Theoretical compensation of static deformations of freeform multimirror substrates

Johannes Hartung; Henrik von Lukowicz; Jan Kinast

doi:10.1364/AO.57.004020

Applied Optics
Vol. 57,
Issue 15,
pp. 4020-4031
(2018)
•https://doi.org/10.1364/AO.57.004020

Theoretical compensation of static deformations of freeform multimirror substrates

Johannes Hartung, Henrik von Lukowicz, and Jan Kinast

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Johannes Hartung, Henrik von Lukowicz, and Jan Kinast, "Theoretical compensation of static deformations of freeform multimirror substrates," Appl. Opt. 57, 4020-4031 (2018)

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Abstract

Varying temperatures influence the figure errors of freeform metal mirrors by thermal expansion. Furthermore, different materials lead to thermo-elastic bending effects. The paper presents a derivation of a compensation approach for general static loads. Utilizing perturbation theory, this approach works for shape compensation of substrates that operate in various temperature environments. Verification is made using a finite element analysis, which is further used to produce manufacturable CAD models. The remaining low spatial frequency errors are deterministically correctable using diamond turning or polishing techniques.

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Mirror	M1	M2	M3
RoC [mm]	−1750.000	−401.923	−465.322
CC [1]	−69.850	27.909	−0.544
A4 [ ${mm}^{- 3}$ ]	$- 3.422 \times 10^{- 10}$	$3.571 \times 10^{- 7}$	$- 1.067 \times 10^{- 9}$
A6 [ ${mm}^{- 5}$ ]	$1.833 \times 10^{- 14}$	$- 3.836 \times 10^{- 10}$	$- 3.351 \times 10^{- 15}$
A8 [ ${mm}^{- 7}$ ]	$- 7.748 \times 10^{- 20}$	$6.820 \times 10^{- 16}$	$- 2.851 \times 10^{- 20}$
Freeform	Zernike Noll	Zernike Noll	Zernike Noll

Surface	$t$ [mm]	$D Y$ [mm]	$R X$ [°]	CA [ ${mm}^{2}$ ]
Object	$\infty$	0	0	—
Entrance ap.	23	0	0	$109 \times 74.5$
Coord. Break	0	0	13.5	—
M1	−220	0	0	user defined
M2	220	0	0	radius 40.5
M3	−230	0	0	user defined
Coord. Break	0	0	−30	—
Fold mirror	0	0	0	$68.5 \times 54.5$
Coord. Break	220	0	−30	—
Coord. Break	−30	88.6	0	—
Front surf. FPA	30	0	0	radius 100
Detector	0	0	0	$40 \times 20$

Name	Al–40Si	NiP
Young’s modulus [MPa]	102000	170000
Poisson number [1]	0.27	0.27
CTE [ $K^{- 1} \times 10^{- 6}$ ] at 20 °C	13.0	12.5

Mirror	M1	M2	M3
RoC [mm]	−1750.000	−401.923	−465.322
CC [1]	−69.850	27.909	−0.544
A4 [ ${mm}^{- 3}$ ]	$- 3.422 \times 10^{- 10}$	$3.571 \times 10^{- 7}$	$- 1.067 \times 10^{- 9}$
A6 [ ${mm}^{- 5}$ ]	$1.833 \times 10^{- 14}$	$- 3.836 \times 10^{- 10}$	$- 3.351 \times 10^{- 15}$
A8 [ ${mm}^{- 7}$ ]	$- 7.748 \times 10^{- 20}$	$6.820 \times 10^{- 16}$	$- 2.851 \times 10^{- 20}$
Freeform	Zernike Noll	Zernike Noll	Zernike Noll

Surface	$t$ [mm]	$D Y$ [mm]	$R X$ [°]	CA [ ${mm}^{2}$ ]
Object	$\infty$	0	0	—
Entrance ap.	23	0	0	$109 \times 74.5$
Coord. Break	0	0	13.5	—
M1	−220	0	0	user defined
M2	220	0	0	radius 40.5
M3	−230	0	0	user defined
Coord. Break	0	0	−30	—
Fold mirror	0	0	0	$68.5 \times 54.5$
Coord. Break	220	0	−30	—
Coord. Break	−30	88.6	0	—
Front surf. FPA	30	0	0	radius 100
Detector	0	0	0	$40 \times 20$

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Equations (29)

Applied Optics