Johannes Hartung, Sebastian Merx, and Henrik von Lukowicz, "Compensation for general asymmetric static loads for a complete optical system of freeform mirrors," Appl. Opt. 59, 1507-1518 (2020)
Optical systems consisting of freeform metal mirrors are state of the art in optical engineering. The freeform shapes allow for more compact designs and offer more degrees of freedom for aberration correction. The metal components allow for the relocation of the effort from the integration to the fabrication stage. Metal mirrors for spaceborne optical systems experience several loads during orbital commissioning or operation. The present paper focuses on describing general static loads within the optical design to close the iteration loop between optical and mechanical design using this knowledge to investigate how to compensate for load-induced surface shape errors within the optical design. First, this analysis is performed for a two-mirror system with an asymmetric force load step. Second, the compensation for this load is discussed by performing another optical design step or a direct mechanical compensation step at mechanical design level. Since thermal loads usually introduce expansion effects, a third point of the paper is the discussion of thermal loads with some general results, to embed them into the shown formalism. The paper concludes by showing residual optical errors of the compensated optical system and comparing them with the nominal design.
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“Res.” means residual spot diagram of the pre-compensation of the mechanical design under the respective load.
This should be comparable to the “Nominal” column. “Deformed” represents the spots of the optical design under load.
All scales are in micrometers. Airy radius is 4.4 µm. All Airy disks are located at the centroid of the spot.
$\Delta$ is difference in spot centroid location of respective optical design minus spot centroid location of nominal optical design.
Notice that the detector aperture half-width is 2.5 mm.
Therefore, for the deformed system, the spot of field point 0°, 2° lies outside the detector aperture.
In the “Type” column, “Std.” means a surface description with only curvature radius and conic constant as parameters.
Type “ZF” stands for the Zernike polynomials in Fringe convention.
“CB” denotes a coordinate break, where TY denotes the decenter in $y$ direction and RX the rotation around the $x$ axis.
Notice that only the surface types “M1,” “M2,” and “Detector” (3, 7, IMA) are changed.
Further, only the 16 Zernike coefficients are changed (the normalization radii stay constant: 29.59 mm, 5.0 mm, 3.978 mm).
The base shape radii are unchanged, and also the relative distances and angles of the different coordinate systems are unchanged.
Notice further that the Zernike polynomials are centered in the respective optical coordinate system.
Further, the single coefficients may not have a distinct meaning, since due to the small sub-apertures, the conversion between them and the full aperture in the optical coordinate system may suffer from numerical instabilities.
“Res.” means residual spot diagram of the pre-compensation of the mechanical design under the respective load.
This should be comparable to the “Nominal” column. “Deformed” represents the spots of the optical design under load.
All scales are in micrometers. Airy radius is 4.4 µm. All Airy disks are located at the centroid of the spot.
$\Delta$ is difference in spot centroid location of respective optical design minus spot centroid location of nominal optical design.
Notice that the detector aperture half-width is 2.5 mm.
Therefore, for the deformed system, the spot of field point 0°, 2° lies outside the detector aperture.
In the “Type” column, “Std.” means a surface description with only curvature radius and conic constant as parameters.
Type “ZF” stands for the Zernike polynomials in Fringe convention.
“CB” denotes a coordinate break, where TY denotes the decenter in $y$ direction and RX the rotation around the $x$ axis.
Notice that only the surface types “M1,” “M2,” and “Detector” (3, 7, IMA) are changed.
Further, only the 16 Zernike coefficients are changed (the normalization radii stay constant: 29.59 mm, 5.0 mm, 3.978 mm).
The base shape radii are unchanged, and also the relative distances and angles of the different coordinate systems are unchanged.
Notice further that the Zernike polynomials are centered in the respective optical coordinate system.
Further, the single coefficients may not have a distinct meaning, since due to the small sub-apertures, the conversion between them and the full aperture in the optical coordinate system may suffer from numerical instabilities.
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