5.1

Stray light characterisation

The Instrument Response Matrix gives the normalised instrument spatial and instrument spectral response to real world spatial and real world spectral quasi-point sources (at the resolution of the measurement). The stray light matrix of the instrument is the IRM minus the direct light, i.e., light from the real world spectral and spatial dimensions that ends up on the intended instrument spectral and spatial pixels.

The real-world spectral range and resolution of the stray light characterisation is determined through the OPD scan step size and range, respectively. These are under control of the operator and not limited by the instrument under investigation, only by the interferometer used to generate the spectral fringes.

The real-world angular dimension of the characterisation is determined by the classical scan of a narrow field source. The angular range and step size are determined by the operator, the angular resolution is determined by the set-up used for the illumination of the instrument.

The instrument spectral and spatial response are fixed and determined by the instrument design, in particular the number of detector pixels. If needed for SNR reasons, spectral- and/or spatial resolution can be sacrificed for reduced noise, by binning spectral and spatial pixels either during or after detector read-out. This reduces the total data volume and may be beneficial for stray light correction calculations.

Figure 5-1 shows two of the characterisation measurements, one with short (10 ms) and one with long (1 s) exposure time. The detector read-out clearly shows the narrow angular (horizontal) range that is illuminated, and the broad spectral (vertical) range coved by the white light source and the instrument.

Figure 5-1

Examples of two measured interferograms. The left-hand image shows an interferogram without saturation. The vertical dimension is detector pixel rows, corresponding to the spectral dimension of the instrument, the horizontal dimension is detector pixel columns, corresponding to the angular dimension of the instrument. The bright vertical stripe is the spectrum of the angular point source of white light with superimposed spectral fringes. The right-hand image shows a similar measurement, but with 100 times longer exposure time resulting in saturation in most directly illuminated pixels, but also better signal to noise ratio in the instrumental stray light. The dark vertical band on the right-hand side is detector crosstalk of the bright pixels of the same exposure.

Figure 5-2 shows two 2-dimensional slices through the 4-dimensional IRM, showing the detector response derived from the interferograms for two fixed real world instrument illumination angles and real-world wavelengths. Ideally, this should correspond to the instrument response to a monochromatic point source illuminating the instrument. The small bright spot in each image is the expected response, effectively that of the directly illuminated pixels. The horizontal slightly curved line extending from the bright spot is predominantly spatial stray light, likely caused by the optics before the entrance slit of the spectrometer of the instrument. The vertically extending line is increased noise, caused by limitations of the method, likely dominated by OPD noise and shot noise in the interferograms. Only pixels which are directly illuminated (the bright pixels in Figure 5-1 left hand image) are affected, since other pixels have their noise decreased by means of the HDR approach to the measurements and analysis. Figure 5-9 shows the typical noise levels of directly illuminated pixels (blue curve) and pixels that benefit from HDR (black curve).

Figure 5-2

Examples of two slices through the instrument response matrix, for all detector pixels, at fixed real world viewing angle and fixed real-world wavelength. The left-hand image shows the IRM for an instrument viewing angle of 89.6 degrees and wavelength of 408 nm, the right-hand image shows the IRM for an instrument viewing angle of 93.8 degrees and wavelength of 472 nm.

Figure 5-3 shows two different slices through the IRM, at fixed detector pixel row and column, showing which real-world angle and real-world wavelength contribute to the signal in the pixel. As the number of characterisation angles was limited to 9 in this investigation, there are 9 columns in the images. The spectral range covers 316.4 nm to 516.4 nm. As the angular sampling (Figure 5-5) was chosen to be quite coarse, the resulting figures are correspondingly coarse in that dimension. The characterisation method however allows in principle arbitrary resolution and sampling for these dimensions of the IRM, of course at the expense of measurement time and data volume. Some noteworthy details in Figure 5-3 are the angular (horizontal) extent of the response of the pixels, and the spectrally (vertically) present noise which is more prominent at the angles that generate the direct illumination.

Figure 5-3

Examples of two slices through the instrument response matrix, for all measured real world viewing angles (columns) and all measured real-world wavelengths between 375 and 484 nm (rows), at fixed detector pixel row and column. The left-hand image shows the IRM for detector pixel row 680 and column 580, the right-hand image shows the IRM for detector pixel row 1050 and column 424. The images show, for the given detector pixel, from which direction and which wavelength the light reaches the pixel. The pixel in the left-hand image was chosen to lie between two characterisation angles, the right hand one very close to one of the characterisation angles.

The dynamic range in the IRM is determined on the one hand by the noise properties of the instrument, but also by the number of OPD steps and OPD scan range, and to very strong degree by the exposure levels used to compose the HDR IRM. Provided that the instrument is not adversely affected by over-exposure of parts of the detector, the dynamic range can be arbitrarily extended by including more over-exposed measurements in the characterisation.

The dynamic range of the measurement results obtained in this study is estimated from the noise in the IRM. The total amount of direct light is normalised to unity for each monochromatic point source, which means that the noise in the IRM is also expressed as a fraction of the direct light and can thus be used to estimate the dynamic range. However, as there are typically 77 pixels in the directly illuminated part of the measurements, corresponding to a certain spectral and spatial resolution of the characterisation, the noise-dominated part of the IRM was smoothed with this typical resolution before the dynamic range was determined. Figure 5-9 shows the typical noise level in (smoothed) instrument response matrix data for both pixels benefiting from the long exposure times in the HDR data (black curve) and those that do not (blue curve). The corresponding dynamic range well exceeds 10⁷ for the wavelength ranges where both the source is bright, and the throughput of the instrument is high. At wavelengths below 380 nm the instrument optics are opaque due to the glass of the telescope lenses, and at wavelengths above 480 nm the instrument no longer detects direct light as the spectrum no longer falls on the detector.

The minimum measurement time for the characterisation performed in this study depends on the desired spectral resolution, determined by the number of OPD steps needed to obtain the desired spectral resolution, or about 3400 steps for a spectral resolution of 0.5 nm at a wavelength of 500 nm, or 20 cm^-1. There will be a minimum time needed to read out the detector, which will set the overall minimum time for an OPD scan. Depending on the brightness of the light source used for characterisation, there will be an additional term to account for the total integration time to collect the required photons. In the case of these measurements and hardware under test, the short exposure measurements were set at 10 ms exposure time and were obtained at slightly over 0.5 seconds per frame. For a full scan of 3400 steps with synchronisation between the interferometer and the spectrometer read-out, this would result in just under 30 minutes. The long exposures at 1000 ms would take slightly over 60 minutes for a full scan. The 9 angles scanned would combine to slightly under 14 hours total acquisition time for the complete set of data presented here. In practice, due to lack of hardware synchronisation between the interferometer and spectrometer, the real measurement time was about a factor 6 longer. In this total measurement time, the stray light properties for the entire input spectral range between 316.4 nm and far into the infrared were characterised, limited by the spectral properties of the light source and the optics of the interferometer, both of which can be configured to cover selections of the wavelength range between 200 nm and about 500 μm.

With a brighter light source (which is a commercially-off-the-shelf option for the interferometer), the exposure time of the measurements can be reduced, resulting in the overall characterisation time to be limited by the overhead of the data acquisition of the instrument, in this study for the acquisition of 3400 * 2 * 9 frames.

5.2

Stray light verification

The verification measurement was performed by scanning the instrument over a pre-defined angular range in a single exposure time. The light source used was a white light source, spectrally limited by a bandpass filter. SNR was improved by repeating the measurement and averaging the result. A matching dark measurement was made, using identical conditions but with the light source blocked. Figure 5-4 (left image) shows the resulting verification scene. The detector rows represent the spectral dimension, with short (UV) wavelengths at the bottom, and long (480 nm) wavelengths at the top. Detector columns represent the angular (spatial) dimension of the scene (Figure 5-5 blue curve). A spatially sharply defined image is expected for a perfect instrument, but due to stray light a loss of contrast close to the sharp edges are expected for a real instrument (Figure 5-7 black curve). Since the bandpass filter has a gradual transition from maximum to minimum transmission, a gentler behaviour of the spectral dimension of the verification scene is expected (Figure 5-6 black curve).

Figure 5-4

Stray light verification image, left the measured image, right the synthetic image, based on the measured image and the characterisation data. The bright spot is a spectrally and spatially confined illumination of the instrument, the dark spot is crosstalk during detector read-out

Figure 5-5

The angular coverage of the characterisation measurements (black) and the verification scene (blue)

Figure 5-6

The spectral behaviour of the verification scene (black) and the synthetic verification scene (blue), integrated over columns 400 to 599

Figure 5-7

The spatial behaviour of the verification scene (black) and the synthetic verification scene (blue), integrated over rows 866 to 944

A synthetic verification scene was created by taking the measured verification scene and selecting only those pixels which likely receive direct illumination. Spatially, the steep edges of the curve in Figure 5-7 were used (between pixel columns 405 and 593), spectrally the range between detector rows 600 and 1101 was used (Figure 5-6), which broadly covers the full range where direct light could be present, but also likely covers pixels affected by (spectral) stray light. For each pixel in the specified ranges, the nearest neighbour IRM entry was found in real world wavelength and angle. The 2-dimensional (detector pixel row and column) IRM for this wavelength and angle was shifted to the pixel coordinates of the pixel under investigation, multiplied by the pixel value, and added to the synthetic scene. This resulted in the synthetic verification scene shown in the right hand of Figure 5-4.

The synthetic verification scene of Figure 5-4 shows the same spectral and spatial features as the measured verification scene, in particular the spatial stray light extending to the left and the right of the illuminated part of the scene. Spectrally, a lot of “blocky” noise is present. This is consistent with the angular sampling, nearest neighbour interpolation scheme, and increased noise in the detector spectral dimension of the IRM as shown in Figure 5-2.

Quantitatively, the measured and synthetic verification scenes are compared by means of integration over parts of the detector spectral or spatial dimensions. Figure 5-6 shows the spatially integrated scenes revealing the average spectral profiles of the measured (black) and synthetic (blue) verification scenes. Overall, the shape and magnitude agree well. In more detail, the synthetic scene seems to have a slightly higher signal at signal levels below half a percent. This is likely due to actual (spectral) stray light being considered as direct signal and counting twice in the synthetic image, once as direct and once as stray light. At pixel row values below 500, there seems to be a slight underestimate of the stray light by the characterisation.

Figure 5-7 shows the spectrally integrated signals of the measured and synthetic verification scene. The match is quite good down to the 0.05% level, with only a slight over-estimate of the stray light in the synthetic scene around pixel column 600. The noise in the integrated synthetic scene is at the 10^-4 level, with a slightly lower average signal level than measured. The crosstalk-effect around column 900 is clearly visible in the measured verification data, but less so in the synthetic data. It is, however, still caught to some degree by the characterisation data, resulting in a slightly lower stray light level than adjacent pixel column ranges. As it turns out (data not shown) the crosstalk in the detector is not linear, and the assumption for stray light is that it behaves strictly linearly with the recorded signal after dark correction.

An interesting region in the verification scene is the part close to the directly illuminated spatial detector columns, which is known to not receive any direct light. This would be columns below 400 and above 600. In these regions, significant amounts of signal are recorded while from the design of the measurement we expect no direct signal to be present. We can thus with confidence state that the recorded signal is dominated by instrumental stray light. The right hand Figure 5-8 shows the spatially integrated signal over columns 600 to 619, in the region where we saw the deviation between measured and synthetic data in Figure 5-7. Spectrally, the match is reasonably good, apart from the peak being over-estimated by about 30% of the stray light, or 0.1% of the level of the direct illumination. The reason for this is not fully understood but could be related to a loss of resolution when convolving the measured scene (already affected by instrumental resolution) with the IRM, also affected by instrumental resolution. The left hand Figure 5-8 shows the spatially integrated signal over columns 375 to 394, basically mirrored in the illuminated part of the verification scene. Here, the match between the measured and synthetic scene is much better and no systematic difference can be discerned.

Figure 5-8

Spatially integrated normalised signal of columns 375 and 394 (left) and of columns 600 and 619 (right), just outside of the directly illuminated part of the verification scene. The black curve is the measured signal, the blue curve is the synthetic scene

Figure 5-9

Typical noise level in the Instrument Response Matrix for resolution elements that benefit of the HDR (black) and those that do not (blue) due to saturation of the long exposure. The total direct signal is unity, the noise is expressed per pixel with respect to the integrated direct signal. The variation of the noise with wavelength is due to the spectral throughput of the instrument and the spectral brightness of the light source used

5.3

Discussion

The WLI-based stray light characterisation of imaging spectrometers and hyperspectral imagers has some clear advantages over existing (monochromator- or laser-based) methods. In view of the goal to perform space instrument calibration in a single day, the main advantage is the speed of the method: a WLI-based method has a measurement overhead of 20 ms for an OPD step, while the alternative typically has an overhead of tens of seconds per wavelength step. For a typical SOI with 2000 independent wavelength bands of interest, and 200 independent viewing angles of interest, and assuming a viewing angle step overhead of 1 minute and a wavelength step overhead of 30 seconds, and no HDR, the minimum time for characterisation would be 139 days overhead time for wavelength and angle setting. A WLI-based characterisation, with e.g., 5000 OPD steps, would take slightly under 9 hours for measurement overhead alone. To both numbers should be added the actual time to collect the light, and the overhead for reading out the detector. If we assume 0.5 seconds for the sum of these two, the total time needed for characterisation of the SOI using a laser or a WLI, would increase to 141 days or 6 days, respectively.

In addition to the significantly shorter overhead time, other advantages of the WLI-based characterisation are the wavelength calibration of all SOI pixels that can be derived from the characterisation results, and the large wavelength range covered, both in-band for the SOI, but at no extra measurement time, also out-of-spectral-band characterisation. The spectral range and spectral resolution of the characterisation can be set by means of the OPD scan parameters, at nearly arbitrary values, only limited by the light source and optics involved, and the highest spectral resolution that can be provided by the WLI (300 000 in the case of the WLI used in this study). This also allows fast characterisation of the instrument spectral response function of all SOI pixels, especially if the full field of view of the SOI can be illuminated in one go.

The parameters of importance in a WLI-based stray light characterisation are the OPD step size, the OPD scan range, and the number of HDR levels with corresponding over-exposure. The OPD step size determines the spectral range covered, with the shortest wavelength being double the OPD step size. Any wavelengths shorter than this will be aliased to longer wavelength, which can not be distinguished from these longer wavelengths without prior knowledge. The OPD scan range determines the spectral resolution, with a longer scan range resulting in higher spectral resolution. The noise in the interferograms is mostly determined by the noise of the SOI, but also the stability of the WLI affects the interferograms through the OPD noise and light source stability. All noise sources combined will result in a maximum dynamic range in the spectra obtained from the interferograms, as well as a noise floor. The noise floor can be lowered by means of HDR measurements, which can be done arbitrarily much. The OPD noise and shot noise in the interferograms limits the dynamic range in the spectra of pixels that receive direct light, which is one of the main limitations of the method as implemented here.

Potential improvements of the method address the dynamic range of the directly illuminated pixels. By spectrally limiting the number of directly illuminated pixels, e.g., by means of a bandpass filter, fewer pixels are affected by the constraint in the dynamic range of the directly illuminated pixels, allowing better characterisation of purely spectral stray light. This will however be at the expense of additional measurement time.

The validity of the stray light characterisation data was tested with a verification measurement, which was used to compose a synthetic verification measurement from the combined characterisation data. Though affected by noise, the agreement between the synthetic and real measurement is good, also in regions only affected by stray light. The main limitation is the dynamic range in the directly illuminated pixels, resulting in higher noise in the purely spectral direction of the detector than in any other directions. We are currently investigating modifications to the characterisation method to reduce the impact of this limitation.

The stray light characterisation data can be used to feed a stray light correction algorithm, as done e.g., in [1] and [2]. This will allow the SOI to achieve higher spectral and spatial contrast after correction than intrinsically possible by the instrument. The WLI-based stray light characterisation is efficient enough to quickly gather large amounts of data, allowing more detailed correction by the stray light correction algorithms than currently possible with only coarse sampling in real world spectral and real-world angular dimensions.