Analysis of the impact of temperature on the spectral shift in ultraviolet hyperspectral imaging spectrometers

Guotao Pan; Guotao Pan; Bo Li; Guochao Gu; Xiangyang Yu; Hanshuang Li; Xiaoxu Wang; Zhanfeng Li; Xiaohu Yang; Junqing Zhu; Diansheng Cao; Bingqiang Li; Qingjun Ma; Heng Wu; Limin He; Guanyu Lin

doi:10.1364/OE.517945

1. Introduction

The imaging spectrometer, recognized as a high-end optical device, performs a critical role in fields such as remote sensing, environmental monitoring, and Earth science [1–3]. Its unique advantage stems from its ability to provide both high-resolution spatial and spectral information, rendering it a powerful tool for scientific research and various applications [4]. However, the high performance of this instrument may be compromised by various environmental factors in practical use, notably temperature variations, which are among the most prevalent and challenging issues.

Temperature fluctuations can induce spectral shift [5]. In the analysis of atmospheric spectroscopy, variations in spectral wavelengths may result in shifts in the positions of crucial absorption lines, utilized for the quantitative assessment of atmospheric components like O₃, NO₂, SO₂, aerosols, etc. A shift in wavelength directly influences the accuracy of absorption line positions, thereby leading to inaccuracies in the measurement of atmospheric components. In practical operation, temperature change serves as a primary cause for spectral movement in spectrometers [6]. Currently, many imaging spectrometers utilize characteristic spectral lines of known wavelengths for on-board spectral calibration, a technique distinct from the monochromator spectral calibration device used by MODIS [7]. Through data processing, the change in spectral line positions of the spectrometer in orbit relative to laboratory spectral calibration results can be determined. Subsequently, by adjusting the central wavelength matrix measured in the laboratory, the appropriate central wavelength matrix for in-orbit operation is obtained. Minimizing spectral shift is a prerequisite and foundation for achieving on-board spectral calibration [8], particularly when using characteristic spectral lines as references. At present, studies, such as the findings by Zheng et al. [6], have revealed that temperature variations result in significant spectral shifts in the detectors of imaging spectrometers. Cui et al. [5] conducted a comprehensive analysis, including simulation and experimental testing, of the temperature shift characteristics observed in a screw-driven spectrometer. During temperature increases, the spectral line at 253 nm showed a shift of 0.028 nm in comparison to the original wavelength scan. This spectrometer employs a reduced number of optical components and lacks spectral imaging capabilities. Xian et al. [9] primarily investigated the influence of temperature on the spectral line shift in a specific airborne imaging spectrometer. In a temperature change range of ±10°C, the average shift in spectral line reached 0.248 nm. Substantial environmental differences exist between airborne and spaceborne platforms, and it cannot meet the design requirements for high calibration accuracy. However, comprehensive analysis of the spectral shift characteristics of multi-channel, high-calibration-accuracy imaging spectrometers remains insufficient. Conducting in-depth research in this area will enhance understanding and control over the performance of imaging spectrometers in complex environments, thus improving their accuracy and reliability in various applications.

This paper concentrates on the Ultraviolet (limb) Hyperspectral Imaging Spectrometer (UV-HIS) and investigates the impact of temperature on spectral shift through simulation analysis and experimental validation.

Initially, the impact of temperature changes on the spectral shift of the spectrometer was assessed based on the optical and mechanical design requirements of the instrument. Subsequently, the research team performed a detailed analysis of the structural design of the spectrometer and deliberated on the temperature load settings in light of actual in-orbit temperature data. Furthermore, using finite element software, the deformation of the mirror surface and the rigid-body displacement under different temperature conditions were determined; the specific impact of these changes on the spectral shift was subsequently analyzed using Ansys Zemax software. Finally, the accuracy of the simulation analysis was corroborated through a thermal vacuum test, thus completing the quantitative evaluation of the spectral shift of the spectrometer under temperature load. This research not only offers valuable references for the performance enhancement of imaging spectrometers in practical applications but also possesses significant practical significance in fields such as environmental monitoring and Earth science.

2. Impact of temperature on spectral shift

Imaging spectrometers, functioning as essential devices mounted on satellites or spacecraft, endure the extreme conditions of space, presenting a major challenge to the long-term safe operation of such onboard instruments [10]. Even though effective thermal design can ensure the maintenance of temperature levels and distribution within an optimal range, satisfying the fundamental requirements of dimensional stability for optical components and mechanical structures, temperature-induced spectral shift continues to be a significant factor impacting the precision of spectral measurements in imaging spectrometers. This shift phenomenon stems from a variety of complex mechanisms.

2.1 Refractive index

In refractive systems, the refractive index of optical materials commonly fluctuates with temperature changes [11], leading to varying degrees of spectral shift at the image plane. This phenomenon is primarily manifested in the temperature coefficient of the absolute refractive index $({d{n_{\textrm{abs}}}({\lambda ,T} )/dT} )$, in the variation of the absolute refractive index $({\Delta {n_{\textrm{abs}}}({\lambda ,T} )} )$, and in the absolute refractive index itself $({{n_{\textrm{abs}}}({\lambda ,T} )} )$. The expressions for these are as follows:

(1)$$\frac{{d{n_{\textrm{abs}}}({\lambda ,T} )}}{{dT}} = \frac{{{n^2}({\lambda ,{T_0}} )- 1}}{{2n({\lambda ,{T_0}} )}}\left[ {{D_0} + 2{D_1}\Delta T + 3{D_2}\Delta {T^2} + \frac{{{E_0} + 2{E_1}\Delta T}}{{{\lambda^2} - \lambda_{tk}^2}}} \right]$$

(2)$${\Delta {n_{\textrm{abs}}}({\lambda ,T} )= \frac{{{n^2}({\lambda ,{T_0}} )- 1}}{{2n({\lambda ,{T_0}} )}}\left[ {{D_0}\Delta T + {D_1}\Delta {T^2} + {D_2}\Delta {T^3} + \frac{{{E_0}\Delta T + {E_1}\Delta {T^2}}}{{{\lambda^2} - \lambda_{\textrm{tk}}^2}}} \right]}$$

(3)$${{n_{\textrm{abs}}}({\lambda ,T} )= {n_{\textrm{abs}}}({\lambda ,{T_0}} )+ \Delta {n_{\textrm{abs}}}({\lambda ,T} )}$$

where $\Delta T$ denotes the temperature difference, specifically the difference between the working environment temperature of the sample and the initial reference temperature ${T_0}$ (20°C). $n({\mathrm{\lambda },{T_0}} )$ represents the absolute refractive index value of glass at a certain wavelength in vacuum at the temperature ${T_0}$ (20°C). $\Delta {n_{\textrm{abs}}}({\lambda ,T} )$ indicates the difference in the absolute refractive index of glass at a certain wavelength and a specific temperature in vacuum relative to the absolute refractive index at the initial reference temperature ${T_0}$ (20°C). ${n_{\textrm{abs}}}({\lambda ,T} )$ is defined as the absolute refractive index value of glass at a certain wavelength and a specific temperature in vacuum. ${D_0}$, ${D_1}$, ${D_2}$, ${E_0}$, ${E_1}$ represent material-specific coefficients, associated with wavelength and temperature. ${\lambda _{tk}}$ (${L_{tk}}$) is exclusively related to the wavelength, typically ranging between 0.08 and 0.33 µm.

Temperature-induced changes in refractive index can result in spectral shift, a factor particularly critical for spectrometers requiring high-precision measurements. In practical applications, minimizing this shift through calibration and temperature control is necessary to ensure the accuracy and repeatability of spectral measurements.

2.2 Surface profile

Variations in the coefficients of thermal expansion among different materials in response to temperature changes can result in surface profile alterations in optical systems [12,13], thereby leading to spectral shifts. This section will derive the relationship between surface curvature changes and thermal expansion, followed by a brief analysis.

Within an optical system, the optical surface is characterized as a curved surface, where ‘z’ denotes the surface height at a specific x and y position. The configuration of an optical element is represented by a three-dimensional height function $z = f({x,y} )$. We will now perform a Taylor expansion of this function.

The Taylor expansion is a method that can approximate the behavior of a function near a point. Consider an optical surface at a point $({{x_0},{y_0}} )$, characterized by a surface height function $f({x,y} )$. In the vicinity of that point, the surface height can be represented by an expansion as follows:

(4)$$\begin{array}{c} {f({x,y} )= f({{x_0},{y_0}} )+ ({x - {x_0}} )\frac{{\partial f}}{{\partial x}} + ({y - {y_0}} )\frac{{\partial f}}{{\partial y}} + }\\ {\frac{1}{{2!}}\left( {{{(x - {x_0})}^2}\frac{{{\partial^2}f}}{{\partial {x^2}}} + 2({x - {x_0}} )({y - {y_0}} )\frac{{{\partial^2}f}}{{\partial x\partial y}} + {{(y - {y_0})}^2}\frac{{{\partial^2}f}}{{\partial {y^2}}}} \right) + \ldots } \end{array}$$

In optical systems, it is common to focus on small regions on the surface, enabling the neglect of higher-order terms. For $\Delta x$ and $\Delta y$ with small variations, the aforementioned surface height function can be approximated as:

(5)$$f({x + \varDelta x,y + \varDelta y} )\approx f({x,y} )+ \varDelta x\frac{{\partial f}}{{\partial x}} + \varDelta y\frac{{\partial f}}{{\partial y}}$$

The curvature K at this point is defined as:

(6)$$K ={-} \frac{1}{R}$$

where R represents the radius of curvature. The radius of curvature is associated with the second-order derivative and can be determined using the following equation:

(7)$$R = \frac{{{{(1 + {{(\frac{{\partial f}}{{\partial x}})}^2})}^{\frac{3}{2}}}}}{{\left|{\frac{{{\partial^2}f}}{{\partial {x^2}}}} \right|}}$$

Replacing $\Delta x$ with $\alpha \cdot \varDelta T\cdot x$, in which $\alpha $ is the coefficient of linear expansion of the material and $\varDelta T$ represents the temperature change, establishes the relationship between the change in curvature and the coefficient of thermal expansion:

(8)$$\mathrm{\Delta }K ={-} \frac{1}{R} \cdot \mathrm{\Delta }L ={-} \frac{1}{R} \cdot L \cdot \alpha \cdot \mathrm{\Delta }T \cdot x$$

This relationship suggests that the length change resulting from temperature change impacts the curvature change of the optical element, thereby influencing its optical performance. Therefore, selecting appropriate materials and thermal expansion coefficients is crucial for the performance of the optical system, as this reduces the amount of spectral shift.

2.3 Rigid-body displacement

Temperature changes can induce rigid-body displacements in optical systems [14], encompassing both rigid-body translations and rotations. This phenomenon is attributable to the varying coefficients of thermal expansion among different materials, leading to changes in the dimensions of system components in response to temperature fluctuations, ultimately resulting in spectral shifts.

The extent of translation correlates with the material's coefficient of linear expansion, the initial dimensions of the element, and the extent of temperature change. Rigid-body displacement resulting from translation is described by the following equation:

(9)$$\varDelta {r_{\textrm{translation}}} = ({\varDelta x,\varDelta y,\varDelta z} )= ({{L_x} \cdot {\alpha_x} \cdot \varDelta T,{L_y} \cdot {\alpha_y} \cdot \varDelta T,{L_z} \cdot {\alpha_z} \cdot \varDelta T} )$$

where $\varDelta x$, $\varDelta y$, and $\varDelta z$ represent the displacements, ${L_x}$, ${L_y}$, and ${L_z}$ denote the initial dimensions of the optical system in the x, y, and z axes, respectively, ${\alpha _x}$, ${\alpha _y}$, and ${\alpha _z}$ are the coefficients of thermal expansion in these directions, and $\varDelta T$ signifies the temperature change.

Rigid body rotation is represented by the rotation matrix R, where $\varDelta {r_{\textrm{rotation}}} = R \cdot \varDelta {r_{\textrm{original}}}$. The rotation matrix can be expressed as:

(10)$$R = \left[ {\begin{array}{ccc} {\cos (\theta )}&{ - \sin (\theta )}&0\\ {\sin (\theta )}&{\cos (\theta )}&0\\ 0&0&1 \end{array}} \right]$$

where $\theta $ is the rotation angle.

(11)$$\varDelta {r_{\textrm{rotation}}} = \left[ {\begin{array}{c} {\cos (\theta ) \cdot \varDelta x - \sin (\theta ) \cdot \varDelta y}\\ {\sin (\theta ) \cdot \varDelta x + \cos (\theta ) \cdot \varDelta y}\\ {\varDelta z} \end{array}} \right]$$

The total rigid displacement is a combination of translations and rotations:

(12)$$\varDelta {r_{\textrm{total}}} = \varDelta {r_{\textrm{translation}}} + \varDelta {r_{\textrm{rotation}}} = \left[ {\begin{array}{c} {{L_x} \cdot {a_x} \cdot \varDelta T + \varDelta x \cdot \cos (\theta ) - \varDelta y \cdot \sin (\theta )}\\ {{L_y} \cdot {a_y} \cdot \varDelta T + \varDelta x \cdot \sin (\theta ) + \varDelta y \cdot \cos (\theta )}\\ {{L_z} \cdot {a_z} \cdot \varDelta T + \varDelta z} \end{array}} \right]$$

This analysis demonstrates that the total displacement comprises a superposition of the linear expansion effect caused by temperature fluctuations and the displacement attributable to rotation. The amalgamation of these two types of displacement dictates the extent of shift that can occur in the spectral lines of the spectrometer within the optical system. Consequently, it is imperative to consider these factors to ensure the accuracy and stability of spectral measurements.

2.4 Grating period

Thermal variations in the grating period affect the diffraction angle, thereby causing spectral shift and impacting spectrometer accuracy.

For reflective gratings, the angle of incidence is generally equal to the angle of reflection. Therefore, the grating equation [15] may be simplified to:

(13)$$m\lambda = d\sin (\theta )$$

where m is the diffraction level; $\lambda $ is the wavelength of the incident light; d is the period of the grating, namely, the distance between two adjacent grating lines; and $\theta $ is the angle between the incident light and the grating normal.

When the temperature changes, the corresponding variation of the grating period with temperature can be expressed as:

(14)$$d(T )= {d_0}({1 + CTE \times \varDelta T} )$$

where $d(T )$ represents the grating period post-temperature change, ${d_0}$ denotes the initial grating period, $CTE$ is the thermal expansion coefficient of the material, and $\varDelta T$ signifies the temperature change

A change in the grating period alters the angle of diffraction of light, consequently affecting the wavelength of the diffracted light, which can be calculated from the grating equation relative to the grating period:

(15)$$\lambda ^{\prime} = d(T )\cdot \sin (\theta ^{\prime})$$

where $\lambda ^{\prime}$ denotes the changed wavelength and $\theta ^{\prime}$ represents the changed diffraction angle.

The spectral shift, namely, the difference between the altered wavelength and the original wavelength, can be expressed as:

(16)$$\varDelta \lambda = \lambda ^{\prime} - \lambda $$

To summarize, when a reflective grating undergoes a change in the grating period d due to temperature variations, this results in a change in the diffraction angle, subsequently leading to a shift in the position of the spectral lines.

2.5 Coating

Temperature changes can lead to thermal expansion of the optical coating, altering the reflection and transmission properties and impacting the spectral shape. The coefficient of thermal expansion for an optical coating is expressed by the equation:

(17)$${\alpha _{\textrm{total}}}(T )= \mathop \sum \nolimits_{i = 1}^n \frac{{{d_i}}}{D} \cdot {\alpha _i}(T )$$

where ${\alpha _{\textrm{total}}}(T )$ denotes the total coefficient of thermal expansion of the coating at temperature T, ${\alpha _i}(T )$ represents the coefficient of thermal expansion of the material of the ith layer at temperature T, n indicates the number of layers of the coating, ${d_i}$ refers to the thickness of the ith layer, and D is the total thickness of the coating, namely, $D = \mathop \sum \nolimits_{i = 1}^n {d_i}$.

In summary, the optical path length undergoes alterations due to the thermal expansion of the membrane layer, potentially resulting in a shift of the spectral. Particularly in multilayer membrane structures, the effect of thermal expansion of each layer on the total optical path accumulates.

Based on the comprehensive analysis above, it is evident that these factors interact and collectively determine the performance of optical systems under temperature variations. Among these factors, refractive index and rigid body displacement are considered the two most significant contributors to spectral shift. Firstly, the temperature dependence of the refractive index has a direct and crucial impact on spectral shift, especially in refractive optical systems. Secondly, the influence of rigid body displacement is fundamentally attributed to variations in the thermal expansion coefficients of materials, leading to changes in the lengths of different components and ultimately resulting in spectral shift. Therefore, prudent material selection becomes a necessary step to ensure the stability of the system.

3. Opto-mechanical-thermal integrated simulation analysis technology

Optical, mechanical, and thermal integrated simulation analysis represents a highly specialized process, encompassing comprehensive analyses in the optical, mechanical, and thermal fields. This method is primarily employed to evaluate and optimize the performance and stability of precision equipment, such as optical and satellite instruments, under various environmental conditions. By integrating these analyses, it becomes possible to gain a more comprehensive understanding and prediction of the system's performance in practical use contexts. In this study, the effect of temperature on spectral shift will be analyzed through the integration of optical, mechanical, and thermal simulation analysis technology. The comprehensive analysis process is illustrated in Fig. 1.

Fig. 1. Opto-mechanical-thermal integrated simulation analysis process.

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4. Spectrometer characterization analysis

4.1 Spectrometer system design

The UV-HIS, boasting an expected in-orbit lifetime of eight years, is tasked primarily with carrying out limbic atmospheric soundings in the light region of each orbit, enabling detailed observations of the Earth's limbic atmosphere due to its high spatial and spectral resolution. Such observations are capable of providing important data on atmospheric ozone (O₃), nitrogen dioxide (NO₂), Sulphur dioxide (SO₂), and stratospheric aerosol profiles. This spectrometer encompasses a spectral range of 290 to 500 nm, spanning two channels: 290 to 400 nm and 390 to 500 nm. It boasts a spectral resolution of 0.6 nm and a wavelength calibration accuracy of 0.01 nm. The spectrometer is outfitted with a 2048 × 2048 detector, featuring a pixel size of 10µm, and combines four pixels in the spectral dimension.

To ensure long-term data accuracy and reliability, the spectrometer is scheduled to perform monthly mercury and tungsten calibrations in the shadow region and solar calibrations in the light region. These in-orbit calibration operations are instrumental in monitoring and correcting the Proximity Atmospheric Sounding data over the long term, thus ensuring the high accuracy and reliability of its scientific observations.

The optical system of the UV-HIS comprises several key components. As depicted in Fig. 2, this encompasses multiple mirrors (M1, M2, M3, M4, M5) in the co-optical path section, pre-dispersive prism (PDP), beam splitters (B-S), and two spectral band detection channels, CH1 (290∼400 nm) and CH2 (390∼500 nm). The overall optical machine structure, illustrated in Fig. 3, comprises a main box assembly, a secondary box assembly, a heat sink assembly, three focal plane assemblies, and a mounting support, among other components. This meticulous structural design is crucial to ensuring the stability and performance of the spectrometer in harsh space environments.

Fig. 2. Optical structure of UV-HIS.

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Fig. 3. UV-HIS composition.

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In the design of this UV-HIS, the main box functions as the mounting reference for the optical system. The optics primarily consist of fused silica, a material widely used in high-precision optical systems due to its excellent optical properties and thermal stability. The mirrors and refractors are mounted in various positions within the main box using two methods: back mandrel support and mirror chamber fixed mounting. This design aims to ensure precise alignment and stability of the optical elements.

To further enhance the thermal stability of the system, the spectrometer employs a tripod flexible structure. This structure is capable of effectively absorbing and minimizing the potential effects of temperature changes. Simultaneously, the optical system can be precisely adjusted to ensure optimal performance via the reserved adjustment pads.

The overall robustness of the system is commendable. To mitigate the processing difficulty and weight of the load, aluminum alloy 7A09 is utilized for both the main and secondary boxes. This material is not only lightweight but also possesses high strength, and via integrated molding technology, it ensures the strength and stiffness of the structure to meet the requirements of harsh space applications. The related materials utilized in the overall optical system and their properties are detailed in Table 1.

Table 1. Main parameters of the material^a

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This design and material selection enable the spectrometer to maintain stable performance in extreme space environments while ensuring its structural lightness and high efficiency, vital for long-term space missions.

In terms of thermal control, the UV-HIS employs a series of carefully designed measures to address the temperature challenges of the cosmic environment. Initially, the main body of the spectrometer is mounted using external insulation to minimize the thermal impact of the mounting platform. This design contributes to maintaining temperature stability inside the instrument and lessens the impact of changes in the external environment on instrument performance. Furthermore, all critical optical components, comprising mirror assemblies, grating assemblies, optical elements, and focal plane assemblies, are mounted in a manner ensuring thermal conductivity to the main box. This approach aids in enhancing the temperature uniformity of the entire unit and guarantees the stability of optical performance under various temperature conditions. Effective heat-insulating mounting has been implemented between the onboard electrical box and the main body to mitigate the impact on the main box from the temperature rise of the electronic components during operation. This measure is aimed at preventing the heat from the electrical box from impacting the optical components, thus ensuring the overall performance of the instrument. Simultaneously, master heating compensation is utilized to fulfill the requirement of constant temperature and uniform temperature distribution operation. This aspect is crucial for ensuring the accuracy and reliability of the optical measurements.

Given the inevitable differences in temperature environments between the laboratory spectral calibration and the on-orbit phase, achieving a completely heatless design for a complex optomechanical system such as an imaging spectrometer is nearly impossible. Consequently, conducting an in-depth study of the effects of temperature variations on spectral shift, and accordingly guiding laboratory spectral calibration and on-orbit imaging, is crucial for enhancing the accuracy of spectral and radiometric measurements.

4.2 Temperature load setting analysis

Utilizing the existing in-orbit work data and through a comparison and analysis of the actual temperature records of similar spectrometers in the in-orbit environment, the normal working temperature of the spectrometer we developed can be deduced, providing important reference information.

Figure 4(a), (b), and (c) display the structural temperature distribution curves at three different locations within the same type of spectrometer. From these data, we conclude that the spectrometer maintains a remarkably stable on-orbit temperature range between 16 ± 0.3°C, with an exceedingly low temperature gradient of no more than 0.02°C, and a minimal variation in the temperature level of only ± 0.3°C, demonstrating the exceptional stability of the thermal control design. The impact of the temperature gradient on the structure of the optical machine is negligible, thereby shifting the focus of the study to the impact of temperature level changes on the optical performance of the instrument. Incorporating the differences among various spectrometers, the spectral shift characteristics under the temperature condition of 16 ± 1°C were ultimately selected for analysis.

Fig. 4. Temperature distribution of internal components of a similar type of on-board spectrometer over time. (a) 200 consecutive point-in-time temperature records of the internal temperature of the CH1 grating (from 08:01:03 on October 01, 2021 to 11:36:49 on October 01, 2021). (b) 700 consecutive point-in-time temperature recordings for channel 2 imaging mirrors (from October 01, 2021 at 13:24:57 to October 02, 2021 at 02:11:22). (c) 550 consecutive point-in-time temperature recordings for channel 2 imaging mirrors (from October 03, 2021 at 11:22:52 to October 03, 2021 at 20:41:01).

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5. Rigid-body displacement solution analysis

When the temperature varies horizontally, the optomechanical structure undergoes thermoelastic deformation, resulting in face shape changes and rigid-body displacements of the optical elements [14,16], which leads to changes in the imaging position of the main light line at each wavelength and spectral shift. Due to the varied approaches in structural design and material selection, the alterations in the face shape of the optical elements of the spectrometer range from a few nm to tens of nm. Consequently, the spectral shift attributable to the face shape change can be deemed negligible (This range of face shape change can be ascertained through face shape fitting). The primary factor affecting the spectral shift remains the rigid-body displacement of the mirrors.

Other mechanisms impacting spectral shift, as outlined in Section 1, include factors such as refractive index, grating period, and coating. The refractive index fluctuates with wavelength and temperature and is capable of being automatically adjusted for temperature via optical design software. The grating period calculation is conducted using Eq. (14), and the resulting grating period value is then allocated to the corresponding material properties. The grating period at an ideal temperature of 20°C stands at 5.55555555555E-04, and the grating period for various temperatures is calculable based on this, as illustrated in Table 2. Regarding the consideration of the membrane layer, in light of the minimal change in the face shape of the optical element and the minor extent of horizontal temperature fluctuation, the membrane layer is simplified in this analysis and presumed to maintain an ideal state.

Table 2. Variation of the grating period with temperature

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In the subsequent analysis, we examine the elastic deformation of optical elements and mechanical structures caused by changes in temperature level, and subsequently assess the effect of the rigid-body displacement resulting from this on the spectral shift.

Thermoelastic analysis is conducted using Ansys software to determine the precise behavior of the optical elements and mechanical structure under specific thermal loads. The output of the FEA software represents the structural deformation value of each node under a specific load, requiring surface fitting to ascertain the face shape error and rigid-body displacement of the mirrors, which is then incorporated into optical software like Zemax for optical performance analysis.

It is postulated that the initial node position is $({{x_0},{y_0},{z_0}} )$ within the local coordinate system ${C_0}$ prior to rigid-body displacement, and the node position becomes $({{x_m},{y_m},{z_m}} )$ post-deformation. However, within the local coordinate system ${C_1}$, the node position remains $({{x_0},{y_0},{z_0}} )$ even post-deformation, following the occurrence of rigid-body displacement in the mirror surface. Assuming the rigid-body displacement induced by the mirror is represented by $({{T_X},{T_Y},{T_Z},{R_X},{R_Y},{R_Z}} )$, the analytical solution for the coordinates $({x_m^\mathrm{^{\prime}},y_m^\mathrm{^{\prime}},z_m^\mathrm{^{\prime}}} )$ can be derived using the chi-square coordinate transformation method.

(18)$$\scalebox{0.88}{$\displaystyle\left\{ \begin{array}{@{}l} x_m^\mathrm{^{\prime}} = {x_m}\textrm{cos}{R_y}\textrm{cos}{R_z} - {y_m}\textrm{cos}{R_\gamma }\textrm{sin}{R_z} + {z_m}\textrm{sin}{R_y} + {T_x}\\ y_m^\mathrm{^{\prime}} = {x_m}({\textrm{sin}{R_X}\textrm{sin}{R_Y}\textrm{cos}{R_Z} + \textrm{cos}{R_X}\textrm{sin}{R_Z}} )- {y_m}({\textrm{sin}{R_X}\textrm{sin}{R_Y}\textrm{sin}{R_Z} - \textrm{cos}{R_X}\textrm{cos}{R_Z}} ) - {z_m}\textrm{sin}{R_X}\textrm{cos}{R_Y} + {T_Y}\\ z_m^\mathrm{^{\prime}} = {x_m}({ - \textrm{cos}{R_X}\textrm{sin}{R_y}\textrm{cos}{R_Z} + \textrm{sin}{R_X}\textrm{sin}{R_Z}} )+ {y_m}({\textrm{cos}{R_X}\textrm{sin}{R_Y}\textrm{sin}{R_Z} - \textrm{sin}{R_X}\textrm{cos}{R_Z}} ) + {z_m}\textrm{cos}{R_X}\textrm{cos}{R_Y} + {T_Z} \end{array} \right.$}$$

Due to the small rotational displacements $({{R_X},{R_Y},{R_Z}} )$ of each mirror, Eq. (18) can be simplified as:

(19)$$\left\{ {\begin{array}{c} {x_m^\mathrm{^{\prime}} = {x_m} - {y_m}{R_Z} + {z_m}{R_Y} + {T_X}}\\ {y_m^\mathrm{^{\prime}} = {x_m}{R_Z} + {y_m} - {z_m}{R_X} + {T_Y}}\\ {z_m^\mathrm{^{\prime}} ={-} {x_m}{R_Y} + {y_m}{R_X} + {z_m} + {T_Z}} \end{array}} \right.$$

Defining the difference between $({{x_m},{y_m},{z_m}} )$ and the analytical solution computed by Eq. (19) as the error $\Delta $, then:

(20)$$\Delta = \mathop \sum \nolimits_m [{{{({x_m^\mathrm{^{\prime}} - {x_m}} )}^2} + {{({y_m^\mathrm{^{\prime}} - {y_m}} )}^2} + {{({z_m^\mathrm{^{\prime}} - {z_m}} )}^2}} ]$$

The partial derivatives can be solved for the six rigid-body displacement components $\Delta $ and set to zero, from which a system of six quadratic equations can be obtained:

(21)$$\left\{ {\begin{array}{c} {\frac{{\partial \Delta }}{{\partial {T_X}}} = 0}\\ {\frac{{\partial \Delta }}{{\partial {T_Y}}} = 0}\\ {\frac{{\partial \Delta }}{{\partial {T_Z}}} = 0}\\ {\frac{{\partial \Delta }}{{\partial {R_X}}} = 0}\\ {\frac{{\partial \Delta }}{{\partial {R_Y}}} = 0}\\ {\frac{{\partial \Delta }}{{\partial {R_Z}}} = 0} \end{array}} \right.$$

The least squares solution for the displacement of the mirror rigid body can be obtained by solving Eq. (21). The algorithm is independent of the shape of the mirror, relatively stable, simple to implement, and efficient to solve.

6. Rigid-body displacement solution analysis

To examine the spectral shift attributes under thermal load, Ansys Workbench was employed for constructing the structural analysis model [17]. This model featured face-to-face friction sliding and fixed connections. Meshing was performed using a blend of tetrahedral and hexahedral meshes [18]. Considering the disparate temperature effects across various system locations, precise meshing was applied to the optical components and their nearby support frameworks. Coarser meshing was adopted for the casing, heat dissipation plates, and additional components, resulting in improved computational speed of the system. The resultant meshed model is illustrated in Fig. 5. The model comprised 1,614,429 cells and 2,711,309 nodes.

Fig. 5. UV-HIS meshing results.

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6.1 Small temperature difference spectral shift analysis

Initially, aligning with the instrument's operating temperature in orbit, 16°C is established as the ideal operating temperature. Subsequently, eight temperature loading conditions: 15°C, 15.25°C, 15.5°C, 15.75°C, 16.25°C, 16.5°C, 16.75°C, and 17°C, were defined, and the corresponding rigid-body displacements were computed. Owing to the numerous temperature conditions, only the deformation cloud diagrams at 15°C, as illustrated in Fig. 6, are presented. For other temperatures, the nodal displacement data is provided in Table 3.

Fig. 6. Deformation cloud at 15°C temperature condition.

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Table 3. Maximum node displacement data of UV-HIS at different temperatures

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The FEA results were transferred to Zemax optical design software for the analysis and computation of the rigid-body displacements of the mirror nodes as well as the face-fitting. Considering the system's complexity and the range of temperature conditions, the results of rigid-body displacement and face shape fitting accuracy are illustrated by examining the optics of channel 1 at a temperature of 15.75°C as an example, with these findings summarized in Table 4. A clear observation emerges from the analysis of Table 4: owing to the interconnected imaging mirror groups, the rigid-body displacements and the angles of rigid-body rotations exhibit a high degree of uniformity from lens 1 to lens 5, aligning with the actual situation. Furthermore, the fitted surface patterns of the front surfaces of mirror 1 and lens 1, as depicted in Figs. 7 and 8, demonstrate remarkably high surface fitting accuracy. This results in minimized error.

Fig. 7. Reflector 1 fitted surface pattern (PV = 7.81 × 10-3 nm, RMS = 2.43 × 10-3 nm).

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Fig. 8. Fitted surface of the front surface of the lens 1 (PV = 1.27 nm, RMS = 8.14 nm).

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Table 4. Mirror rigid-body displacement and face shape accuracy at 15.75°C temperature for CH1

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Integrating the mirror rigid-body displacement and face shape accuracy data obtained from the previous analysis, Zemax software was employed to conduct ray tracing on the deformed optical system, aiming to determine the spectral shift resulting from the aforementioned eight temperature conditions. Given that the system comprises two channels, 290∼400 nm and 390∼500 nm, an analysis was conducted on the amount of spectral shift for channel 1 and channel 2 at various wavelengths and fields of view, as illustrated in Figs. 9(a), (b) and 10(a), (b), respectively.

Fig. 9. Channel 1 wavelength spectral shift data (a) 15∼16°C (b) 16∼17°C.

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An analysis of the data from Figs. 9 and 10 yields the following insights:

(1) Within the temperature range of 15∼17°C, CH1 experiences a maximum spectral shift of around 0.018 nm. Similarly, CH2 exhibits a maximum spectral shift of about 0.010 nm under the same temperature conditions.
(2) Assuming that the positive spectral dimension aligns with the + Y direction, as the temperature increases, the spectral shift tends to occur towards the -Y direction.
(3) The wavelength shift in the central field of view (FOV) of CH1 exhibits a distinct linear trend, while the wavelength shift in the central FOV of CH2 demonstrates a more quasi-linear pattern. This variation could be attributed to the differing locations and extents of deformation experienced by the two channels in the system.
(4) As the temperature difference escalates, the slope of the curve correspondingly increases, suggesting a more rapid increase in the shift with an increasing temperature difference.
(5) In non-central fields of view, such as 0.7FOV and 1FOV, a pronounced non-linear trend is evident, indicating that the optical system's response to wavelength shift is influenced not only by the magnitude of the temperature difference but also by the angle of incidence of the light.
(6) The effects of temperature and FOV are interdependent. The interplay between these two factors can amplify or mitigate the spectral shift. For instance, a higher FOV at a marginally elevated temperature may result in a larger shift than anticipated by the individual effects alone.

Fig. 10. Channel 2 wavelength spectral shift data (a) 15∼16°C (b) 16∼17°C.

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6.2 Large temperature difference spectral shift analysis

Acknowledging that minor temperature variations may not present noticeable regularity, 16°C was established as the ideal working temperature. In conjunction with the characteristic spectral lines of a mercury lamp (296.73 nm, 302.15 nm, 334.15 nm, 365.01 nm, 404.66 nm, 435.84 nm), the system's spectral shift was analyzed over a broader temperature range of 15∼22°C, as depicted in Fig. 11.

Fig. 11. Spectral shift amount at 10°C to 22°C (simulation data).

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Analysis of data from Fig. 11 reveals the following:

(1) At the designated ideal operating temperature of 16°C, all spectral curves demonstrate a turning point.
(2) In CH1, within the temperature range of 10∼22°C, the maximum spectral shift is approximately 0.06 nm. Similarly, in CH2, the maximum shift under the same conditions is about 0.03 nm. This suggests that the placement of channels in the system design influences the magnitude of their spectral shift.
(3) The spectral performance of the CH1 and CH2 channels displays distinct shift patterns. CH1 demonstrates a linear change, while CH2 presents a non-linear pattern. This could indicate varying temperature dependencies across different wavelengths.
(4) Wavelengths exhibit differing levels of temperature sensitivity. For instance, within CH1, the 365.01 nm wavelength exhibits a more pronounced central wavelength shift in response to temperature variations, in contrast to the 296.73 nm wavelength, which demonstrates more subtle changes. This phenomenon may be attributable to the material's differential response to varying wavelengths.

7. Experimental

The vacuum thermal test of the UV-HIS is depicted in Fig. 12. In the left image, the outer surface of the instrument is enveloped in multi-layer insulation (MLI) to mitigate the alternating effects of the sun and the cold, dark environment. The instrument is equipped with two heat sinks for efficient heat dissipation. Resistance heating plates are affixed to key positions on the detector and optical components to offset thermal losses under low-temperature conditions, thereby ensuring the overall structure's temperature remains within the operational temperature range [19].

Fig. 12. UV-HIS thermal test.

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Between June 22 and June 27, 2022, a thermal vacuum test was carried out at the environmental test station, featuring temperatures ranging from approximately 12°C to 21°C and a heating rate of about 1°C. Prior to, during, and following the test, the instrument's engineering telemetry parameters and analog telemetry data remained within normal ranges. The test results are presented in Fig. 13.

Fig. 13. Spectral shift from 12°C to 23°C (ground vacuum thermal test).

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The experimental data indicate that the trends and numerical values of spectral shift observed in the simulation are closely aligned with those in the vacuum test data. This affirms the strong correlation between the simulation analysis and the actual test results. Notably, the CH1 channel demonstrates a linear trend, with its spectral shift experiencing significant fluctuations with temperature variations; conversely, the CH2 channel exhibits a non-linear trend, with more subtle changes in spectral shift due to temperature, mirroring the simulation analysis.

Based on the foregoing analysis, it can be concluded that:

(1) Within a temperature range of 16 ± 1°C, the spectral shift remains about 0.01 nm, satisfying the precision requirements of spectral calibration and eliminating the need for further calibration and correction.
(2) Under varying temperature differentials, the CH1 and CH2 channels demonstrate distinct shift patterns. With minor temperature differences, both channels exhibit a linear trend, whereas at more significant differences, CH1 maintains a linear pattern, and CH2 displays a nonlinear distribution. This suggests varying temperature dependencies across different wavelengths.
(3) Wavelengths demonstrate differing sensitivities to temperature fluctuations. For example, within CH1, the 365.01 nm wavelength undergoes a more substantial central wavelength shift due to temperature changes, in contrast to the 296.73 nm wavelength, which exhibits lesser alterations. This phenomenon could be attributed to the differential material responses to various wavelengths of light.
(4) With an increase in temperature differential, the curve’s slope also escalates, indicating an accelerated shift with larger temperature differences.
(5) Nonlinear patterns are observed in non-central fields of view, like 0.7FOV and 1FOV, suggesting the optical system’s response to wavelength shifts is affected by both the magnitude of temperature differences and the angle of incident light.
(6) Temperature and FOV effects are interrelated, with their combination potentially amplifying or mitigating spectral shifts. For instance, a higher FOV at marginally increased temperatures may result in a more significant shift than expected from individual effects alone.
(7) Despite the minor discrepancies between the experimental and simulation results, these discrepancies are deemed acceptable. However, the experimental results prove to be more accurate than the simulation results. This is primarily attributed to the simulation model being predicated on a series of assumptions and simplifications, failing to encapsulate the entirety of the experimental environment; employing measures such as precise temperature control and accurate calibration of the spectrometer results in smaller deviations in the experimental results; the employment of meticulous data processing methods further diminishes the spectral shift deviation observed in the experiments. Plans are underway to meticulously refine our simulation models and experimental methods in subsequent work, aiming to enhance the accuracy and reliability of the results.

8. Conclusions

Based on the preceding analysis, it is evident that temperature-induced spectral shifts exert complex effects on the accuracy of atmospheric composition measurements by spaceborne spectrometers. Firstly, spectral shifts can result in changes in the positions of absorption lines, significantly impacting the accuracy of inversion. Secondly, spectral shifts may further influence the precision of spectral resolution and wavelength calibration. In the analysis of atmospheric spectra, both high spectral resolution and strict inversion accuracy rely on reliable spectral calibration. Reductions in resolution or inaccuracies in wavelength calibration will impact the precise monitoring of atmospheric composition. Additionally, spectral shifts may compromise the performance of optical components, such as lenses and filters, thereby affecting the system's overall performance. Consequently, in the design and operation of spaceborne spectrometers, controlling temperature fluctuations is critical to maintaining optical system stability under varied temperature conditions, thus ensuring high accuracy and reliability in atmospheric composition measurements.

This study comprehensively examines the impact of temperature on spectral shift in UV-HIS. The research has detailed the characteristics of the temperature load on the instrument in a space-borne environment and elucidated the mechanisms and manifestations of temperature load. Additionally, this research delves into the characteristics of spectral shift and includes a thermal vacuum test. Estimations of spectral shift were made based on temperature variations. Simulation results indicated that the maximum deviation of spectral shift is estimated at 0.018 nm under a temperature condition of 16 ± 1°C. Under a more controlled orbital temperature condition (16 ± 0.3°C), the maximum deviation of spectral shift decreased to 0.01 nm. Experimental data revealed that at 16 ± 1°C, the maximum deviation of spectral shift did not exceed 0.01 nm. This effectively corroborates our theoretical analysis. The relationship between temperature and spectral shift offers a crucial theoretical foundation for calibrating spectral measurements and managing the thermal conditions of the instrument.

Funding

The Strategic Priority Research Program of the Chinese Academy of Sciences (XDA28050102); National Natural Science Foundation of China (62205330); National Key Research and Development Program of China (2022YFB3903202).

Acknowledgment

Thanks for the fund support.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

References

1. J. C. Zhu, X. H. Chen, Z. C. Zhao, et al., “Design and manufacture of miniaturized immersed imaging spectrometer for remote sensing,” Opt. Express 29(14), 22603–22613 (2021). [CrossRef]

2. J. C. Zhu, X. H. Chen, Z. C. Zhao, et al., “Long-slit polarization-insensitive imaging spectrometer for wide-swath hyperspectral remote sensing from a geostationary orbit,” Opt. Express 29(17), 26851–26864 (2021). [CrossRef]

3. T. Wang, L. Yu, and J. Lin, “Coastal shallow waters explorer imaging spectrometer for aerial remote sensing of shallow waters in UV-VIS-NIR broadband,” Appl. Opt. 60(6), 1566–1573 (2021). [CrossRef]

4. Y. R. Chen, H. Zhang, Y. N. Wang, et al., “ADMM-DSP: A deep spectral image prior for snapshot spectral image demosaicing,” IEEE Trans. Ind. Inf. 99, 1–11 (2023). [CrossRef]

5. Q. L. Cui, Z. F. Li, Z. H. Zhang, et al., “Analysis of temperature-induced spectral drift in the solar spectrometer driven by leadscrew and bar mechanism,” Optik 225, 165783 (2020). [CrossRef]

6. Y. Q. Zheng, “Precise spectral calibration for hyperspectral imager,” Optics and Precision Engineering 18(11), 2347–2354 (2010).

7. X. Xiong, K. Chiang, J. Esposito, et al., “MODIS on-orbit calibration and characterization,” Metrologia 40(1), 89–92 (2003). [CrossRef]

8. T. Choi and C. Y. Cao, “S-NPP VIIRS day night band on-board solar diffuser calibration validation using the scheduled lunar collections,” Remote Sens. 13(6), 1093 (2021). [CrossRef]

9. G. Xian, C. X. Yan, and J. B. Shao, “Thermal effect on spectral-line shift of a airborne imaging spectrometer,” Acta Optics Sinica 35(4), 383–389 (2015). [CrossRef]

10. G. Thuillier, T. Foujols, D. Bolsée, et al., “SOLAR/SOLSPEC: scientific objectives, instrument performance and its absolute calibration using a blackbody as primary standard source,” Sol. Phys. 257(1), 185–213 (2009). [CrossRef]

11. P. J. Herve and L. K. J. Vandamme, “Empirical temperature dependence of the refractive index of semiconductors,” J. Appl. Phys. 77(10), 5476–5477 (1995). [CrossRef]

12. R. Y. Wang, Z. S. Gao, L. J. Wang, et al., “Thermo-optical analysis and correction method for an optical window in low temperature and vacuum,” Curr. Opt. Photonics 77(2), 213–221 (2023).

13. E. Segato, V. Da Deppo, S. Debei, et al., “Method for studying the effects of thermal deformations on optical systems for space application,” Appl. Opt. 50(18), 2836–2845 (2011). [CrossRef]

14. L. Hahn and P. Eberhard, “Transient dynamical-thermal-optical system modeling and simulation,” J. Eur. Opt. Soc.-Rapid Publ. 17(1), 5 (2021). [CrossRef]

15. T. Puegner, J. Knobbe, and H. Lakner, “Basic angles in microelectromechanical system scanning grating spectrometers,” Appl. Opt. 50(24), 4894–4902 (2011). [CrossRef]

16. F. Shakeriaski, M. Ghodrat, J. Escobedo-Diaz, et al., “Recent advances in generalized thermoelasticity theory and the modified models: a review,” Journal of Computational Design and Engineering 8(1), 15–35 (2021). [CrossRef]

17. Y. Zheng, M. H. Liu, B. S. Li, et al., “Structural optimization of a pipe-climbing robot based on ANSYS,” Mech. Sci. 13(2), 725–733 (2022). [CrossRef]

18. G. J. Li, W. J. Wang, L. An, et al., “Research on hexahedral and tetrahedral mesh applied to strength analysis of bogie frame,” Appl. Mech. Mater. 477-478, 150–154 (2014). [CrossRef]

19. Q. L. Cui, G. Y. Lin, D. S. Cao, et al., “Thermal design parameters analysis and model updating using Kriging model for space instruments,” Int. J. Therm. Sci. 171, 107239 (2022). [CrossRef]

Material	Density $\mathbf{g}/\boldsymbol{c}{\boldsymbol{m}^3}$)	EM (GPa)	Poisson's ratio	LEC (10⁻⁶/K)	TC (W/m·K)	Parts and Components
7A09	2.8	71	0.33	23.6	142	Boxes, Supports
2A12	2.8	68	0.33	22.7	130	Electric control Boxes
TC4	4.4	114	0.34	8.6	7.3	Shaft and Bearing Inlay Sleeves
9Cr18	7.7	210	0.3	10.5	29.3	Shaft Parts
Silica	2.205	73	0.17	0.58	1.4	Optics
45#	7.85	206	0.3	11.7	35	Bearing Sleeves, Glands

Temperature /°C	Grating Period /mm
15.00	5.55489997E-04
15.25	5.55493272E-04
15.50	5.55496550E-04
15.75	5.55499827E-04
16.00	5.55503105E-04
16.25	5.55506383E-04
16.50	5.55509661E-04
16.75	5.55512938E-04
17.00	5.55516216E-04

Temperature/°C	Nodal deformation displacement /mm
15.0	0.10168
15.25	0.096599
15.5	0.091515
15.75	0.086431
16.0	0.081347
16.25	0.076262
16.5	0.071178
16.75	0.066094
17.0	0.06101

Optics	Dx (mm)	Dy (mm)	Dz (mm)	Rx (°)	Ry (°)	Rz (°)	RMS (nm)	PV (nm)
Mirror 1	-0.001	0.035	-0.042	0.001	-0.001	0.000	2.43 × 10⁻³	7.81 × 10⁻³
Mirror 2	0.004	0.042	0.007	0.002	0.000	-0.002	1.43 × 10⁻²	4.57 × 10⁻²
PSP Front Surface	0.002	0.032	-0.013	0.002	-0.005	-0.005	2.22 × 10⁻²	8.84 × 10⁻²
PSP Rear Surface	-0.001	0.017	-0.027	0.002	-0.007	-0.001	0.1	1.75
Mirror 3	0.000	0.025	-0.033	0.003	0.000	-0.001	8.69 × 10⁻³	4.69 × 10⁻²
Mirror 4	0.007	0.034	0.010	0.000	0.000	-0.001	4.91 × 10⁻³	3.09 × 10⁻²
Mirror 5	-0.001	0.012	-0.037	0.001	0.000	-0.001	9.61 × 10⁻³	5.03 × 10⁻²
B-S Front Surface	0.006	0.025	-0.001	0.002	-0.003	-0.006	1.33	10.4
Mirror 6	0.006	0.014	-0.002	0.002	-0.008	-0.003	1.90	14.4
Grating_CH1	0.008	0.012	0.003	0.002	-0.001	0.001	2.8 × 10⁻²	0.118
Lens1 Front Surface	0.005	0.003	0.003	0.002	0.001	-0.001	1.27	8.14
Lens 1 Rear Surface	0.005	0.003	0.003	0.002	0.001	-0.001	1.06	4.23
Lens 2 Front Surface	0.005	0.003	0.003	0.002	0.001	-0.001	0.96	6.41
Lens 2 Rear Surface	0.005	0.002	0.003	0.002	0.001	-0.001	0.24	1.95
Lens 3 Front Surface	0.006	0.001	0.002	0.002	0.001	-0.001	0.54	4.59
Lens 3 Rear Surface	0.006	0.001	0.002	0.002	0.001	-0.001	1.39	10.5
Lens 4 Front Surface	0.006	0.001	0.001	0.002	0.001	-0.001	0.97	8.76
Lens 4 Rear Surface	0.006	0.000	0.001	0.002	0.001	-0.001	0.34	1.91
Lens 5 Front Surface	0.006	0.002	-0.001	0.006	0.002	-0.001	3.13	18.1
Lens 5 Rear Surface	0.007	0.001	-0.001	0.006	0.002	-0.001	3.61	21.5

Material	Density $\mathbf{g}/\boldsymbol{c}{\boldsymbol{m}^3}$)	EM (GPa)	Poisson's ratio	LEC (10⁻⁶/K)	TC (W/m·K)	Parts and Components
7A09	2.8	71	0.33	23.6	142	Boxes, Supports
2A12	2.8	68	0.33	22.7	130	Electric control Boxes
TC4	4.4	114	0.34	8.6	7.3	Shaft and Bearing Inlay Sleeves
9Cr18	7.7	210	0.3	10.5	29.3	Shaft Parts
Silica	2.205	73	0.17	0.58	1.4	Optics
45#	7.85	206	0.3	11.7	35	Bearing Sleeves, Glands

Analysis of the impact of temperature on the spectral shift in ultraviolet hyperspectral imaging spectrometers

Abstract

1. Introduction

2. Impact of temperature on spectral shift

2.1 Refractive index

2.2 Surface profile

2.3 Rigid-body displacement

2.4 Grating period

2.5 Coating

3. Opto-mechanical-thermal integrated simulation analysis technology

4. Spectrometer characterization analysis

4.1 Spectrometer system design

4.2 Temperature load setting analysis

5. Rigid-body displacement solution analysis

6. Rigid-body displacement solution analysis

6.1 Small temperature difference spectral shift analysis

6.2 Large temperature difference spectral shift analysis

7. Experimental

8. Conclusions

Funding

Acknowledgment

Disclosures

Data availability

References

Data availability

Cited By

Figures (13)

Tables (4)

Equations (21)

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