20 November 2017 Grating scattering BRDF and imaging performances: A test survey performed in the frame of the flex mission
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Proceedings Volume 10564, International Conference on Space Optics — ICSO 2012; 105642P (2017) https://doi.org/10.1117/12.2309031
Event: International Conference on Space Optics 2012, 2012, Ajaccio, Corsica, France
Key components in optical spectrometers are the gratings. Their influence on the overall infield straylight of the spectrometer depends not only on the technology used for grating fabrication but also on the potential existence of ghost images caused by irregularities of the grating constant. For the straylight analysis of spectrometer no general Bidirectional Reflectance Distribution Function (BRDF) model of gratings exist, as it does for optically smooth surfaces. These models are needed for the determination of spectrometer straylight background and for the calculation of spectrometer out of band rejection performances.

Within the frame of the Fluorescence Earth Explorer mission (FLEX), gratings manufactured using different technologies have been investigated in terms of straylight background and imaging performance in the used diffraction order. The gratings which have been investigated cover a lithographically written grating, a volume Bragg grating, two holographic gratings and an off-the-shelf ruled grating. In this paper we present a survey of the measured bidirectional reflectance/transmittance distribution function and the determination of an equivalent surface micro-roughness of the gratings, describing the scattering of the grating around the diffraction order. This is specifically needed for the straylight modeling of the spectrometer.
Harnisch, Deep, Vink, and Coatantiec: Grating Scattering BRDF and Imaging Performances – A Test Survey performed in the frame of the FLEX Mission


Gratings measured within the survey

The goal of this measurement survey was to measure the BRDF/BTDF of gratings manufactured by different technologies and compare their straylight performance using the same test bench. The following grating technologies have been investigated: holographic grating technology, lithographic grating technology, volume Bragg grating technology and ruled grating.

The ideal case would have been to measure the gratings with the same specifications on the size, groove density, diffraction efficiency and polarization sensitivity. However, this was not possible since the selection of gratings was partly dictated by the available time and budget but also by the resulting different spectrometer designs, which were considered in the spectrometer trade-off study. Nevertheless, all gratings have been selected to have groove densities above 1000 grooves per mm and all gratings had been measured in the Littrow configuration. The gratings measured in the trade-off are shown in Table 1 below.

Table 1

Gratings of the measurement survey

ManufacturerFraunhofer Institute for Applied Optics and Precision Engineering JenaHoriba Jobin YvonZeissCentre Spatial de LiegeEdmund Optics
Techno-logylithographicholographicholographicholographic Dichromate Gelatine Volume Bragg GratingRuled
Sample IDUZE079a _1 _C1521 12 040  43210
ShapeflatConcave – radius of curvature 201.4 mmflatflatflat
Dimen-sion31x31x6.35 mm3Useful area: 29x29 mm230x30 mm2Useful area 24x24 mm260x60x10 mm3100x100x20 mm325x25x9.5 mm3Useful area: 22x22 mm2
Groovedensity1250 grooves / mm1200 grooves / mm1400 grooves / mm – sinusoidal groove shape1200 grooves / mm1200 grooves / mm
Spectral rangeOptimized for 1100 nm340-800 nm (aluminium coating)680 – 780 nm (efficiency # 60%)677 – 697 nm (efficiency # 60%)Optimized for 750 nm
Normal AOI43.5°23.3 (Littrow under 632 nm)22.3° (Littrow under 632 nm)26.25° (Littrow under 632 nm)22.3° (Littrow under 632 nm)22.3° (Littrow under 632 nm)
Usefuldiffract-tionorder-1-1 (± 6 ° around order -1 to avoid vignetting of the illumination beam by the detector)-1 (± 6° around order -1 to avoid vignetting of the illumination beam by the detector)-1-1 (± 6 ° around order -1 to avoid vignetting of the illumination beam by the detector)

The lithographic technology applied by the Fraunhofer Institute is currently limited to flat gratings. This technology allows fabrication of large gratings with very high accuracy groove density and low pitching error. The grating profile has been etched with an etching depth of 1800 nm. Such grating has already been manufactured, space qualified and integrated in the radial velocity spectrometer of the ESA GAIA mission [2,3].

The holographic grating manufactured by Horiba Jobin Yvon is a replica of a master grating. It is a convex reflective grating, which required the test set-up to focus of the illumination beam in front of the grating, such that the grating conjugated diffraction image falls onto the detector.

The ZEISS grating is also a holographic reflection grating, however, it is flat and the grooves are sinusoidal.

The Dichromate Gelatine Volume Bragg grating has been developed by CSL within an ESA Technology Research Programme contract [4]. It is a flat transmission grating. The grating itself consists out of two fuses silica substrates attached to each other with the grating in between.

The ruled grating is a commercial off-the-shelf grating from Edmund Optics [5]. Although, not comparable in terms of price and effort with respect to the above mentioned gratings, it has been included in the survey to get an idea about the differences in the straylight level one could expect from ruled gratings.


Measurement set-up

The BRDF of the different gratings has been measured on a commercial CASI test bench from Schmitt Industries INC. [1]. Figure 1 shows the optical lay-out of the CASI system. The laser acts as a source for the measurement of BRDF/BTDF. The laser output is passing through a chopper where part of the light is directed towards a reference detector. The reference detector continuously monitors the laser energy and when a measurement is performed, any deviation of the optimal power is automatically taken in account by the software making the system insensitive to (small) laser power drifts. The laser beam is cleaned by a spatial filter which is a combination of a microscope objective with a matched pinhole. The light is finally focussed by a parabolic mirror onto the detector mounted on a goniometer stage.

Figure 1

CASI BRDF test bench concept


The procedure for measurement of optically smooth flat samples, either reflective or transmissive, is as follows: the first step is the measurement of the instrument signature, this means the measurement of the instrument BRDF itself. This signature provides the background limit of the measurement. In a second step the sample is mounted in the rotation centre of the goniometer, such that the converging laser beam after reflection/transmission from the sample is focussed onto the goniometer circle along which the detector is scanning the grating BRDF/BTDF.

This measurement procedure is only strictly valid for reflecting smooth optical surface and infinitesimal thin transmission surfaces.

The measurement of gratings in the dispersion plane has to be modified because of an additional effect: since the grating is illuminated with a convergent F/100 beam the angle of the incidence beam is varying over the grating surface resulting in a focus position away from the goniometer circle. A BRDF measurement without refocussing of the beam leads to defocussed images in the diffraction orders. Since in general the imaging performance of the grating around the diffraction order is needed, this defocus can be corrected by the CASI illumination system.



In this section we show the measurement results for the different gratings that were investigated. The BRDF/BTDF measurements for the gratings were done in dispersion as well as cross-dispersion direction. For all gratings the performance of the Littrow diffraction order is provided in an angular range of +/- 2°.

As a reference we provide BRDF curves of optically smooth samples with a surface micro-roughness of 2nm and 5nm, 10nm and 25nm. The BRDF curves of smooth surfaces are modelled according to the Wein formula [6]:


Where 00072_PSISDG10564_105642P_page_4_3.jpg

σ … surface micro-roughness

β … scatter angle

λ … wavelength

Δ n. change in index of refraction

These reference plots allow at one hand side a quantitative comparison of the different gratings and on the other hand side the possibility to define the grating scattering by a simple ABg description for the development of the grating spectrometer straylight model.

In the following sections A) to E) we provide the measurement results for all gratings of the survey. Two plots are provided for each grating, the BRDF or BTDF in dispersion and in cross-dispersion direction. While the measurement of the dispersion direction shows the grating scatter performance around the -1st Littrow order, while the measurement in cross dispersion direction shows the scatter performance around the 0th order.


Fraunhofer Institute IOF lithographic grating

The lithographic grating manufactured by the Fraunhofer Institute IOF Jena is shown in Figure 4. The grating is a flat transmission grating.

Figure 2

Dispersion directi


Figure 3

Cross-dispersion direction


Figure 4

IOF lithographic grating


In the test configuration the grating surface was positioned on the back surface. The unstructured front surface of the grating did not have an anti-reflection coating. The grating BTDF shows a relative large plateau around the diffraction peak within an angular range of ± 0.5 ° which intensity is larger a smooth surface of a surface micro-roughness of 10 nm.

The grating shows two spikes symmetric around the diffraction order. A similar spike is also visible in the crossdispersion direction. These spikes are the effect of the grating internal reflection. It is suspected that they can be minimized by an AR coating.

  • 1) Dispersion direction (file: IOF_results)

  • 2) Cross-dispersion direction (file: IOF_results)


Horiba Jobin Yvon holographic grating

  • 1) Dispersion direction (file: JY_results)

  • 2) Cross-dispersion direction (file: JY_results)

The grating is a convex reflection grating and shown in Figure 7.

Figure 5

IOF lithographic grating in dispersion direction


Figure 6

IOF lithographic grating in cross-dispersion direction


Figure 7

Horiba Jobin Yvon holographic grating


The reflective convex grating manufactured by Horiba Jobin Yvon provides a very good straylight performance. The central plateau around the diffraction peak is limited to ± 0.2 °. The grating can be approximated by an equivalent surface rms micro-roughness between 5 nm and 10 nm.

The grating is free of any ghosts.


ZEISS holographic grating

  • 1) Dispersion direction (ZEISS_results)

  • 2) Cross-dispersion direction ZEISS_results)

The holographic grating manufactured by ZEISS is a flat reflective grating and is shown in Figure 10.

Figure 8

Horiba JobinYvon holographic grating in dispersion direction


Figure 9

Horiba JobinYvon holographic grating in cross-dispersion direction


Figure 10

ZEISS holographic grating


The straylight performance of the ZEISS grating is dominated by a large scattering plateau around the diffraction peak, which is larger an equivalent surface micro-roughness of 25 nm ranging until ± 0.2 ° around the diffraction peak which falls down to a second plateau of around 10 nm equivalent surface micro-roughness until ± 0.5 °. For angles larger ± 1° off the diffraction peak, the grating equivalent surface microroughness is about 5 nm.

The equivalent surface microroughness of the grating in cross-dispersion direction is between 10 nm and 25 nm.

The grating is free of any ghosts.


Centre Spatial de Liege Volume Bragg grating

  • 1) Dispersion direction (file: VBG results)

  • 2) Cross-dispersion direction (file: VBG results)

The Volume Bragg grating, shown in Figure 13, is based on a volume grating realized in di-chromate gelatine, which is covered in between two fused silica plates.

Figure 11

ZEISS holographic grating in dispersion direction


Figure 12

ZEISS holographic grating in cross-dispersion direction


Figure 13

CSL Volume Bragg grating


Figure 14

CSL Volume Bragg grating in dispersion direction


Figure 15

CSL Volume Bragg grating in cross-dispersion direction


Figure 16

Edmund Optics ruled grating


Figure 17

Edmund Optics ruled grating in dispersion direction


Figure 18

Edmund Optics ruled grating in cross-dispersion direction


The straylight performance of the CSL volume Bragg grating shows a steeper fall-off than the other gratings.

For an angular range lower than ± 0.5° around the diffraction peak the equivalent surface micro-roughness is between 25 nm and 10 nm, but it falls off to lower 5 nm at angles larger ±1.5°.

The transmission grating has an internal reflection, causing a ghost image.


Edmund Optics ruled grating

  • 1) Dispersion direction (file:Edmund_results)

  • 2) Cross-dispersion direction (file:Edmund_results)

The straylight performance of the ruled Edmund Scientific grating has a plateau larger 25 nm equivalent surface microroughness for an angular range of less than ±0.5° around the diffraction peak. For larger angles the scattering performance can be approximated by a 10 nm equivalent surface microroughness.

The grating is free of ghost images.



The measurement results shown in the previous section give an indication about the straylight performances that can be expected from gratings manufactured using different technologies. It shows as well, that the selection of a technology does not guarantee automatically a minimum of grating straylight, as shown with the holographic gratings.

Although the differences in the plots seem to be marginal it must be considered that the plots are given on a logarithmic scale.

Since the grating is usually located in an image of the pupil instrument plane its scattering will cover the field of view of the instrument.





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© (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Bernd Harnisch, Bernd Harnisch, Atul Deep, Atul Deep, Ramon Vink, Ramon Vink, Claude Coatantiec, Claude Coatantiec, } "Grating scattering BRDF and imaging performances: A test survey performed in the frame of the flex mission", Proc. SPIE 10564, International Conference on Space Optics — ICSO 2012, 105642P (20 November 2017); doi: 10.1117/12.2309031; https://doi.org/10.1117/12.2309031

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