed that the peak value of the Kerr coefficient is inversely proportional to the Rabi frequencies.

V2O5 has the highest oxygen state in vanadium-oxygen systems and is the most stable member of the series of vanadium oxides. V2O5 is an n-type semiconductor at room temperature with wide bandgap between 2.2 eV and 2.4 eV, high absorption coefficient, and unique orthorhombic layered structure. Multi-walled carbon nanotubes have unique high mechanical strength, high electrical conductivity, high thermal stability and good electrochemical properties, usually considered as a p-type semiconductor. The synthesis of p-type multi-walled carbon nanotubes with n-type V2O5 will form p-n heterojunction, which increases the Schottky barrier, mobility and quantum effect, and can achieve excellent optoelectronic properties which is conducive to the preparation of optoelectronic devices, such as ultra-high-speed switches, high-frequency and high-speed components, and solar cells. Ions have been doped into V2O5 thin films to improve their optical and electrical properties, and the results show that doping other elemental ions to fill gaps or replace atoms in the lattice can effectively enhance the optical and electrical properties of thin films by forming additional donors or acceptors to facilitate the interband jumps of the phase transition process. In this paper, V2O5/MWCNT nanocomposite films were prepared on quartz substrates by sol-gel method and post-annealing process due to its advantages of being environmental friendly, inexpensive, and requiring simple fabrication. Firstly, 0.5 g V2O5 and 0.33 g MWCNT power were progressively added to the 40 ml H2O2 solution at room temperature while the solution was continuously stirred. After stirring for 3 hours, continued stirring in 75 ℃ water bath until the exothermic reaction was complete, the multi-walled carbon nanotubes were ultrasonically dispersed in the solution at a certain molar ratio of V2O5 to multi-walled carbon nanotubes for 0.5 hour. The solution was continued to be stirred in the water bath for more than 1 hour until the composite gel was formed. Finally, the V2O5/MWCNT composite film was fabricated on quartz substrates by the homogenizer and annealed at 400 ℃ for 2 hours in the furnace. The surface morphology, structure, chemical composition and elements, and optical-electrical properties of the V2O5/MWCNT composite films have been investigated. The SEM image of the surface morphology of the V2O5/MWCNT composite film measured by scanning electron microscopy clearly shows that the composite film has a fine and uniform surface with good crystallinity and lamellar nanostructure. The profiles of V2O5/MWCNT composite films measured by X-ray diffractometer obviously confirm the presence of V2O5 in the composite films. X-ray photoelectron spectra demonstrate that the V2O5/MWCNT composite films contained oxygen, vanadium, carbon and no other elements. The ratio of the areas of C1s and V2p confirms that there is no loss of material content in the preparation process of the composite film. Raman spectra clearly manifest the presence of MWCNT in V2O5/MWCNT composite films. The photoelectric properties of the composite films are analyzed by using spectrophotometry and other instruments. The results show that the doping of MWCNT broadens the band gap of the composite films to 2.42 eV which is wider than that of films without doping of MWCNT, and its resistance is decreased from 52.38 MΩ to 0.97 MΩ when the temperature is increased from room temperature to 270 °C with 5 ℃/min rise rate, which has a change of nearly two orders of magnitude. In the wavelength range of 600~1 200 nm, the average transmittance of the composite film is 58%, and the transmittance variation before and after the phase transition is changed up to 2%. The transmittance is increased under the applied voltage from 0 to 7 V. The composite films have been tested undergoing many high and low temperature cycles with stable performance. Its photoelectric properties have both stable and great reversible thermotropic photoelectric properties, which are expected to be applied in the fields of optoelectronic integration, new photoelectric devices and sensors.

Infrared imaging systems have extensive applications in remote sensing, detection, and reconnaissance, with effective apertures increasingly trending towards larger sizes. The performance of infrared optical systems critically depends on high performance large-aperture infrared materials, particularly since the optical homogeneity of these materials typically ranges from 10-5 to 10-4. The optical homogeneity introduces additional aberrations in the optical systems, leading to an increase in wavefront errors and decrease in imaging quality. High-precision testing of the optical homogeneity of large-aperture infrared materials is essential for optimizing manufacturing processes and serves as a pivotal means for evaluating and compensating for impacts on the performance of infrared transmission optical systems. In response to the growing demand for precise optical homogeneity measurements, this paper employs an infrared interferometer equipped with a spherical standard mirror combined with a collimator to create a large-aperture infrared collimated wavefront. In order to solve the problem that the reflection wavefront of the material's back surface cannot be measured in the traditional four-step method due to the low contrast of the fringes with the increasing thickness of infrared materials, an auxiliary measurement with visible light interferometer is used to test the back surface of the sample, achieving absolute measurement of the material's optical homogeneity without increasing measurement. This method uses the TF of a visible light interferometer as the standard reflector in the testing system, and then uses the TF as the reference surface to measure the back surface maps of infrared materials. The measured wavefront results are analyzed using the proposed Eq. 7 for absolute determination of optical homogeneity in large-aperture infrared materials. The theoretical analysis alongside the testing scheme is illustrated, encompassing four steps: the reflected wavefront of the sample's front surface, the transmitted wavefront, the cavity wavefront of the test optical path, and the reflected wavefront of the sample's back surface. The optical homogeneity testing experiments of the large aperture infrared materials are carried out with the proposed method. A Φ400 mm aperture, 70 mm thickness infrared Ge material is measured and the four steps measurement results are shown, with the homogeneity testing result is 8.89×10-5. In addition, the optical homogeneity of different apertures and thicknesses SI and Ge materials are measured. The experiments indicate that the four step interferometry method based on beam expansion and auxiliary measurement proposed in this paper can effectively measure the optical homogeneity of large aperture infrared material samples. The proposed method successfully resolves the limitations associated with measuring the reflected wavefront on the back surface due to increasing sample thickness. The measurement uncertainty of the proposed method is specifically analyzed in this paper. Furthermore, the study provides a thorough analysis of measurement uncertainty, primarily attributed to system measurement repeatability, TF alignment errors caused by sample wedge angles and positioning inaccuracies, as well as calibration errors in sample thickness and refractive index. The measurement uncertainty for different materials is determined to be better than 3.4×10-5, as summarized in Table 3. This paper validates the feasibility and accuracy of the proposed method through comprehensive optical homogeneity testing and uncertainty analysis for Si and Ge materials across various apertures and thicknesses. By analyzing the optical homogeneity results of several materials, substantial improvements have been achieved—from 10-4 to 10-5-effectively guiding enhancements in the manufacturing processes of large-aperture infrared materials.

Wide bandgap semiconductors, such as AlN, can effectively suppress the temperature quenching effect and expand the spectral range due to their large band gap width. Through the doping of rare earth ions, it is hoped that the excellent optical and magnetic properties of rare earth ions and the good electrical properties of AlN can be integrated. Single-doped and co-doped wide-bandgap materials with different rare earth ions have bright application prospects and high commercial value in many fields such as photoelectric detection and lighting display. Doped rare earth ions usually form a variety of light-emitting centers under the action of defects, and the properties of different light-emitting centers are different, and the complex defect environment also plays an important role in the luminescence of rare earth ions. However, the luminescence intensity of rare earth ions doped with nitride needs to be improved, and the interaction of rare earth ions after co-doping is not clear.In this study, ion implantation was employed to co-dope Tb3+ and Pr3+ into AlN thin films grown on sapphire by metal-organic chemical vapor deposition method and annealed at 1 000 ℃ under normal pressure for 2 h under NH3 atmosphere. During ion implantation, the beam is tilted approximately 10° relative to the normal of the AlN thin film (0002) surface, and the accelerating voltage is 200 keV. In order to characterize the stress changes of the annealed samples with different injection doses, HRXRD and Raman spectroscopy were performed on the samples. Its luminescence performance was measured by a Mono CL3+ cathode fluorescence spectrometer mounted on a Quanta400FEG field emission scanning electron microscope. The influence of varying Pr3+ doses on the structural integrity and luminescence behavior of the samples was systematically investigated. The sample and parabolic mirror remain in the same position throughout the test. The height of the parabolic mirror and the working distance during the test also remain constant. The instrument's acceleration voltage, spot size, aperture size, and integration time are all consistent. All tests were performed at room temperature. Results indicate that, under a constant Tb3+ doses, the introduction of Pr3+ ions increases internal lattice stress. As the doses of Pr3+ increases, due to the cumulative effect, stacking faults or large clusters will be formed in the cascade, making the stacking network denser, and the point defects are easier to pass through the network, and the excess vacancies reaching the surface layer will cause the ion implantation area of the surface layer to shrink, thereby releasing the compressive stress to a certain extent.CL spectroscopy reveals divergent trends in the emission intensities of Tb3+ and Pr3+ with increasing Pr3+ doses. The interaction between Tb3+ and Pr3+ were investigated. It was found that there may be exit energy transfer pathway from Tb3+ and Pr3+in AlN, and the method that regulated the luminescence chromaticity by adjusting the ratio of Tb3+ and Pr3+ was proved. Further analysis suggests the occurrence of resonant energy transfer from Tb3+ to Pr3+, described by the transition 5D4[Tb3+]+3H5[Pr3+]→7F5[Tb3+]+3P1[Pr3+]. CIE software coordinates the luminescent colors in the material to form chromaticity coordinates. Color temperature indicates the temperature at which black will be heated to the desired color, measured in Kelvin. As the Pr3+ doses increases, the chromaticity coordinate shifts from (0.268 2, 0.305 0) to (0.293 7, 0.320 7), with the emission color transitioning from blue-green to yellow-green and the color temperature rising from 7 336 K to 10 260 K. This thesis shows that it is feasible to obtain light emission through Tb3+ and Pr3+ doped AlN, especially the energy transfer between Tb3+ and Pr3+ provides a new idea for the development of novel nitride photoelectric materials.

Quantum cutting is a promising approach to enhance the efficiency of silicon solar cells.The Yb3+ is chosen as the acceptor ion since it has been extensively used for its near-infrared emission around 980 nm (2F5/2→2F7/2), which is just above the bandgap of Si-based solar cells.The efficiency of quantum cutting mechanism via two-step energy transfer from Tm3+ to Yb3+ is investigated in Tm3+/Yb3+ co-doped NaLu(WO4)2 phosphors. Tm3+-doped and Tm3+/Yb3+ co-doped NaLu(WO4)2 phosphors were prepared by a high temperature solid-state reaction method. The crystal structure of the samples was analyzed by X-ray Diffraction (XRD). X-ray diffraction shows that all of samples are pure tetragonal-phased NaLu(WO4)2 powders. It is known that the high doping concentration will result in the concentration quenching which further depresses the quantum cutting efficiency.Through the dependences of emission intensities for all transitions of Tm3+ ,it can indicated that the population of the metastable levels reaches its maximum at around 1 mol%. To achieve effective quantum cutting, the optimum concentration of Tm3+ was determined to be 1 mol% through optical spectral measurements. By analyzing the spectra and luminescence decays of Tm3+/Yb3+ co-doped samples, it was confirmed that Tm3+-sensitized-Yb3+ quantum cutting is achieved via two-step energy transfer processes, namely, the first energy transfer 1G4(Tm)+2F7/2(Yb)→3H4(Tm)+2F5/2(Yb) results in the emission of a 980 nm photon from Yb3+, and the second energy transfer 3H4(Tm)+2F7/2(Yb)→3H6(Tm)+2F5/2(Yb) results in the emission of another 980 nm photon from Yb3+. The luminescence lifetime decay curve of Tm3+ with different Yb3+ concentrations is gradually shortened with the increase of Yb3+ ions concentration, which indicates energy transfer efficiency and quantum efficiency can be improved with the increase of Yb3+ ions concentration.The quantum cutting efficiencies of Tm3+/Yb3+ co-doped NaLu(WO4)2 phosphors were calculated using fluorescence lifetimes of corresponding levels of Tm3+ and Yb3+.The Yb3+ concentration dependent energy transfer efficiency from Tm3+ to Yb3+ has also been evaluated. The results indicate that the quantum cutting efficiencies are relatively low that is because the energy transfer efficiencies are low. The low energy transfer efficiencies are caused by the large energy mismatch in the two-step energy transfers. Meanwhile, it was also found that the back energy transfer from Yb3+ to Tm3+, viz, 3H6(Tm)+2F5/2(Yb) →3H5(Tm)+2F7/2(Yb), displays bad influence to the quantum cutting and depresses quantum cutting efficiency of Tm3+/Yb3+ co-doped materials.The results further complements the theory of quantum cutting that convert one blue photon to two near-infrared photons. This material indicate the potential application in improving the photoelectric conversion efficiency of the silicon based solar cells.

Low-loss chalcogenide optical waveguide is the key basis of chalcogenide integrated photonic devices. At present, the traditional lithography and etching techniques are mainly used to prepare chalcogenide optical waveguide, but chalcogenide glass is easily corroded by alkaline solution and plasma gas during the etching process, which makes it difficult to control the size and shape of the waveguide, and deteriorates the roughness of the waveguide sidewall and surface. Hot stamping technology is a novel technique for preparing nano or submicron scale structures, which is particularly suitable for use in chalcogenide glass film materials with low glass transition temperature. The sidewall and surface of ridge optical waveguide prepared by this method are smoother, thereby reducing surface light scattering and transmission loss. In this paper, As2S3 chalcogenide ridge optical waveguide was prepared by hot stamping method. Through the experiment, it is found that only shallow indentation appeared on the chalcogenide film when the thermoplastic temperature was near the glass transition temperature of As2S3 chalcogenide glass (197 ℃). In order to better fill the mold with the chalcogenide film, the thermoplastic temperature should be increased to 250 ℃. However, the surface of the As2S3 waveguide prepared at the high thermoplastic temperature will have a large number of crystallization and adhesion problems during demolding, resulting in poor surface quality and incomplete profile of the waveguide, and making it difficult to obtain high quality As2S3 chalcogenide ridge optical waveguide. By depositing a layer of Ge20Sb15Se65 chalcogenide film with thickness of about 70 nm on the As2S3 chalcogenide film as a covering layer, the surface degradation of the waveguide layer is inhibited by means of the similar topological connection of chalcogenide glass and the excellent thermal stability of Ge20Sb15Se65. And the simulation results show that after adding the covering layer, the energy of the basic mode optical field is mainly concentrated in the As2S3 waveguide layer, and the optical field in the covering layer area is weak, so the influence of the covering layer on the optical field can be ignored. The experimental results show that a complete waveguide profile can be obtained under the action of Ge20Sb15Se65 covering layer at a thermoplastic temperature of 290 ℃. This thermoplastic temperature can maintain the low viscosity of As2S3 chalcogenide film to fully fill the mold, and also soften the Ge20Sb15Se65 covering layer to easily shape a complete waveguide profile. In addition, in order to obtain high quality waveguide profile after hot stamping, the demolding temperature is also an important parameter affecting the quality of waveguide. The experiments show that too low or too high demolding temperature will increase the difficulty of demolding, resulting in incomplete surface of chalcogenide films. Continuously optimizing the preparation process parameters through extensive experiments, the As2S3 chalcogenide ridge optical waveguide with ridge width of 4 μm and ridge height of 950 nm was prepared with a 70 nm thick Ge20Sb15Se65 chalcogenide film covering layer under the hot stamping process with thermoplastic temperature of 290 ℃, pressure of 0.5 MPa, hot pressing time of 8 min and demolding temperature of 140 ℃, exhibiting complete waveguide morphology. The experiment shows that this covering layer can effectively inhibit the degradation of the As2S3 chalcogenide film during the hot stamping process, and solve the adhesion problem during demolding. By using the cut-back method to measure the insertion loss and linear fitting, the transmission loss of As2S3 chalcogenide ridge optical waveguide is about 0.48 dB/cm@1 550 nm, indicating that the prepared As2S3 chalcogenide ridge optical waveguide with Ge20Sb15Se65 covering layer has low transmission loss. These works provide a new method for preparing low-loss chalcogenide integrated photonic devices.

Photoacoustic Spectroscopy (PAS) technology is an essential technique for detecting gas concentrations due to its rapid response time, strong anti-interference capabilities, high sensitivity, and excellent resolution. These features have made PAS broadly applicable across fields such as atmospheric monitoring, power diagnostics, healthcare, and environmental analysis. In PAS, a modulated laser beam targets gas molecules contained within a sealed photoacoustic cell. Upon absorbing the laser energy, these molecules transition to a high-energy state and subsequently release the absorbed energy through non-radiative decay, returning to their initial state. This process converts the absorbed energy into kinetic energy, causing the periodic heating of the sample and surrounding medium, synchronized with the laser's modulation frequency. This periodic heating induces pressure fluctuations, which generate an acoustic signal. A micro-acoustic sensor then converts this acoustic signal into an electrical signal, enabling the precise measurement of gas concentration through data acquisition and processing. The photoacoustic cell, as the core component of the PAS detection system, serves as the medium for the sample's photoacoustic effect and is crucial for amplifying the signal while maintaining immunity to external interference. The cell’s shape and configuration significantly impact the system's sensitivity and signal-to-noise ratio, underscoring the importance of optimized cell design for advancing both theoretical understanding and practical applications. To enhance photoacoustic cell performance, various structural optimizations have been explored, including resonant cylindrical photoacoustic cells, H-type and T-type cells, ellipsoidal resonant cavities, and hyperbolic busbars. Conventional photoacoustic cell design often relies on finite element analysis to determine optimal dimensions by controlling variables and scanning parameters. However, for complex geometries, this process is time-intensive, creating demand for streamlined methods that can effectively optimize the acoustic and flow characteristics of photoacoustic cells, even with intricate designs. This study proposes a novel parameter optimization approach specifically for irregularly shaped photoacoustic cells, integrating the Design of Experiments (DOE) methodology with the Non-dominated Sorting Genetic Algorithm (NSGA-II). Using this integrated approach, a synaptic photoacoustic cell was designed, and its performance was validated against that of conventional cylindrical photoacoustic cells. The synaptic photoacoustic cell includes several structural components: a resonant cavity, two buffer chambers (both arc-shaped and cylindrical), an acoustic sensor, one air inlet, one air outlet, and two window panes. Key design parameters include the length and radius of the resonant cavity, the radius of the buffer chamber, and the respective lengths of the arc-shaped and cylindrical buffer chambers. The arc-shaped buffer chamber connects tangentially to the resonant cavity, thereby optimizing sound and flow characteristics within the photoacoustic cell. Compared with conventional cylindrical photoacoustic cells, the synaptic photoacoustic cell design offers distinct advantages, including enhanced acoustic signal strength, sound energy efficiency, and reduced noise caused by vortex-induced gas flow disturbances. Additionally, the smaller cavity volume of the synaptic photoacoustic cell reduces sample fill time, enabling faster response rates and a more efficient analysis process. A modal analysis of the first eight acoustic modes reveals increasing complexity with higher modal orders, indicating a sophisticated internal sound distribution. In the second-order mode, sound pressure is maximized in the center of the resonant cavity, where the acoustic sensor can detect signals with enhanced effectiveness. Meanwhile, minimal sound pressure in the buffer chamber makes this area optimal for placing inlets and outlets, as it minimizes external interference with the cell’s performance. This study applies DOE to assess photoacoustic cell parameters with high efficiency, reducing the number of necessary trials while enabling comprehensive evaluation of variable interactions. Specifically, the Box-Behnken response surface method was applied in 41 experiments to analyze sound pressure and quality factor. The response surface proxy model generated from the experimental results reveals nonlinear relationships among the parameters, necessitating a balanced optimization approach. The NSGA-II algorithm, configured with 500 generations and a population size of 50, produced a Pareto-optimal solution set for sound pressure and quality factor. From this solution set, an optimal design was identified, yielding improvements in both parameters over traditional cylindrical photoacoustic cells. The optimized dimensions for the synaptic photoacoustic cell include a resonant cavity length of 30.03 mm, a radius of 3.42 mm, a buffer chamber radius of 29.99 mm, an arc-shaped buffer chamber length of 50 mm, a cylindrical buffer chamber length of 20 mm, and an arc radius of 56.68 mm. Using COMSOL software, this study further simulates and compares the acoustic and flow field characteristics of the optimized synaptic photoacoustic cell against those of traditional cylindrical photoacoustic cells. Results demonstrate a 41.8% increase in sound pressure and a 16.03% improvement in the quality factor. Additionally, the synaptic photoacoustic cell reduces vortex flow area by 62.75% and achieves a 66.27% reduction in volume, enhancing overall system efficiency. In practical NO? gas detection experiments, the synaptic photoacoustic cell exhibits a resonant frequency of 2 553 Hz, a quality factor of approximately 70.16, a rising edge response time of 32 seconds, and a falling edge response time of 28 seconds. Stability tests conducted over five hours indicate a mean signal variance of (3.851±0.023) V, underscoring the synaptic photoacoustic cell's robust acoustic focusing ability, rapid response, and compact structural design. In summary, the synaptic photoacoustic cell developed in this study demonstrates significant improvements in both acoustic and flow field performance. These enhancements provide a substantial upgrade over traditional photoacoustic cells and offer valuable insights for future PAS detection system optimization, enabling more efficient and precise gas detection across various applications.

Space gravitational wave detection is significant for further verifying the theory of general relativity and studying the formation and evolution of the universe. However, in space gravitational wave detection constellations, the interstellar laser links are distant, which puts new requirements on the pointing accuracy of laser precision pointing systems. To compensate for the non-conservative forces on the satellite platform to follow the motion of the test mass, this is usually achieved by a drag-free system utilizing microthruster actuation. However, while the drag-free system compensates for the external non-conservative forces, the perturbation of the microthruster, the measurement noise of the sensors, and the small adjustments of the platform's attitude and position may lead to the angular perturbation of the precision pointing system and thus reduce the pointing accuracy. Therefore, it is necessary to conduct modeling research on the mechanism of micro-perturbations of the drag-free system. Considering that the satellite platform may be affected by various micro-perturbations, including solar light pressure perturbation, temperature interference, and control system micro-perturbations, this paper models the micro-perturbations from three different aspects: mechanics, thermodynamics, and control. In the micro-perturbation dynamics modeling, this paper mainly considers the solar light pressure modeling and the dynamic modeling of the test mass micro-perturbation. Additionally, the modeling and analysis of the mechanism of high-order coupling effect micro-perturbations are carried out. For the solar light pressure modeling, this paper refers to the data of VIRGO to establish a solar light pressure perturbation model considering the influence of random fluctuations in solar light pressure. Since the test mass tracked by the satellite platform does not directly apply a disturbing force to the platform, but the small adjustments in position and attitude when tracking the test mass, as well as the control force applied by the actuator, can both cause disturbances to the precision pointing system. Therefore, dynamic modeling is performed for the test mass. In the part of high-order coupling effect micro-perturbation modeling, this paper conducts perturbation simulation analysis and compares it with the perturbation levels of the former two. Because the perturbation level of high-order coupling effect micro-perturbation is much smaller than the former two, this paper mainly considers the effect of low-order micro-perturbations in the micro-perturbation simulation analysis of the drag-free control system. In the part of micro-perturbation thermodynamics modeling, considering that changes in the orbit cause changes in external heat flow, leading to temperature fluctuations in the detection satellite. Thermoelastic deformation and interference can cause deformation in some structures of the satellite, resulting in optical axis pointing errors and affecting its pointing and tracking performance. Therefore, in this part, the impact of temperature fluctuations induced by solar heat flux on the laser precision pointing system is modeled and analyzed. In the part of control system disturbance source modeling, this paper mainly considers the disturbance modeling of the control system actuator, i.e., the microthruster, and the modeling of the measurement noise of the control system star sensor. Because different micro-perturbations have different response characteristics when transmitted to the target node, and there may be coupling effects between them while propagating in the satellite structure, the modeling of the perturbation transmission model of multiple micro-perturbations in the satellite structure has the problem of transmission coupling. Analyzing and calculating the transfer function of each micro-perturbation to the precision pointing system and simply superimposing the responses does not match the actual situation. In addition, considering that it is difficult to completely replicate the space environment on the ground, it is also difficult to directly analyze the coupling effects of multi-disciplinary micro-perturbations through experiments. Therefore, this paper establishes a micro-vibration transfer function model through finite element modeling. Subsequently, an integrated simulation framework for the micro-vibration of the drag-free system was established to deeply analyze the impact of the micro-vibration of the drag-free system on the laser precision pointing system. Through the integrated simulation analysis of multiple perturbation sources, the results show that under the open-loop condition of the pointing system, the angular response amplitude of the precision pointing mechanism is the largest around the Y-axis, but does not exceed 2.5×10-7 rad, the angular response amplitude around the Z-axis is the smallest, which is below 4×10-8 rad, and that around the Y-axis the angular response amplitude is around 1.5×10-7 rad. In addition, it is noted that the angular response around the Z-axis oscillates within the range of -3.5×10-8 rad, which is due to the dead zone nonlinearity of the microthruster control system. Subsequently, this paper analyzes the role played by each disturbance source of the drag-free system in this process. The simulation results of each perturbation source show that the effects of small adjustments in platform attitude and position and sensor measurement noise on the pointing system are relatively small. However, the microthruster perturbation during the operation of the drag-free system plays a major role in the angular perturbation response of the precision pointing system and can cause system resonance and modal vibration. In summary, when designing the control loop of the space gravitational wave detection satellite, it is necessary to consider the perturbation of the precision pointing system by the drag-free system and to suppress the microthruster perturbation.

Detecting Gravitational Waves (GWs) in the 0.1 mHz to 1 Hz range is a crucial step in exploring the longstanding astrophysical mysteries surrounding the coevolution of supermassive black holes at galactic centers and their host galaxies. It is estimated that GWs can only induce spatial changes on the order of 10-21, which poses a significant challenge for ground-based observatories due to spatial constraints and interference from the ground and atmosphere. Fortunately, space-based GWs observatories can offer promising solutions, where signals are expected to be larger in number and characterized by larger amplitudes. Notable examples include the Laser Interferometer Space Antenna (LISA), Tianqin, and Taiji. All these missions deploy three synchronized satellites in a triangular configuration, separated by arm lengths of 10?~10? meters, forming a colossal interferometer in space. Each satellite houses two free-falling test masses, whose relative displacements are monitored via laser interferometry. By analyzing the movement between these masses with ultra-stable clocks, scientists aim to extract faint GWs buried in noise. The detection of GWs necessitates displacement measurements with an extraordinary precision of tens of picometers. Achieving such precision demands the suppression of noise sources, particularly laser frequency fluctuations, to an extraordinary degree. In addition to optimizing the structure of the interferometer using Pound-Drever-Hall (PDH) frequency stabilization and arm-locking techniques, researchers are now using Time-Delay Interferometer (TDI) techniques to improve the accuracy of gravitational wave detection. TDI represents a computational tour de force: it processes phase data collected from satellites at varying light-travel times and combines them algorithmically to cancel laser frequency fluctuations. For example, differential measurements between satellites are delayed and summed to nullify phase drifts caused by imperfect laser coherence. This approach effectively mitigates noise while preserving GW signatures. A critical subsystem is the timing system. To meet the requirements of GWs detection, phase measurements require clock stability better than 10-15. Traditional atomic clocks meet the stability requirements but are impractical for space missions due to their size, weight, and power consumption. In contrast, quartz clocks offer advantages in size and weight but fall short in stability. Under this circumstance, improving the clock's stability while optimizing its size and structure has become a critical challenge to address. The optical frequency comb-based TDI (OFC-TDI) technique was proposed to simplify the difficulty. OFCs generate ultra-stable, evenly spaced spectral lines across a broad frequency range. OFC-TDI technique uses the repetition frequency of the OFC as the clock for the heterodyne measurements, allowing phase fluctuations to be coherently transferred to microwave signals through its broad spectral characteristics. This approach directly eliminates laser noise, significantly simplifying the system structure and reducing the likelihood of subsystem failures. Recent advancements in miniaturizing mode-locked lasers, the core components of OFCs, have accelerated the development of compact, space-qualified systems. Compared to fiber lasers, solid-state lasers provide superior beam quality and longer lifetime. This paper presents an integrated Kerr lens-locked laser based on an irradiation-resistant Yb∶Y2O3 ceramic for the low-noise clock. The laser is fully integrated into a compact volume of 61 mL. By optimizing the pump structure, all optical components of the laser are confined to an area of 34×78 mm2, which allows for precise temperature control. The temperature control helps the laser achieve a timing jitter of 28 fs. The low power consumption of the laser is only 4 W. The small size, low noise, low power consumption, and long lifetime make the integrated ceramic laser as an ideal tool for gravitational wave detection. In addition, the laser operates near a center wavelength of 1 076.5 nm with a spectral width of 8.58 nm. The relative power stability of the laser is within 0.4% over a two-hour period.

Space gravitational wave detection is a groundbreaking effort to observe spacetime ripples caused by cosmic events. It requires deploying laser interferometry systems with inter-satellite baselines ranging from hundreds of thousands to millions of kilometers. These systems need detect picometer-scale displacements induced by gravitational waves. However, this task faces significant technical challenges. Key challenges include ultra-long interferometric baselines (~1 million kilometers), small telescope apertures (~100 mm), and beam degradation due to space environmental factors such as thermal fluctuations, radiation, and residual gas interactions. These effects lead to substantial laser power attenuation (down to ~100 picowatts at the receiver) and distortions in beam parameters, including wavefront, polarization, and pointing stability. Achieving sub-nanoradian precision in beam pointing control is critical to maintaining phase stability and ensuring a sufficient signal-to-noise ratio. To address these issues, this study introduces an innovative electro-optic beam-pointing control system using lithium niobate (LiNbO3) crystals. This system is designed for high precision, environmental robustness, and scalability. We analyzed various beam-steering technologies, including non-mechanical methods (e.g., electro-optic, acousto-optic, and liquid crystal) and mechanical methods (e.g., fast steering mirrors and rotating prisms). Our analysis highlighted the limitations of current technologies, particularly in terms of precision, adaptability to space environments, and wavefront preservation. The proposed system leverages the superior electro-optic properties of LiNbO? crystals. These crystals have a high electro-optic coefficient (r33=30.9 pm/V at 632.8 nm, r33=29.49 pm/V at 1 064 nm) and excellent optical transparency in the near-infrared range, making them ideal for high-precision beam steering. The core innovation is in the system's symmetric optical design. It actively compensates for effective thermo-optic effects, a critical bottleneck in conventional devices. By placing paired LiNbO? crystal prisms in an antiparallel alignment of the optical axes, the design cancels out thermally induced refractive index gradients. The effective thermo-optic induced refractive index is about 9.3×10??, smaller than the refractive index gradient of LiNbO?, ensuring stability in the harsh temperature conditions of space. We rigorously evaluated the system's performance through simulations and experiments. Voltage-deflection modeling showed a linear response, with 720 nrad of beam steering at 5 V and a resolution of <1 nrad/mV. These results demonstrate the feasibility of real-time adjustments in dynamic space conditions. Prototype devices were fabricated using ultra-precision diamond turning and optical bonding techniques. They achieved a central clear aperture of 2 mm with minimal wavefront distortion. Zygo interferometric measurements (λ=632.8 nm) showed a transmitted wavefront error of 0.2λ RMS, mainly due to limitations in the optical bonding process and surface roughness. However, the error meets the minimal optical requirements for high-voltage deflection testing. Beam deflection tests using a high-resolution infrared CCD camera measured a maximum angular displacement of 1.88 milliradians (mrad) under a 15 kV driving voltage. This result closely matched theoretical predictions. Other metrics include a deflection sensitivity of 125 μrad/kV, allowing precise control with moderate voltage inputs. The beam profile distribution was nearly Gaussian across the temperature range, ensuring minimal sensitivity degradation. These advancements demonstrate the feasibility of LiNbO?-based electro-optic systems for next-generation gravitational wave observatories like LISA (Laser Interferometer Space Antenna), TianQin, and Taiji. Our work contributes to ground verification platforms for testing million-kilometer-scale laser links, filling critical gaps in system-level testing. Moreover, the design is adaptable to other high-precision applications, including quantum communication terminals requiring sub-μrad beam alignment and deep-space laser ranging systems that need robust performance in varying thermal environments. By solving thermo-optic stability and precision issues, this research accelerates the development of reliable large-scale space interferometry and opens new possibilities for advanced photonic technologies in astrophysics and beyond.

Space gravitational wave detection refers to the method of using satellite formation or constellation to construct a large laser interferometer with interference arms of more than ten kilometers or even millions of kilometers in space to detect gravitational waves. One of the key indicators is that the ranging accuracy of laser interferometry needs to be better than 1~10 pm/Hz1/2@0.1 mHz~1Hz. In the intersatellite laser interferometer, which was necessary to use the telescope to collimate and expand the laser beam. Due to wavefront distortion of telescope, light field transmitted to spacecraft 2 will deviate from ideal spherical wave during the intersatellite transmission. After coupling pointing jitter of telescope caused by non-conservative forces and other reasons, the phase of light field received by spacecraft 2 will change with the pointing jitter, which will eventually introduce noise in the measurement system. In order to study the error caused by the coupling of wavefront distortion and pointing jitter, the far-field phase distribution with wavefront distortion was obtained by using Kirchhoff scalar diffraction model and Zernike aberration model. After linearization, the phase and displacement noise related to pointing jitter can be obtained. Using this method, the predecessors established the noise generated by the telescope wavefront composed of different order aberrations and wavefront RMS values after far-field transmission, and analyzed the pointing direction of the telescope to reduce the coupling noise and gave how to make the optimal pointing of the telescope close to the intersatellite visual axis to assist pointing. The above research mainly focuses on analyzing the wavefront quality and aberration distribution of the outgoing pupil of the telescope, and the coupling noise can be quickly extracted by linearizing the far-field phase formula. Due to the accuracy loss in the process of linearizing the far-field phase, the numerical simulation is carried out by using the traversal method with higher accuracy and the traditional method. The simulation results show that there is 25%~100% relative error in the coupled noise distribution field in the range of±100 nrad. To solve this problem, this paper uses the differential evolution algorithm to extract the coupling noise, which solves the optimization problem through the process of biological evolution. It can take the jitter range centered on the static pointing of the telescope as search space, randomly select individuals within the jitter range to get the initial displacement, then judge the new individual position by comparing the difference between individuals, finally converge to the extreme value of the function to get the coupling noise. In the same case of wavefront distortion, the relative error between differential evolution method and traversal method is less than 2%. Finally, differential evolution method is used to extract coupling noise and combined with Monte Carlo simulation to give the pointing jitter index of the telescope transmitter required to achieve the gravitational wave measurement accuracy when different wavefront quality RMS values are given. The simulation results show that if the RMS value of the telescope wavefront quality is λ/60~λ/20, for the couple noise of 10 pm/Hz1/2@0.1 mHz~1 Hz, the pointing jitter of the transmitting telescope should be about 19~34 nrad/Hz1/2@0.1 mHz~1 Hz, and the pointing jitter corresponding to the noise index of 1 pm/Hz1/2@0.1 mHz~1 Hz should be better than 2.1~7.0 nrad/Hz1/2@0.1 mHz~1 Hz. According to the existing design parameters of the outgoing pupil wavefront RMS value of λ/30 in LISA, Taiji and Tianqin, the pointing jitter needs to be better than 21 nrad/Hz1/2 @0.1m Hz~1 Hz and 2.2 nrad/Hz1/2 @0.1 mHz~1 Hz respectively in the measurement frequency band. This result provides a target and reference for the manufacturing and pointing control system of the telescope in the later stage.

Along with the continuous development of aerospace technology, human exploration of outer space has made great progress. During this period, a large number of vehicles have been launched into orbit around the Earth by various countries, led by the United States, but due to a lack of awareness and technology to recover them, they have resulted in space garbage and debris remaining in outer space. According to incomplete statistics, there are thousands of pieces of space debris with a diameter of 10 cm around the Earth, which pose potential hazards for future space exploration and research. Early detection and identification of space debris and timely avoidance are the primary means to ensure the safe operation of satellites and spacecraft. Long-range detection and imaging technology is key to obtaining the relative position information of space debris.For space-based detection and imaging tasks, a reflection system without chromatic aberration is generally used due to the strict requirements on aberration. Among these systems, the three-mirror anastigmat system (Three-Mirror Anastigmat, TMA) is a reflective optical system that can meet the requirements of anastigmatism and a flat image field. Generally, it can be divided into a coaxial three-reflection optical system and an off-axis three-reflection optical system. The coaxial tri-reflective system has the advantages of small size, light weight, good thermal stability, and mature technology, but the disadvantage of reduced system resolution due to central blocking; while the off-axis tri-reflective optical system has a large field of view, no central blocking, and a simple structure, but is difficult to process and adjust and is also susceptible to the influence of external environmental factors, which limits its use under certain conditions. In this paper, by designing the co-axial eccentric-pupil, the center blocking is avoided. The structure is simpler than the traditional coaxial system, while retaining the advantages of the coaxial system in processing and assembly. To further improve space utilization and achieve lightweight and miniaturization, a common aperture spectroscopic structure is adopted. This allows for both high-resolution passive visible light imaging and three-dimensional imaging capabilities using active short-wave infrared imaging. The working principles of the two detection methods differ, as do their applicable occasions, thus eliminating the limitations of a single detection mode and greatly extending the application scope of the entire system.In the front-end optical system design, through the optimization of the initial off-axis structure, we complete the design of the co-axial eccentric-pupil afocal system, with an entrance pupil aperture of 300 mm, an F-number of 8.33, and a full field of view of 0.12°×0.12°. The reflected light from the beam splitter enters the passive imaging system in the back-end optical system. The passive imaging system operates in the 450~850 nm spectral range; the energy distribution within the circular area surrounding the image element is greater than 80%, and the dispersion spots for each field of view are within the Airy disk, indicating strong system detection capabilities and long-distance detection imaging capabilities. Additionally, the optical system's MTF is close to the diffraction limit, providing high-resolution imaging. Furthermore, this paper adopts 4th、5th lens as the compensation mirror group, realizing the design of a continuously adjustable focusing system under conditions ranging from 15 °C to 25 °C and from 1 km to infinity. The image plane position remains unchanged, so there is no need to adjust the position of the focusing plane, reducing the power consumption of the camera. The light transmitted through the beam splitter enters the active imaging system. The active imaging system adopts a common aperture beam splitter structure with integrated transceiver, which improves the coaxial stability of the system and reduces the processing and assembly requirements. The working wavelength of the active imaging system is 1 550 nm, and the wave aberration is better than 1/300λ, which can meet the requirements of laser heterodyne coherent imaging. Finally, the tolerance analysis shows that the system meets the design parameters and actual processing requirements, thus, the design is both effective and rational. In summary, the system has the advantages of high resolution, long focal length, short total length, strong thermal resistance, continuous focus adjustment, and fine imaging quality. To realize long-range tracking imaging of space debris, this design provides a reference for the realization of an integrated optical system for detection and imaging.

When an object with mass accelerates, it produces Gravitational Waves (GWs) that are not easily absorbed or scattered. GW is the only means to study some extreme astronomical phenomena. To overcome the limitations from seismic gravity-gradient noise in ground-based GW observatories, several spaced-based GW observatory projects: LISA, DECIGO, Taiji, and TianQin, have been initiated world widely in the past two decades, aiming to detect GWs in the frequency range from 0.1 mHz to 1 Hz (science band).Spaced-based GW observatory is essentially a laser interferometer consisting of three spacecrafts. Because GW is extremely weak, the frequency noise of the lasers inside the interferometer needs to be suppressed by at least 8 to 10 orders of magnitude to meet the detection requirements. To achieve this goal, three techniques are typically employed. The laser's frequency is first prestabilized to a fixed-length ultrastable optical cavity using Pound-Drever-Hall (PDH) locking method; then the arm length of the constellation, which is much more stable than the laser's frequency in the science band, is used as a reference to further reduce the laser's phase noise, and this is called arm locking technique; finally, the residual laser frequency noise can be canceled by Time Delay Interferometry (TDI), with the help of virtual delays introduced in data postprocessing.Despite significant advances in arm locking techniques over the past two decades, all arm locking controllers reported so far have been based on the traditional forward design approach: first giving the concrete form of the controller and then fine-tuning a small number of parameters. This method has a very limited degree of freedom for optimization, which severely limits the noise suppression performance of the arm locking system.In this paper, for the first time, the inverse design idea is employed for the design of the arm locking controller. A layer structure is used for the controller optimization. The data input layer is responsible for modeling noise, gravitational wave signal and controller parameters; the control architecture layer determines the structure of the arm locking system; and the optimization output layer is responsible for parameter optimization and output. During the optimization, several key characteristics, such as laser frequency noise suppression ratio, peak gain of other noises, gravitational wave sensitivity and zeros and poles of the closed-loop system, are firstly obtained by analyzing the data collected by the phase meter. These characteristics are then combined linearly or nonlinearly to obtain a figure of merit (FoM) function whose independent variables are the feedback controller parameters in the data input layer. Finally, a specific optimization algorithm, such as gradient descent algorithm, is used to obtain the optimal value of the FoM function, and the corresponding controller parameters are returned to the data input layer, thus updating the controller structure in the control architecture layer.Using the method above, the controllers of three noise-coupled architectures, single arm locking, dual arm locking and common arm locking systems, are optimized respectively. The optimization parameters are obtained by searching the local minimal of the FoM function, under the constrains of the arm locking stability criterions we summarized recently.After optimization, the laser phase noise suppression ratio of noise-coupled single arm locking system is above 75.9 dB within the full scientific band, except for those frequencies near the dead zone of the interferometer, and the maximum suppression ratio exceeds 112.7 dB. The laser phase noise suppression ratio for dual arm locking is more than 74.0 dB within the full science band (no dead zones), and approaches 234.0 dB at 0.1 mHz. And for common arm locking this suppression ratio is more than 75.5 dB in the full science band (except for a few frequencies around the dead zones) and can exceed 196 dB at 0.1 mHz. In all the three systems, the GW and technical noise at low frequency range can be amplified, therefore, the signal-to-noise ratio of GW relative to laser phase noise are significantly improved. To verify the performance of the optimized controllers, time domain MATLAB/Simulink simulation is performed for all the three noise-coupled architectures, respectively. By choosing appropriate out-of-loop measurement ports, the technical noise can be well suppressed while GW is still amplified by the locking system. The experimental results show that the signal-to-noise ratio of GW relative to all other noises can be increased by 149.05 dB, 179.62 dB and 171.20 dB, for single arm locking, dual arm locking and common arm locking system, respectively. This work can be generalized to different kinds of arm locking controller design and will effectively improve the sensitivity of the space-based GW observatories.

At the dawn of the 20th century, Einstein's theory of general relativity predicted the existence of Gravitational Waves (GWs). In the early 1 980 s, several ground-based interferometers, such as LIGO and VIRGO, were proposed for GW detection. Due to constraints like limited arm lengths and sensitivity to ground vibrations, these detectors are restricted to detecting GWs with frequencies above 30 Hz. Consequently, the focus of GW research has shifted towards space-based detectors. Noteworthy initiatives in this domain include NASA and ESA's Laser Interferometer Space Antenna (LISA) and China's “Taiji” program, both aiming to measure GWs within the 0.1 mHz to 1 Hz frequency band. The detection of GWs, which induce extremely subtle distance changes, necessitates measurement systems with picometer (pm) precision. To achieve this sensitivity, it is crucial to reduce laser frequency noise by 10 to 12 orders of magnitude from current levels. The prevailing strategy involves a three-tiered noise suppression approach: pre-frequency stabilization, arm locking technology, and Time-Delay Interferometry (TDI). Despite pre-stabilization, laser frequency noise typically remains 2 to 3 orders of magnitude above the TDI requirements, making arm locking frequency stabilization a pivotal intermediate step in further noise reduction. Arm locking systems exploit the relative stability of the spacecraft's arm length within the target frequency band to suppress laser frequency noise. While substantial progress has been made in developing arm locking controllers, there remains a relative paucity of studies focused on the optimization of controller parameters.This paper proposes a controller design method based on a bilayer optimization strategy. The bilayer synchronized optimization strategy consists of two layers: a controller structure optimization layer and a parameter optimization layer. The two optimization layers are synchronized through feedback, with the optimized parameters from the parameter optimization layer fed back into the structure optimization layer to refine the controller design iteratively. In the structure optimization layer, the noise rejection capabilities and stability of different controller structures vary significantly. Implementing zero-pole controllers in parallel with integrators can provide enhanced noise suppression without requiring excessive gain. However, it is important to note that while increasing the number of zero-pole pairs and integrator orders can improve laser frequency noise suppression, it also increases the complexity of the controller design, thereby compromising system stability. At the same time, the different values of the controller zero-pole parameters will also affect the above performance, so the controller parameters need to be optimized by an iterative algorithm after the structure is determined.In the parameter optimization layer, accordingly, in order to compare the performance of controllers with different structures, it is necessary to update the controller structure by feeding back to the structure layer after determining the zero-pole parameter, i.e., forming a two-layer simultaneous optimization strategy in which the controller structure layer and the parameter optimization layer are nested with each other, which can be used to adjust the controller structure through iterative calculations until convergence in a relatively perfect structural model and determine the optimal controller parameters under the structure in a simultaneous manner.In the process of optimization, the objective function for this feedback loop is a linear combination of the amplification at the zero point of the transfer function and the noise suppression ratio at other frequencies to minimize the effect of noise amplification due to the transfer function zeros. The stability and the relative stability of the close-loop system serve as constraints. To ensure absolute system stability, meaning that all poles of the system's closed-loop transfer function are located in the left half-plane of the s-domain, the padé approximation is applied to address the issue of unsolvable characteristic equation poles caused by delay elements. With the delay margin considered as a posteriori condition due to the real-time variations in arm length, the 60th-order approximation is chosen in this paper, after comparing the effects of different order approximations. Once the absolute stability constraints are established, the relative stability of the system can be constrained by evaluating phase margins. Given that the delay time of the actual laser signal fluctuates in real time, robustness against delay fluctuations should be considered as a posteriori condition, in addition to absolute and relative stability as optimization constraints. The range of these fluctuations can be approximately determined by calculating the system's orbital parameters, which can then be used to define the delay margin. Ultimately, this method yields a controller that meets the noise rejection requirements by synchronously optimizing the structure and parameters of the controller, and meanwhile remains stably throughout the system's operational cycle. The final controller can suppress noise by up to 6 orders of magnitude, with the system maintaining a phase margin of 37° at the first zero point.Simulation analysis of the optimized controller demonstrates that it can suppress laser frequency noise by 5 to 6 orders of magnitude in the frequency band below 0.01 Hz, and by 2 to 3 orders of magnitude in the 0.01 Hz to 1 Hz range (excluding the zeros). However, the system's sensitivity to different noise input positions can lead to the amplification of technical noise. Specifically, below 1 mHz, this amplified technical noise may surpass the laser frequency noise, potentially becoming the dominant factor. While this does not significantly affect the overall noise suppression performance of the system, it does limit further improvements in the noise suppression of the single arm locking system. Finally, the accuracy of the simulated system is verified by solving the frequency domain analytical solution, while further showing that the designed controller meets the system requirements.

The high-intensity noises of free-running lasers cannot meet the stringent requirements in the field of precision measurements such as gravitational wave detection. Taking ground-based gravitational wave detection project The Laser Interferometer Gravitational Wave Observatory (LIGO) as an example, its detection sensitivity was significantly improved after suppressing the laser intensity noises in the frequency range of 10 Hz to 10 kHz, which helps to directly observe the first gravitational wave signal in 2015. In order to obtain more information about the universe, researchers have attempted to expand the detection range of gravitational wave to the millihertz frequency range. So far, a few projects on space gravitational wave detection have been initiated around the world. Taking The Laser Interferometer Space Antenna (LISA) and Tianqin as examples, the space gravitational wave projects require laser sources to have their relative intensity noises below 2×10-4 Hz-1/2 in the millihertz frequency range, 2×10-6 Hz-1/2 in the 100 s kilohertz frequency range and 1×10-8 Hz-1/2 in the megahertz frequency range. The seed lasers used in such projects are Non-Planar-Ring-Oscillators (NPRO) solid-state lasers, which have high intensity noises in the millihertz frequency range and high relaxation-oscillation noises in the 100 s kilohertz frequency range. Active noise suppression using feedback control loop must be applied on such lasers to meet the low-intensity noise requirements. The photodetector is one of the key components in active feedback control loop to convert optical signal to electrical signal with high efficiency and low noise. Motivated by the simultaneous suppression of millihertz intensity noise and 100 s kilohertz relaxation-oscillation noises in NPRO lasers, a wide-bandwidth and low-noise photodetector has been designed and tested in this work. The design strategies of this photodetector mainly include the following four points: firstly, select low-noise and high-response PIN-type InGaAs photodiodes to operate in photovoltaic mode to achieve low-noise measurement of weak signals; secondly, use low-noise zero-drift operational amplifiers to build integrators to reduce the contribution to total output noise at low frequencies from the high-speed operational amplifiers; thirdly, select low-noise high-speed operational amplifiers to meet the requirements of high-gain and high-bandwidth; fourthly, build a resistive capacitive network around the high-speed operational amplifier to enhance the cable driving capability. Configurations on the frequency response and noise level of the photodetector are theoretically calculated. Calculation results show that the detection bandwidth of the photodetector is approximate to 16 MHz; the noise level of the photodetector is lower than 1×10-7 V/Hz1/2 in 0.1 mHz to 1 Hz frequency range, and lower than 2×10-8 V/Hz1/2 in 100 kHz to 1 MHz frequency range. Experimental measurements show that the detection bandwidth of the photodetector is approximately 15 MHz; the noise level of the photodetector is lower than 1×10-6 V/Hz1/2 in 0.1 mHz to 1 Hz frequency range, and lower than 5×10-8 V/Hz1/2 in 100 kHz to 1 MHz frequency range. When the output voltage of the photodetector is larger than 1 V,the photodetector is possible to measure a laser with relative intensity noise lower than 1×10-6 Hz-1/2 in the millihertz frequency range, and lower than 5×10-8 Hz-1/2 in the 100 s kilohertz range. Therefore, this photodetector will provide a key support for achieving simultaneous suppression of millihertz intensity noises and relaxation-oscillation noises of NPRO lasers used for space gravitational wave detection or simultaneous suppression of multiband intensity noises of other similar lasers.

Asteroids are inextricably linked to the fate of humanity: their structure and composition provide crucial insights into the evolution of the solar system, and the mineral resources they harbor hold the potential to alleviate Earth's energy crisis. However, the risk of asteroid impacts on Earth is equally significant and cannot be overlooked. Conducting imaging and exploration of asteroids can significantly enhance our understanding of these celestial bodies. In practical asteroid exploration missions, the functions of detection and imaging are typically achieved through either a single camera with multiple optical paths or multiple cameras. To reduce system complexity and manufacturing challenges, this paper proposes an optical system design that integrates both detection and imaging functionalities within a single optical path. Initially, based on the requirements of the asteroid detection mission, the limiting magnitude for detection was determined to be 14th magnitude. This allowed for the calculation of the irradiance at the entrance pupil of the optical system corresponding to this magnitude. Subsequently, by considering the specifications of the selected detector and the signal-to-noise ratio threshold requirements, the necessary entrance pupil diameter was calculated to be 280 mm, with a focal length of 1 472 mm and a full field of view angle of 0.895°. In terms of optical system configuration, the need for a long focal length and large aperture to detect faint stars was taken into consideration. A fully transmissive system would inevitably result in an excessively long overall size, making it susceptible to temperature variations. Additionally, correcting chromatic aberration would require a combination of lenses made from different materials, complicating the achievement of a lightweight design. On the other hand, a fully reflective system could achieve a large field of view and long focal length design without chromatic aberration, but compared to coaxial systems, it might face challenges in overall assembly and alignment. Therefore, this paper combines the advantages of both transmissive and reflective systems by adopting a Ritchey-Chrétien configuration with corrective lenses: the front group eliminates spherical aberration and coma, compressing the axial distance of the system, while the rear group incorporates corrective lenses to address other types of aberrations and simultaneously expand the system's overall field of view. Building upon the calculated initial R-C structure, corrective lenses were incorporated and optimized, resulting in a relatively simple catadioptric optical system with excellent imaging quality. When operating in detection mode, the detector employs 2×2 pixel binning to increase the received light flux, while the focal plane is positioned 0.04 mm outside the ideal focal plane to ensure that 80% of the encircled energy diameter is approximately equal to one binned pixel. In imaging mode, through appropriate focusing adjustments, the system can achieve clear imaging of targets at distances ranging from 10 to 150 km. Tolerance analysis indicates that under reasonable manufacturing and assembly conditions, the modulation transfer function at the edge of the field of view decreases by a maximum of 0.036 compared to the design phase, and the maximum dispersion range of the encircled energy is 5.7 μm. Both values remain within acceptable limits and do not affect the system's normal operation. In terms of stray light suppression, an approximate calculation method was employed to allocate the roughness of each optical surface, resulting in a final backscattered light flux reaching the imaging plane of 3.52×10-16 W. This value is one order of magnitude lower than the target light flux, ensuring that it does not interfere with the system's normal operation. For out-of-field stray light, the suppression requirements for stray light Point Source Transmittance (PST) were calculated using parameters such as the solar constant. To mitigate out-of-field stray light, an external baffle with gradient vertical vanes and internal baffles for the primary and secondary mirrors were designed specifically for this optical system. The optomechanical system, configured with optical surfaces of varying roughness, was then simulated in Tracepro. The results demonstrate that the PST value can reach the order of 10-4 at a 30° off-axis angle, indicating that the overall system meets the operational requirements.

To achieve high-precision terrain mapping and centimeter level surface deformation detection for the new generation of remote sensing satellites, it is necessary to improve the quality and accuracy of Earth observation remote sensing images. In addition to improving the resolution of payloads, satellite platforms also need to provide high-precision attitudes. Star sensors are high-precision satellite attitude measurement sensors, whose measurement accuracy directly determines the accuracy of satellite attitude determination. Their measurement accuracy is mainly affected by factors such as measurement noise of star sensors, installation matrix calibration errors, line of sight drift errors caused by changes in solar irradiation angles, thermal deformation of satellite structures, and optical orbit errors. Therefore, it is necessary to classify the in orbit measurement errors of star sensors, and then calculate, analyze, and correct each type of in orbit error. For this purpose, this article introduces a method for correcting in orbit measurement errors of star sensors.By adjusting detector parameters and optimizing attitude calculation methods, the random noise, noise equivalent angle, and low-frequency error of the star sensor can be reduced ; to improve the design of star sensors through simulation and experimental verification, the thermal stability ability is improved by isolating the installation of the light shield and main frame, optimizing the structural materials and design, and optimizing the optical lens adjustment method ; by calculating the sum of the Earth's revolution speed and satellite motion speed in the coordinate system measured by the star sensor, the angle of optical aberration error is obtained, and the optical aberration correction is performed on the in orbit star sensor .After optimizing the detection parameters, the accuracy of the star sensor's X direction centroid positioning increased by 19.35% and the Y direction centroid positioning accuracy increased by 48.52%. After optimization using dynamic weight algorithm, the equivalent angle of ground observation experiment noise increased by 46.27% in the X direction, 52.17% in the Y direction, and 42.87% in the Z direction . The above optimization methods are validated on the ground and solidified in the internal parameters and software of the star sensor. The star sensor can self correct during in orbit operation, output high-precision measurement data in real time, and do not require satellite attitude and orbit control backend processing. Through in orbit data verification, the random noise of the star sensor is 1.35″ with an equivalent noise angle of 0.99″ and a low-frequency error of 0.91″, which meets the requirements for attitude measurement random error and attitude measurement low-frequency error in the allocation of accuracy indicators for satellite positioning.The independent installation of the sunshade and the optimization method of the optomechanical structural material have been verified through ground simulation and thermal stability tests. It can ensure that the thermal drift effect of the star sensor's line of sight is controlled to 0.1"/℃ when the sun irradiation angle changes alternately in different environmental temperatures during orbit, and high-precision measurement data is output in real-time. The star attitude and orbit control computer can directly use it without the need for backend fitting processing. Through the analysis of four-dimensional satellite in orbit data, the thermal drift of the star sensor's line of sight pointing has been reduced from 7.35" to 1.11", meeting the requirements for thermal drift of the star sensor's line of sight pointing in the accuracy index allocation of remote sensing satellite positioning.This article provides a detailed classification of the in orbit errors of star sensors, analyzes the error sources, and corrects the errors.Firstly, after optimizing the detection parameters and dynamic weight algorithm, and verifying with ground observation and in orbit data, the random noise of the star sensor is 1.35″, which meets the requirements of the accuracy index allocation for satellite positioning in remote sensing.Secondly, through simulation and thermal stability tests, the structure and material optimization design of the main frame material, weight reduction groove, optical lens installation, and independent insulation installation of the light shield of the star sensor are verified. Analysis of in orbit data shows that the thermal drift of the star sensor's line of sight pointing is 1.11″, which is consistent with the results of ground thermal stability tests. At the same time, it meets the requirements for thermal drift of the star sensor's line of sight pointing in the allocation of accuracy indicators for remote sensing satellite positioning.Finally, through the method of correcting optical aberration, the peak value of the trend term of the angle between the optical axes of the star sensor 2a and star sensor 2b in orbit decreased from 15.92″ to 3.63″, a decrease of 12.29″.The above in orbit measurement error correction method is independently completed by star sensors and outputted in real time, without the need for satellite platform backend processing and fitting. It has great engineering application value for obtaining high-quality Earth observation remote sensing images and can meet the needs of the new generation of remote sensing satellites for high accuracy and stability.

Space gravitational wave detection is highly sensitive to low-frequency gravitational radiation within the range of 0.1 mHz to 1 Hz. This frequency band is rich in astronomical events and high-intensity gravitational wave sources, making it a crucial area of research at the forefront of fundamental science. A space-based detector consists of three identical spacecraft flying in an equilateral triangle formation, essentially a giant Michelson interferometer placed in space. The space-time metric is altered when gravitational waves pass through. This "ripples in spacetime" can be reconstructed by observing variations in the distance between two freely suspended test masses. However, the point-ahead angle, which arises during the transmission of laser light over distances ranging from tens to millions of kilometers between two satellites in the gravitational wave constellation, varies due to residual seasonal variations and orbital evolution, making it challenging to fully optimize through orbital parameters alone. The Point Ahead Angle Mechanism (PAAM) is used to correct the beam offset and the residual point-ahead angle errors. It is a prerequisite for establishing inter-satellite laser links and ensuring that the space-based gravitational wave detection laser interferometry system enters the stage of scientific measurement. Additionally, since the disturbances acting on the test masses are extremely minimal, any change in the path length measured by the interferometer arms is attributed to gravitational waves. Thus, the PAAM is required to overcome parasitic displacement to the pico-meter level and ensure very rigid rotation perpendicular to the beam propagation direction to achieve nano-radian accuracy.It is an unprecedented challenge to evaluate the essential performance of the PAAM in terms of both precise pointing accuracy and displacement measurements. The RIJNEVEL N research team developed a picometer-stable scanning PAAM for the LISA mission and tested its performance using a triangular resonant cavity. Specifically, the mechanism was in a closed-loop state at three different positions in a vacuum tank of 10-4 mbar and a temperature environment of 14 μK/Hz1/2. The experimental results proved that the angle jitter noise amounted to below 8 nrad/Hz1/2 (0.1 mHz~1 Hz) and the parasitic displacement noise was within 1.4 pm/Hz1/2 (0.1 mHz~1 Hz), meeting LISA's requirements. However, only displacement noise can be directly measured using the method based on a triangular resonant cavity. Angle noise is indirectly decoupled from angle jitter and path length. Consequently, the accuracy of angle measurement is affected by length measurement noise. Differential Power Sensing (DPS) technology detects the optical axis misalignments along horizontal and vertical direction by received optical power in four quadrants. This technique for measuring variations in laser angles is quick and accurate. Nevertheless, the precision and noise level of incoherent measurements are restricted to microradians, which is inadequate for determining the relative laser angles in space gravitational wave detection applications. Another promising precision angle measurement technology for space applications is Differential Wavefront Sensing (DWS) technology, which is a phase angle sensitive approach with a sensitivity of three to four orders of magnitude using a Quadrant Photodiode (QPD) as the detector. It can integrate angle and displacement measurement in a compact optical path by designing a reasonable laser interference system. Angle values are solved by differential phase of the QPD, while displacement values are computed using the average phase. The correlation problem between displacement and angle noise is essentially resolved by DWS technology, effectively enhancing system stability and dependability compared to the triangle resonant cavity method. DWS technology outperforms DPS technology in terms of measurement accuracy. In 2023, researchers such as ZHU Weizhou from Institute of Technical Physics and GAO Ruihong from Institute of Mechanics, Chinese Academy of Sciences, utilized DWS technology to evaluate the performance of a developed PAAM. The result showed that the optical path delay noise introduced by the mechanism's deflection was less than 10 pm/Hz1/2 (1 Hz~10 Hz). However, there is still significant measurement noise in the low-frequency band below 1Hz, which requires further exploration.This paper presents a heterodyne interferometric optical system designed on the foundation of Gaussian beam interference theory, incorporating DWS technology to achieve high-precision, integrated measurements of both angle and distance. In contrast to the displacement decoupling method utilized in triangular resonant cavity systems, the DWS approach to angle measurement has demonstrated enhanced reliability. The PAAM is placed on the measurement optical path of the heterodyne interference system, establishing a self-closing loop for one-dimensional deflection using angle values from piezoelectric ceramics and capacitive sensors. The angle noise and displacement noise were independently decoupled with the readout phases of the measuring and reference interferometers. The experimental results show that the pointing control noise was better than 10 nrad/Hz1/2 (10 mHz~1 Hz), and the parasitic displacement noise stayed within 10 pm/Hz1/2 (20 mHz~1 Hz) after the system was placed in a vacuum chamber for 72 hours and reached a thermal equilibrium with a temperature of 0.67 mK/Hz1/2 (10 mHz~1 Hz). This mechanism exhibited lower pointing control noise and parasitic displacement noise in the low-frequency range, compared to the test results of domestically advanced PAAM. This validates the PAAM performance indicators and offers a reference for advancing space gravitational wave detection. However, it still lags behind international PAAM and needs further optimization. Meanwhile, according to the noise analysis results of the testing system, it is necessary to focus on overcoming the temperature drift effect and using high-precision positioning stage to further reduce the alignment deviation of the optical path in subsequent testing, thereby suppressing the tilt length coupling noise caused by lateral offset. Overall, this work contributes to enhancing the system resolution of pointing and displacement measurement and is widely applicable to optical precision measurement systems based on laser interference.