Subaperture stitching computation time optimization using a system of linear equations

Marek Stašík; Pavel Psota; Vít Lédl; Jan Kredba

doi:10.1364/AO.433312

Applied Optics
Vol. 60,
Issue 27,
pp. 8556-8568
(2021)
•https://doi.org/10.1364/AO.433312

Subaperture stitching computation time optimization using a system of linear equations

Marek Stašík, Pavel Psota, Vít Lédl, and Jan Kredba

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Marek Stašík, Pavel Psota, Vít Lédl, and Jan Kredba, "Subaperture stitching computation time optimization using a system of linear equations," Appl. Opt. 60, 8556-8568 (2021)

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- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: June 7, 2021
- Revised Manuscript: August 13, 2021
- Manuscript Accepted: August 19, 2021
- Published: September 20, 2021

Abstract

Measurement of large or aspheric optical surface shapes as a single aperture using interferometry is problematic for many reasons. A typical problem is the numerical aperture limitation of the interferometer transmission element and the surface slope deviation of aspheres. This deviation typically causes vignetting and spatial aliasing on the camera. A solution is subaperture measurement and subsequent subaperture stitching. A stitching algorithm, in principle, uses overlaps between subapertures to eliminate aberrations of each subaperture to obtain a full aperture for further analysis. This process is computation time demanding and requires optimization in order to obtain a result in a reasonable time to reduce, in turn, the overall manufacturing time. In this paper, a novel, to the best of our knowledge, and fast stitching method based on a system of linear equations is proposed and mathematically described. The developed method was compared with other algorithms, and theoretical computation complexity was calculated and compared. The method was tested practically, with real data measured on spherical surfaces using QED ASI (QED Technologies aspheric stitching interferometer) and an experimental interferometer, and the results are presented. Stitching quality was quantified for results and compared to other algorithms.

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Supplementary Material (3)

Name	Description
Dataset 1	Sub-apertures measured on the first experimental surface using QED ASI.
Dataset 2	Sub-apertures measured on the second experimental surface using QED ASI.
Dataset 3	Sub-apertures measured on the LA1256 using TOPTEC AWA.

Data Availability

The measured data used in this paper are available in Dataset 1, Ref. [18], Dataset 2, Ref. [19], Dataset 3, Ref. [20].

18. M. Stašík, P. Psota, V. Lédl, and J. Kredba, “Sub-apertures measured on the LA1256 using TOPTEC AWA,” figshare, (2021) https://doi.org/10.6084/m9.figshare.15163842.

19. M. Stašík, P. Psota, V. Lédl, and J. Kredba, “Sub-apertures measure on the first experimental surface using QED ASI,” figshare, (2021) https://doi.org/10.6084/m9.figshare.15163677.

20. M. Stašík, P. Psota, V. Lédl, and J. Kredba, “Sub-apertures measure on the second experimental surface using QED ASI,” figshare, (2021) https://doi.org/10.6084/m9.figshare.15163680.

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Equations (61)

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	First Surface	Second Surface	LA1256
R [m]	0.13335	0.10399	0.1545
D [m]	0.088	0.088	0.0508
Material	N-KS	N-KS	N-BK7
Device	QED ASI	QED ASI	TOPTEC AWA
Transmission element	Melles Griot 6” F1.5	Melles Griot 6” F1.5	TOPTEC R585 4”
Number of subapertures	11	12	12
Pixel size [m/px]	$9.4786 \cdot 10^{- 5}$	$7.3917 \cdot 10^{- 5}$	$1.1995 \cdot 10^{- 5}$

Measurement	Used Algorithm	Initial RMS	Preprocessed Mismatch RMS	Final Mismatch RMS	Dilution of the Input Data	Computation Time	Output Resolution
First surface	Developed algorithm	233 nm	6.67 nm	2.88 nm	0.0016	$\sim 4 s$	$1000 \times 1000 p x$
	Chunyu Zhao			4.60 nm	1	$\sim 15 s$	$1000 \times 1000 p x$
	QED algorithm			1.2 nm		$\sim 50 s$	$500 \times 5000 p x$
Second surface	Developed algorithm	361 nm	5.31 nm	2.12 nm	0.0016	$\sim 4 s$	$1300 \times 1300 p x$
	Chunyu Zhao			2.11 nm	1	$\sim 15 s$	$1300 \times 1300 p x$
	QED algorithm			1.2 nm		$\sim 50 s$	$500 \times 500 p x$
LA1256	Developed algorithm	12900 nm	34.4 nm	9.16 nm	0.0016	$\sim 26 s$	$3908 \times 3887 p x$
LA1256	Chunyu Zhao	12900 nm	34.4 nm	21.7 nm	1	$\sim 68 s$	$3908 \times 3887 p x$

	First Surface	Second Surface	LA1256
R [m]	0.13335	0.10399	0.1545
D [m]	0.088	0.088	0.0508
Material	N-KS	N-KS	N-BK7
Device	QED ASI	QED ASI	TOPTEC AWA
Transmission element	Melles Griot 6” F1.5	Melles Griot 6” F1.5	TOPTEC R585 4”
Number of subapertures	11	12	12
Pixel size [m/px]	$9.4786 \cdot 10^{- 5}$	$7.3917 \cdot 10^{- 5}$	$1.1995 \cdot 10^{- 5}$

Measurement	Used Algorithm	Initial RMS	Preprocessed Mismatch RMS	Final Mismatch RMS	Dilution of the Input Data	Computation Time	Output Resolution
First surface	Developed algorithm	233 nm	6.67 nm	2.88 nm	0.0016	$\sim 4 s$	$1000 \times 1000 p x$
	Chunyu Zhao			4.60 nm	1	$\sim 15 s$	$1000 \times 1000 p x$
	QED algorithm			1.2 nm		$\sim 50 s$	$500 \times 5000 p x$
Second surface	Developed algorithm	361 nm	5.31 nm	2.12 nm	0.0016	$\sim 4 s$	$1300 \times 1300 p x$
	Chunyu Zhao			2.11 nm	1	$\sim 15 s$	$1300 \times 1300 p x$
	QED algorithm			1.2 nm		$\sim 50 s$	$500 \times 500 p x$
LA1256	Developed algorithm	12900 nm	34.4 nm	9.16 nm	0.0016	$\sim 26 s$	$3908 \times 3887 p x$
LA1256	Chunyu Zhao	12900 nm	34.4 nm	21.7 nm	1	$\sim 68 s$	$3908 \times 3887 p x$

Abstract

Supplementary Material (3)

Data Availability

Cited By

Figures (21)

Tables (2)

Equations (61)

Applied Optics