Threshold algorithm to recover the deformation of optical surfaces

Porfirio Nanco-Hernández; Carlos I. Robledo-Sánchez; Rosa García-Olivares; Gustavo Rodríguez-Zurita; Víctor I. Moreno-Oliva

doi:10.1364/AO.45.004652

Threshold algorithm to recover the deformation of optical surfaces

Porfirio Nanco-Hernández, Carlos I. Robledo-Sánchez, Rosa García-Olivares, Gustavo Rodríguez-Zurita, and Víctor I. Moreno-Oliva

Applied Optics
Vol. 45,
Issue 19,
pp. 4652-4657
(2006)
•https://doi.org/10.1364/AO.45.004652

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Porfirio Nanco-Hernández, Carlos I. Robledo-Sánchez, Rosa García-Olivares, Gustavo Rodríguez-Zurita, and Víctor I. Moreno-Oliva, "Threshold algorithm to recover the deformation of optical surfaces," Appl. Opt. 45, 4652-4657 (2006)

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Previously assigned OCIS codes
- Aberrations (global) (080.1010)
- Optical fabrication (120.4610)
- Testing (220.4840)

About this Article
History
- Original Manuscript: September 6, 2005
- Revised Manuscript: November 21, 2005
- Manuscript Accepted: November 25, 2005

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Abstract

The global optimization threshold algorithm is reported to obtain the deformations of an optical surface. The advantage of these types of algorithm is that they can be solved for the correlation problem presented in Seidel polynomials. We obtain the 2D deformations of a surface test with the transversal aberration along one direction only. In order to apply this algorithm we used exact ray tracing to simulate the transversal aberration adapting the same mathematical theory for the Ronchi test. The error obtained in sagitta recovering deformation was $1 μm$ .

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Surface	Conic
Spherical	K = 0
Parabolic	K = −1
Hyperboloid	K < −1
Ellipsoid (greater axis)	−1 < K < 0
Ellipsoid (minor axis)	k > 0

Deformation	Coefficient of Deformation	Simulation (λ)	Threshold (λ)
Spherical	A	0.020 000	0.026 697
Coma	B	0.200 000	0.187 463
Astigmatism	C	0.010 000	0.036 899
Defocus	D	0.010 000	0.013 291
Tilt in x	E	0.040 000	0.064 405
Tilt in y	F	0.000 000	0.005 127

Deformation	Coefficient of Deformation	Simulation (λ)	Threshold (λ)
Spherical	A	0.002 000	0.002 237
Coma	B	0.200 000	0.199 977
Astigmatism	C	0.010 000	0.004 667
Defocus	D	0.010 000	0.000 047
Tilt in x	E	0.040 000	0.040 075
Tilt in y	F	0.000 000	−0.307 487

Deformation	Coefficient of Deformation	Simulation (λ)	Threshold (λ)
Spherical	A	0.020 000	0.020 084
Coma	B	0.003 000	0.003 031
Astigmatism	C	0.002 000	0.010 206
Defocus	D	0.020 000	0.006 301
Tilt in x	E	0.007 000	0.006 972
Tilt in y	F	0.050 000	0.063 799

Surface	Conic
Spherical	K = 0
Parabolic	K = −1
Hyperboloid	K < −1
Ellipsoid (greater axis)	−1 < K < 0
Ellipsoid (minor axis)	k > 0

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