Doppler asymmetric spatial heterodyne (DASH) interference spectrum technology inherits many advantages of spatial heterodyne interference spectroscopy^[1] to obtain a more significant interferometric phase^[2]. Since the Doppler differential technology was proposed by Englert et al in 2006, the ARROW prototype was developed by the US Air Force laboratory in 2011^[3], and the speed accuracy was 2 m/s after indoor test. In 2015, the SWIFT-DASH prototype was developed by York University in Canada^[4], the inversion accuracy under 24~60 km wind field can reach 3 m/s. In 2023, the wind field detection instrument MIGHTI^[5], led by the United States Naval Laboratory, has a wind speed detection accuracy of 5 m/s. The DASH interferometer^[6] developed by Xi'an Institute of Optics and Precision Mechanics of CAS in 2023 has an atmospheric wind speed error of about 12 m/s. In the above wind speed detection errors, there are all wind speed errors caused by temperature changes, and this kind of thermal drift error can not be ignored, so it is necessary to study wind speed errors caused by thermal drift of DASH interferometer.

At present, Englert et al.^[7] studied the interferometer reference phase thermal drift, proposed a scheme of synchronous detection of calibration lines, and analyzed the degree of phase thermal drift through the interferometer temperature test conclusion; in Ref. [8], by taking the spatial heterodyne interferometer as the research object, Luo Hai yan et al. analyzed the impact of temperature change on the performance parameters of the mirror group in the spectrometer and each optical system component of the interferometer assembly. The theoretical model was validated by software simulations and thermo-optical experiments; Fu Di et al.^[9] analyzed three factors, namely asymmetric amount phase drift, phase slope drift and interferogram phase drift, by separating the factors influencing thermal stability.

The above research mainly focuses on the evaluation and monitoring of various thermal stability influencing factors of interferometer phase drift, and discusses the thermal influencing factors of interferometer optical elements separately, without thermal integration analysis based on the mutual thermal influence between interferometer optical components and mechanical components, and discussion of the influence degree of optical-mechanical thermal deformation of interference module and imaging optical system on interference phase.

This paper is based on the operating principles of the interference module and imaging optics system of DASH interferometer, the thermal drift of the interference module and imaging optical system is discussed and analyzed according to the error requirements of wind speed detection of the project. In Section 2, the working principle of DASH interferometer is described. In section 3, the optical mechanical thermal analysis model and thermal deformation data acquisition model of the interferometer module and imaging optical system are designed and modeled. In section 4, the thermal deformation and phase drift between the interference arm elements of the interference module are effectively analyzed, and the influence of the deformation of each element of the two arms on the Littrow wavenumber, Littrow angle and optical path difference of the system is given separately and quantitatively. The phase errors caused by the thermal drift of the magnification of the imaging optics system, and the phase drift caused by the relative positions between the imaging optics system and the detector are discussed, and the wind speed error caused by the phase error is given. On the basis, a reasonable temperature control scheme is given. In section 5, the targeted suggestions and summary are given.

The target airglow light ray enters the interferometer through the fore-optical system， the light is split into two beams of comparable intensity by a beam-splitting prism. One reaches the grating G2 and diffracts back to the beam splitting prism, while the other arm reaches the grating G1 and diffracts back to the beam splitting prism. The optical path difference between the beam returned from G2 and the beam returned from G1 is 2Δd, and the two beams meet at the beam splitting prism to form interference fringes. Then, the interference fringes are imaged on the detector by the imaging optical system^[10-16], as shown in Fig 1.

The function of the fore-optical system is to guide the target airglow into the interferometer with a certain field of view, the interference module mainly realizes the beam splitting and merging of the airglow, and realizes the interference of the airglow, and the imaging optical system mainly scales the interference fringe out of the interference module into a certain proportion to image on the detector.

The interference fringe I(x) formed^[17] by two beams on the detector is shown in formula (1) :

$ \left\{\begin{split} &I\left(x\right)={\int }_{0}^{\infty }B\left(\sigma \right)\cdot T\left(\sigma \right)[1+\cos\varphi (x\left)\right]{\mathrm{d}}\sigma \\ &\varphi \left(x\right)=2{\text{π}} \left[4(\sigma -{\sigma }_{{\mathrm{L}}})\tan{\theta }_{{\mathrm{L}}}\frac{x}{{R}_{\text{im}}}+2\sigma \Delta d\right]\end{split}\right. \quad,$ (1)

At this time, the frequency of the interference fringe formed by the interference of two beams of light is shown in formula (2)^[12]:

$ f\left(x\right)=4\cdot (\sigma -{\sigma }_{\rm{L}})\tan{\theta }_{\rm{L}}\quad, $ (2)

where σ is the target airglow wavenumber，σ_L is Littrow wavenumber, θ_L is Littrow angle, ∆d is the single optical path difference of airglow, x is the pixel coordinate of the detector, representing optical path differences, B(σ) is the radiation brightness of the incident spectrum, T(σ) is the wavenumber responsivity function of the optical system, and R_im is the magnification of the imaging optical system.

Based on the working principle of the Doppler heterodyne interferometer and formula (1), it can be seen that the interference phase is related to Littrow angle, Littrow wavenumber, imaging magnification and optical path difference. The fore optical system will not affect the interference phase, but the optical machine structure of the interference module and imaging optical system will directly affect the interference phase. Therefore, this paper mainly implements the optical, mechanical and thermal integration analysis of interference module and imaging optical system, and discusses the wind speed detection error.

The DASH interferometer mainly uses the Fourier transform method to obtain the interference phase, and then obtains the wind speed by interference-based the absolute phase difference. Because the two arms of the interferometer are fixed, the two dimensional interference fringes are obtained within a large optical path difference interval by static interference. The interferogram consists of hundreds of sampling points of optical path difference, and the phase information at the near-point of each optical can be obtained by Fourier transform method. The interference phase difference corresponding to the frequency can be obtained through subtracting the reference phase of zero wind speed from the absolute phase in equation (1) ^[14,18]:

$ \delta \varphi =\varphi -{\varphi }_{0} \quad.$ (3)

Then the wind speed is calculated by equation (4):

$ v=\frac{c\cdot \delta \varphi }{4{\text{π}} \sigma \Delta d} \quad,$ (4)

where c is the speed of light.

The interferometer opto-mechanical-thermal integration analysis involves the optical system structure, mechanical structure and thermodynamic coupling analysis. Through the data interaction analysis, the heat situation of the system in the real environment was simulated. Thermal integration analysis process is shown in Fig. 2. Firstly, the overall design of the interferometer was given based on the DASH interferometer principle, and the finite element model was built by importing the designed model to analysis software. The thermal analysis model was generated by adding the mechanical load and ambient temperature of the system, the original data and deformation data of the thermal analysis model were obtained. At last, the performance of the optical-mechanical system under different thermal loads was discussed^[19].

Based on the principle of DASH interferometer, and considering the sensitivity of interference module in interferometer system to temperature change, the interference module was designed by using thermal compensation design^[20]. The beam-splitting prism adopts the existing product specifications. The design of field-widening prism, wedge spacer and detector design are described in detail in the Refs. [14-16]. The overall parameters of the interferometer are shown in Table 1.

In order to verify the correctness of the interferometer system design, the interferometer model was established in the optical analysis software ZEMAX according to the design results. The non-sequential mode was used for tracking simulation, and the dot matrix light sources with the object plane of 1000×1000 and the light source interval of 0.01 mm were set to simulate the target light source entering the interferometer^[21]. The interferometer model is shown in Fig. 3, and the simulation interference fringe is shown in Fig. 4 (color online).

According to formula (2), when the wavelength of the target spectral line is 557.7 nm, the interference fringe frequency is 1.2287. Since the detector size is from −6.66 mm to 6.66 mm, the theoretical interference fringe number is 16.36. From simulation result in Fig.4, it can obtain not only the fringe number, but also the fringe spectrum under different columns. The simulation interference fringe number is 15.61, which differs from the theoretical number of interference fringes by 0.75 fringes. The error is caused by the dispersion effect of glass^[21]. After the grating inclination is fine-tuned to 0.0015° in the simulation, the number of interference fringes is consistent with the theoretical value. As shown in Fig. 5, the design results are consistent with the design index, and the final physical diagram of the interferometer is shown in Fig. 6.

Interference module and imaging optical system are the core components of the optical machine system of the interferometer. Although the reasonable thermal compensation design has been adopted to weaken the composite effect of external heat flow on the interference module, but the thermal compensation design is specifically targeted at optical elements. Furthermore, optical materials and mechanical materials are different, and the changes of external thermal radiation flow will cause position changes in each optical and mechanical element, resulting in deviation from the design value^[22-24]. Moreover, the spectral line drift and phase error still exist^[25-31]. Therefore, thermal analysis models of optical and mechanical components are established separately.

The interference module is made up of beam-splitting prism, field-widening prism, wedge spacer and diffraction grating. Fig. 7 shows the overall design structure of the interference module, including the design angles between components, the optical axis represented by the dotted line and the light beam represented by the solid line.

The relationship between the wedge angle of the wedge spacer, the vertex angle of the field-widening prism and the wedge angle of the grating spacer is given^[17] by formula (5), which can ensure that the light parallel to the optical axis in the detection field of view enters the grating at a Littrow angle through any arm：

$ \left\{\begin{split} &\frac{{n}^{2}-1}{{n}^{2}}\cdot \frac{2{n}^{2}-{\rm{sin}}^{2}\gamma }{{n}^{2}-{\rm{sin}}^{2}\gamma }\cdot \rm{tan}\gamma =\rm{tan}{\theta }_{\rm{L}}\\ &n\rm{sin}\left(\frac{\alpha }{2}\right)=\rm{sin}\gamma \\ &{\theta }_{\rm{L}}=\eta +\gamma \\ &{\sigma }_{\rm{L}}=\frac{m}{2d\cdot \text{sin}{\theta }_{\rm{L}}}\end{split}\right. \quad,$ (5)

where n is the refractive index of the field-widening prism, m is the diffraction order, usually set as 1.

When the temperature changes, the thermal effect of the interference module comes from the thermal changes of the refractive indexes of the beam-splitting prism and the two arms of the field-widening prism, and the thermal expansion of the wedge spacer. The thermal effect will cause the above components to deviate from the initial design, and change the optical path difference (∆L) of the system, Littrow angle, Littrow wavenumber, and the magnification (R_im) of the imaging optical system, thus affecting the interference phase and reducing the accuracy of wind speed measurement. Assuming that d₁ and d₂ are the thickness of the wedge spacer, n₁ is the refractive index of the parallel bias, t₁ is the thickness of the parallel bias, and the optical path difference meets:

$ \Delta L=2\Delta d=2({n}_{1}{t}_{1}+{d}_{1}-{d}_{2})\quad. $ (6)

When the environmental temperature changes, the thermal change of the component will lead to the thermal change of the optical path difference:

$ \begin{split} &\Delta L\left(T\right)=2\Delta d\left(T\right)=\\ & 2\left({n}_{1}\right(\Delta T)\cdot {t}_{1}(\Delta T)+{d}_{1}(\Delta T)-{d}_{2}(\Delta T\left)\right)\quad. \end{split} $ (7)

According to formula (5), when thermal deformation occurs in the optical-mechanical structure of the interference module, the Littrow angle can be regarded as being influenced by the angles of various elements and the temperature drift of refractive index of the field-widening prism, and the Littrow wavenumber can be regarded as being affected by the Littrow angle and the thermal variation of grating grooving density. Thus the Littrow wavenumber and Littrow angle with respect to the temperature change can be described as^[18]:

$ \left\{\begin{split} &{\theta }_{\rm{L}}\left(\Delta T\right)=\eta \left(\Delta T\right)+{\mathrm{arc}}{\rm{sin}}\left(n\left(\Delta T\right)\cdot {\rm{sin}}\left(\alpha \left(\Delta T\right)-{\rm{arc}\sin}\left(\frac{1}{n\left(\Delta T\right)}{\rm{sin}}\left(\gamma \left(\Delta T\right)\right)\right)\right)\right)\\ &{\sigma }_{\rm{L}}\left(\Delta T\right)=\left(\frac{1}{d}\left(\Delta T\right)\right)\frac{m}{\text{2sin}\left({\theta }_{\rm{L}}\left(\Delta T\right)\right)}\\ &n\left(\Delta T\right)=n\left(\lambda,{T}_{\text{20} \;\text{°C}}\right)+\frac{{n}^{2}\left(\lambda,{T}_{\text{20} \;\text{°C}}\right)-1}{2n\left(\lambda,{T}_{\text{20} \;\text{°C}}\right)}\left({D}_{0}\Delta T+{D}_{1}\Delta {T}^{2}+{D}_{2}\Delta {T}^{3}+\frac{{E}_{0}\Delta T+{E}_{1}\Delta {T}^{2}}{{\lambda }^{2}-{{\lambda }^{2}}_{TK}}\right)\\ &\frac{1}{d}\left(\Delta t\right)=\frac{\dfrac{1}{d}\left({T}_{20 \;\text{°C}}\right)}{1+{\alpha }_{{\mathrm{T}}}\Delta T}\end{split}\right.\quad, $ (8)

where n(λ,T_{20 °C}) is the relative refractive index at the design temperature and D₀、D₁、D₂、E₀、E₁、λ_TK is the refractive index temperature coefficient constant, α_T is the thermal expansion coefficient of diffraction grating.

As the DASH interferometer belongs to localized interference, the size of the actual interference fringes formed by coherent light from two arms can not be directly matched with the size of the detector, so the imaging optical system needs to image the interference fringes onto the detector with a certain magnification (R_im). The interference fringe size of the interferometer can be obtained as W'cosθ_L, and the theoretical imaging scaling ratio of the final imaging optical system^[19] is shown in formula (9) :

$ {R}_{{\mathrm{im}}}=\frac{N\times P}{W'\times {\rm{cos}}{\theta }_{\rm{L}}}\quad, $ (9)

where N is the number of pixels, P is the pixel size, and W' is the effective width in the diffraction direction. Thermal deformation of imaging optical systems usually includes rigid body displacement and surface deformation. Rigid body displacement is caused by thermal expansion and cold contraction deformation of external mechanical structure, and surface deformation is caused by optical element stress^[23]. The combination of these four kinds of thermal changes will cause magnification drift. Therefore, when the interferometer performs wind speed inversion by interferometric phase, the drift of the magnification will directly affect the interferometric phase. Thermal drift of imaging optical system mainly includes two ways. Firstly, the thermal drift of the magnification of optical system directly affects the interference phase^[9]:

$ \left\{\begin{split} &{R}_{\text{shift}}={R}_{\text{im}}+{R}_{\text{im}}\left(\Delta T\right)\\ &{\varphi }_{1}\left(x\right)=8{\text{π}} (\sigma -{\sigma }_{\rm{L}})\tan{\theta }_{\rm{L}}\frac{x}{{R}_{\text{im}}\left(\Delta T\right)}\end{split}\right. \quad,$ (10)

where R_im(∆T) is the thermal drift value of the imaging magnification, and $ {\varphi }_{1} $ is the phase difference caused by the thermal drift of the magnification.

Secondly, when the temperature changes, there will be a relative displacement between the imaging optical system and the detector with a displacement amount of:

$ {\varphi }_{2}=\frac{2{\text{π}} \cdot D\left(\Delta T\right)\cdot {R}_{\text{im}}}{{M}_{\text{pixel}}\cdot {N}_{\text{pixel}}}\quad, $ (11)

where D(∆T) is the thermal drift value of the relative position between the imaging optical system and the detector, M_piexl is the number of pixels of the detector, N_piexl is the number of pixels corresponding to the single-period fringe, and $ {\varphi }_{2} $ is the phase thermal drift value caused by the thermal change of the relative position between the imaging optical system and the detector.

In summary, based on the above Littrow wavenumber thermal drift value σ_L(∆T), Littrow angle thermal drift value θ_L(∆T), optical path difference thermal drift value ∆d(∆T), and the thermal changes and the relative position changes of imaging optical system, when there is a thermal change in the environment, the phase of the interference changes as:

$ \begin{split} \varphi \left(x\right)= &2{\text{π}} \left[4\left(\sigma -\left({\sigma }_{\rm{L}}+{\sigma }_{\rm{L}}\left(\Delta T\right)\right)\right)\tan\left({\theta }_{\rm{L}}+{\theta }_{\rm{L}}\left(\Delta T\right)\right)\times\right. \\ &\frac{x}{{R}_{\text{im}}+{R}_{\text{im}}\left(\Delta T\right)}+2\sigma \left(\Delta d+\Delta d\left(\Delta T\right)\right)+\\ &\left.\frac{D\left(\Delta T\right)\cdot {R}_{\text{im}}}{{M}_{{\mathrm{pixel}}}\cdot {N}_{{\mathrm{pixel}}}}\right] \quad.\\[-9pt] \end{split}$ (12)

In order to effectively monitor the Littrow wavenumber thermal drift, Littrow angle thermal drift and optical path difference thermal drift caused by the deformation of the above components, based on the parameters of the interferometer described in section 3.1, an optical model and its physical diagram are established, as shown in Fig. 8.

The optical-mechanical model is modeled by linear material characteristics, and the glass material parameters are set based on the data provided by the manufacturer. The working platform is made of aluminum alloy. The fore- and back of the interference module are connected by mechanical structure, and the components are fixed to the working platform through adhesive bonding and nut to ensure the operation stability of the system. The fluid domain within the interferometer’s optical chamber is filled with air, and the density, specific heat capacity and thermal conductivity are 1.127 kg/m³, 1.004 kJ/kg·K and 0.271 W/mK, respectively. The optical-mechanical model and physical picture are shown in Fig. 9. The materials and indicators are shown in Table 2.

The finite element selection and thermal integration analysis of the optical mechanical structure of the interference module and imaging optical system was carried out by using the thermodynamic analysis software ANSYS^[17]. These finite element cells provide data sources for the subsequent analysis for the temperature changes of each component at different temperature loads. This article adopts a hexahedral finite element mesh, and the nodes and elements of the hexahedral finite element mesh can better approach the real experimental conditions, and the density of the finite element mesh in this paper is relatively dense and closer to the real results. Other constraints are completely consistent with the actual working conditions, and the mesh type and element density are simulated by adopting more accurate data, which improves the authenticity and accuracy of the simulation. The finite element model is shown in Figure 10.

In this case, the thermal integration analysis software can not directly get the component angle and thickness change caused by thermal deformation, so it is necessary to establish reference points to monitor thermal deformation. According to the working principle of the interferometer module, the thermal deformation of each element in the X direction will not affect the overall working performance of the interferometer module, while the deformation of the elements in the Z and Y directions will affect the performance of the interferometer module^[17]. Therefore, 8 reference points are selected in each of the G1 and G2 arms of the interferometer, they are located on one side of the prism, on both sides of the field-widening prism and on one side of the grating diffraction surface, respectively. They are all located in the center of the interference module in the X direction, and each reference point is 15 mm away from the optical axis, as shown in Fig. 11. The local coordinate system is established at the reference point. By extracting the coordinate changes in the local coordinate system in the thermal analysis software, the changes of the wedge angle and thickness of the wedge spacer, the field-widening prism and the grating spacer under different thermal loads can be monitored, as shown in Fig. 12.

The imaging optical system is selected as a double telecentric structure to ensure that the system has a large depth of field range^[31]. When the environment temperature changes, the light emitted by the lens has better optical performance to a certain extent. The housing is made of aluminum alloy 2A12 material, the structure of the optical machine is shown in Fig. 13, and the physical picture is shown in Fig. 14 . The finite element model is established in thermal analysis software to analyze the working performance of the imaging optical system after being affected by heat.

The detector is connected to the detector support base through a flange, maintaining a coaxial relative position with the detector branch, and finally fixed to the bottom plate. Adjustable pads are placed between the detector and support base, as well as between the support base and the bottom plate. A light shield is placed between the detector branch and the detector to eliminate the influence of the external light source on the detection target source. The flange, support base, adjustment pads and bottom plate are all made of aluminum alloy 2A12, and the material characteristics are described in Table 2. In order to monitor the relative position changes between the imaging optical system and the detector, the models of the imaging optical system and the detector were established, as shown in Fig. 15. A coordinate system was established with the center of the detector’s image plane position as the origin, setting the initial position at 20 °C and as the coordinate origin. In the software, the relative position thermal drift between the imaging optical system and the detector is monitored by the relative change of coordinate position.

Based on the thermal analysis model of the interference module in Section 3.1, the basic temperature of the optical-mechanical system of the interference module is 20 °C, the boundary temperature are 12 °C and 28 °C, and the temperature rise step is 0.05 °C. The heating situation at each temperature is described by a separate load, which can illustrate the deformation of the optical-mechanical structure of the interference module under the influence of the environment temperature during operation. The thermal analysis cloud map of the interference module is shown in Fig. 16 (color online), and the thermal deformation cloud map of the interference module is shown in Fig. 17 (color online).

As the optical analysis software cannot analyze the mechanical part of the thermal analysis model, after the thermal analysis, it is necessary to carry out optical and mechanical separation of the obtained data, to extract the original and deformed data of the optical part in the optical and mechanical structure. At this time, the extracted optical part has been influenced by the mechanical part, and the position coordinates of the 16 reference points established in the model have included the angle change between components. Then, the thermal deformation analysis is carried out based on formula (8). The relationship between Littrow angle and temperature of G1 arm and G2 arm of interferometer are shown in Fig. 18 (color online), and the relationship between Littrow wavenumber and temperature is shown in Fig. 19 (color online).

The analysis of the above data shows that the thermal drift of each element angle will affect Littrow wave number, Littrow angle and optical path difference. The variation of interference phase error caused by the drift of the interference G1 arm and the interference G2 arm at different temperatures is shown in Figure 20 (color online).

Based on formula (6) and formula (7), the relationship between the thermal drift value of the optical path difference of the interferometer and temperature can be obtained as shown in Fig. 21, and the interference phase change caused by the optical path difference is shown in Fig. 22.

For interference module G1 arm, the thermal deformations of grating spacer’s wedge angle and wedge spacer’s wedge angle have a great influence on Littrow wavenumber and Littrow angle, occupying the main influencing factor. For interference module G2 arm, the thermal deformations of the wedge angle of wedge spacer and the vertex angle of field-widening prism have a great influence on Littrow wavenumber and Littrow angle. In summary, the phase drift of the G1 arm is more serious than that of the G2 arm, and the phase error caused by the thermal drift of G1 arm has reached 0.09750 rad/ °C and the phase error caused by the thermal drift of G2 arm has reached 0.06506 rad/°C. The phase thermal drifts of G1 arm and G2 arm are different, due to the different materials used by the two arms and the different placement methods of the two arms in the mechanical structure. Fig. 23 (color online) shows the wind speed error caused by thermal drift of G1 arm and G2 arm. Due to its large wind speed error, only the wind speed error caused by thermal deformation at 19.5 °C-20.5 °C is given in Figure 23 (color online).

The phase error caused by thermal drift of optical path difference reaches 3.4285×10⁻⁵ rad/°C. The wind speed error caused by optical path difference thermal drift at different temperatures is shown in Fig. 24. It can be seen that the phase drift caused by thermal drift is small, because the thermal compensation design is adopted in the design of interference module, and the thermal deformation between components can compensate each other, and the thermal drift of optical path difference can be reduced to a certain extent.

Therefore, referring to the current research status of detection accuracy of atmospheric wind field^[32], and in consideration of current temperature control means and technical challenges, it can be concluded that controlling the overall temperature of the interference module at (20±0.05) °C can control the phase drift caused by the heating of the interference module, and correspondingly the wind speed error within 3.8 m/s. In addition, the temperature control device should be mainly installed on the grating spacer and the wedge spacer of G1 arm, the wedge spacer and the field-widening prism of G2 arm for more stable and accurate temperature control, and reducing the wind speed error caused by temperature changes.

Aiming at the the thermal drift of imaging optical system, based on the thermal analysis model constructed in section 3.3, the basic temperature of the optical-mechanical system of the interference module is 20 °C, the boundary temperatures are set as 12 °C and 28 °C, and temperature rise step is 0.2 °C. The cloud map of the thermal analysis of the imaging optical system is shown in Fig. 25 (color online), and the thermal deformation cloud map of the imaging optical system is shown in Fig. 26 (color online).

After thermal analysis of optical-mechanical structures, the deformation data of the optical element can be obtained by processing the finite element node data. The deformation data includes two parts: surface deformation and rigid body displacement, which cannot be analyzed directly in the optical analysis software, so it is necessary to separate the two parts. Then, the rigid body displacement coordinates of translation and rotation between the surfaces are fitted by using Zernike coefficients, and the corresponding data are imported into the optical analysis software ZEMAX for analysis^[33]. The changes of magnification of the imaging optical system at different temperatures are shown in Fig. 27. The variation error of magnification at different temperatures is shown in Fig. 28 . The phase error caused by the thermal drift of magnification at different temperatures is shown in Fig. 29.

Aiming at the changes in the relative positions of the imaging optical system and the detector, the initial temperature of the imaging optical system and the detector as a whole is set as 20 °C, the boundary temperatures are set as 12 °C and 28 °C, and the temperature rise step is 0.2 °C. The thermal analysis cloud map of the relative position between the imaging optical system and detector is shown in Fig. 30 (color online).

By analyzing the coordinate information of the detector’s image plane, the changes of relative position between the imaging optical system and the detector can be obtained as shown in Fig. 31. The relationship between the phase thermal drift caused by relative position change and temperature is shown in Fig. 32.

According to the above phase error results, the drift of magnification of the imaging optical system is affected by the combined effect of rigid body displacement and surface deformation. The wind speed error caused by magnification thermal drift at different temperatures is shown in Fig. 33. The wind speed inversion error caused by the change of magnification of the imaging optical system cannot be ignored. According to the detection accuracy requirements of current wind interferometer and temperature control technology, it is necessary to control the temperature fluctuation of the imaging optical system within (20±2) °C, and ensure that the wind speed error is within 3.05 m/s.

In addition, the wind speed error caused by thermal drift of the changes of relative position between the imaging optical system and the detector at different temperatures is shown in Fig. 34. It can be seen that the error is small and can be ignored.

In this work, based on DASH interferometer, an opto-mechanical-thermal integrated analysis model of interference module and imaging optical system is designed and established. Through software simulation and data fitting, it is shown that the interference module occupies the main influence factor in the optical-mechanical-thermal deformation. It is necessary to control the temperature fluctuation of the overall interference module within (20±0.05) °C, especially focusing on the temperature control of the grating spacer and wedge spacer in the interference G1 arm, wedge spacer and field-widening prism in the G2 arm, correspondingly the temperature control components should be installed in these positions. The wind speed error caused by the part is 3.8 m/s. The thermal deformation of the imaging optical system and the changes of relative position between the imaging optical system and the detector are secondary factors, and their temperature needs to be controlled at (20±2) °C, and the wind speed error caused by the part is 3.05 m/s. In summary, the wind measurement error caused by interference module, imaging optical system, the relative position between the imaging optical system and the detector can be controlled within 6.85 m/s. This paper proposes targeted temperature control for temperature sensitive components, analyzes the degree of error in imaging optical systems, and suggests the corresponding temperature control measures, offering a theoretical support for the engineering implementation of the DASH interferometer.

多普勒非对称空间外差干涉光谱技术(DASH)继承了空间外差干涉光谱技术诸多优点，并拥有更大光程差^[1]，可以获得更加显著的干涉相位^[2]。2006 年，Englert 等人首次提出多普勒差分技术，在此基础上，2011年，美国空军实验室研制ARROW样机^[3]。经室内测试速度精度为2 m/s。2015年，加拿大约克大学^[4]研制出SWIFT-DASH 样机，24~60 km 风场反演精度可达 3 m/s。2023年，由美国海军实验室^[5]主导研制的风场探测仪器MIGHTI，其风速探测精度为5 m/s。2023年，中国科学院西安光学精密机械研究所研制的DASH干涉仪^[6]，其大气风速误差约为12 m/s。以上的风速探测误差均包含由温度变化导致的风速误差。该类热漂移误差不可忽略，因此有必要对DASH干涉仪由于热漂移造成的风速误差进行研究。

目前Englert等人对干涉仪基准相位热漂移进行了研究，提出校准线同步检测方案，并根据干涉仪温度试验结论分析了相位热漂移的程度^[7]。罗海燕等人以空间外差干涉仪为对象，分析了温度变化对光谱仪中镜组以及干涉仪各光学系统组成部分性能参数的影响，通过软件仿真和热光学实验对理论模型进行了验证^[8]。傅頔等人通过分离热稳定影响因素，对非对称量相位漂移、相位斜率漂移及干涉图相位漂移这3项因素进行了分析^[9]。

上述研究主要针对干涉仪相位漂移的多种热稳定性影响因素进行评估和监测，对于干涉仪光学元件的热影响因素进行了分离讨论，但并没有对基于干涉仪光学部件和机械部件之间的相互热影响进行热集成分析，也没有研究多普勒差分干涉仪干涉模块和成像光学系统热变形对于干涉相位的影响程度。

本文基于DASH干涉仪干涉模块和成像光学系统的工作原理，结合数值分析和软件仿真，根据项目风速探测误差要求，对干涉模块和成像光学系统的热漂移进行讨论和分析。在第2节，介绍了DASH干涉仪的工作原理和风速反演原理。在第3节，设计并建模了干涉仪的干涉模块和成像光学系统的光机热分析模型和热变形数据获取模型。在第4节中，有效地分析了干涉模块干涉臂元件之间的热变形和相位漂移，并分别定量给出了两臂各元件变形对系统的Littrow波数、Littrow角和光程差的影响，以及由这些因素造成的相位误差，讨论了成像光学系统放大倍率的热漂移和成像光学系统与探测器相对位置的热漂移所产生的相位误差，并给出相位误差所导致的风速误差，进而给出了合理的温控方案。在第5部节，给出了针对性的建议和总结。

目标气辉光线通过前置光学系统进入干涉仪内部，光线经过分束棱镜形成两束强度相当的光束，其中一臂到达光栅G2发生衍射后返回分束棱镜，另一臂经过反射到达光栅G1后发生衍射，返回分束棱镜。从G2返回的光束与从G1返回的光束光程差相差2 Δd，两光束于分束面相遇并形成干涉条纹，再由成像光学系统将干涉条纹成像于探测器，如图1所示^[10-16]。

其中前置光学系统的作用在于引导目标气辉以一定视场进入干涉仪内部。干涉模块主要用于气辉的分束和合束，实现气辉的干涉。成像光学系统主要将干涉模块出口处的干涉条纹以一定比例进行缩放成像至探测器。

两束相干光在探测器上所形成的干涉条纹I(x)为^[17]：

$ \left\{\begin{split} &I\left(x\right)={\int }_{0}^{\infty }B\left(\sigma \right)\cdot T\left(\sigma \right)[1+\cos\varphi (x\left)\right]{\mathrm{d}}\sigma \\ &\varphi \left(x\right)=2{\text{π}} \left[4(\sigma -{\sigma }_{\rm{L}})\tan{\theta }_{\rm{L}}\frac{x}{{R}_{\text{im}}}+2\sigma \Delta d\right]\end{split}\right. \quad,$ (1)

此时，两束光干涉形成的干涉条纹的频率如式（2）所示^[12]：

$ f\left(x\right)=4\cdot (\sigma -{\sigma }_{\rm{L}})\tan{\theta }_{\rm{L}}\quad, $ (2)

其中，σ 为目标气辉波数，σ_L 为Littrow波数，θ_L为Littrow角，∆d 为气辉经过的单次光程差，x为探测器像元坐标，不同的取值代表不同的光程差，B(σ)为入射光谱辐射亮度，T(σ)为光学系统波数响应度函数，R_im为成像光学系统的放大倍率。

由多普勒外差干涉仪的工作原理和式（1）可知，干涉相位与Littrow角、Littrow波数、成像倍率和光程差有关，前置光学系统不会对干涉相位造成影响，但干涉模块和成像光学系统的光机系统将直接影响干涉相位，因此本文主要针对干涉模块和成像光学系统进行光机热集成分析，讨论其风速探测误差。

多普勒外差干涉仪主要利用傅立叶变换法获取干涉相位，再通过干涉绝对相位差分获得风速。由于干涉仪两臂固定，通过静态干涉在一个大光程差间隔内可获得二维干涉条纹。干涉图由几百个光程差采样点组成，每个光程差点处的相位信息可以通过傅立叶变换求解。式（1）中绝对相位中减去零风速的基准相位，即可得到该频率所对应的干涉相位差^[14,18]：

$ \delta \varphi =\varphi -{\varphi }_{0} \quad,$ (3)

进而求出风速：

$ v=\frac{c\cdot \delta \varphi }{4{\text{π}} \sigma \Delta d} \quad,$ (4)

其中c为光速。

干涉仪光机热集成分析涉及光学系统结构、机械结构以及热力学耦合分析。通过数据交互分析，模拟系统在真实环境的受热情况，热集成分析流程如图2所示。给出干涉仪的总体设计图，建立分析模型，将其导入分析软件中建立有限元模型，同时附加机械载荷和环境温度生成热分析模型。获取热分析模型的原始数据和变形数据，讨论在不同热载荷下的系统工作性能^[19]。

基于DASH干涉仪原理，并考虑到干涉仪系统中干涉模块对于温度变化的敏感性，在进行干涉模块设计时常采用消热差设计^[20]。分束棱镜采取现有产品规格，扩视场棱镜、楔形垫片和探测器规格选取方案均在文献[14-16]中有详细叙述，本文不再赘述，干涉仪总体参数如表1所示。

为验证干涉仪系统设计的正确性，依据设计结果在光学分析软件ZEMAX中建立干涉仪模型，采用非序列模式进行追迹仿真，设置物面为1000×1000的点阵光源，光源间隔为0.01 mm，以模拟目标光源进入干涉仪的工作状态^[21]。干涉仪模型如图3所示，仿真干涉条纹如图4（彩图见期刊电子版）所示。根据式（2）可知，当目标光谱线波长为 557.7 nm 时，干涉条纹频率为1.228 7。由于探测器尺寸为−6.66~6.66 mm ，理论干涉条纹数为16.36。ZEMAX仿真干涉条纹图如图4所示，不仅得到了条纹数，还得到了不同列下的条纹数谱。可以看出仿真干涉条纹数为15.61，与理论干涉条纹数相差 0.75个条纹。这个误差是由玻璃的色散效应造成的^[21]。在模拟中将光栅倾角微调到 0.001 5°后，干涉条纹数与理论值一致，如图 5（彩图见期刊电子版）所示。表明该设计结果符合设计指标，最终干涉仪实物图如图6所示。

干涉模块和成像光学系统是干涉仪光机系统的核心部件，虽然在设计中采用了合理的热补偿设计来减弱外部热流对干涉模块的复合效应，但热补偿设计仅针对光学元件，而光学材料和机械材料是不同的，另外，外部热辐射流的变化会引起光学和机械元件的变化，从而偏离设计值^[22-24]，并且光谱线漂移和相位误差仍然存在^[25-30]，因此，分别建立两者的热分析模型进行讨论。

干涉模块由分束棱镜、扩视场棱镜、楔形垫片与衍射光栅胶合而成。图7为干涉模块光学元件结构图，图中标出了各元件之间的角度，虚线代表光轴，实线代表光线束。

楔形垫片楔角、扩视场棱镜顶角与光栅垫片倾角的相互制约关系由式(5)给出^[17]。这样可以保证探测视场内平行于光轴的光经过任意一臂时都以Littrow角入射光栅。

$ \left\{\begin{split} &\frac{{n}^{2}-1}{{n}^{2}}\cdot \frac{2{n}^{2}-{\rm{sin}}^{2}\gamma }{{n}^{2}-{\rm{sin}}^{2}\gamma }\cdot \rm{tan}\gamma =\rm{tan}{\theta }_{\rm{L}}\\ &n\rm{sin}\left(\frac{\alpha }{2}\right)=\rm{sin}\gamma \\ &{\theta }_{\rm{L}}=\eta +\gamma \\ &{\sigma }_{\rm{L}}=\frac{m}{2d\cdot \text{sin}{\theta }_{\rm{L}}}\end{split}\right. \quad,$ (5)

其中n为扩视场棱镜折射率，m为衍射级次，通常取1。

当温度发生变化时，干涉模块的热效应来源于分束器、两臂扩视场棱镜折射率的热变化，以及垫片的热膨胀。热效应会使以上元件偏离设计值，从而使光程差(∆L)、Littrow角、Littrow波数、成像光学系统成像放大倍率R_im改变，降低风速测量精度。

针对系统光程差(∆L = 2∆d)的热漂移，设d₁、d₂分别为空气间隔厚度，n₁为平行偏置板的折射率，t₁为平行偏置板的厚度，两臂上分束器和垫片差异产生的光程差满足：

$ \Delta L=2\Delta d=2({n}_{1}{t}_{1}+{d}_{1}-{d}_{2})\quad, $ (6)

当环境温度发生变化时，元件的热变化会导致光程差的热变化:

$ \begin{split} &\Delta L\left(T\right)=2\Delta d\left(T\right)=\\ & 2\left({n}_{1}\right(\Delta T)\cdot {t}_{1}(\Delta T)+{d}_{1}(\Delta T)-{d}_{2}(\Delta T\left)\right)\quad, \end{split} $ (7)

由式(5)可知，当干涉模块的光机械结构发生热变形时，Littrow角可视为受各元件角度、扩视场棱镜折射率温漂所影响，Littrow波数可视为受Littrow角、光栅凹槽密度的温漂所影响，由此得到描述Littrow波数与Littrow角与温度变化^[18]的关联公式(8)：

$ \left\{\begin{split} &{\theta }_{\rm{L}}\left(\Delta T\right)=\eta \left(\Delta T\right)+{\rm{arcsin}}\left(n\left(\Delta T\right)\cdot {\rm{sin}}\left(\alpha \left(\Delta T\right)-{\rm{arcsin}}\left(\frac{1}{n\left(\Delta T\right)}{\rm{sin}}\left(\gamma \left(\Delta T\right)\right)\right)\right)\right)\\ &{\sigma }_{\rm{L}}\left(\Delta T\right)=\left(\frac{1}{d}\left(\Delta T\right)\right)\frac{m}{\text{2sin}\left({\theta }_{\rm{L}}\left(\Delta T\right)\right)}\\ &n\left(\Delta T\right)=n\left(\lambda,{T}_{\text{20} \;\text{°C}}\right)+\frac{{n}^{2}\left(\lambda,{T}_{\text{20} \;\text{°C}}\right)-1}{2n\left(\lambda,{T}_{\text{20} \;\text{°C}}\right)}\left({D}_{0}\Delta T+{D}_{1}\Delta {T}^{2}+{D}_{2}\Delta {T}^{3}+\frac{{E}_{0}\Delta T+{E}_{1}\Delta {T}^{2}}{{\lambda }^{2}-{{\lambda }^{2}}_{TK}}\right)\\ &\frac{1}{d}\left(\Delta t\right)=\frac{\dfrac{1}{d}\left({T}_{20 \;\text{°C}}\right)}{1+{\alpha }_{{\mathrm{T}}}\Delta T}\end{split}\right.\quad, $ (8)

其中n(λ,T_20℃)为设计温度下的相对折射率，D₀、D₁、D₂、E₀、E₁、λ_TK为折射率温度系数常数，α_T为衍射光栅热膨胀系数。

由于DASH干涉仪属于定域干涉，两臂的相干光所形成的干涉条纹尺寸与实际探测器尺寸无法直接匹配探测，需要成像光学系统以一定放大倍率R_im将干涉条纹缩放成像至探测器上。通过计算可得到干涉仪出射面的干涉条纹尺寸为W'cosθ_L，最终成像光学系统理论成像缩放比为^[15]：

$ {R}_{{\mathrm{im}}}=\frac{N\times P}{W'\times {\rm{cos}}{\theta }_{\rm{L}}}\quad, $ (9)

其中N为像元数，P为像元尺寸，W' 为衍射方向的有效宽度。成像光学系统的受热变形通常包含刚体位移和面变形，刚体位移是由于外部机械结构热胀冷缩所导致的，面变形是由于光学元件应力造成的^[23]，这4种热变形共同作用将导致放大倍率漂移。当干涉仪通过干涉相位进行风速反演时，放大倍率的漂移将直接影响干涉相位。成像光学系统的热漂移影响主要包含两种方式：

首先，光学系统放大倍率的热漂移直接影响干涉相位^[9]：

$ \left\{\begin{split} &{R}_{\text{shift}}={R}_{\text{im}}+{R}_{\text{im}}\left(\Delta T\right)\\ &{\varphi }_{1}\left(x\right)=8{\text{π}} (\sigma -{\sigma }_{\rm{L}})\tan{\theta }_{\rm{L}}\frac{x}{{R}_{\text{im}}\left(\Delta T\right)}\end{split}\right. \quad,$ (10)

其中R_in(∆T)为成像放大倍率热漂移值，$ {\varphi }_{1} $为放大倍率热漂移所造成的相位差。

其次，当温度发生变化时，成像光学系统与探测器将会发生相对位移，位移量如下：

$ {\varphi }_{2}=\frac{2{\text{π}} \cdot D\left(\Delta T\right)\cdot {R}_{\text{im}}}{{M}_{\text{pixel}}\cdot {N}_{\text{pixel}}}\quad, $ (11)

其中，D(∆T) 为成像光学系统与探测器之间相对位置的热漂移值，M_piexl 为探测器像元数，N_piexl为单周期条纹对应像元数，$ {\varphi }_{2} $为成像光学系统与探测器相对位置由于热变化所造成的相位差。

综上所述，基于以上Littrow波数热漂移值σ_L(∆T)，Littrow角热漂移值θ_L(∆T)，光程差热漂移值∆d(∆T)及成像光学系统的热变化和相对位置的变化可知，当干涉仪环境发生热变化时，干涉仪的相位变为：

$ \begin{split} \varphi \left(x\right)= &2{\text{π}} \left[4\left(\sigma -\left({\sigma }_{\rm{L}}+{\sigma }_{\rm{L}}\left(\Delta T\right)\right)\right)\tan\left({\theta }_{\rm{L}}+{\theta }_{\rm{L}}\left(\Delta T\right)\right)\times\right. \\ &\frac{x}{{R}_{\text{im}}+{R}_{\text{im}}\left(\Delta T\right)}+2\sigma \left(\Delta d+\Delta d\left(\Delta T\right)\right)+\\ &\left.\frac{D\left(\Delta T\right)\cdot {R}_{\text{im}}}{{M}_{\rm{pixel}}\cdot {N}_{\rm{pixel}}}\right] \quad.\\[-9pt] \end{split}$ (12)

为有效监测干涉模块受热发生形变时产生的Littrow波数、Littrow角和光程差的热漂移，基于3.1节干涉仪系统参数，建立光学模型和实物图如图8所示。光机模型均采用线性材料特性进行建模，玻璃材料参数均基于生产厂家提供的数据没定，工作平台采用铝合金加工，干涉模块的正面和背面通过机械结构相连，元件之间通过胶粘和螺母接触，固定于工作平台，以保证系统的工作稳定性。干涉仪光室流体域内为空气，其密度、比热容和热导率分别为1.127 kg/m³、1.005 kJ/kgK和0.271 W/mK，光机模型和实物图如图9所示。材料及各项指标如表2所示。

利用热力学分析软件ANSYS对干涉模块和成像光学系统的光机结构进行有限元选取^[17]和热集成分析。这些有限元单元将为后续分析提供数据源，用以反应不同温度载荷下各元件的热变化。本文采用六面体有限元网格，六面体有限元网格的节点以及单元更接近真实的实验工况，并且本文有限元网格密度相对较密，这也更接近于真实结果。其它约束与真实工况完全一致，网格类型与单元密度均采用更加准确的数据模拟，从而提高了仿真的真实性和准确性，有限元模型如图10所示。

热集成分析软件无法直接得到热变形所引起的元件角度和厚度的变化值，因此，需要建立参考点来监测热变形。由干涉仪原理可知，各元件在X方向的热变形将不会影响干涉模块的整体工作性能，而Z和Y方向的元件变形将会影响干涉模块性能^[17]，于是在干涉仪的G1臂和G2臂各选取8个参考点，分别位于棱镜一侧，扩视场棱镜两侧和光栅衍射面一侧，处于干涉模块X方向中心，各参考点距离光轴均为15 mm，如图11所示。在参考点处建立局部坐标系，通过在热分析软件中提取局部坐标系中的坐标变化，可监测不同热载荷下楔形垫片、扩视场棱镜、光栅垫片的倾角和厚度的变化情况，如图12所示。

成像光学系统为双远心结构，以保证系统有较大的景深范围^[31]。当环境温度发生变化时，可在一定程度上使得镜头出射光具有较佳的光学性能。镜筒外壳采用铝合金2A12材料，其光机布局如图13所示，实物图如图14所示。在热分析软件中建立有限元模型以分析受热影响后系统的工作性能。

探测器通过法兰与探测器支撑座连接，并与探测器支路保持同轴相对位置，固定在底板上。探测器和支撑座，支撑座和底板上设有调节垫。在探测器支路和探测器之间设计了遮光罩，以消除外部光源对探测目标源的影响。法兰、支撑座、调节垫和底板均由2A12铝合金制成，材料特性如表2所示。为了监测成像光学系统与探测器之间的相对位置变化，建立了成像光学系统和探测器的模型，如图15所示。以探测器像面位置中心为原点建立坐标系，设20 ℃时的初始位置为坐标原点。在软件中，通过坐标位置的相对变化来监测成像光学系统和探测器之间的相对位置热漂移。

基于3.1节干涉模块的热分析模型，在软件中设置干涉模块光机系统基本温度为20 ℃，边界温度为12 ℃和28 ℃，温升步长为0.05 ℃ 的温度载荷。每个温度下的受热情况由单独的负载描述，可说明干涉模块光机结构在工作时受环境温度影响的形变情况。干涉模块的热分析云图如图16所示，干涉模块热变形云图如图17所示。

热分析结束后，光学分析软件无法对热分析模型中的机械部分进行分析，需要对所获得的数据进行光机分离，即提取光机结构中光学部分的原始和变形后的数据。此时所提取的光学部分已经受到机械部分的影响，模型中所建立的16个参考点位置坐标已包含各元件角度的变化，再基于式(8)进行热变形分析，干涉仪G1臂和G2臂的Littrow角与温度的关系如图18所示，Littrow波数与温度的关系如图19所示。

分析上述数据可知，每个元件角度的热漂移都会影响Littrow波数、Littrow角和光程差。得到不同温度下干涉仪G1臂和干涉仪G2臂漂移引起的干涉相位误差变化如图20所示。

由式(6)和式(7)可得到干涉仪光程差热漂移值与温度的关系，如图21所示，不同温度下由光程差变化引起的干涉相位变化情况如图22所示。

对于干涉模块G1臂，光栅垫片楔角和楔形垫片楔角的热变形对Littrow波数和Littrow角影响较大，是主要影响因素，干涉仪G2臂的楔形垫片楔角和扩视场棱镜顶角的热变形对Littrow波数和Littrow角的影响均较大。综上所述，干涉模块G1臂的相位漂移较G2臂更为严重，G1臂受热漂移引起的相位误差己经达到0.097 50 rad/℃，G2臂受热漂移引起的相位误差为0.061 05 rad/℃。干涉仪G1臂和G2臂相位变化趋势不同，这是由于两臂所采用的元件材料不同，且在机械结构中放置方式不同所导致的。图23（彩图见期刊电子版）为G1臂和G2臂的热漂移引起的风速误差，由于其产生的风速误差较大，只在图23中给出19.5℃~20.5℃的热变形所导致的风速误差。

光程差受热漂移引起的相位误差达到3.428 5×10⁻⁵ rad/℃，不同温度下光程差热漂移引起的风速误差如图24所示。可见，热漂移所导致的相位漂移较小，这是由于在干涉模块的设计中采用了消热差设计，元件之间的热变形可以相互补偿从而使光程差热漂移减小。

参考当前大气风场探测精度的研究现状^[32]，并结合目前温控手段和技术难点可得出以下结论：将干涉模块整体温度控制在（20±0.05） ℃，可将相位漂移所产生的风速误差在3.8 m/s内，此外，在干涉仪进行温度控制装置安装时，应将温度控制装置着重安装在G1臂的光栅垫片和楔形垫片及G2臂的楔形垫片和扩视场棱镜上，这样可以进行更加稳定且精准的温度控制，进一步有针对性地降低温度变化造成的风速误差。

针对成像光学系统的热漂移，基于3.2节的热分析模型，在软件中设置成像光学系统基本温度为20℃，边界温度为12℃和28℃，逐步温升为0.2℃的温度载荷，成像光学系统热分析云图如图25所示，成像光学系统的热变形云图如图26所示。

光机热分析结束后，通过处理有限元数据可以得到光学元件的变形数据。此时的数据包括面变形和刚体位移两部分，无法直接在光学分析软件中进行分析，需要将其进行分离处理，并采用Zernike系数拟合获得各表面之间的平动和转动的刚体位移坐标，再将相应数据导入光学分析软件ZEMAX中进行分析和校验^[33]。不同温度下，成像光学系统的放大倍率变化情况如图27所示。不同温度下，放大倍率变化误差如图28所示。放大倍率热漂移引起的相位误差与温度的关系如图29所示。

针对成像光学系统与相机相对位置的变化，在软件中设置成像光学系统和相机整体的基本温度为20℃，边界温度为12℃和28℃，逐步温升为0.2℃的温度载荷，成像光学系统与探测器的相对位置的热分析云图如图30所示。

通过分析探测器像面的坐标信息，成像光学系统与探测器的相对位置热漂移如图31所示，相对位置热漂移引起的相位热漂移与温度的关系如图32所示。

由上述相位误差结果可知，成像光学系统的放大倍率漂移受刚体位移和表面变形的综合影响。不同温度下，放大倍率热漂移引起的风速误差如图33所示。由于成像光学系统放大倍率的变化引起的风速反演误差不可忽视，根据当前风干涉仪的检测精度要求和控温技术，需要将成像光学系统的温度波动控制在（20±2） ℃以内，并保证风速误差在3.05 m/s以内。

此外，不同温度下的成像光学系统和探测器之间的相对位置的热漂移引起的风速误差如图34所示。不同温度下相对位置的热漂移所造成的风速误差较小，误差可以忽略。

本文基于DASH干涉仪，设计并建立了干涉模块与成像光学系统的光机热集成分析模型。通过软件仿真和数据拟合表明，干涉模块在光机热变形中占据主要影响因素，需将干涉模块光机结构整体的温度波动控制在（20±0.05） ℃内，并重点对干涉G1臂中光栅垫片和楔形垫片，G2臂中的楔形垫片和扩视场棱镜进行温度控制，将温度控制部件安装在相应位置，此时该部件造成的风速误差为3.8 m/s。成像光学系统热变形、成像光学系统与探测器的相对位置受热变化为第二影响原因，需将其温度控制在（20±2）℃，此时该部件造成的风速误差为3.05 m/s。通过上述方法可将干涉模块、成像光学系统、成像光学系统与探测器相对位置三者共同造成的风速测量误差控制在6.85 m/s 内。本文提出了对温度敏感元件的针对性温控，分析给出成像光学系统的误差程度，并提出了相应的温控措施，为DASH干涉仪工程实施提供理论依据。