We have focused on the optical form that is low cost while maintaining high performance for airborne application. We report the optical design as well as the alignment and test results for a push-broom imaging spectrometer. The smart architecture of the prism-grating based spectrometer ensures high uniformity and image quality. Moreover, an effective method for aligning the spectrometer is also proposed. The results of laboratory-based optical tests and a flight test confirm the easy manufacture and excellent performance. Thus, the proposed system should be suitable for use as a hyperspectral instrument that can be loaded onto airborne and unmanned aerial vehicles.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Rapid improvements in optics and computer technology led to the development of imaging spectrometers in the late 1970s . These instruments have since been used widely for scientific instrumentation for earth-based, airborne, and space-based applications [2,3]. Many practical imaging spectrometers have been developed, and most of them are based on gratings or prisms. A few examples are the Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) , the Compact Airborne Spectrographic Imager (CASI) , the compact prism spectrometer for hyperspectral imaging developed by the Environmental Mapping and Analysis Program (EnMAP) , and the Landsat-swath imaging spectrometer . Among these, AVIRIS is a whisk-broom imaging spectrometer while the other three are all push-broom imaging spectrometers. Push-broom imaging spectrometers can achieve higher signal-to-noise ratios (SNR) compared to their whisk-broom counterparts  and need not depend on the scanning mechanism. Thus, they are employed widely for both research and practical applications, including mineral identification, environment monitoring, and agriculture studies, to name a few. However, in contrast to the high spectral and spatial uniformity of whisk-broom imaging spectrometers, “smile” and “keystone” distortions plague most push-broom instruments if no special control over them during the design stage.
The “smile” distortion (sometimes named as spectral line curvature or slit curvature), which refers to a curvature of the monochromatic image of the slit in the spectral dimension, leads to the misregistration of the detector pixels across the field of view (FOV) of the spectrometer in the spectral dimension. On the other hand, the “keystone” distortion, which refers to variations in the slit magnification with the wavelength, leads to the interband spatial misregistration in the spectral dimension. In general, these geometric distortions can be caused by aberrations in the spectrometer optics. The smile is primarily caused by the dispersive element, which is a prism or grating. The field stop of push-broom imaging spectrometers is a straight-entrance slit at the focal plane of the fore-optics. In the case of a grating or prism spectrometer, the smile derives from the grating equation or the prism dispersion equation. The smile and keystone increase the difficulty of the calibration and correction tasks . Thus, they should be corrected in the optical system design stage.
In the case of dispersive-type spectrometers, in order to minimize distortions, the optical design is usually based on a concentric system with a spherical grating or curved prism or a combination of the two. Examples of spectrometers based on a spherical grating include spectrometers of the Offner and Dyson forms, wherein the grating is convex and concave, respectively. Both have been shown to result in perfect image quality at low distortion levels [10–13]. An example of a system with a curved prism is the spectrometer developed by EnMAP, whose dispersive component is a Féry prism . The use of a combination of dispersive components (a grating and two prisms) was proposed by Mauri Aikio in 1991, with the first such system developed being the Airborne Imaging Spectrometer for Applications (AISA) in 1993 . Other combination have also been proposed, such as that based on a flat grating and a decenter lens. Besides, in recent years, the prevalence of free-form surfaces has resulted in novel spectrometer designs [16,17].
Here, we propose a novel design for prism-grating imaging spectrometers, wherein a flat grating is employed as the dispersive component. The spectrometer exhibits low distortion and good image quality, in making some concession to the compactness with its more expensive curve grating based counterpart. However, compared to classical prism-grating spectrometers wherein both the collimator and the re-imager are lenses and the core dispersive element is a transmission volume phase grating made of gelatin, the proposed spectrometer has the following advantages: (1) it has a simpler optical system and higher throughout—a single spherical mirror is employed as the collimator instead of a multipiece lens; the former is also more suitable for a long-slit design and (2) it uses a low-cost, high-stability dispersive component. The grating is a reflective flat blazed grating fabricated by lithography, making it suitable for low-groove-density manufacture. In this study, the optical architecture of the instrument is described, including its optomechanical design, assembly, and alignment, and the results of laboratory assessments and preliminary flight tests are discussed.
2. Optical design
2.1 System design specifications and performance
The design specifications of the system and its performance are listed in Table 1. The system has a speed of f/3.6 with a cross-track FOV of 14.58° and spectral range of 400–1000 nm. A silicon-based charge coupled device (CCD) with 2048 spatial elements and 256 spectral elements is used. The instantaneous FOV is 0.125 mrad; thus, the pixel size at a flight altitude of 1000 m is 0.125 m.
It should be noted that the proposed visible and near-infrared (VNIR) waveband imaging spectrometer is composed of three identical submodules. The total FOV of the spectrometer is as high as 40°. Thus, here we only focus on the design of its submodules.
The submodule is a prism-grating imaging spectrometer, and its optical system features an off-axis three-mirror anastigmatic (TMA) fore-optics that feeds a reflective-refractive dispersive spectrometer, as shown in Fig. 1. The spectrometer employs a prism-grating combination as its dispersive component, a single sphere mirror as the collimator, and a six-piece lens as the re-imager. The slit is set on the focal plane of the single-sphere mirror. Thus, the dispersive component lies in the semi-collimated beam.
2.2 Dispersive component
We propose a spectrometer design that utilizes a prism-grating dispersive component, which has the advantages of being simple, low cost, and highly feasible. The dispersive component is composed of a prism and a flat blazed grating. We have a better foundation and cooperation for the manufacture of the low-groove-density reflective grating, so we use a reflective grating rather than transmission grating. The reflective flat grating is the core dispersive element, while the prism is the auxiliary one and is attached to compensate for spectral distortions. For convenience of analysis, the prism-grating dispersive component can be divided into the two dependent elements, namely, the prism and the grating, as shown in Fig. 2.
First, as shown in Fig. 2.(a), for pupil matching with the TMA fore-optics, the stop of the spectrometer is set on the rear of the prism. For convenience of alignment, the prism is designed to be a right prism, and its rear is parallel to the surface xoz; the output chief ray of the center field from the grating is controlled to be parallel to the z-axis. The geometric relationship between the mirror and the prism-grating component can be expressed as
Second, as shown in Fig. 2.(b), according to refraction law, we get
According to the refraction law and based on the similarity between the object and the image, it can be deduced that
Thus, the refraction equation of the non-center chief ray of the slit in the principle section can be obtained from Eqs. (2) and (3) and can be expressed as
By taking the differential of the second expression of Eq. (4), we get the differential of the dispersion angle of the non-center chief ray of the slit in the principle section, which can be expressed as
According to the above equations, is a function of (which corresponds to the ratio of the slit height and the focal length of the collimator), (refraction index of the prism), (which corresponds to the position of the prism), and (which corresponds to the shape of the prism), that is, . Thus, can be obtained once the initial values of the above-mentioned parameters are set. The chief rays from the slit pass through the different dispersive sections with different vertex angles, which results in . Generally, a prism spectrometer suffers from geometrical distortion, because the smile of the prism leads to . Besides, it also bends forward the short end of the wave.Eq. (7) into Eq. (6), we can obtain the difference in the angles, which can be expressed as
Based on the above equations, it can be concluded that is a function of (which corresponds to the ratio of the slit height and the focal length of the collimator), (diffraction order), (grating spacing), (position of the grating), that is, . Thus, can also be obtained once the initial values of the above-mentioned parameters are set. The chief rays from the slit pass through the different diffractive sections with different diffraction angles, which results in . Generally, a flat-grating spectrometer also suffers from geometrical distortions, because the smile of the grating leads to . Besides, it also bends forward the long end of the wave.
In theory, the problem of smile distortion at a certain wavelength can be overcome by combining a prism and a grating, owing to the compensation resulting from the inverse dispersion characteristics of the components. Given the initial values of some of the parameters, including the slit length, focal length of the collimating lens, refractive index of the prism, diffraction order, and grating spacing and using Eqs. (1), (5), and (8), the shape and position of the prism and the position of the grating can be determined.
2.3 Spectrometer design
The optical design of the proposed imaging spectrometer for hyperspectral application meets the stringent requirements related to distortion and image quality, which are controlled by the fore-optics and the spectrometer, respectively.
In most grating-prism-based spectrometers, both the collimator and the re-imager are multipiece lenses. Thus, there are more than ten refractive elements in the spectrometer; this decreases the throughput and in some case increases the difficulty of aberration correction for a long-slit design. To achieve a relatively higher throughput and simplify the optical structure, the proposed spectrometer employs a reflective-refractive form. A single on-axis spherical mirror replaces the lens as the collimator; this does not cause achromaticity. To be easier for aberration correction and alignment, and moderate for volume and cost, the multipiece lens is retained as re-imager rather than aspherical mirrors. The re-imager is a six-piece lens and can readily compensate for other aberrations arising from the collimator.
The design process of the prism-grating spectrometer is as follows:
- (1) Set the magnification of the spectrometer and the slit length and subsequently set the focal length of the collimator and the re-imager.
- (2) Simulate the paraxial model of the spectrometer using the Zemax design software and calculate the grating spacing.
- (3) Calculate the position of the plane mirror, wedge angle of the prism, and position of the flat grating using Eqs. (1), (5), and (8).
- (4) Obtain the six-piece lens model.
- (5) Establish the initial model of the spectrometer.
- (6) Edit the merit function for image quality, distortion, and constraint conditions.
- (7) Perform optimization.
We set the magnification to −1 × , so the slit length was 32.768 mm. We set the focal lengths of the collimator and the re-imager to 160 mm. Next, we chose the glass material and optimized the six-piece lens to obtain the initially aberration corrected re-imager. This was then incorporated into the initial model of spectrometer. As mentioned in Section 2.2, the stop was set on the rear of the prism. Based on this initial model, subsequent optimization led to a design that resulted in low distortion and good imaging performance for all the spherical surfaces and was also compact.
The design results for the image quality and the spectral response of the spectrometer are shown in Fig. 3. The RMS radii of three field points are less than 5.7 μm over the entire spectrum, which is less than the unit pixel size. The full width at half maximum (FWHM) of the designed spectral response function (SRF) spanning the entire spectrum is approximately 1.15. The maximum smile occurs at the end of the slit at a wavelength of 0.4 μm, which is less than 3% of a pixel. The maximum keystone occurs at the end of the slit at 1000 nm, which is less than 4% of a pixel. Thus, using a prism and a flat blazed grating together as the dispersive component has an obvious positive effect on distortion.
The dispersion curve is almost a straight line spanning from 400 to 1000 nm; this suggests that the spectral nonlinearity arising from the prism can be neglected in the prism-grating spectrometer. With the exception of the general stray light related to the multiple reflections (of the filter, the window of the detector, and the other optical surfaces) and scattering, which are suppressed by the coating, by using the appropriate mechanical design, and by blackening, the other-order diffraction rays of the grating make the greatest contribution to stray light. As other orders re-image at the imaging plane shown in Fig. 4(a), an order-sorting filter (OSF), whose design is shown in Fig. 4(b), is placed near the CCD. The OSF has two coating segments, which weaken the second-order and other-order strays effectively.
2.4 Fore-optics design
The fore-optics and the spectrometer are designed separately. The image quality, distortion, and pupil position are controlled reasonably well in both parts. The fore-optics is designed to meet the requirements for good image quality, low distortion, compact volume, high throughput, and suitable clearance and has an appropriate pupil for integration with the spectrometer. The entrance pupil of the spectrometer lies 695 mm in front of the slit. Thus, the TMA form is selected for the fore-optics. The design specifications and performance of the TMA are listed in Table 2. The TMA exhibited excellent performance in terms of image quality as well as very low distortion.
2.5 Optical system integration
The TMA and the spectrometer are then combined, such that the stop is located on the rear of the prism. The virtual stop of the TMA permits the system stop within the spectrometer to act as the limiting aperture. This method of pupil matching is a reasonable one. The optical layout of the imaging spectrometer is shown in Fig. 1.
The system design results are shown in Fig. 5. The RMS radii in all the fields are less than 5.6 μm at wavelengths of 400, 550, 700, 850, and 1000 nm; this is less than a single pixel. The modulation transfer functions (MTF) are greater than 0.83 at 15.625 lp/mm and 0.64 at 31.25 lp/mm in each field at wavelengths of 400, 700, and 1000 nm. Moreover, the designed CRF FWHM spanning the entire spectrum is approximately 1.05. These data confirm the suitability of the optical design.
2.6 Prediction of signal-to-noise ratio
The two main factors affecting the SNR of a prism-grating imaging spectrometer are the quantum efficiency of the detector and the optical throughout. A Jaguar sensor bought from DALSA. Inc. is used as the electronic sensor. The simulated quantum efficiency is higher than 60% for approximately 75% of the spectrum, as shown in Fig. 6(a). All the reflective mirrors as well as the grating are aluminum coated. All the lenses as well as the prism are coated with an antireflection material. The optical efficiency of the order-sorting filter is more than 95%. The grating has a determining effect on the optical efficiency. The groove density of the grating is 30 lines per mm. Owing to the tight tolerance of the blaze angle, which is very small (approximately 0.6°), a single-blaze design is employed rather than a double-blaze one. The absolute difference between the measured and simulated diffraction efficiencies was less than 6%, as shown in Fig. 6(b), highlighting the precision of the reflective flat grating with a low groove density and small blaze angle.
The SNR was predicted under the following conditions: solar zenith of 60°, surface reflectance of 0.3, standard atmospheric conditions, integration of 12.5 ms, and spectral sampling of 2.34 nm. The SNR shown in Fig. 7, which was determined while considering the atmospheric effects, is not less than 200 for more than 75% of the spectral region. Moreover, the SNR will be higher in the case of the overlaying of the frame frequency or spatial merging.
3. Tolerance, assembly and alignment
Tolerance analyses that only focus on the image quality are not sufficient in the case of imaging spectrometers . The spatial and spectral characteristics should both be considered together in the merit function (MT) for tolerance analysis, which should account for spatial sampling and spectral sampling as well as the smile and keystone effects. The tolerances are determined based on the feasibility and accuracy of the manufacturing and alignment processes along with the environment effects. The error budget for the imaging spectrometer is listed in Table 3. With the exception of the budget for the manufacturing and alignment processes, the other items correspond to the environment and testing.
The tolerances of the fore-optics and the spectrometer are first analyzed separately and then in the case of the integrated system. The MT for the fore-optics includes the RMS spot size and the focal length related to spatial sampling. The MT for the spectrometer includes the MTF, magnification, smile, and keystone, among other factors.
The tolerance analyses revealed that the tightest offenders were the 2nd and 4th lenses, including the front surface tilt of the 2nd lens (approximately 45″), and the rear surface and element tilts of the 4th lens (approximately 44″ and 30″, respectively). Each of these tight tiles can be ensured using the centering technique. Overall, the set tolerances were acceptable and readily achieved in the case of the manufacturing and alignment processes. Under these tolerances, the MTF for the system may be more than 90% of the designed value. Thus, one can expect that the system can be built as required.
3.2 Assembly and alignment
The overall system consists of a fore-optics and the spectrometer itself, with the latter containing three parts: the collimator, the prism-grating component, and the re-imager, as shown in Fig. 8. The collimator housing is the main frame of the system, into which the other parts are assembled. Details of each part are listed in Table 4.
The main principles of the assembly and alignment of the system are as follows. First, the mechanical brackets and optical elements are fabricated and tested to ensure that they strictly meet the designed tolerances. The optical elements and components are then assembled based on their precisely fabricated edges and subsequently aligned with the compensator to ensure good performance. Next, the fore-optics and the spectrometer are assembled and aligned separately. They are then integrated together by aligning the fore-optics relative to the spectrometer.
The assembly and alignment of the fore-optics is strictly based on the first principle mentioned above. The mirrors are assembled against the optical and mechanical edges. Next, the tertiary is aligned as the compensator to improve the wavefront performance as determined based on interferometrical measurements. The RMS error of the wavefront as measured based on the representative field points is shown in Fig. 9; the deviations from the design values are less than 0.02, confirming good alignment.
The assembly of the spectrometer includes the separate assembly of the collimator, prism-grating dispersive component, and re-imager. The assembly process for the first two parts is similar to that for the fore-optics. The re-imager is assembled using the centering technique. The lowest tilt tolerance of the re-imager is less than 30″ as measured with an OptiCentricsystem. After the separate assembly of each component, the mirror, collimator, dispersive component, and re-imager are bonded to the main frame.
The alignment of the spectrometer refers to the clocking of the grating relative to the slit and the precise positioning of the CCD. For this, an auxiliary two-dimensional slit is used, as shown in Fig. 10(a). The mechanical parameters of the substrate and the fabrication process of the auxiliary slit are the same as those for the formal slit. The connection of the horizontal slits is equivalent to the spectrometer slit, which is used to monitor the spectral location and spectral response; the vertical bars are used to monitor the field points and the spatial response during alignment, as shown in Figs. 10(b) and (c). The source can be an integrating ball with a laser or a mercury or tungsten halogen lamp. Hence, the clocking of the grating and the spatial and spectral responses can be monitored simultaneously. Compared to a formal slit, the two-dimensional slit results in better alignment. After the precise adjustment and assembly of the grating and CCD detector, the auxiliary two-dimensional slit is replaced by the formal slit by monitoring the spectral response obtained using the same monochromatic source.
The system is integrated after the alignment of the fore-optics and the spectrometer. The fore-optics is attached to the spectrometer relative to the slit by monitoring the MTF of the system, wherein the fore-optics acts as the compensator. The platform used for system integration consists of a parabolic collimator (focal length is 2 m and aperture is 300 mm), a goniometric stage (loads the under-test imaging spectrometer, ensuring an adjustable field), and a bars target at the focal plane of the collimator illuminated by a laser or tungsten halogen lamp. The MTF measured over the entire imaging plane is listed in Table 5; 90% of the data are beyond 80% of the designed value (MTF of the CCD is approximately 0.6), confirming that the imaging spectrometer was well aligned.
4. Performance measurements and assessment
The performance of the prism-grating imaging spectrometer was assessed in the laboratory, primarily based on measurements of its spatial and spectral characteristics. In addition, hyperspectral image of engineering flight was also provided.
4.1 Spatial characteristics
The spatial characteristics, including the across-track response function (CRF) and along-track spatial response function (ARF), were measured on the described platform. A subpixel slit was placed instead of the bars as the target on the focal plane of the collimator. This subpixel slit was oriented perpendicular (CRF measurements) or parallel (ARF measurements) to the spectrometer slit and scanned across or along the track. Both the CRF and the ARF were measured for different fields and wavelengths.
The representative normalized CRF and ARF values are shown in Fig. 11 (left and right, respectively). The FWHM of the CRF is approximately 1.12 pixel units, and its variation with the wavelength is less than 10% for each spatial field. The FWHM of the ARF is also approximately 1.08 pixel units, and even its variation with the wavelength is less than 10%. Other locations yielded similar results.
The keystone was obtained by measuring the centroids of the CRF for different wavelengths. The keystone values for five fields are shown in Fig. 12. The 95% centroids of the CRF disturb within ± 5% of a pixel, while the designed values are also within ± 5% of a pixel.
4.2 Spectral characteristics
The spectral characteristics were also measured using the above-described platform. The collimator was replaced by one with a shorter focal length to increase the signal entering the instrument entrance, and the subpixel slit was replaced by a monochromator for wavelength scanning; the exit slit was placed at the focal plane of the collimator and was perpendicular to the instrument slit. A low-pressure Hg lamp with known wavelengths was employed to calibrate the monochromator. The width of the exit slit was set appropriately, so that the signal was as large as possible and the output spectral bandwidth was narrower than 1/6 the spectral sampling size of the test undertest instrument.
The SRF was measured for five different field points through a wavelength scan of the monochromator. The representative normalized SRF values of the center field from spectral rows 53 to 61 are shown in Fig. 13(a). The curves are almost Gaussian. The FWHM of the measured SRF, shown in Fig. 13(b), is approximately 1.18 pixel units while the variation in the FWHM is less than 15% of a pixel.
The smile was obtained by measuring the centroids of the SRF through the fields. The smile values for three wavelengths (approximately 435, 589, and 915 nm) are shown in Fig. 14. The horizontal axis represents the spatial pixels. The curves were obtained through second or fourth-order polynomial fitting. The locking misalignment was negligible. It can be seen that 95% of the centroids of the SRF disturb within the ± 5% of a pixel.
4.3 Flight image
We have developed the wideband and multimodule instrument, which is the abbreviation of ultra-violet (UV), VNIR, short-wave infrared (SWIR) and long-wave infrared bands (LWIR ). The instrument exhibits a large FOV (40°) for each band. The VNIR imaging spectrometer was composed by three identical submodules described in this study.
The VNIR imaging spectrometer was integrated with the subsystems for the other bands (UV, SWIR, and LWIR) at the Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics. The system was mounted on a Leica PAV80 gyro-stabilized platform in June 2018, and all the bands were tested during flight. A rectified RGB-bands image from VNIR imaging spectrometer is shown in Fig. 15, confirming the good alignment and high resolution of the system.
The VNIR submodule has 256 channels spanning from 400 to 1000 nm. Its optical system is composed of an off-axis TMA fore-optics and a reflective-refractive spectrometer. The smart spectrometer uses a single spherical mirror as the collimator, a prism grating as the dispersive component, and a six-piece lens as the re-imager. The blazed reflective flat grating is the core dispersive element, while the prism is used as an auxiliary one to compensate for spectral distortion. Laboratory tests confirmed that the instrument exhibits good performance, including desirable spatial and spectral characteristics. In addition, a flight test of the instrument was performed, and hyperspectral images were collected in June, 2018, during a land and resource survey.
The proposed instrument design results in low distortion and high image quality as well as feasible tolerances for the manufacture and alignment processes. Further, the manufacturing price of the instrument is low, and it has high reliability. Thus, it is anticipated that the instrument will find wide use in various aerial applications.
Youth Innovation Promotion Association CAS (2017286); National Natural Science Foundation of China (NSFC) (61775227, 61627804).
We would like to acknowledge the following for helpful work: Qiujie Yang, Hongxuan Yu, Gang Lv, Daogang He and Shengwei Wang regarding the design and alignment.
1. P. Z. Mouroulis and R. O. Green, “Review of high fidelity imaging spectrometer design for remote sensing,” Opt. Eng. 57(4), 040901 (2018). [CrossRef]
2. A. F. H. Goetz, “Three decades of hyperspectral remote sensing of the Earth: A personal view,” Remote Sens. Environ. 113, S5–S16 (2009). [CrossRef]
3. F. Sigernes, M. Syrjäsuo, R. Storvold, J. Fortuna, M. E. Grøtte, and T. A. Johansen, “Do it yourself hyperspectral imager for handheld to airborne operations,” Opt. Express 26(5), 6021–6035 (2018). [CrossRef] [PubMed]
4. R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998). [CrossRef]
6. B. Sang, J. Schubert, S. Kaiser, V. Mogulsky, C. Neumann, K. Förster, S. Hofer, T. Stufflera, H. Kaufmann, A. Müllerc, T. Eversberg, and C. Chlebekd, “The EnMAP hyperspectral imaging spectrometer: instrument concept, calibration and technologies,” Proc. SPIE 7086, 708605 (2008). [CrossRef]
7. P. Z. Mouroulis, R. O. Green, B. V. Gorp, L. B. Moore, D. W. Wilson, and H. A. Bender, “Landsat swath imaging spectrometer design,” Opt. Eng. 55(1), 015104 (2016). [CrossRef]
8. P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. 39(13), 2210–2220 (2000). [CrossRef] [PubMed]
9. S. Qian, Optical Satellite: Signal Processing and Enhancement (SPIE, 2013), Chap. 8.
11. P. Z. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” J. Geophys. Opt. Eng. 46(6), 063001 (2007). [CrossRef]
12. D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high-performance infrared applications,” Opt. Eng. 47(10), 103601 (2008). [CrossRef]
14. J. Kolmeder, A. Kuisl, B. Sang, M. Lettner, A. Godenir, M. Glier, M. Sornig, and S. Fischer, “Optical intergration process for the earth-observing satellite mission ENMAP,” Proc. SPIE 10562, 1056226 (2016).
15. B. M. Braam, J. T. Okkonen, M. Aikio, K. Makisara, and J. F. Bolton, “I Design and first test results of the Finnish Airborne Imaging Spectrometer for different Applications, AISA,” Proc. SPIE 1937, 142–151 (1993). [CrossRef]
17. L. Yuan, J. Xie, J. Hou, G. Lv, and Z. He, “Optical design of compact infrared imaging spectrometer,” Infrared Laser Eng. 47(4), 0418001 (2018). [CrossRef]
18. G. Wu, Design of spectrograph (Science, 1978), Chap. 4.
19. L. B. Moore and P. Mouroulis, “Tolerancing methods and metrics for imaging spectrometers,” Proc. SPIE 10590, 105900Q–1 (2017).
20. L. Yuan, Z. He, G. Lv, Y. Wang, C. Li, J. Xie, and J. Wang, “Optical design, laboratory test, and calibration of airborne long wave infrared imaging spectrometer,” Opt. Express 25(19), 22440–22454 (2017). [CrossRef] [PubMed]