Technology for detecting spectral radiance by a snapshot multi-imaging spectroradiometer

Technologies to determine spectral sky radiance distributions have evolved in recent years and have enabled new applications in remote sensing, for sky radiance measurements, in biological/diagnostic applications and luminance measurements. Most classical spectral imaging radiance technologies are based on mechanical and/or spectral scans. However, these methods require scanning time in which the spectral radiance distribution might change. To overcome this limitation, different so-called snapshot spectral imaging technologies have been developed that enable spectral and spatial non-scanning measurements. We present a new setup based on a facet mirror that is already used in imaging slicing spectrometers. By duplicating the input image instead of slicing it and using a specially designed entrance slit, we are able to select nearly 200 (14 × 14) channels within the field of view (FOV) for detecting spectral radiance in different directions. In addition, a megapixel image of the FOV is captured by an additional RGB camera. This image can be mapped onto the snapshot spectral image. In this paper, the mechanical setup, technical design considerations and first measurement results of a prototype are presented. For a proof of concept, the device is radiometrically calibrated and a 10 mm × 10 mm test pattern measured within a spectral range of 380 nm–800 nm with an optical bandwidth of 10 nm (full width at half maximum or FWHM). To show its potential in the UV spectral region, zenith sky radiance measurements in the UV of a clear sky were performed. Hence, the prototype was equipped with an entrance optic with a FOV of 0.5° and modified to obtain a radiometrically calibrated spectral range of 280 nm–470 nm with a FWHM of 3 nm. The measurement results have been compared to modeled data processed by UVSPEC, which showed deviations of less than 30%. This is far from being ideal, but an acceptable result with respect to available state-of-the-art intercomparisons.


Introduction
Historically, technologies for assessing spectral imaging radiance data (also called hyperspectral imaging) are based on scanning in either the spectral (Hardeberg et al 2002, Gupta and Voloshinov 2004, Mathews 2008, Sigernes et al 2012 or spatial domain (Hu et al 2005). However, non-scanning, socalled snapshot spectral imaging technologies have become more popular in recent years (Content 1997, Matsuoka et al 2002, Henault et al 2004, Laurent et al 2006, Gehm et al 2007, Wagadarikar et al 2008, Gao et al 2010, Riechelmann et al 2013. These technologies allow time-resolved invest igations of, e.g. cloud movements in atmospheric science, OLED (organic light emitting diode) panel investigations, chemical process analysis, mineralogy of planet surfaces (Brown et al 2010) and many more applications (Brown 2006). A detailed overview of the known spectral snapshot imaging technologies and applications is given in (Hagen and Kudenov 2013). In the following paragraph, a short appraisal is presented to explain the important differences between spectral-scanning, mechanical-scanning and spectral snapshot measurements (figure 1).
Spectral scans (figure 1, second from left) are achieved using, for example optical filter glasses, acousto-optical filters or interferometers. The spectral resolution and spectral domain of this approach is determined by the filtering technology and the measurement time. For higher resolution, a large number of measurements is needed. Furthermore, in some wavelength regions like the UV, only a few types of filters are available whereby the optical performance is limited. However, the advantage of these technologies is a very high spatial resolution since, in principle, highresolution photographic cameras can be used (Bianco et al 2010). Mechanical scans (figure 1, point scanning on the left or line-scanning second from right) vary the field of view (FOV) by either moving the whole spectroradiometer (e.g. remote sensing with the help of satellites or aircraft) or by using mirror-based scanners. As a result, the spatial resolution of point-scanning devices (1D array detector) in both dimensions (x, y) depends on the number of scans. When using line-scanning devices (2D array detector), one spatial dimension (e.g. x) depends on the number of scans, the other (e.g. y) on the number of pixels that can be resolved by the device within the measurement line. This technology is also called push-broom scanning (Davis et al 2002, Brown et al 2008. Hence, the spatial resolution is limited by the measurement time. The advantage of this technology is based on the freedom in the choice of the spectrometer design and performance.
However, all scanning technologies have the common disadvantage that time-resolved effects can only be analyzed when they are significantly slower than the scanning itself. Spectral and point-scanning measurements take time and thus fast temporal effects like cloud movement cannot be resolved.
To analyze such kind of tasks, snapshot spectral imaging technologies are needed. One of many existent approaches is based on imaging a coded spatial and spectral information mixture on the detector and mathematically reconstructing the spectral snapshot image (Gehm et al 2007, Wagadarikar et al 2008. Another approach is the so-called integral field spectroscopy (IFS) snapshot technology, such as fiber bundlebased technologies (IFS-F), where single fibers capture the signal of one measurement channel (Hagen and Kudenov 2013). These fibers are lined up on the entrance slit of a linescanning spectrometer. Subsequently, the maximum spatial resolution is limited by the number of fibers that can be mechanically lined up and optically imaged without channel crosstalk on the detector. A higher resolution system has been achieved by Riechelmann et al (2013) with a spatial resolution of 113 channels. Furthermore, a couple of image slicing spectro meter (ISS) technologies (one example being IFS-M) are known for applications in astronomy or for microscopy purposes (Content 1997, Henault et al 2004, Laurent et al 2006, Gao et al 2009. These approaches are based on a facet mirror optical design, which slices the image into single parts that are spectrally resolved.
In this paper, a new type of IFS approach is presented. A facet mirror is used to produce duplicated images instead of slicing the image as with known IFS-M technologies. For the spatial resolution, different parts of each duplicated image are selected by the entrance slit of a line-scanning spectrometer. These parts are spectrally resolved and can be rearranged by software to obtain the spectral snapshot image afterwards. In addition, a RGB camera can take a high resolution image of one duplicated image by the facet mirror. These data can be used as meta information to simplify further data analysis. For example, the image can be mapped to the lower resolution spectral snapshot imaging data.
The new design is based on very few optical parts and a well-known line-scanning spectrometer with freedom in design of spectral range, spectral resolution and optical bandwidth (full width at half maximum or FWHM Seckmeyer et al (2001)). The new system is called 4D Imager since measurements of an image (2D), spectral resolution (1D) and snapshot in time (1D) with well-balanced performance in all four dimensions could be achieved.

Fundamental concept of the 4D Imager
The essential part of the 4D Imager is a facet mirror (figure 2(b)), which is reflecting the incoming image (figure 2(a)) in different directions. The reflection angle α depends on the specific facet angle β : (1) As shown in figure 2 with one larger mirror (figure 2(c)), these signals can be imaged at the image plane d. Depending on their reflecting angle α, multiple images are generated since they are lined up as duplicated images in the imaging plane (figure 2(d)) in different heights h. The height h depends on the reflection angle α, focal length of the mirror, object and imaging distance. These quantities can be determined by the well-known imaging formulas. For gathering further information about the object, one part of the signal can imaged on an additional camera to obtain a higher spatial resolution image (figure 2(e)).
The lined up images (figure 2(d)) are physically identical and contain the same information. The number of images is determined by the number of facets. In order to extract different information, or parts, out of each image, a customized aperture is used. After the aperture, the lined up image parts enter a well-known line-scanning spectrometer and can be spectrally resolved. Due to a fixed correlation between the slit position and image pixel, the measured data can be rearranged to get the spectral snapshot image voxels ( x, y, λ). This imaging process is schematically shown in figure 3.
This technology has been successfully patented (Zuber 2015).

Design considerations
The size and angle of the mirror facets have to be chosen in such a way that they fit to the whole spectrometer design. The number of facets m of the facet mirror defines the spatial nominal resolution in one dimension (e.g. x). The spatial resolution in the other dimension ( y) is given by the following formula: where n represents the number of pixels, which can be resolved spectrally by the line-scanning spectrometer. u is a parameter depending on the system design and represents the amount of pixels that cannot be used per measurement (see figure 3(e)). The width of the single slits of the customized aperture (figure 3(c)) is not only determining the part of the image that is selected, it directly affects the optical bandwidth (FWHM) since it represents the entrance slit of the spectro meter. The spectral range and resolution of this technology only depends on the design of the line-scanning spectro meter (l/mm of the grating, etc). Due to the image duplication and selection process, the entrance slit of the spectrometer is shaped like a saw tooth (figure 3(c)). This directly affects the spectral range, which is slightly shifted (o n ) at each set of channels (figure 3(e)). In terms of alignment, the key task of this technology is the mapping of the customized aperture (figure 3(c)) to the duplicated images (figure 3(b)). Tilts, rotation, and a shifting of the aperture would directly lead to an incorrect selection of spatial pixels of the duplicated images.

Characterization of the 4D Imager prototype
In order to perform proof of concept measurements, a 4D Imager prototype has been developed and configured for the visible spectral region with a spatial resolution of 14 × 14 channels. The measurement object is a 10 mm × 10 mm test pattern with a distance of 1 m. An additional facet is used to provide a spatially higher resolution image, captured with an RGB camera. The prototype is based on UV enhanced mirrors (Edmund Optics) and optical gratings (Newport) from stock. As a detector a Princeton Instruments Pixis 400B has been choosen. As a RGB camera, for the additional image, a AVT MAKO G-125C POE was used. The facet mirror has been produced by Gigahertz-Optik GmbH.
In the following, the calibration steps of this setup and measurement results are presented.

Channel calibration (object position to detector position)
The incoming signal is spectrally analyzed by a line-scanning spectrometer. To assign each pixel on the chip with the dimensions ( x, λ) to a measurement point (channel) in the 3D cube with the dimensions ( x, y, λ), the measured data need to be rearranged to the original image. Therefore, the correlation between the pixels of the detector and the channels of the image has to be determined (figure 3, step (e)-(f)). This was achieved by observing an unambiguous test pattern and identifying the position of each channel of the test pattern on the detector.  Due to image distortions within the spectrometer, the single channels are not imaged exactly along one pixel row in the spectral domain of the detector. An additional curve fitting individual for each channel on the detector along the signal in the spectral domain similar to Gao et al (2010) has been applied to correct these image distortions. In addition, the higher resolution data gained from the additional camera can be mapped to the spatial lower resolution spectral snapshot imaging measurement.

Wavelength calibration and optical bandwidth
The wavelength calibration of each channel has been achieved with the help of intrinsic lines of several pen ray lamps. The spectral range of a single channel enables a delta of 500 nm, e.g. 380 nm-880 nm in this configuration. However, as shown in figure 3(e), each set of channels is slightly shifted in the spectral domain. Thus, the common spectral range of all channels is 380 nm-800 nm with an optical bandwidth (FWHM) of 10 nm.

Radiometric calibration
The radiometric calibration of the 4D Imager has been performed by using a 210 mm integrating sphere based uniform light source traceable to the Physikalische Technische Bundesanstalt (PTB). The calibration uncertainty of this standard is 2% (k = 2) in the spectral range above 450 nm and is linearly increasing below 450 nm to 3.2% at 380 nm. The radiance distribution of the 65 mm exit port of the integrating sphere has to be very homogeneous within the FOV of the 4D Imager to ensure low calibration uncertainties. The inhomogeneity of the calibration source used is better than ± 0.20%. The 4D Imager has been calibrated at the measurement location so that no movement of the instrument between calibration and measurement is needed.

Measurement results
A proof of concept measurement has been performed to analyze the spatial performance (channel separation) of the 4D Imager. As a measurement object, a 10 mm × 10 mm laser cut test pattern with 14 × 14 pixels has been backside illuminated with a tungsten lamp. To clarify the channel separation, the raw signal on the detector chip is presented in figure 4. The raw signal   . The different spatial information gets selected by a customized aperture (c). The selected data (d) are entering a line-scanning spectrometer where the single pixels are spectrally resolved (e). This data can be rearranged to get the spectral snapshot imaging voxels (f). Details of (e): between two sets of channels, such as ( x 1 , y m ) and ( x 2 , y m ), a few channels cannot be used (u n ). According to the saw tooth shape of the entrance slit (c), the wavelength range of each set is slightly shifted (o n ) to the next set. The measurement data can be remapped (f) into voxels ( x, y, λ).
shows 14 imaged channel sets from which 14 channels can be used each. In principle, more detector pixels than could be used in each channel set. However, only 14 are clearly separated by a channel crosstalk of less than 4% (see figure 5). This investigation of the crosstalk is based on a perfectly aligned test pattern to the FOV of the 4D Imager. A slight offset, which might be present, leads to signals that appear like channel crosstalk.
The described calibration process has been applied to this raw data. Furthermore, the measured spectral snapshot imaging data have been mapped by the measurement software to the higher resolution image (0.58 megapixels) taken with the additional camera. In addition, the spectral data of two channels are illustrated in figure 6.
The measurement has been performed for all 196 channels simultaneously with an integration time of 3 s. No averaging or smoothing has been applied.
This measurement indicates a successful separation of the channels on the detector chip. However, to show the spectral radiometric capabilities of the new instrument, measurements     11°04′46.3″E) and ratio to UVSPEC generated data (convolved to 3 nm FWHM) are illustrated. In addition, the standard deviation of 196 channels (all) and 164 channels is shown. Some channels exhibit significant stray light, which can be recognized by the increase of the standard deviation, especially below 340 nm. of an object with a different spectral distribution compared to the calibration lamp have to be performed.

Application of the 4D Imager for spectral sky radiance measurements
For the analysis of the spectral radiometric performance of the 4D Imager and its capability in the UV, snapshot radiance measurements of the sky zenith were performed. Due to a large dynamic and high spectral stray light, solar radiation is difficult to measure, especially in the UV (Seckmeyer et al 2001). Hence, the optical design of the 4D Imager has been modified to access the UV spectral range and to achieve a smaller optical bandwidth (FWHM). Furthermore, the device has been equipped with an entrance optic to achieve a 0.5° FOV of zenith sky radiance, see figure 7, left.

Calibration
The calibration process was performed in the same manner as the VIS setup as described before. The calibration uncertainty of the standard increases linearly in the UV from 2% (k = 2) at 450 nm to 5% (k = 2) at 280 nm. A spectral range of 280 nm to 470 nm with a mean optical bandwidth of 3 nm (FWHM) was achieved (see figure 8). The measurements are corrected for stray light using a simple method similar to Riechelmann et al (2013), which is based on subtracting stray light signals from the measurement channel signals using detector channels that are not illuminated by the light source (see figure 3(e), channels u).

Measurement results
In figure 9 a measurement of a uniform spectral radiance calibration standard, which is as well traceable to PTB, has been performed to check the absolute radiometric capability of the measurement system. This standard is different to the used standard during calibration. The calibration uncertainty of this standard is 3.5% (k = 2) in the spectral range above 350 nm and is linearly increasing with decreasing wavelength below 350 nm to 6.5% at 280 nm. The measurement results show an agreement with a deviation of less than ±3% in the spectral range 370 nm-470 nm. Below 370 nm the residual deviation is rising to about −15% in maximum mainly due to an insufficient signal to noise ratio.
The measurement results show that all channels of the 4D Imager possess an offset of about −30% compared to the UVSPEC simulation results within the wavelength range 330 nm-470 nm. In addition, this offset shows a spectral variation due to not perfectly matched optical bandwidths for all channels at the Fraunhofer lines since every channel has a different FWHM (see figure 8). Furthermore, the standard deviation for the mean of 164 channels compared the standard deviation of 196 channels (all) shows that 32 channels exhibit significant stray light, especially below 340 nm.
In figure 11, a first measurement of a spectral sky radiance distribution using a wide angle entrance optic (FOV: 16.8° to 73.5°) is shown. This entrance optic (see figure 6, right) is mirror based and its design is according to Chahl and Srinivasan (1997). The measurement was captured within an integration time of 1 s.

Discussion and conclusions
Spectral snapshot imaging measurements have been performed with the 4D Imager, which is a new type of IFS technology. This technology is based on only a few optical parts which key component is a facet mirror that duplicates the object image. For the spectral analysis, a line-scanning spectrometer can be used. Hence, the spectral range and resolution of this technology is defined by the design of the spectro meter (l/mm of the grating, etc) whereby applications in the UV are also possible. These are the key advantages compared to other IFS approaches. The achievable spatial resolution can be as well designed with freedom since it depends on the number of facets, the detector resolution and the quality of the image selection process (customized aperture) connected with the imaging quality of the line-scanning spectrometer. The challenge of this technology is to image the duplicated images precisely on the entrance slit of the line-scanning spectrometer to support the selection process. An overview of the 4D Imager compared to different IFS technologies is presented in table 1. In this paper, proof of concept radiance measurements of a 10 mm × 10 mm test pattern with a distance of 1 m and a spatial resolution of 14 × 14 channels (196) are shown. A channel crosstalk of less than 4% was attained. The channel crosstalk could be even smaller since the investigated signal is a mixture of the real channel crosstalk (optical imaging performance) and the alignment of the test pattern to the FOV of the 4D Imager. The device has been radiometrically calibrated, traceable to PTB, in the spectral range of 380 nm-800 nm with an optical bandwidth of 10 nm (FWHM). Furthermore, the spectral snapshot imaging data (196 channels) have been mapped with a higher resolution RGB image that was captured by an additional facet and camera.
To demonstrate the spectral capabilities of this technology, spectral zenith sky radiance measurements in the UV region have been performed. Therefore, the prototype was adapted for a spectral range of 280 nm-470 nm with a mean optical bandwidth of 3 nm (FWHM), a FOV of 0.5° and 196 channels. To check the radiometric capabilities of the measurement system a radiance measurement of a calibration standard was carried out. The results show a good agreement with a residual deviation of less then ±3% in the spectral range 370 nm-470 nm where sufficient signal to noise ratio is given by the used calibration standard. After this validation a spectral zenith sky radiance measurement was realized. The comparison of this measurement with UVSPEC generated data showed an average offset of −30% in the range of 330 nm-470 nm. The reason for this deviation could not been determined exactly. The uncertainty of any radiation measuring instrument is given by the combined calibration and measurement uncertainty. When comparing with modeled values, the uncertainty of the model and its input parameters must be considered as well. The UVSPEC model uncertainty is mainly dominated by the input parameters, e.g. aerosol characteristics of the atmosphere. This uncertainty has been investigated by Cordero et al (2013) for spectral UV irradiance. He found uncertainties for the UV-A range of about 3% for unpolluted atmospheres and about 5% for polluted atmospheres if realistic input uncertainties are assumed. The publication from van Weele et al (2000) showed that a difference of up to 20% at 305 nm between different UV models exists. Mayer et al (1997) found systematic differences between irradiance measurements and the UVSPEC model in the range between −11% to +2% for wavelengths between 295 nm and 400 nm and solar zenith sky angles up to 80°. The uncertainty of spectral UV irradiance measurements have been systematically assessed by Bernhard and Seckmeyer (1999) and found to be about 13% at 300 nm under ideal circumstances. Such uncertainties were later confirmed with a Monte-Carlo-approach by Cordero et al (2013). Pissulla et al (2009) showed that five independent calibrated systems exhibit a spectral radiance difference to UVSPEC between 3% and about 35%.
This suggests that an offset of −30% for spectral radiance is not very good, but still in the range of an acceptable agreement between the UVSPEC model and the 4D Imager. Furthermore, this comparison between UVSPEC and the 4D Imager measurement is based on the assumption of a clear sky, which might be not the case during the measurement (2017-02-15 14:15 UTC + 1 48°06′03.6″N 11°04′46.3″E).
It should be noted that the measurement showed that 36 channels exhibit significant stray light, especially below 340 nm. This is mainly caused by the prototype using an optical table setup at which the spectrometer housing was not yet completely light tight.
In this publication we do not want to show the possible endpoint of longer development, but just want to describe a proof of a new concept. The measurement results show the potential of the 4D Imager technology to measure spectral radiance using snapshot imaging. However, for high accuracy measurements, especially in the UV, a fixed setup with optimized light traps and a machine processed spectrometer housing would be needed. The optical table-based prototype used for these measurements clearly showed its limits when using it outdoors.