As the demand for survey observations continues to grow, the apertures and fields of view of telescopes are expanding correspondingly. This trend results in an increased need for large detectors^[1]. However, material and technological limitations present significant challenges in producing sufficiently large detectors. Consequently, the segmented detector approach has emerged as a key solution to this issue^[2]. Meanwhile，the new technology also introduces its own challenges.

In traditional large aperture telescopes, the smaller focal plane size allows a single detector to meet imaging requirements while maintaining excellent flatness relative to the depth of focus. However, as the field of view expands, larger target planes may lead to imaging quality issues stemming from flatness deviations and errors associated with segmented detectors^[3-6]. Currently, large focal plane detection relies primarily on two methods: contact and non-contact. Contact methods utilize coordinate measuring machines to provide direct, large-span measurements with an accuracy of up to 10 microns. However, these methods risk scratching detector surfaces. Non-contact methods include visual inspection, confocal scanning, geometric triangulation, structured light measurement, and white light interferometry^[7]. Other non-contact techniques involve Hartmann masks and coaxial laser displacement sensors^[8].

The European Southern Observatory (ESO) employs a visual method to measure the displacement of the microscope objective lens using a micrometer scale on the CCD surface. However, due to the close proximity of the microscope lens to the CCD, direct measurement is impossible with a window in front of it. Interferometric surface measurements are limited by their dynamic range and coverage, while the confocal scanning method faces challenges related to axial chromatic dispersion. Structured light measurement can struggle with detector surface reflectivity and microstructure interference, which negatively affects the signal-to-noise ratio. A white light interferometer developed by Ulm achieves approximately 20 nm accuracy using a coherent beam method^[9].

The Royal Observatory at Greenwich (RGO) developed a Hartmann mask method that projects two converging light cones onto a CCD. If the detector is precisely at the focal plane, only one point appears; otherwise, two points indicate surface deviation. Scanning the surface during a single exposure allows for the measurement of height differences. At the ESO’s 2.6-meter VST at Paranal Observatory, 32 stitched 2k×4k CCD sensors are used for its focal plane. Flatness is measured with Keyence’s LK-H082 triangulation laser probe, achieving a peak-to-valley flatness of approximately 18 μm^[10].

Moreover, the methods mentioned above depend on point detection, necessitating translation stages for operation, which limits their ability to achieve rapid in-situ measurements. For larger step differences, mechanical motion along the normal vector can reduce detection precision, hindering the establishment of a continuous traceability chain for optical accuracy. Therefore, future large focal plane detection systems must incorporate a real-time, high-throughput monitoring capability to collect flatness data during system integration.

The flat detection method for segmented detector differs from traditional flat mirror detection, which typically involves continuous surfaces and requires a smaller dynamic range. In contrast, stitched detectors often exhibit significant geometric and angular errors. The Hartmann method, which reconstructs surface figures using slope measurements without requiring a pupil-conversion optical path, offers a wider dynamic range that is particularly suitable for detecting low-order aberrations on a large scale. By leveraging robust slope information and frequency-based reconstruction techniques, we can effectively assess and adjust the flatness of segmented detectors.

Detector tiling involves establishing a final baseline by aligning detectors on the same plane through pairwise measurements. However, any shifts in the benchmark plane can extend the outer edge detectors and complicate the integration of different layouts, ultimately affecting the assembly and positioning accuracy of subsequent detectors, especially for weak and precise measurements^[11-13]. Such shifts and slight tilting can degrade the accuracy of the final data, which is crucial for exoplanet detection. An integrated approach for the front-end optical system ensures continuity with offsets in the micron to nanometer range, while the back-end detector comprises hundreds of tiled segments. System errors from rotation, defocus, and sensitivity differences can result in fluctuations in light intensity, negatively impacting detection accuracy^[14-16].

An architecture for detecting detector flatness is proposed based on optical fiber interconnection, utilizing channel spectroscopy with two-dimensional scanning using a red laser to detect seams on the plane. By measuring the dispersion fringes for coplanar adjustment, the final adjustment residual is improved. Initially, a frequency positioning method locates steps, followed by geometric slope measurements for fine step differences. Some systems can achieve broader accuracy ranges using frequency algorithms. The tolerance of the system’s detector is less than one image circle due to focal plane blur, making the focal plane error dependent on its F-number and vector size. Depending on the required accuracy, either frequency or fringe slope measurement methods are utilized^[17-18].

This paper presents a fiber interconnect architecture that enables multi-point, high-throughput detection by simultaneously measuring at the edges of the detectors. We employ Fourier transform techniques to analyse the interference fringes, determining their step differences, which are then utilized to reconstruct the system's detectors, as illustrated in Fig. 1 (color online).

First, the basic principles of dispersive fringe interference are analyzed, followed by the derivation of the theory of dispersive fringe difference. To verify the consistency and convergence of the final adjustment, the single-point interference intensity is given by:

$ I = {I_1} + {I_2} + 2\left| {{\gamma _{12}}} \right|\sqrt {{I_1}{I_2}} \cos \left( {\frac{{2\Delta L}}{{{\lambda _0}}}2{\text{π}} } \right) \quad,$ (1)

where, I₁ and I₂ are the light intensities of two paths, |γ₁₂| is the multiplex coherence, ΔL is the step difference, and λ₀ is the central wavelength.

Let I₁= I₂= I₀

$ I = 2{I_0}\left[ {1 + \left| {{\gamma _{12}}} \right|\cos \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _0}}}} \right)} \right] \quad,$ (2)

the transverse light intensity distribution is:

$ I\left( {{\lambda _i},y} \right) = 2{I_0}\left[ {1 + \left| {{\gamma _{12}}} \right|\cos \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _i}}} + \frac{{2{\text{π}} d}}{{{\lambda _i}f}}y} \right)} \right] \quad, $ (3)

where, d is the length of the baseline equivalence, and f is the focal length.

$ \frac{{\partial I\left( {{\lambda _i},y} \right)}}{{\partial y}} = 2{I_0}\left| {{\gamma _{12}}} \right|\sin \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _i}}} + \frac{{2{\text{π}} d}}{{{\lambda _i}f}}y} \right) \cdot \frac{{2{\text{π}} d}}{{{\lambda _i}f}} , $ (4)

Performing Fourier transformation on the transverse light intensity distribution as in Equation (4) yields:

$ \begin{split} &FFT\left[ {\frac{{\partial I\left( {{\lambda _i},y} \right)}}{{\partial y}}} \right] = FFT\left[ \frac{{4{\text{π}} {L_0}d}}{{{\lambda _i}f}}\sin \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _i}}}} \right)\cos \left( {\frac{{2{\text{π}} }}{{{\lambda _i}}} \cdot \frac{d}{f} \cdot y} \right) + \sin \left( {\frac{{2{\text{π}} }}{{{\lambda _i}}} \cdot \frac{d}{f} \cdot y} \right)\cos \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _i}}}} \right) \right] {\text{ = }}\\ &\frac{{4{{\text{π}} ^2}{{\bar L}_0}d}}{{{\lambda _i}f}}\left\{ \sin \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _i}}}} \right)\left[ {\delta \left( {\omega + \frac{{2{\text{π}} }}{{{\lambda _i}}} \cdot \frac{d}{f}} \right) + \delta \left( {\omega - \frac{{2{\text{π}} }}{{{\lambda _i}}} \cdot \frac{d}{f}} \right)} \right] + j\cos \left( {\frac{{4{\text{π}} \Delta L}}{{{\lambda _i}}}} \right)\left[ {\delta \left( {\omega + \frac{{2{\text{π}} }}{{{\lambda _i}}} \cdot \frac{d}{f}} \right) - \delta \left( {\omega - \frac{{2{\text{π}} }}{{{\lambda _i}}} \cdot \frac{d}{f}} \right)} \right] \right\} , \end{split} $ (5)

where, $ \omega $ is the frequency domain coordinate, L₀ is the initial distance, λ_i is the wavelength, allowing the detector plane to be adjusted through the FFT of fringe difference.

In terms of detector surface figure reconstruction, it is necessary to employ orthogonal decomposition using basis functions. In practical applications, using an orthogonal basis in a circular domain, such as the Zernike polynomial, can lead to orthogonality degradation in non-circular domains and a corresponding decrease in representation accuracy when discrete sampling is performed. Here, Fourier series are chosen to characterize the wavefront, as the Fourier transform benefits from fast algorithms, significantly improving computation speed.

The discrete Fourier transform is as shown in Equation (6):

$ X\left( k \right) = \sum\limits_{n = 0}^{N - 1} {x\left( n \right){e^{ - j\tfrac{{2{\text{π}} }}{N}kn}}}\quad. $ (6)

Assuming $ x\left( n \right) $ is obtained by differentiation of $ y\left( n \right) $, as shown in Equation (7), we substitute it into Equation (6) to get the intrinsic Equation (8):

$ x\left( n \right) = y\left( {n + 1} \right) - y\left( n \right) \quad,$ (7)

$ \begin{split} X\left( k \right) =& \sum\limits_{n = 0}^{N - 1} {\left[ {y\left( {n + 1} \right) - y\left( n \right)} \right]{e^{ - j\tfrac{{2{\text{π}} }}{N}kn}}} =\\ &\sum\limits_{n = 0}^{N - 1} {y\left( {n + 1} \right){e^{ - j\tfrac{{2{\text{π}} }}{N}kn}}} - \sum\limits_{n = 0}^{N - 1} {y\left( n \right){e^{ - j\tfrac{{2{\text{π}} }}{N}kn}}} \quad, \end{split} $ (8)

$ y\left( n \right) = \frac{1}{N}\sum\limits_{k = 1}^{N - 1} {\left[ {\frac{{X\left( k \right)}}{{{e^{j\tfrac{{2{\text{π}} }}{N}k}} - 1}}{e^{j\tfrac{{2{\text{π}} }}{N}nk}} + \frac{{{e^{j\tfrac{{2{\text{π}} }}{N}k}}y\left( N \right)}}{{{e^{j\tfrac{{2{\text{π}} }}{N}k}} - 1}}{e^{j\tfrac{{2{\text{π}} }}{N}nk}}} \right]} + \frac{{y\left( N \right)}}{N} = \frac{1}{N}\sum\limits_{k = 1}^{N - 1} {\frac{{X\left( k \right)}}{{{e^{j\tfrac{{2{\text{π}} }}{N}k}} - 1}}{e^{j\tfrac{{2{\text{π}} }}{N}nk}}} + \frac{1}{N}\left[ {y\left( N \right) + \sum\limits_{k = 1}^{N - 1} {\frac{{{e^{j\tfrac{{2{\text{π}} }}{N}k}}y\left( N \right)}}{{{e^{j\tfrac{{2{\text{π}} }}{N}k}} - 1}}{e^{j\tfrac{{2{\text{π}} }}{N}nk}}} } \right], $ (9)

Set the highest fitting order be N, and represent the wavefront $ \Phi ({x_1},{x_2}) $ as a discrete Fourier series, as shown in Equation (10):

$ \Phi ({x_1},{x_2}) = \sum\limits_{n = 1}^N {\sum\limits_{m = 1}^N {\tilde \Phi \left( {k,j} \right)} } {e^{j\tfrac{{n{x_1} + m{x_2}}}{N}}} \quad,$ (10)

where n and m are integers, x and y are discrete spatial coordinates, and $ \tilde \Phi $(n, m) are the coefficients of the discrete Fourier series. Transforming Equation (10) yields Equation (11):

$ \tilde \Phi (k,j) = \sum\limits_{x = 1}^N {\sum\limits_{y = 1}^N {\Phi \left( {{x_1},{x_2}} \right)} } {e^{ - j\tfrac{{n{x_1} + m{x_2}}}{N}}} \quad.$ (11)

Based on these formulas, slope sampling and surface figure reconstruction are conducted for segmented detector surfaces. The final results are characterized using a structure function, a sub-scale characterization method. As shown in Fig. 2 (color online), there is a correspondence in the feature space frequencies, and the amplitude differences resulting from the sampling points can be compensated through subsequent calibration. Additionally, amplitude discrepancies caused by sampling can be adjusted during post-calibration. Inspired by concepts from the KECK telescope's edge sensor control matrix, dispersive fringe interference is performed using a non-narrow band light source to obtain local step differences. These step differences are utilized to determine the local slope gradient, aiding in the reconstruction of the overall shape of the target plane. Since the overall tilt of the detector cannot be controlled, precise adjustment of the reference detector's posture is essential.

Here, different resolutions are utilized to measure the surface figure of segmented detectors. Initially, a smaller aperture is employed to facilitate the rapid acquisition of large-range slope gradients of the detector. Additionally, multi-point detection enables comprehensive surface figure acquisition, providing a foundation for subsequent fine focusing. The results of the multi-stage surface figure reconstruction accuracy analysis, based on simulation, are presented in Fig. 3 (color online). The rows of images illustrate the reconstructed surface shapes of the detector at varying sampling rates. The low-resolution reconstruction achieved during the initial system integration can be performed using the existing projection measurement system. As the integration process nears the required accuracy, high spatial resolution calibration through movement becomes essential.

Low-resolution reconstruction sampling, original surface figure, and reconstructed surface figure are represented in Fig 3(a)–(c). Mid-resolution reconstruction sampling, original surface figure, and reconstruction sampling locations are shown in Fig. 3(d)–(f). High-resolution reconstruction sampling, original surface figure, and reconstruction sampling locations are shown in Fig. 3(g)–(i).

A broadband light source illuminates the edges of the detector. Initial rough adjustments are achieved by varying the position of the system’s single component within the coherent length. Fine positional adjustments are then made at the edges using dispersion elements. Simultaneously, a fiber optic interconnection system emits multiple light points on one side of the wide-angle optical system. The shear test is performed on the test piece by observing deviations in the pupil position. The piston error between the two points is utilized to determine the slope of the original piece, from which the required adjustment is inversely calculated. The entire adjustment process is illustrated in Fig. 4 (color online).

Large-aperture optical systems seek longer focal lengths and larger target surfaces to maximize detection capabilities, including resolving power and detection efficiency. However, due to limitations in detector materials and manufacturing processes, larger detectors must be spliced and integrated, requiring the use of multiple detectors for imaging. The unevenness of the spliced surface directly affects the focusing quality of the final energy and the overall image clarity. For spliced detectors, it is essential that the image blur remains smaller than the pixel size; thus, the flatness tolerance depends on both the pixel size and the product of the system's focal ratio. Typically, after splicing, flatness is required to be within 20-30 μm. For dispersive terminals (such as imaging and seamless spectroscopy), the target surface flatness must be better than half the product of the pixel size and the system's focal ratio. The performance parameters detected by stitched detectors are summarized in Table 1.

Referring to Table 1, it can be observed that the detector splices are approximately 1 mm or less. Therefore, assuming that the splice proportion is below 10%, the detection aperture can be set to 10 mm, with the step difference detection accuracy required to be better than 1 μm.

The system employs narrow-band measurement in conjunction with high-dispersion-capability devices to mitigate additional dispersion caused by the periodic structure of the detector itself. Additionally, a standard block made of indium composites, which supports microcrystalline glass, is positioned at the edge of the detector's target surface to serve as the overall tilt reference.

Two segmented mirrors function as equivalent segmented detectors, as illustrated in Fig. 5. The fiber interconnect system projects light into the corresponding positions. During the multi-point measurement process of the boundary, the image is transformed into the frequency domain, enabling the calibration of frequency-related differences.

The direct measurement of fringes and the results of differential detection are presented in Fig. 6. This figure demonstrates that differential detection effectively suppresses background noise. Furthermore, in non-in-phase conditions, differential signals can be obtained in both dimensions. As the system transitions into the in-phase period, the frequency of the differential signal in the non-dispersion direction gradually decreases, as shown in Fig. 7. With improved in-phase accuracy, the signal-to-noise ratio of the differential signal also increases. The measurements were taken using a red-light source with a wavelength of 632.8 nm. Considering the mapping relationship between voltage and displacement in the PZT, the residual achieved through final adjustments is better than 300 nm.

The frequency transformation for high-throughput testing is depicted in Fig. 8, illustrating that the Fourier transformation can be sensed and controlled in parallel.

Future astronomical research will focus on characterizing the cosmos on a larger scale, at deeper levels, and in higher dimensions. Key areas of interest include the space near Earth, the Earth–Moon system within the solar system, and the laws governing matter and life in extragalactic systems. Significant breakthroughs are expected at the forefront of science, including deep, large-area sky surveys that combine multiple wavelengths and methods; the detection of dark matter and dark energy; the discovery of optical counterparts to gravitational waves; exploration of the cosmic dark ages and the dawn of the universe; and a better understanding of the laws governing interactions among celestial bodies within the solar system.

To achieve high integration and uniform near-field projection of beams, a new architecture for multi-field-of-view transmitted wavefront detection is proposed, utilizing densely packed arrayed waveguide gratings (AWG) and telecentric optical paths. This approach overcomes the limitations of bulk optical elements, such as large volume, susceptibility to external vibrations, and temperature gradients. By employing innovative methods of multi-angle, non-perfect imaging testing and leveraging the constraints of discrete apertures instead of whole wavefront testing, the need for large-aperture, high-precision compensation components is eliminated. Consequently, the detection accuracy of the spliced detector step difference exceeds 300 nm, meeting the requirements for future large-aperture, large-field-of-view telescopes.