Abstract

A new method to design Hartmann type null screens to test either qualitatively or quantitatively fast plano-convex aspherical lenses is presented. We design both radial and square null screens that produce arrays of circular spots uniformly distributed at predefined planes, considering that the CCD sensor is solely placed inside the caustic region. The designs of these null screens are based on knowledge of the caustic by refraction and on exact ray tracing. The null screens also serve to improve the alignment in optical systems.

© 2016 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), 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]
  4. R. Díaz-Uribe and M. Campos-García, “Null-screen testing of fast convex aspheric surfaces,” Appl. Opt. 39, 2670–2677 (2000).
    [Crossref]
  5. 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]
  6. D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 8, 1778–1780 (1974).
    [Crossref]
  7. A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, “Null Hartmann and Ronchi-Hartmann test,” Appl. Opt. 29, 4618–4621 (1990).
    [Crossref] [PubMed]
  8. J. F. Forkner, “Computer generation of null masks for Ronchi lens tests,” Opt. Eng. 39, 1840–1844 (2000).
    [Crossref]
  9. 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]
  10. M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
    [Crossref]
  11. M. C. Roggemann and T. J. Schulz, “Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements,” Appl. Opt. 37, 4321–4329 (1998).
    [Crossref]
  12. D. P. Salas-Peimbert, D. Malacara-Doblado, V. M. Durán-Ramírez, G. Trujillo-Schiaffino, and D. Malacara-Hernández, “Wave-front retrieval from Hartmann test data,” Appl. Opt. 44, 4228–4238 (2005).
    [Crossref] [PubMed]
  13. D. Liu, H. Huang, B. Ren, A. Zeng, Y. Yan, and X. Wang, “Scanning Hartmann test method and its application to lens aberration measurement,” Chin. Opt. Lett. 4, 725–728 (2006).
  14. C. Canovas and E. N. Ribak, “Comparison of Hartmann analysis methods,” Appl. Opt. 46, 1830–1835 (2007).
    [Crossref] [PubMed]
  15. D. Malacara and Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 37, 1151–1555 (1992).
  16. E. Román-Hernández, J. G. Santiago-Santiago, G. Silva-Ortigoza, R. Silva-Ortigoza, and J. Velázquez-Castro, “Describing the structure of ronchigrams when the grating is placed at the caustic region: the parabolical mirror,” J. Opt. Soc. Am. A 27, 832–845 (2010).
    [Crossref]
  17. S. A. Juárez-Reyes, M. Marciano-Melchor, P. Ortega-Vidals, E. Román-Hernández, G. Silva-Ortigoza, R. Silva-Ortigoza, R. Suárez-Xique, G. Torres del Castillo, and M. Velázquez-Quesada, “Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens,” J. Opt. Soc. Am. A 31, 448–459 (2014).
    [Crossref]
  18. 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]
  19. M. Avendaño-Alejo, “Caustics in a meridional plane produced by plano-convex aspheric lenses,” J. Opt. Soc. Am. A 30, 501–508 (2013).
    [Crossref]
  20. D. Gonzalez-Utrera and M. Avendaño-Alejo, “Quantitative evaluation of a plano-convex parabolic lens,” Proc. SPIE 8011, 80111G (2011).
    [Crossref]
  21. D. Castán-Ricaño and M. Avendaño-Alejo, “Designing null screens type sub-structured Ronchi to test a fast plano-convex aspheric lens,” Proc. SPIE 9195, 919509 (2014).
    [Crossref]
  22. G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
    [Crossref]
  23. A. Téllez-Quiñones, D. Malacara-Doblado, R. Flores-Hernández, D. A. Gutiérrez-Hernández, and M. León-Rodríguez, “Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances,” Appl. Opt. 55, 2160–2168 (2016).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
[Crossref]

2014 (2)

2013 (1)

2011 (1)

D. Gonzalez-Utrera and M. Avendaño-Alejo, “Quantitative evaluation of a plano-convex parabolic lens,” Proc. SPIE 8011, 80111G (2011).
[Crossref]

2010 (2)

2009 (1)

2007 (1)

2006 (1)

2005 (1)

2000 (3)

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]

1998 (1)

1992 (2)

D. Malacara and Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 37, 1151–1555 (1992).

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]

1990 (1)

1981 (1)

1975 (1)

1974 (1)

D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 8, 1778–1780 (1974).
[Crossref]

Avendaño-Alejo, M.

G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
[Crossref]

D. Castán-Ricaño and M. Avendaño-Alejo, “Designing null screens type sub-structured Ronchi to test a fast plano-convex aspheric lens,” Proc. SPIE 9195, 919509 (2014).
[Crossref]

M. Avendaño-Alejo, “Caustics in a meridional plane produced by plano-convex aspheric lenses,” J. Opt. Soc. Am. A 30, 501–508 (2013).
[Crossref]

D. Gonzalez-Utrera and M. Avendaño-Alejo, “Quantitative evaluation of a plano-convex parabolic lens,” Proc. SPIE 8011, 80111G (2011).
[Crossref]

M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
[Crossref]

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]

Campos-García, M.

Canovas, C.

Cardona-Nunez, O.

Castañeda, L.

M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
[Crossref]

Castán-Ricaño, D.

G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
[Crossref]

D. Castán-Ricaño and M. Avendaño-Alejo, “Designing null screens type sub-structured Ronchi to test a fast plano-convex aspheric lens,” Proc. SPIE 9195, 919509 (2014).
[Crossref]

Castillo-Santiago, G.

G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
[Crossref]

Caulfield, H. J.

Cordero-Davila, A.

Cornejo, A.

D. Malacara, A. Cornejo, and M. V. R. K. Murty, “Bibliography of various optical testing methods,” Appl. Opt. 14, 1065–1080 (1975).
[Crossref] [PubMed]

D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 8, 1778–1780 (1974).
[Crossref]

Cornejo-Rodriguez, A.

Díaz-Uribe, R.

Durán-Ramírez, V. M.

Flores-Hernández, 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.

Gonzalez-Galindo, A.

G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
[Crossref]

Gonzalez-Utrera, D.

D. Gonzalez-Utrera and M. Avendaño-Alejo, “Quantitative evaluation of a plano-convex parabolic lens,” Proc. SPIE 8011, 80111G (2011).
[Crossref]

M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
[Crossref]

Gutiérrez-Hernández, D. A.

Huang, H.

Juárez-Reyes, S. A.

León-Rodríguez, M.

Liu, D.

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.

D. Malacara and Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 37, 1151–1555 (1992).

D. Malacara, A. Cornejo, and M. V. R. K. Murty, “Bibliography of various optical testing methods,” Appl. Opt. 14, 1065–1080 (1975).
[Crossref] [PubMed]

D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 8, 1778–1780 (1974).
[Crossref]

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 361–397.
[Crossref]

Malacara, Z.

D. Malacara and Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 37, 1151–1555 (1992).

Malacara-Doblado, D.

Malacara-Hernández, D.

D. P. Salas-Peimbert, D. Malacara-Doblado, V. M. Durán-Ramírez, G. Trujillo-Schiaffino, and D. Malacara-Hernández, “Wave-front retrieval from Hartmann test data,” Appl. Opt. 44, 4228–4238 (2005).
[Crossref] [PubMed]

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]

Marciano-Melchor, M.

Moreno-Oliva, I.

Murty, M. V. R. K.

Ordóñez-Romero, C. L.

M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
[Crossref]

Ortega-Vidals, P.

Qureshi, N.

M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
[Crossref]

Ren, B.

Ribak, E. N.

Roggemann, M. C.

Román-Hernández, E.

Salas-Peimbert, D. P.

Santiago-Santiago, J. G.

Schulz, T. J.

Silva-Ortigoza, G.

Silva-Ortigoza, R.

Suárez-Xique, R.

Téllez-Quiñones, A.

Torres del Castillo, G.

Trujillo-Schiaffino, G.

Velázquez-Castro, J.

Velázquez-Quesada, M.

Wang, X.

Yan, Y.

Zeng, A.

Appl. Opt. (11)

D. Malacara, A. Cornejo, and M. V. R. K. Murty, “Bibliography of various optical testing methods,” Appl. Opt. 14, 1065–1080 (1975).
[Crossref] [PubMed]

A. Cornejo-Rodriguez, H. J. Caulfield, and W. Friday, “Testing of optical surface: a bibliography,” Appl. Opt. 20, 4148 (1981).
[Crossref]

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

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]

D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 8, 1778–1780 (1974).
[Crossref]

A. Cordero-Davila, A. Cornejo-Rodriguez, and O. Cardona-Nunez, “Null Hartmann and Ronchi-Hartmann test,” Appl. Opt. 29, 4618–4621 (1990).
[Crossref] [PubMed]

M. C. Roggemann and T. J. Schulz, “Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements,” Appl. Opt. 37, 4321–4329 (1998).
[Crossref]

D. P. Salas-Peimbert, D. Malacara-Doblado, V. M. Durán-Ramírez, G. Trujillo-Schiaffino, and D. Malacara-Hernández, “Wave-front retrieval from Hartmann test data,” Appl. Opt. 44, 4228–4238 (2005).
[Crossref] [PubMed]

C. Canovas and E. N. Ribak, “Comparison of Hartmann analysis methods,” Appl. Opt. 46, 1830–1835 (2007).
[Crossref] [PubMed]

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]

A. Téllez-Quiñones, D. Malacara-Doblado, R. Flores-Hernández, D. A. Gutiérrez-Hernández, and M. León-Rodríguez, “Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances,” Appl. Opt. 55, 2160–2168 (2016).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (3)

D. Malacara and Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 37, 1151–1555 (1992).

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]

Opt. Exp. (1)

M. Avendaño-Alejo, D. Gonzalez-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Exp. 18, 21131–21137 (2010).
[Crossref]

Proc. SPIE (3)

D. Gonzalez-Utrera and M. Avendaño-Alejo, “Quantitative evaluation of a plano-convex parabolic lens,” Proc. SPIE 8011, 80111G (2011).
[Crossref]

D. Castán-Ricaño and M. Avendaño-Alejo, “Designing null screens type sub-structured Ronchi to test a fast plano-convex aspheric lens,” Proc. SPIE 9195, 919509 (2014).
[Crossref]

G. Castillo-Santiago, D. Castán-Ricaño, A. Gonzalez-Galindo, M. Avendaño-Alejo, and R. Díaz-Uribe, “Null screens type Hartmann to test simple lenses,” Proc. SPIE 9575, 95751H (2015).
[Crossref]

Other (1)

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 361–397.
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (2784 KB)      Hartmann type null screens

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Figures (10)

Fig. 1
Fig. 1 (a) Caustic produced by refraction through a plano-convex aspheric lens and their associated parameters considering that the point source is located at infinity. (b) Diagram of the experimental setup to test a plano-convex aspherical lens considering a ccd sensor placed inside the caustic surface.
Fig. 2
Fig. 2 (a) Square array of circular spots at detection plane to design null screens with P = 13, n = 113 spots, lm = 6.6mm and Δ = 0.264mm. (b) Distribution of quasi-angular array of circular spots at detection plane to design the null screen with n = 133 spots.
Fig. 3
Fig. 3 (a) Three different polygons with M sides forming part of the null screens, which will be overlapping at plane z0, the points whose distance are hs1, hs2 and hs3 are brought in coincidence at the point y0. (b) Distribution of the regions along the optical axis showing the coincidence of three refracted rays at the point (z0, y0). (c) Parameters involved in the process to design a circular bright spot at detection’s plane.
Fig. 4
Fig. 4 (a) Designing null screens placing the ccd sensor at different planes of detection. (b) Zoom of a square array of bright spots on CCD sensor to design the null screens. (C) Zoom of a quasi-angular array of bright points on CCD sensor to design the null screens.
Fig. 5
Fig. 5 Design of square null screens where Q is the number of holes, whose images are recorded at different planes of detection z0, for all cases supplying n = 113 bright spots (see Visualization 1).
Fig. 6
Fig. 6 Design of radial null screens where Q is the number of holes, whose images are recorded at different planes of detection z0, for all cases supplying n = 133 bright spots (see Visualization 1).
Fig. 7
Fig. 7 Design of square and quasi-angular null screens to be recorded at z0 = 22 mm for P = 9, 11 and 13 drop spots along Y-axis and its ray tracing process on a meridional plane.
Fig. 8
Fig. 8 Images recorded at ccd sensor for (a) square and (b) quasi-angular arrays null screens considering three different holes being illuminated by a plane wavefront and brought in coincidence at detection plane, which is placed at CLC.
Fig. 9
Fig. 9 Images recorded at ccd sensor reducing slightly the illuminance at entrance aperture for (a) square and (b) quasi-angular arrays null screens being illuminated by a plane wavefront and brought in coincidence at detection plane z0 = 22mm.
Fig. 10
Fig. 10 (a)–(c) and (e)–(f) CCD sensor has been placed slightly toward the lens under test for square and quasi-angular arrays respectively. (d) and (h) the null screen has been misalignments. (i)–(l) CCD sensor has been placed slightly outward of the lens under test for square and quasi-angular arrays respectively.

Equations (8)

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S h N = c h 2 1 + 1 ( k + 1 ) c 2 h 2 + i = 1 N A 2 i h 2 i ,
z d ( h ) = t + S h N + [ n a 2 + ( n a 2 n i 2 ) S h N 2 ] [ n a 2 + n i n a 2 + ( n a 2 n i 2 ) S h N 2 ] n a 2 ( n a 2 n i 2 ) S h N y d ( h ) = h [ n a 2 + ( n a 2 n i 2 ) S h N 2 ] S h N n a 2 S h N ,
y 0 = [ n a 2 n i 2 ] [ z 0 ( t + S h N ) ] S h N n a 2 + n i n a 2 + ( n a 2 n i 2 ) S h N 2 + h .
n i 2 [ ( z 0 t S h N ) 2 + ( y 0 h ) 2 ] S h N 2 = n a 2 [ ( z 0 t S h N ] ) S h N ( y 0 h ) ] 2 ,
( x H i ) 2 + ( y K j ) 2 = r s 2 ,
H i = 2 i Δ , for i = P 1 2 , , 1 , 0 , 1 , , P 1 2 , K j = 2 j Δ , for j = P 1 2 , , 1 , 0 , 1 , , P 1 2 .
( x i q , y j q ) = ( H i + r s cos [ q θ M ] , K j + r s sin [ q θ M ] ) , for q = 0 , 1 , , M ,
( x s , y s ) = ( h s cos φ i j , h s sin φ i j ) ,

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