Improving fast aspheric convex surface tests with dynamic null screens using LCDs

Manuel Campos-García; Víctor Iván Moreno-Oliva; Rufino Díaz-Uribe; Fermín Granados-Agustín; Agustín Santiago-Alvarado

doi:10.1364/AO.50.003101

Applied Optics
Vol. 50,
Issue 19,
pp. 3101-3109
(2011)
•https://doi.org/10.1364/AO.50.003101

Improving fast aspheric convex surface tests with dynamic null screens using LCDs

Manuel Campos-García, Víctor Iván Moreno-Oliva, Rufino Díaz-Uribe, Fermín Granados-Agustín, and Agustín Santiago-Alvarado

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Manuel Campos-García, Víctor Iván Moreno-Oliva, Rufino Díaz-Uribe, Fermín Granados-Agustín, and Agustín Santiago-Alvarado, "Improving fast aspheric convex surface tests with dynamic null screens using LCDs," Appl. Opt. 50, 3101-3109 (2011)

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Abstract

A method for testing fast aspheric convex surfaces with dynamic null screens using LCDs is shown. A flat null screen is designed and displayed on an LCD monitor with drop-shaped spots in such a way that the image, which is formed by reflection on the test surface, becomes an exactly square array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. Here the whole surface is tested at once. The position of the spots on the LCD can be changed in a dynamic way, to perform point-shifting of the image spots. The proposed procedure improves the dynamic point-shifting method. As has been shown previously, this process reduces the numerical error during the integration procedure, thereby improving the sensitivity of the test. The positioning accuracy for the screen spots is related to the LCD’s spatial resolution. Results of the evaluation of a parabolic convex surface with $f / # = 0.22$ are shown.

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Element	Symbol	Size
Radius of curvature	r	$44.93 mm$
Diameter	D	$100 mm$
Conic constant	k	$- 1$
CCD–pinhole distance	a	$50 mm$
Stop aperture–surface vertex distance	b	$729.75 mm$
CCD length	d	$6.6 mm$
Optical axis–LCD1 distance	ρ	$492.5 mm$
Optical axis–LCD2 distance	$ρ^{'}$	$150 mm$

Method	r (mm)	A	B	$x_{o}$ (mm)	$y_{o}$ (mm)	$z_{o}$ (mm)
Point-shifting LCD	42.505	0.309	0.351	$- 2.010$	$- 0.002$	0.001
Point-shifting radial null screen	42.259	1.995	2.297	$- 0.147$	0.033	0.052
Laser deflectometry	43.975	-	-	-	-	-

Deformation Coefficients	$D_{1}$	$D_{2}$	$D_{3}$	$D_{4}$
Point-shifting LCD	$- 7.59 \times 10^{- 7}$	$1.29 \times 10^{- 9}$	$- 6.89 \times 10^{- 13}$	$1.41 \times 10^{- 16}$
Point-shifting radial null screen	$- 7.37 \times 10^{- 7}$	$1.34 \times 10^{- 9}$	$- 7.72 \times 10^{- 13}$	$1.48 \times 10^{- 16}$
Laser deflectometry	$- 8.22 \times 10^{- 7}$	$1.33 \times 10^{- 9}$	$- 7.63 \times 10^{- 13}$	$1.40 \times 10^{- 16}$

Element	Symbol	Size
Radius of curvature	r	$44.93 mm$
Diameter	D	$100 mm$
Conic constant	k	$- 1$
CCD–pinhole distance	a	$50 mm$
Stop aperture–surface vertex distance	b	$729.75 mm$
CCD length	d	$6.6 mm$
Optical axis–LCD1 distance	ρ	$492.5 mm$
Optical axis–LCD2 distance	$ρ^{'}$	$150 mm$

Method	r (mm)	A	B	$x_{o}$ (mm)	$y_{o}$ (mm)	$z_{o}$ (mm)
Point-shifting LCD	42.505	0.309	0.351	$- 2.010$	$- 0.002$	0.001
Point-shifting radial null screen	42.259	1.995	2.297	$- 0.147$	0.033	0.052
Laser deflectometry	43.975	-	-	-	-	-

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Equations (14)

Applied Optics