Abstract

A method to design Ronchi-Hartmann screens for improved alignment in the testing of fast plano-convex spherical lenses is presented. We design null screens that produce aligned straight fringes for observed patterns. The designs of these null screens are based on knowledge of the caustic by refraction. A qualitative test for a lens is presented.

© 2010 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing, 3rd Edition, (Wiley, 2007), Chap. 10, pp. 361-397.
    [CrossRef]
  2. D. Malacara, A. Cornejo, and M. V. R. K. Murty, "Bibliography of various Optical Testing Methods," Appl. Opt. 14, 1065-1080 (1975).
    [CrossRef] [PubMed]
  3. A. Cornejo-Rodriguez, H. J. Caulfield, and W. Friday, "Testing of Optical Surface: A bibliography," Appl. Opt. 20, 4148 (1981).
    [CrossRef] [PubMed]
  4. D. Malacara, and A. Cornejo, "Null Ronchi Test for Aspherical Surfaces," Appl. Opt. 8, 1778-1780 (1974).
    [CrossRef]
  5. A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, "Null Hartmann and Ronchi-Hartmann test," Appl. Opt. 29, 4618-4621 (1990).
    [CrossRef] [PubMed]
  6. R. Díaz-Uribe, and M. Campos-García, "Null-screen testing of fast convex aspheric surfaces," Appl. Opt. 39, 2670-2677 (2000).
    [CrossRef]
  7. M. Avendaño-Alejo, and R. Díaz-Uribe, "Testing a fast off-axis parabolic mirror using tilted null-screens," Appl. Opt. 45, 2607-2614 (2006).
    [CrossRef] [PubMed]
  8. M. Avendaño-Alejo, I. Moreno-Oliva, M. Campos-García, and R. Díaz-Uribe, "Quantitative evaluation of an off-axis parabolic mirror by using a tilted null screen," Appl. Opt. 48, 1008-1015 (2009).
    [CrossRef] [PubMed]
  9. J. F. Forkner, "Computer generation of null masks for Ronchi lens tests," Opt. Eng. 39, 1840-1844 (2000).
    [CrossRef]
  10. J. M. López-Ramírez, D. Malacara-Doblado, and D. Malacara-Hernández, "New simple geometrical test for aspheric lenses and mirrors," Opt. Eng. 39, 2143-2148 (2000).
    [CrossRef]
  11. A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, "Ronchi and Hartmann tests with the same mathematical theory," Appl. Opt. 31, 2370-2376 (1992).
    [CrossRef] [PubMed]
  12. M. Avendaño-Alejo, L. Castañeda, and I. Moreno, "Properties of caustics produced by a positive lens: meridional rays," accepted to be published in J. Opt. Soc. Am. A, (2010).
    [CrossRef]
  13. D. M. González-Utrera, "Desarrollo Teórico-Experimental de Pantallas Nulas para la Caracterización de Lentes Plano-Convexas," Thesis, Faculty of Sciences, UNAM, (2009).

2009

2006

2000

R. Díaz-Uribe, and M. Campos-García, "Null-screen testing of fast convex aspheric surfaces," Appl. Opt. 39, 2670-2677 (2000).
[CrossRef]

J. F. Forkner, "Computer generation of null masks for Ronchi lens tests," Opt. Eng. 39, 1840-1844 (2000).
[CrossRef]

J. M. López-Ramírez, D. Malacara-Doblado, and D. Malacara-Hernández, "New simple geometrical test for aspheric lenses and mirrors," Opt. Eng. 39, 2143-2148 (2000).
[CrossRef]

1992

1990

1981

1975

1974

D. Malacara, and A. Cornejo, "Null Ronchi Test for Aspherical Surfaces," Appl. Opt. 8, 1778-1780 (1974).
[CrossRef]

Avendaño-Alejo, M.

Campos-García, M.

Cardona-Nunez, O.

Caulfield, H. J.

Cordero-Davila, A.

Cornejo, A.

Cornejo-Rodriguez, A.

Díaz-Uribe, R.

Forkner, J. F.

J. F. Forkner, "Computer generation of null masks for Ronchi lens tests," Opt. Eng. 39, 1840-1844 (2000).
[CrossRef]

Friday, W.

López-Ramírez, J. M.

J. M. López-Ramírez, D. Malacara-Doblado, and D. Malacara-Hernández, "New simple geometrical test for aspheric lenses and mirrors," Opt. Eng. 39, 2143-2148 (2000).
[CrossRef]

Malacara, D.

Malacara-Doblado, D.

J. M. López-Ramírez, D. Malacara-Doblado, and D. Malacara-Hernández, "New simple geometrical test for aspheric lenses and mirrors," Opt. Eng. 39, 2143-2148 (2000).
[CrossRef]

Malacara-Hernández, D.

J. M. López-Ramírez, D. Malacara-Doblado, and D. Malacara-Hernández, "New simple geometrical test for aspheric lenses and mirrors," Opt. Eng. 39, 2143-2148 (2000).
[CrossRef]

Moreno-Oliva, I.

Murty, M. V. R. K.

Appl. Opt.

Opt. Eng.

J. F. Forkner, "Computer generation of null masks for Ronchi lens tests," Opt. Eng. 39, 1840-1844 (2000).
[CrossRef]

J. M. López-Ramírez, D. Malacara-Doblado, and D. Malacara-Hernández, "New simple geometrical test for aspheric lenses and mirrors," Opt. Eng. 39, 2143-2148 (2000).
[CrossRef]

Other

M. Avendaño-Alejo, L. Castañeda, and I. Moreno, "Properties of caustics produced by a positive lens: meridional rays," accepted to be published in J. Opt. Soc. Am. A, (2010).
[CrossRef]

D. M. González-Utrera, "Desarrollo Teórico-Experimental de Pantallas Nulas para la Caracterización de Lentes Plano-Convexas," Thesis, Faculty of Sciences, UNAM, (2009).

D. Malacara, Optical Shop Testing, 3rd Edition, (Wiley, 2007), Chap. 10, pp. 361-397.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Caustic produced by refraction through a Plano-Convex spherical lens and the associated parameters considering that the point source is located at infinity. (b) Diagram of the experimental setup to test a plano-convex spherical lens using null screens.

Fig. 2
Fig. 2

(a) Procedure to design null screens. (b) Array of points on CCD sensor to design the null screens and their associated parameters.

Fig. 3
Fig. 3

(a) Computed Lines of the Null Screen. (b) Design of the null screen. (c) Image of the null screen after refraction through a plano-convex spherical lens at the detection plane.

Fig. 4
Fig. 4

(a) The CCD sensor is decentered and lies inside the caustic. (b) The CCD sensor is centered and lies inside the caustic. (c) Zoom of the center of figure b by reducing the intensity of the laser beam. (d) CCD sensor is placed near of the circle of least confusion.

Fig. 5
Fig. 5

(a) Design of the null Hartmann screen. (b) Image recorded at the design plane. (c) Zoom of the center for a null screen inside the caustic by reducing the intensity of the laser beam. (d) Zoom of the center for a null screen when it is further away from the surface than the design distance.

Equations (5)

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( z ( h ) , y ( h ) ) = ( n i [ n i n a 2 ( R 2 h 2 ) 3 / 2 + ( R 2 n a 2 h 2 n i 2 ) 3 / 2 ] n a 2 ( n i 2 n a 2 ) R 2 R , h 3 n i 2 R 2 n a 2 ) ,
tan ψ = y 0 h 3 n i 2 R 2 n a 2 z 0 + R n i [ n i n a 2 ( R 2 h 2 ) 3 / 2 + ( R 2 n a 2 h 2 n i 2 ) 3 / 2 ] n a 2 ( n i 2 n a 2 ) R 2 .
tan ψ = ( n a 2 n i 2 ) h n a 2 R 2 h 2 + n i n a 2 R 2 n i 2 h 2 .
h { n a 2 ( n i 2 n a 2 ) ( z 0 + R ) R 2 n i [ n i n a 2 ( R 2 h 2 ) 3 / 2 + ( R 2 n a 2 h 2 n i 2 ) 3 / 2 ] } = ( h 3 n i 2 y 0 R 2 n a 2 ) ( n a 2 R 2 h 2 + n i n a 2 R 2 n i 2 h 2 ) .
( x s , y s ) = ( h s cos ϕ i j , h s sin ϕ i j ) ,

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