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Abstract
A multiple sub-pupil ultra-spectral imaging system designed with a single spectrometer and detector can simultaneously detect multiple-channel spectra with ultra-high spectral resolution. However, due to using a prism in the system's front end, the nonlinear dispersion introduces spectral line tilt in the imaging spectra. This phenomenon can lead to bias in the final spectral data. To eliminate this issue, we propose a new design by introducing a second prism to correct this spectral tilt in the system. The angle of spectral line tilt generated by the nonlinear dispersion of the first prism is derived. It provides the theoretical basis for characterizing the second complementary prism. Finally, a UV multiple sub-pupil ultra-spectral imaging system is designed. The system employs two pupil separation prisms and one flat panel array to segment the pupil in three channels, each operating within spectral ranges of 180∼210 nm, 275∼305 nm, and 370∼400 nm, respectively. The spectral resolutions in all three channels are better than 0.1 nm. The corrected spectral line tilt is less than 1/3 of a pixel in the two channels with pupil separation prisms. At a Nyquist frequency of 30 lp/mm, the modulation transfer functions of all three channels are greater than 0.7, ensuring imaging quality. The design results indicate that the method proposed in this paper, utilizing complementary prisms, can effectively correct the spectral line tilt caused by the nonlinear dispersion of the pupil separation prisms. This design approach can be a reference for developing multiple sub-pupil ultra-spectral imaging systems.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As the most crucial instrument in space remote sensing, the spectral imager can acquire two-dimensional spatial information of target objects while capturing continuous spectral information. This results in a multi-band continuous spectral image, creating an image data cube arranged in spectral order [1]. The imager can not only capture the spectral information of the target under measurement but also acquire its image information [2]. The spectral information collected by the imager can identify the target object type, while the spatial image information can provide the outline characteristics of the target object. It possesses the integrated features of spectra and imagery [3].
In the current imager development, miniaturization, high spectral resolution, and simultaneous multi-channel measurements are vital trends. The requirements for spaceborne atmospheric remote sensing imagers have gradually increased in terms of system size, weight, spectral resolution, and operational efficiency. Traditional imager system designs are often single-channel, requiring multiple spectrometers to simultaneously detect multiple targets. Alternatively, a multi-channel design may be employed, but it necessitates the use of multiple spectral imaging systems for individual imaging tasks. This leads to issues such as low spectral resolution and large size. Prisms not only serve as dispersive elements [4,5], but also enable the separation of large-aperture incident light. Therefore, multiple prisms can be placed at the entrance pupil of the front telescope system to divide the incident light pupil into several sub-pupils, each corresponding to a different channel. All channels undergo collimation and focus using a shared optical path spectral imaging system [6]. A diffraction grating with various diffraction orders in the spectral imaging system disperses different spectral segments for each channel, ultimately forming images on the same detector surface. The design scheme achieves high-resolution detection of different channel spectra by a single spectrometer system and detector. The significant advantage of this system design lies in its capability for multi-channel, ultra-high spectral resolution detection. While their high-resolution features are crucial, the design of a multiple sub-pupil ultra-spectral imaging system faces challenges due to the nonlinear dispersion of prisms, resulting in spectral line tilting in the acquired images. The presence of spectral line tilting can result in significant bias in the spectral image, affecting the detection accuracy. This introduces spectral calibration and adjustment challenges, complicating subsequent image processing.
The spectral line tilting is induced by the crossed dispersion of prisms and gratings is essentially attributed to the nonlinear dispersion of prisms [7]. In recent years, many scholars have conducted research to correct the nonlinear dispersion of prisms. Yang et al. conducted research on the method of achieving linear dispersion combined prisms through material compensation, employing mathematical modeling, simulation calculations, and experimental validation. They established a dispersion model for materials, proposed a design method for linear dispersion combined prisms, and utilized two materials with similar nonlinear coefficients but different linear coefficients. By controlling the parameters of the combined prisms and the angle of incident light, linear dispersion can be achieved [8]. Jin Yang et al. proposed the design of a Dyson spectrometer using an achromatic Féry prism to eliminate the nonlinear dispersion produced by a single prism. By employing a combination of quartz and flint glass prisms, they achieved high linearity in the dispersion of the prism system, with 206 spectral bands within the working wavelength range of 400 to 2500 nm [9]. Ebizuka et al. proposed the use of a combination of prisms with three different materials to achieve linear dispersion prisms through dispersion compensation between the materials [10].
The correction methods mentioned above are applicable to spectrometer systems where prisms serve as the primary dispersive elements. However, in this study, the prism is positioned at the entrance pupil of the telescope system, which is slightly different from the imaging spectrometer mentioned earlier. To address the issue of spectral line tilting in the design of a multiple sub-pupil imaging spectrometer, this paper proposes a new design method using complementary prisms made with the same material to correct spectral line tilting. We first derive the angle of spectral line tilting caused by prism nonlinear dispersion and the theoretical equation for correcting spectral line tilting using complementary prisms. Subsequently, based on this method, a UV multiple sub-pupil ultra-spectral imaging system is designed to eliminate spectral line tilting. Simulation results confirm the feasibility of the correction method. Finally, evaluation metrics for the designed example are presented, demonstrating that the imaging quality meets the requirements. The spectral line tilting in the two channels containing pupil separation prisms, after correction with complementary prisms, is less than 1/3 of a pixel.
2. MSPUI system layout and design principles
The optical system layout of the multiple sub-pupil ultra-spectral imaging system (MSPUI) is illustrated in Fig. 1. It comprises the front telescope system, slit, and spectral imaging system. The front telescope system includes a pupil separation prism and an optical lens group. The spectral imaging system consists of a collimation system, planar grating, focus system, and detector, which achieves ultra-high spectral resolution detection of different channels spectra through a single spectrometer system and detector. The entire instrument has been optimized to reduce volume and consolidated into a single telescope and spectral imaging system.
The front telescope system utilizes a prism at the front end to split the entrance pupil, forming multiple channels. Different channels can be used for detecting different objects, and this prism is referred to as the pupil separation prisms. Light from the same field of view for different channels is imaged to the slit, as shown in Fig. 2. The presence of the prism spatially separates the slit, preventing spectral overlap.
The separated slits correspond to different spectral channels, and they then enter a multi-channel shared spectral imaging system. To ensure that the spectra from different channels achieve ultra-high spectral resolution dispersion through the grating and are imaged onto a single detector surface, apart from using the pupil separation prisms in the telescope system to ensure spatial separation of the imaging spectra, it is also necessary to ensure that in the spectral dimension, they do not exceed the effective working area of a single detector. This is achieved through the use of grating multilevel spectra. Different spectral channels use different diffraction orders, and if the diffraction angles are not significantly different, imaging onto a single detector can be realized [11].
High groove density or high-order diffraction can be used to improve the spectral resolution. In this study, as a single detector is employed for imaging different spectral channels, based on Eq. (1), the grating equation [12]. If the same diffraction order is used, the imaged spectra for different channels form a step-like distribution, exceeding the effective working area of the detector, as illustrated in Fig. 3(a). Therefore, we apply different diffraction order to different spectral channels to solve this issue, as depicted in Fig. 3(b). assuming that the diffraction angles for various spectral channels are not significantly different. As a result, the spectra from different channels are dispersed within the effective working area of the detector in the spectral dimension. Further, this approach significantly improves the spectral resolution.
Fig. 3. Diffraction results for different spectral channels with the same order and different orders. (Note: The spectral distribution on the detector surface when applying the (a) same or (b) different diffraction order as the grating for different spectral channels.)
Grating equation:
d is the grating constant, $\sigma $ is the incident angle, $\theta $ is the diffraction angle, m is the diffraction order, and $\lambda $ is the operating wavelength.3. Principle of spectral line tilt correction
3.1 Causes of spectral line tilt
A pupil separation prism positioned at the entrance pupil of the telescope system could introduce a specific level of chromatic dispersion to the incident polychromatic light. The surface of the pupil separation prisms is tilted around the Y-axis, with the dispersion direction perpendicular to the grating dispersion direction. The spatial separation of images at the detector for different spectral ranges is determined not only by the physical spacing of the split slits at the focal plane of the telescope but also influenced by the chromatic dispersion of the pupil separation prisms.
Assuming the system's outgoing light path, as illustrated in Fig. 4, OP0 represents the exit light path. Pλ is the image plane imaging point for wavelength λ without transverse dispersion through the prism, and Qλ is the image plane imaging point for wavelength λ after transverse dispersion through the prism. ${\gamma _\lambda }$ represents the exit angle for wavelength λ, and ${\gamma _0}$ represents the exit angle for wavelength λ0. M0Q0 is the half height of the slit, and f is the focal length of the system. The geometric relation can be obtained as follows.
In the equation, ‘$\varepsilon $‘ represents the angular component in the slit direction, and x = M0Q0, then there is $\tan \varepsilon = {\raise0.7ex\hbox{$x$} \!\mathord{/ {\vphantom {x f}}}\!\lower0.7ex\hbox{$f$}}$.
After solving Eq. (2), we get:
Under the same field of view on the image plane, the X-direction imaging coordinates after different wavelengths are transversely dispersed by the prism are:
The difference between the spatial coordinates of the central wavelength and the non-central wavelength of the same field of view:
When ${\gamma _\lambda } - {\gamma _0}$ is small, $\sec ({\gamma _\lambda } - {\gamma _0})$ can be approximated as 1+${\raise0.7ex\hbox{${{{({\gamma _\lambda } - {\gamma _0})}^{_2}}}$} \!\mathord{/ {\vphantom {{{{({\gamma_\lambda } - {\gamma_0})}^{_2}}} 2}}}\!\lower0.7ex\hbox{$2$}}$, so we can get:
The difference in the X-direction coordinates between the central wavelength and non-central wavelengths within the same field of view is proportional to the square difference between the exit angles of non-central wavelengths and the exit angle of the central wavelength. Due to the typical nonlinear dispersion characteristics of the prism, different wavelengths in the X-direction have different exit angles, resulting in a microscopic tilt in the spectrum within the same channel, as illustrated in Fig. 5. This issue leads to discrepancies between the actual and theoretical wavelength image plane position, impacting the calibration accuracy.
Fig. 5. MSPUI spectral line tilt phenomenon based on pupil separation prisms. (Note: Figure 5 shows the microscopic distribution of the imaging spectrum; m, m-i, m + j are diffraction orders.)
Traditional methods for correcting spectral line tilt often involve post-establishment of a spectral chart restoration model, but this method still introduces errors in data processing. Alternatively, lens or image plane tilting may be employed, but this approach fails to achieve simultaneous correction of multi-channel spectral line tilt. Another approach involves using prisms made of different materials, yet there are limitations in correcting spectral line tilt, especially in the ultraviolet range where fewer materials are available. In summary, this paper derives the angle of spectral line tilt caused by the nonlinear dispersion of prisms and provides a theoretical equation for complementary prism correction of spectral line tilt. By designing complementary prisms with the same material as the pupil separation prisms in the system, not only is the correction of spectral line tilt achieved by the optical system itself, but it also addresses the issue in spectral regions with limited available materials.
3.2 Principle of prism dispersion
When polychromatic light enters a prism, the monochromatic light with different wavelengths experiences different angles of deviation upon exiting the prism interface due to the principle that materials have different refractive indices for different wavelengths [13]. The light-splitting principle of a prism is illustrated in Fig. 6.
The relationship between the deflection angle ‘$\delta $‘ and the incident angle ‘${\alpha _1}$‘ of the light, the apex angle ‘A’ of the prism, and the refractive index ‘n’ of the prism material is as follows [14,15]:
From formula (7), it can be determined that when the incident angle of the light is constant, the refractive index ‘n’ of the prism material and the apex angle ‘A’ of the prism determine the degree of deflection of the outgoing light.
When the angle of the incident light is constant [16]:
From Eq. (7) and the trigonometric function relationship, we can get:
Again:
Combining equations (9), and (10):
Differentiate Eq. (11):
To sum up, the formula for the angular dispersion rate of a prism for light at any incident angle is as follows:
According to formula (13), it can be seen that the prism angular dispersion rate is related to the incident angle ${\alpha _1}$, the prism vertex angle A, and the material dispersion rate ${\raise0.7ex\hbox{${dn}$} \!\mathord{/ {\vphantom {{dn} {d\lambda }}}}\!\lower0.7ex\hbox{${d\lambda }$}}$. Among them, according to Cauchy’s empirical formula [17], the expression of ${\raise0.7ex\hbox{${dn}$} \!\mathord{/ {\vphantom {{dn} {d\lambda }}}}\!\lower0.7ex\hbox{${d\lambda }$}}$ can be derived as follows:
where a, b, and c are constants determined by the characteristics of the prism material. When the wavelength change range is not too broad, Eq. (14) can be simplified to the following equation:The dispersion rate of the prism material is:
The prism angular dispersion rate can be obtained by combining Eqs. (13) and (16).
3.3 Principle of spectral line tilt correction
The presence of the pupil separation prisms in the front telescope system causes the imaging spectrum of the spectrometer not only to disperse in the direction of grating dispersion but also to experience dispersion in the direction perpendicular to it, leading to the movement of positions for different wavelengths. The typical nonlinear dispersion characteristics of the prism result in the spatial pixels of the imaging instrument's slits undergoing dispersion. The spectrum undergoes a shift, presenting a tilted state known as spectral line tilt, as shown in Fig. 7. In the figure, $\Delta h$ represents the transverse spacing caused by prism transverse dispersion, $\varphi $ represents the tilt angle caused by prism transverse dispersion, and $\Delta z$ is defined as the spectral line tilt. The following theoretical derivation explores the factors related to $\varphi $ and proposes a theoretical solution.
From the above derivation of the prism dispersion principle in Section 3.2, the pupil separation prisms angular dispersion rate is defined as:
Assuming the focal length of the spectrometer is f, and the spectral width of the working band is $\varDelta \lambda $, the transverse dispersion caused by the pupil separation prisms results in the lateral movement of spectra in the spatial dimension. Therefore, the lateral distance $\varDelta h$ caused by prism dispersion between spectral lines is:
Differentiating both sides of grating Eq. (1) simultaneously, the formula for the grating angular dispersion rate is obtained as:
Due to the nonlinearity of the transverse dispersion caused by the pupil separation prisms, different wavelengths result in different lateral positions after dispersion, leading to spectral line tilt:
Equation (20) indicates that the pupil separation prisms placed at the entrance pupil of the telescope system will cause spectral line tilt in the transverse dispersion direction. The tilt angle ‘$\varphi $‘ is related to the prism apex angle, prism incident angle, prism material dispersion rate, grating groove density, and diffraction order.
Given constant grating parameters, prism incident angle, and prism material, formula (20) reveals that the spectral line tilt angle is only related to the prism apex angle. When the incident angle of light, denoted by ‘${\alpha _1}$,’ is known, correction of spectral line tilt can be achieved by designing a complementary prism. Different complementary prisms are designed for the pupil separation prisms in different channels to correct the spectral line tilt they induce. The complementary prism has an opposite deflection direction to the original prism. The complementary prism for correcting spectral line tilt should satisfy the following formula:
From formulas (20), (21), and (22), it is known that complementary prisms can be used to generate spectral line tilt angles equal in magnitude but opposite in direction to those induced by the pupil separation prisms, thus correcting the spectral line tilt in the system. Complementary prisms can be placed behind the slit, effectively addressing the spectral line tilt issue before light enters the grating. The MSPUI design process using this method involves several steps. First, system design parameters are determined, followed by the selection of different channel pupil prism apex angle parameters A and incident angles ${\alpha _1}$ based on the effective working area of the chosen detector. Next, grating constants d and diffraction orders m for different channels is calculated based on spectral resolution and imaging system focal length. The spectral line tilt angle caused by the pupil separation prisms dispersion is then calculated, and the complementary prism apex angle parameters for correction are determined. Finally, these design parameters are input into the initial module of the multiple sub-pupil ultra-spectral imager (MSPUI) to validate the rationality of the initial structure. If it is deemed unreasonable, the design is iterated for pupil separation prisms apex angles, incident angles, and complementary prism parameters. Ultimately, the optically reasonable initial structure is subjected to optimization using optical design software to obtain an MSPUI system that meets the requirements for eliminating spectral line tilt.
4. Method validation and analysis
4.1 Optical layout
To demonstrate the performance of the proposed design method, we designed a UV MSPUI instance, as shown in Fig. 8. The overall system consists of a telescope system, slit, and spectral imaging system. To separate the image plane from the slit and reduce the system size further, the light emitted from the slit is deflected by a flat mirror. The telescope system includes the pupil separation prisms and lens assembly. The spectral imaging system consists of a complementary prism, reflective grating, and a mirror assembly. The light beam is divided by the pupil separation prisms at the entrance pupil of the telescope system, obtaining different spectral channels. Different channel working spectral ranges are imaged at the slit after being focused by the lens assembly in the telescope system, creating a split slit. The light emitted from the slit passes through the complementary prism, then is collimated by the mirror assembly. The collimated beam reaches the plane reflective grating for dispersion. After dispersion, the beam is focused again by the same mirror assembly and finally reaches the surface of the detector.
The design of the pupil separation prisms and the multi-order spectrum of the grating enables a single spectrometer system and simultaneous detection of multiple substances under a single detector. Additionally, a high diffraction order can improve the spectral resolution of the imaging spectrometer. Collimation of the beam and focusing imaging are achieved using the same system, which further reduces the system's volume and facilitates the correction of system aberrations. This not only meets the requirements for ultra-high spectral resolution but also achieves high-quality imaging. Furthermore, a complementary prism is designed behind the slit to address the spectral line tilt issue caused by the pupil separation prisms. This reduces the difficulty of subsequent image processing and improves the accuracy of spectral calibration. In summary, the design of this optical path not only resolves the spectral line tilt issue but also offers advantages such as ultra-high spectral resolution, simultaneous detection of multiple substances, and miniaturization.
4.2 System design example
Based on the above optical system layout, a UV MSPUI is designed to eliminate spectral line tilt. The system operates in the ultraviolet wavelength range, chosen for its capability to detect SO2 and unknown UV absorbers in the Venusian clouds. High-precision spectral detection of SO2 and unknown UV absorbers in the Venusian atmosphere plays a crucial role in discovering potential signs of life on Venus and exploring planetary habitability.
At the entrance of the front telescope system, two pupil separation prisms (P1, P2) and a flat panel (F1) are placed to divide the entrance pupil into three channels. Based on the requirements for the split slit size and physical spacing, the pupil separation prisms deflection angle is designed to be 3.3°, and the material used is Silica. The corresponding working spectral ranges for the three channels are: T1 = 180∼210 nm, T2 = 275∼305 nm, and T3 = 370∼400 nm. The F-number of the telescope system is 6.25, with a focal length of 125 mm. The system adopts a transmissive structure, and the lens assembly is made of Silica and CaF2. After the slit, a complementary prism (p1, p2) and a flat panel (f1) are placed, as calculated based on the principles of spectral line tilt correction. With deflection angles of p1 = 1.45° and p2 = 1.25° for the Silica complementary prisms, the spectral line tilt correction for channels T1 and T3 is less than 1/3 of a pixel, meeting the usage requirements. The spectral imaging system uses an off-axis three-mirror self-collimating system, where collimation and imaging are multiplexed to avoid beam compression caused by large grating diffraction angles. The dispersion element is a flat reflective grating with a groove density of 286gr/mm. Diffraction orders for the three channels are selected as +6, + 4, and +3, corresponding to channels T1, T2, and T3.
The front telescope system and spectral imaging system, shown in Figs. 9,10, are optimized and integrated with optical design software to enhance the imaging quality. The parameters of the designed example system are presented in Table 1. The overall magnification ratio of the system is 1, and the spectral resolution for all three channels is better than 0.1 nm at the Nyquist frequency of 30lp/mm, with an overall Modulation Transfer Function (MTF) exceeding 0.7 across the entire field of view. The system dimensions are 205 × 450 × 525 (mm) (XYZ). The imaging system design, based on the proposed method in this paper, not only meets the requirements for ultra-high spectral resolution and simultaneous detection of multiple substances but also exhibits the characteristic of miniaturization.
Table 1. Eliminate spectral line tilt UV MSPUI design index parameters
4.3 Evaluation indicator
4.3.1 MTF
The MTF is a comprehensive indicator of optical system imaging quality as suggested [18–20]. Figures 11–13 illustrate the modulation transfer function at the Nyquist frequency of 30lp/mm for the shortwave and longwave in T1, T2, and T3 channels. From the results, it can be observed that the MTF values for each channel's wavelength at the Nyquist frequency of 30lp/mm are all greater than 0.7, indicating good image quality and meeting the requirements for imaging quality.
Fig. 11. MTF curves for shortwave and longwave in T1 channel. (Note: (a) MTF curve for shortwave at 180 nm in T1 channel, Nyquist frequency 30lp/mm; (b) MTF curve for longwave at 210 nm in T1 channel, Nyquist frequency 30lp/mm.)
Fig. 12. MTF curves for shortwave and longwave in T2 channel. (Note: (a) MTF curve for shortwave at 275 nm in T2 channel, Nyquist frequency 30lp/mm; (b) MTF curve for longwave at 305 nm in T2 channel, Nyquist frequency 30lp/mm.)
Fig. 13. MTF curves for shortwave and longwave in T3 channel. (Note: (a) MTF curve for shortwave at 370 nm in T3 channel, Nyquist frequency 30lp/mm; (b) MTF curve for longwave at 400 nm in T3 channel, Nyquist frequency 30lp/mm.)
4.3.2 Spectral line tilt
Since the dispersion direction of the pupil separation prisms is perpendicular to the grating dispersion direction, the spectral line tilt caused by its dispersion nonlinearity not only affects the image fidelity of the spectral imaging system, but also affects the accuracy of spectral calibration. According to the spectral tilt correction method proposed in this study, a complementary prism is designed at the slit, and the material of the complementary prism is the same as that of the pupil separation prisms. In addition, optical design software was used to design an imager spectrometer with only a pupil split prism. Except for the absence of a complementary prism, the content is the same and the imaging quality is similar. This system is used for spectral line tilt comparison. In the UV MSPUI system, the pupil splitting prisms are placed in the T1 and T3 channels respectively, and the T2 channel is placed with a flat plate. Therefore, only the tilt of the spectral lines of the T1 and T3 channel image planes is studied. The comparison of the image plane spectral distributions of the two systems after magnification is shown in Fig. 14(a) (b). It can be intuitively seen that when there is only have pupil separation prism in the MSPUI system and no complementary prism, the image plane spectral lines are more inclined. When there is a complementary prism in the MSPUI system, the image plane spectrum line tilt is smaller after correction by the complementary prism.
Fig. 14. Image surface spectral distribution diagram of UV MSPUI system with or without complementary prism. (Note: (a) There are only pupil separation prisms in the UV MSPUI system, and the schematic diagram of the image plane spectrum line tilt after magnification when there is no complementary prism correction. (b) There are pupil separation prisms and complementary prisms image plane spectrum in the UV MSPUI system. A schematic diagram of the spectral line tilt after enlargement.)
The comparison of system spectral line tilt data before and after correction is shown in Fig. 15. The maximum spectral tilt of channels T1 and T3 is less than 3μm after correction with the complementary prism, while the maximum spectral tilt before correction is ten times that after correction. This indicates that the spectral tilt correction method proposed in this study can effectively correct the spectral tilt.
Fig. 15. Comparison of the spectral line tilt of different channels before and after correction. (Note: (a) Spectral line tilt contrast curves in the T1 channel imager with or without complementary prisms. (b) Spectral line tilt contrast curves in the T3 channel imager with or without complementary prisms.)
5. Conclusion
The MSPUI system based on pupil separation prisms achieve ultra-high spectral resolution while enabling simultaneous detection in multiple channels. However, due to the perpendicular dispersion direction of the pupil separation prisms to the grating dispersion direction, nonlinear dispersion could cause spectral line tilting in the images. This phenomenon leads to complications in post-processing and a decrease in spectral calibration accuracy. To solve this issue, we propose a new design method in this paper to eliminate the spectral line tilt of the MSPUI system, and designs an UV MSPUI system based on the spectral line tilt correction principle. By designing the parameters of the pupil separation prisms and deriving the parameters for the complementary prism, determining the initial structure, and combining subsequent optimizations, the resulting design achieves low spectral line tilting, ultra-high spectral resolution, and simultaneous detection in multiple channels, demonstrating favorable performance.
For demonstration, a UV multiple sub-pupil ultra-spectral imager that eliminates spectral line tilt is designed. The entire system consists of a telescope system and a spectral imaging system. Through independent design and integrated optimization, the design results indicate that in the ultraviolet wavelength range, the three channels T1 = 180∼210 nm, T2 = 275∼305 nm, T3 = 370∼400 nm all achieve spectral resolutions better than 0.1 nm. The system has an F-number of 6.25, and after complementary prism correction, the spectral line tilting in channels T1 and T3 is within 1/3 of a pixel, meeting the usage requirements. When the Nyquist frequency is 30lp/mm, the MTF for all three channels exceeds 0.7, and the RMS radius of the spot diagram for all three channels is less than 9μm. The collimation system and imaging system share the same off-axis three-mirror structure, which is easy to manufacture and adjust, further achieving a compact structure. The UV multiple sub-pupil ultra-spectral imager designed based on the spectral line tilt correction principle can meet practical application requirements. This work can provide a reference for researchers addressing the spectral line tilt issue in designing of multiple sub-pupil imagers.
Funding
National Natural Science Foundation of China (62205330); National Key Research and Development Program of China (2022YFB3903202); Strategic Priority Research Program of the Chinese Academy of Sciences (XDA28050102); B-type Strategic Priority Program of the Chinese Academy of Sciences (XDB41000000).
Acknowledgments
Thanks for the funding support.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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