The observing strategy of the Geostationary Carbon Observatory (GeoCarb), which is a “step and stare” approach, can lead to distortions in the instrument spectral response function (ISRF) when there are gradients in brightness across instrument field of view. These distortions induce errors in the retrieved trace gases. In order to minimize these errors, the GeoCarb instrument design was modified to include a “slit homogenizer” whose purpose is to scramble the pattern of the incoming light and effectively remove the ISRF distortions caused by the variations in illumination across the slit. As a risk reduction, GeoCarb procured six different homogenizers and had them tested for performance in a benchtop optical system. The major finding is that the homogenizer performance depends strongly on the polarization of the incoming light, with the sensitivity growing as a function of wavelength. The width of the ISRF is substantially smaller when the light is vertically polarized (orthogonal to the slit length) compared to horizontally polarized (parallel to the slit length), and the throughput is accordingly reduced. These effects are due to the effects of the gold coating and high incidence angles present in the GeoCarb homogenizer design, which was verified using a polarization-dependent model generalized from previous homogenizer modeling work. The results strongly recommend controlling the polarization of the light entering a similar implementation using a polarizer, depolarizer, or polarization scrambler for other instruments attempting to mitigate scene illumination non-uniformity effects, as well as a robust characterization of the polarization sensitivity of all key subsystems.
The Geostationary Carbon Observatory (GeoCarb;
With these considerations in mind, SH test articles with three different depths were procured from two vendors for performance testing. In parallel, existing models
The paper is structured as follows. Section
The Geostationary Carbon Cycle Observatory (GeoCarb) was selected as the recipient of NASA’s second Earth Venture Mission (EVM-2) in 2016 and will make daily measurements of total column carbon dioxide (
Additional instrument specifications are given in Table
GeoCarb instrument requirements. The top row gives the designation for the four GeoCarb spectral bands: the oxygen A-band (O2A), the weak CO
Following PSF
In trace gas retrievals, high-resolution radiance spectra are convolved with the assumed ISRF, typically measured during pre-flight instrument characterization (e.g.,
Variation in MODIS Band 2 (0.85
One-dimensional SHs have been discussed previously
The slit homogenizer is composed of two parallel mirrors separated by spacers. The slit opening is defined by its length (
The simulated GeoCarb 1-D SHs are defined by two parameters: the slit width
Modeling the SH response was discussed in detail in other references
Let us assume that a point source is imaged on the SH entrance. When the SH entrance is observed from the SH output it appears to be illuminated with multiple point sources, which are aligned and placed at regular intervals: the original point source as well as all its mirror images after reflection on the two mirrors, as is shown in Fig.
This can be done in two ways:
The interference model uses simple complex addition. The input stimuli are source points emitting light within a cone that corresponds to the system The diffraction model expresses the input stimuli as a diffraction point spread function (PSF) obtained with the optical system placed in front of the SH input plane, and a diffraction integral is used for propagation through the SH. This type of model is more accurate, but its computation time is significantly longer. For a rectangular pupil, thanks to the separability of the along-slit (
In the experiments that follow, we utilize the diffraction integral technique for maximum accuracy.
In this work, existing SH models The sign of the phase is changed depending on the complex notation that is used, with positive or negative complex exponentials If, at normal incidence, the vectors for incident and reflected electric fields are equal or differ by a minus sign, a 180
Our equations to compute the gold reflectance are taken from
A point source
Phase shift at reflection on a thick gold layer, computed from Rakić gold index parametrization (Rakić et al., 1998) with definitions
of polarization axes from
In order to incorporate the complex reflectance in the SH model, as discussed in
Definition of phase reflectance in P polarization.
When the angle of incidence is increased to large values, the angle between incident and reflected rays increases by 180
An earlier version of the SH simulator (without polarization dependence) detailed in
If only pure geometric optics is considered and if the instrument has a rectangular pupil, it can be easily shown that after a propagation distance equal to multiples of
To determine the optimum depth for the slit homogenizer for GeoCarb,
we simulated polarization-independent transfer matrices for depths from 0.1 to 2 mm at all four wavelengths of interest (listed in Table 1) using the previously documented SH model
After an initial ramp-up in performance at the lowest depths, the
reduction factors were relatively independent of the homogenizer depth;
however, there were conspicuous dips in performance at specific depths
that were not coincident for all four wavelengths. These dips are due
to some periodicity in the interference patterns as the light
propagates along the depth of the slit. GeoCarb uses a single 36
In order to assess the performance of the six different SH prototypes, a breadboard test setup was constructed at the Institut für Technische Optik (ITO). This section details the optical design and fabrication employed in the testing.
The homogenization performance was evaluated based on recordings of
the near-field intensity distribution at the exit of each SH, while
the input was illuminated
with different illumination patterns (realized by a knife edge). All measurements were performed at four different
wavelengths (0.76, 1.62,
2.05, and 2.33
Figure
The following mono-mode fiber-coupled monochromatic sources have been
employed:
0.76 1.62 2.05 2.33
The knife edge (Edmund optics no. 36-137) with variable orientation (micromechanical adjustable mount) serves to obscure part of the slit and thus to introduce a sharp cutoff in illumination across the homogenizer, simulating an extreme version of the typical image taken from space by the GeoCarb instrument.
The knife edge is imaged
by a double-sided telecentric system at an
Setup for the near-field measurements.
Coherence reduction and homogeneity were verified by measurement of the
speckle contrast in the plane of the SH. To validate the image quality and homogeneity at 0.76
The slit homogenizer can be moved in all three dimensions using high-precision piezo stages (Physik Instrumente PI Q-545.240 linear
stage, PI E-873.3QTU controller, repeatability error of 200 nm).
The orientation of the SH mount is parallel to the optical axis to better than
The intensity distribution at the exit of the SH is imaged by
a double-sided telecentric system (L6 and L7 in Fig.
For the measurements at
In order to be able to judge homogenization performance and to see
possible crosstalk it is preferable to use anamorphotic imaging so
that vertical structures in the output plane of the device
are resolved, while still the lateral position along the slit on the
input side is maintained on the image sensor side. To this end we used an additional cylindrical lens (
For
The polarizer (
In the NIR, a scientific CMOS image sensor (PCO edge
3.1
The beam splitters and image sensors 2, 3, and 4 were only used for alignment and were removed while taking the measurements.
Some interference effects were caused by the cover glass of the main
image sensor. For
For the other wavelengths and image sensors this method does not work, but since the interference fringes are spatially constant, we eliminated the fringes by averaging of spatially shifted images. The image sensor is mounted on a vertically movable stage (Thorlabs MLJ050). Images are taken for different heights of the sensor with a displacement of multiples of the pixel pitch. The image of the slit moves over the sensor area and thus appears at different positions compared to the interference pattern for each image. Image processing is then used to digitally shift the captured image back considering the difference in the sensor height. This is possible since the accuracy of the stage is high compared to the pixel pitch. Averaging of the shifted images results in a significant reduction in the interference effect.
Measurements were performed for the six devices mentioned previously (two vendors supplied devices with depths of 0.5, 1.0, and 1.5 mm) for different input and output polarizer settings (S/P) for different positions of the device with respect to the input knife edge illumination (in steps of 2.5
The throughput was measured with a slightly modified configuration for simplicity. The pick-off mirror was replaced by a circular aperture to illuminate only a defined area. Images were taken under parallel and orthogonal input polarization. Reference images were taken with thin slits (Edmund no. 58-541 and no. 58-542) of known width (measured using a confocal microscope), as well as without an air slit or slit homogenizer to account for potential laser intensity fluctuations. The slit homogenizer throughput values are treated as relative to the air slit measurements as the design trade for GeoCarb is between these two options.
The performance test results and model simulations are presented in this section, as well as some further investigations with the model to explain some of the unexpected findings uncovered during testing.
The measurements were taken as described in the previous sections for different positions of the knife edge, and the resulting 2-D images were averaged to produce the 1-D profile of the homogenized slit images. We compare the results for fully illuminated and 50 % illuminated test data, as well as the throughput performance, below.
As described above, 2-D images were taken for each SH as it was moved across the knife edge, gradually obscuring larger and larger portions of the SH. The efficacy of the SH is judged by how well it reproduces the normalized profile of illumination of the fully illuminated SH when the input illumination is partially obscured by the knife edge after averaging in the across-slit direction. Importantly, the image of a fully illuminated SH is not the same as that of a typical air slit due to the interference effects. However, these effects are measured and would be taken into account during the pre-flight ISRF characterization (e.g.,
Across-slit illumination as a function of slit position for horizontally (left column) and vertically (right column) polarized light. The colors represent the different devices (D1–D6) detailed in Table
Figure
The relative throughput measurements show a strong reduction for vertically polarized light, especially at increased device depth (see Table
Throughput as compared to a thin slit for different devices with an
In order to explain the polarization-dependent features in the SH measurement data, we employ the diffraction SH model. To validate our model, a comparison with simulations using the Zemax software package was performed. A 1-D SH was entered in Zemax non-sequential mode. Two parallel mirrors were defined, coated with gold (using the Rakić parameterization from
More elaborate models could be set up in Zemax with a source emitting a 2-D cone of light, but this would require a more complicated design to create an astigmatic beam, which was not done in this work. Monte Carlo simulations were used with 10
The SH analytical model assumes a scalar wave in the sense that optical path differences and phase shifts are calculated for each ray and combined directly to compute the intensity where the rays interfere. By contrast, Zemax propagates the real electric field along the ray and computes interferences with real electric field vectors: interferences are computed separately for the
We found a reasonable qualitative agreement between the Zemax and analytical model results. In Fig.
We investigated the cause of the polarization dependence in the simulated and measured ISRFs using the interference SH model. This effect was linked to the different phase shifts gained by the electric field at the reflection on the gold layer. When both dephasings are artificially set to the same value in the model, simulations show nearly identical transfer functions in P and S polarization and nearly no variation in the ISRF width, which implies that the difference in reflectance amplitude with polarization plays almost no role.
SH output illumination and resulting ISRF in P and S polarization for a SH length of 1 mm,
P-polarized and S-polarized phase shifts at reflection on gold as a function of the angle of incidence, for
To understand the role of the phase shift, it is necessary to look at its variations with angle of incidence. In Fig.
This applies for the relatively low
Next, the SH transmittance was investigated. The amount of intensity transmitted by the SH when its input is illuminated with a uniform intensity profile was computed using a diffraction model. Diffraction models are not only more accurate than interference models; they also rigorously conserve energy thanks to the properties of diffraction integrals, so they are well suited for transmittance calculations. The SH transmittance was obtained with a summation of the transfer matrix along one dimension, which corresponds to the case where the SH input is fully and uniformly illuminated.
The results are presented in Fig.
We immediately see that the three models predict a nearly identical transmittance in S polarization that is close to 100 %, while they give very different losses in P polarization. Taking the simulation without interferences (first curve) as a reference, we notice that including diffraction effects with a 180
SH transmittance vs. polarization and wavelength for
Ratio between P-polarized and S-polarized transmittances predicted for GeoCarb (
The measurements and modeling together provide a strong argument that performance of 1-D slit homogenizers of the type considered for GeoCarb (i.e., plane-parallel, gold-coated mirrors) is highly sensitive to the polarization of incoming light. The polarization response of the instrument itself, including important components such as the grating, can be characterized in pre-flight calibration, but the polarization state of the incident reflected sunlight is itself unknown and is a function of particles in the atmosphere that scatter light as well as the surface properties. This could lead to significant errors in trace gas retrievals using spectra through the difficulty in disambiguation of albedo and polarization states. For example, two scenes with identical trace gas column mole fractions but different polarization states would be hard to distinguish from scenes with identical polarization states but different trace gas amounts, even if the instrument were perfectly characterized. Another important challenge is the implication that the ISRF will be strongly polarization-dependent and thus change from scene to scene in a similar way as it would with no slit homogenizer present due to the scene brightness variations. Further, there is the potential of using other space-based sensors to try to get a handle on surface brightness, but no such information exists for polarization. Finally, the signal-to-noise ratio will also be highly dependent on polarization, and the lower efficiency of the SH would almost certainly lead to poorer-quality retrievals. In a very real sense, the 1-D devices add complexity to the instrument design but do not reduce uncertainty. For this reason, the slit homogenizer was removed from the GeoCarb design.
The upcoming Sentinel-5 mission includes a 1-D slit homogenizer in their design, as is discussed in
We have presented both experimental and simulated results related to the performance of 1-D SH devices consistent with the GeoCarb optical design. We found that the devices exhibited a strong sensitivity to the polarization of the light incident on the slit. This was apparent in both the width of the slit image and the relative throughput of the different devices. The difference between the two orthogonal polarization states grew worse as wavelengths got longer. We then augmented a model of the slit homogenizer to demonstrate that this narrowing is caused by the reflection on the gold coatings on the mirrors that lead to a phase shift between the P and S polarizations. It seems likely that different materials could be used with better results, but the space application required for GeoCarb limited our interest in that investigation.
Future work involves the implementation of these measurement results in a retrieval framework similar to that described in
All analysis code and all data analyzed can be accessed at
SC drafted the manuscript and analyzed the measurements and model simulations. TH and MT collected the measurements. JC developed the polarization-dependent SH model. EB analyzed the data. BM and all coauthors provided feedback on the manuscript drafts prior to finalization.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors acknowledge funding from NASA through the GeoCarb mission under award 80LARC17C0001.
This research has been supported by the National Aeronautics and Space Administration (grant no. 80LARC17C0001).
This paper was edited by Ulrich Platt and reviewed by two anonymous referees.