Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine

Junzheng Peng; Qingquan Wang; Xiang Peng; Yingjie Yu

doi:10.1364/JOSAA.32.001964

Journal of the Optical Society of America A
Vol. 32,
Issue 11,
pp. 1964-1972
(2015)
•https://doi.org/10.1364/JOSAA.32.001964

Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine

Junzheng Peng, Qingquan Wang, Xiang Peng, and Yingjie Yu

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Junzheng Peng, Qingquan Wang, Xiang Peng, and Yingjie Yu, "Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine," J. Opt. Soc. Am. A 32, 1964-1972 (2015)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: July 2, 2015
- Revised Manuscript: August 23, 2015
- Manuscript Accepted: September 8, 2015
- Published: October 8, 2015

Abstract

Stitching interferometry is a common method for measuring the figure error of high numerical aperture optics. However, subaperture measurement usually requires a fringe-nulling routine, thus making the stitching procedure complex and time-consuming. The challenge when measuring a surface without a fringe-nulling routine is that the rays no longer perpendicularly hit the surface. This violation of the null-test condition can lead to high fringe density and introduce high-order misalignment aberrations into the measurement result. This paper demonstrates that the high-order misalignment aberrations can be characterized by low-order misalignment aberrations; then, an efficient method is proposed to separate the high-order misalignment aberrations from subaperture data. With the proposed method, the fringe-nulling routine is not required. Instead, the subaperture data is measured under a nonzero fringe pattern. Then, all possible misalignment aberrations are removed with the proposed method. Finally, the full aperture map is acquired by connecting all subaperture data together. Experimental results showing the feasibility of the proposed procedure are presented.

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Equations (27)

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No.	Aberration Name	Polynomial
$L_{1}$	Piston	1
$L_{2}$	$X$ tilt	$X$
$L_{3}$	$Y$ tilt	$Y$
$L_{4}$	$X$ power	$1 / 2 (3 X^{2} - 1)$
$L_{5}$	45° astigmatism	$X Y$
$L_{6}$	$Y$ power	$1 / 2 (3 Y^{2} - 1)$
$L_{7}$	$X$ -primary coma	$1 / 2 (5 X^{3} - 3 X)$
$L_{8}$		$1 / 2 (3 X^{2} - 1) Y$
$L_{9}$		$1 / 2 (3 Y^{2} - 1) X$
$L_{10}$	$Y$ -primary coma	$1 / 2 (5 Y^{3} - 3 Y)$
$L_{11}$	$X$ -primary spherical	$1 / 8 (35 X^{4} - 30 Y^{2} + 3)$
$L_{12}$		$1 / 2 (5 X^{3} y - 3 X Y)$
$L_{13}$		$1 / 4 (3 X^{2} - 1) (3 Y^{2} - 1)$
$L_{14}$		$1 / 2 (5 Y^{3} X - 3 Y X)$
$L_{15}$	$Y$ -primary spherical	$1 / 8 (35 Y^{4} - 30 Y^{2} + 3)$

No.	Without Preprocessed		With Preprocessed
No.	PV	RMS	PV	RMS
1	1.6480	0.2788	1.0529	0.1985
2	2.4342	0.4132	0.9979	0.1895
3	2.4874	0.3746	0.9402	0.1822
4	1.1323	0.2071	0.9220	0.1800
5	3.0626	0.4707	1.0929	0.1796
6	1.019	0.1636	1.0054	0.1744
7	2.4256	0.3078	1.1475	0.1831
Mean	2.0299	0.3165	1.0227	0.1839
$σ$	0.7713	0.1106	0.0809	0.0079

No.	Aberration Name	Polynomial
$L_{1}$	Piston	1
$L_{2}$	$X$ tilt	$X$
$L_{3}$	$Y$ tilt	$Y$
$L_{4}$	$X$ power	$1 / 2 (3 X^{2} - 1)$
$L_{5}$	45° astigmatism	$X Y$
$L_{6}$	$Y$ power	$1 / 2 (3 Y^{2} - 1)$
$L_{7}$	$X$ -primary coma	$1 / 2 (5 X^{3} - 3 X)$
$L_{8}$		$1 / 2 (3 X^{2} - 1) Y$
$L_{9}$		$1 / 2 (3 Y^{2} - 1) X$
$L_{10}$	$Y$ -primary coma	$1 / 2 (5 Y^{3} - 3 Y)$
$L_{11}$	$X$ -primary spherical	$1 / 8 (35 X^{4} - 30 Y^{2} + 3)$
$L_{12}$		$1 / 2 (5 X^{3} y - 3 X Y)$
$L_{13}$		$1 / 4 (3 X^{2} - 1) (3 Y^{2} - 1)$
$L_{14}$		$1 / 2 (5 Y^{3} X - 3 Y X)$
$L_{15}$	$Y$ -primary spherical	$1 / 8 (35 Y^{4} - 30 Y^{2} + 3)$

No.	Without Preprocessed		With Preprocessed
No.	PV	RMS	PV	RMS
1	1.6480	0.2788	1.0529	0.1985
2	2.4342	0.4132	0.9979	0.1895
3	2.4874	0.3746	0.9402	0.1822
4	1.1323	0.2071	0.9220	0.1800
5	3.0626	0.4707	1.0929	0.1796
6	1.019	0.1636	1.0054	0.1744
7	2.4256	0.3078	1.1475	0.1831
Mean	2.0299	0.3165	1.0227	0.1839
$σ$	0.7713	0.1106	0.0809	0.0079

Abstract

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Figures (11)

Tables (2)

Equations (27)

Journal of the Optical Society of America A