Spatially heterogeneous Earth radiance scenes affect the atmospheric composition measurements of high-resolution Earth observation spectrometer missions. The scene heterogeneity creates a pseudo-random deformation of the instrument spectral response function (ISRF). The ISRF is the direct link between the forward radiative transfer model, used to retrieve the atmospheric state, and the spectra measured by the instrument. Hence, distortions of the ISRF owing to radiometric inhomogeneity of the imaged Earth scene will degrade the precision of the Level-2 retrievals. Therefore, the spectral requirements of an instrument are often parameterized in the knowledge of the ISRF over non-uniform scenes in terms of shape, centroid position of the spectral channel and the full width at half maximum (FWHM).

The Sentinel-5/UVNS instrument is the first push-broom spectrometer that makes use of a concept referred to as a slit homogenizer (SH) for the mitigation of spatially non-uniform scenes. This is done by employing a spectrometer slit formed by two parallel mirrors scrambling the scene in the along track direction (ALT) and hence averaging the scene contrast only in the spectral direction. The flat mirrors do not affect imaging in the across track direction (ACT) and thus preserve the spatial information in that direction. The multiple reflections inside the SH act as coherent virtual light sources and the resulting interference pattern at the SH exit plane can be described by simulations using scalar diffraction theory. By homogenizing the slit illumination, the SH strongly modifies the spectrograph pupil illumination as a function of the input scene. In this work we investigate the impact and strength of the variations of the spectrograph pupil illumination for different scene cases and quantify the impact on the ISRF stability for different types of aberration present in the spectrograph optics.

The Ozone Monitoring Instrument (OMI) was the first instrument identifying the issue arising from non-uniform Earth scenes on the shape and maximum position of the spectral response of the instrument

The ISRF of an imaging spectrometer is given by the convolution of the slit illumination, pixel response and the optical PSF of the spectrograph optics. In the context of heterogeneous scenes, the ISRF can be altered due to non-uniform illumination and instabilities in the optical PSF. This leads to deformation in the ISRF with respect to the centroid, shape and FWHM.

Depending on the observed scene heterogeneity, the entrance slit will be inhomogeneously illuminated. In the case of a classical slit, this will alter the shape of the ISRF (see Fig.

This effect is particularly prominent for instruments with a high spatial resolution. The along track motion of the satellite during the integration times results in a temporal averaging of the ISRF variation, which reduces the impact of scene heterogeneity. The impact of, e.g., albedo variations depends on the instantaneous field of view (IFOV) and the sampling distance in ALT (for Sentinel-5/UVNS: IFOV

Sentinel-5/UVNS

The outline of this paper is as follows: Sect. 2 describes the model we deployed to propagate the light through the SH by Huygens–Fresnel diffraction formula. Applying Fourier optics, we formulate the propagation of the complex electric field from the SH exit plane up to the grating position, representing the reference plane for the evaluation of the spectrograph pupil intensity distribution. In Sect. 3 we quantify the spectrograph pupil intensity distribution for several Earth scene cases. The scene-dependent weighting of the aberration in the spectrograph and its impact on the ISRF properties is discussed and quantified in Sect. 4. Finally, we summarize our results in Sect. 5.

This section describes the underlying models and the working principle of the SH. The first part briefly summarizes the model developed by

The light from objects on the Earth that are imaged at one spatial position (along slit) within the homogenizer entrance slit arrive at the Sentinel-5/UVNS telescope entrance pupil as plane waves, where the incidence angle

A full experimental validation of the propagation model through the SH is still missing. An initial approach to validate the model in a breadboard activity was conducted by ITO Stuttgart and published in

In a space-based imaging spectrometer equipped with a classical slit acting as a field stop, a point source on the Earth surface enters the instrument as a plane wavefront with a uniform intensity over the telescope pupil. As this principle applies for every point source in a spatial sample on the Earth, the telescope pupil intensity homogeneity is independent of the radiance variation among the point sources in a spatial sample. Besides some diffraction edge effects in the slit plane, the telescope pupil intensity distribution gets retrieved in the spectrograph pupil. This is not the case when introducing a mirror-based SH.
Existing SH models (

Generic setup of the SH in the Sentinel-5/UVNS instrument. A plane wavefront gets focused in the SH entrance plane and the propagation of such a stimulus is shown in blue as the square modulus of the electric field. The incoming light undergoes several reflections in the ALT direction, whereas the SH in ACT is similar to a classical slit acting as a field stop. The collimator contains an astigmatic correction that is adjusted to the slit length. The SH homogenizes the scene in the ALT direction but also modifies the spectrograph pupil illumination. The grating disperses the light in ALT. The pupil distribution in the ACT direction is conserved except for diffraction effects due to truncation of the telescope PSF in the slit plane.

In the following we make the geometrical argument rigorous using diffraction theory.
A general case for the connection between slit exit plane and spectrograph pupil plane is considered by

In order to keep the full image information in ACT while imaging the homogenized SH output image, the collimator needs an astigmatism. In our model, this is implemented via Zernike polynomial terms on the collimation lens. We follow the OSA/ANSI convention for the definitions of the Zernike polynomials and the indexing of the Zernike modes

The Zernike polynomials are given by

The primary goal of the spectrometer is to distinguish the intensity of the light as a function of the wavelength and spatial position. In order to separate the wavelengths, a diffractive element is placed in the spectrograph pupil and disperses the light in the ALT direction. For our analysis, we place the diffraction grating at a distance

The implementation of the diffraction grating is a simplified model, which is an approximation of the real, more complex case. In Sentinel-5/UVNS, the SWIR spectrograph is equipped with a silicon immersed grating. The simplified approach is also valid for this case, as the SH does not affect the general behavior of the grating.

The far-field intensity distribution is dependent on the contrast of the Earth scene in ALT and therefore on the SH entrance plane illumination.
We characterize the amplitude of the variations of the spectrograph pupil illumination by introducing two types of heterogeneous scenes. The first is an applicable Earth scene as defined by the ESA for the Sentinel-5/UVNS mission, which aims at representing a realistic Earth scene case. The on-ground albedo variations of this scene can be parameterized as a linear interpolation between two spectra representing the same atmospheric state but obtained with either a dark or bright albedo

Realistic Earth scenes in the SWIR-3 derived from MODIS images corresponding to the slit illumination in ALT. The on-ground surface albedo is given in terms of weight factors

Simulation results of the spectrograph pupil intensity distribution in the SWIR-3 (

Figure

In the next section we will investigate the impact of non-uniform pupil illumination in combination with spectrograph aberration on the ISRF stability.

The main impact of the above described variations in the spectrometer pupil illumination is the scene-dependent weighting of the aberration inherent to the spectrograph optics. In the case of a classical slit, it is valid to calculate the ISRF of an imaging spectrometer as the convolution of the slit illumination, the pixel response on the FPA and the optical PSF of the spectrograph optics. When using an SH, a scene dependency of the spectrograph pupil illumination will weight the aberration of the system accordingly and thereby create a variation in the PSF, which will ultimately also change the ISRF properties. Therefore, it is necessary to keep the complex phase of the electric field during the propagation through the instrument.

Instead of a convolution, we propagate the spectrograph pupil illumination through the imaging optics by diffraction integrals. For the description of the aberration present in the Sentinel-5/UVNS instrument we use again the formulation of Zernike theory. We know the expected PSF size on the FPA of the Sentinel-5/UVNS SWIR-3 channel, which in the case of a classical slit can be approximated by the standard deviation of a normal distribution. In order to assess the impact of aberration, we impinge different types of aberration on the spectrograph imaging optics and match the PSF size to the instrument prediction. As the shape of the PSF for an arbitrary aberration is not given by a normal distribution, we define the PSF size as the area where

In order to assess the stability of the ISRF we define three merit functions:

shape error: the maximum difference of the ISRF calculated for a homogeneous and heterogeneous scene, respectively:

centroid error: the shift of the position of the spectral channel centroid, where the centroid is defined as

the spectral resolution of the ISRF given by the FWHM.

In the following, we present the ISRF figures of merit resulting from the simulation of several Zernike polynomials for the Sentinel-5/UVNS applicable heterogeneous Earth scene and a

Applicable Earth scene – ISRF stability. Requirements: shape error

This argument is supported by Fig.

Progression of ISRF shape error from pure oblique quadrafoil aberration to pure defocus aberration. Between the values, we decreased the quadrafoil Zernike coefficient in

Although the phenomena of the variations of the pupil illumination in combination with spectrometer aberration increases the errors, the SH still homogenizes the scene well and significantly improves the stability of the ISRF compared to a classical slit. In Fig.

In certain scenarios, Sentinel-5/UVNS will fly over Earth scenes with higher contrasts than specified in the applicable Earth scene. This will be the case when flying over cloud fields, water bodies or city to vegetation transitions. However, these scenes are excluded from the mission requirements in terms of scene homogenization. Although sufficient for the purposes of Sentinel-5/UVNS, the capability of the SH to homogenize the scene is not perfect. This imperfection is particularly prominent when considering the calibration scenes. The imperfections originate from the remaining interference fluctuations in the SH transfer function and are dependent on the wavelength. Higher wavelengths show smaller frequencies and larger peak-to-valley amplitudes of the maxima in the SH transfer function, which leads to reduced homogenization efficiency. Therefore, the SWIR-3 wavelength channel is the most challenging in terms of scene homogenization.

We observe that increasing the number of reflections inside the SH will increase the number of stripes in the spectrometer pupil illumination (see Fig.

The simulation results of this study still require experimental validation. An initial approach to validate the SH transfer functions was published in

Apart from the mirror-based SH discussed in this study, future remote sensing instruments investigate the technology of another slit homogenizer technology, which is based on rectangular multimode fiber bundles. These devices are based on the same principle as the mirror-based SH but enable one to homogenize the scene in the ACT and ALT direction

The presented study continues the investigation by

We observe that the impact of spectrograph pupil illumination variations is small compared to the error due to non-uniform slit illumination, and the ISRF distortion is primarily driven by the remaining near-field variations after the SH. The inhomogeneity remnants arise from the fluctuations of the interference pattern at the SH exit plane. The strength of the variations increases with wavelength. Therefore, this study was conducted in the SWIR-3 channel in order to cover the worst case.

We quantify the ISRF in terms of shape error, FWHM error and centroid error at

The datasets generated and/or analyzed for this work are available from the corresponding author on reasonable request, subject to confirmation of Airbus Defence and Space GmbH.

TH developed, implemented, applied and evaluated the methods for the end-to-end modelling of the Sentinel-5/UVNS instrument with input from CM. TH performed the performance gain analysis which was supported by CM and CK and revised by JK and MW. TH prepared the paper, with contributions and critical revision from all co-authors.

The authors declare that they have no conflict of interest.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Tobias Lamour, Jess Köhler and Markus Melf (all at Airbus Defence and Space) for the helpful comments on a previous version of the manuscript.

This paper was edited by Ulrich Platt and reviewed by Bernd Sierk and Ruediger Lang.