Abstract

A method for increasing the precision and sensitivity of the quantitative evaluation of fast aspheric surfaces through the null screen method is presented. This consists of applying small displacements to the cylindrical null screen along the optical axis. These movements allow a scan of the image spots over zones that with the analysis of a single image are more difficult to evaluate. The precision of the test is increased due to a greater density of sampling reducing the numerical errors during the integration. Results of the evaluation of an elliptical concave mirror on axis show that the numerical integration errors can be reduced from 20% for short paths to 80% for larger integration paths.

© 2008 Optical Society of America

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References

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  1. R. Díaz-Uribe and Manuel Campos-García, "Null-screen testing of fast convex aspheric surfaces," Appl. Opt. 39, 2670-2677 (2000).
    [CrossRef]
  2. E. Ghozeil, "Hartmann and other screen tests," in Optical Shop Testing, 2nd ed., D.Malacara, ed. (Wiley, 1992), pp. 367-396.
  3. D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, 1964), Chap. 6, pp. 178-183.
  4. Campos-García, R. Díaz-Uribe, and F. S. Granados-Agustin, "Testing fast aspheric surfaces with a linear array of sources," Appl. Opt. 43, 6255-6264 (2004).
    [CrossRef] [PubMed]
  5. 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]
  6. R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
    [CrossRef]
  7. L. Carmona Paredes, "Imágenes de aberturas elípticas en la prueba de superficies convexas con pantallas nulas," Tesis de Maestría, Posgrado en Ciencias Físicas (Universidad Nacional Autónoma de México, 2005).
  8. M. Avendaño-Alejo, M. Campos-García, and R. Díaz-Uribe, "Tilted null screens with drop shaped spots: radial and square arrays," in Proceedings of Frontiers in Optics 2006 90th Annual Meeting, Optical Fabrication and Testing, Topical Meeting, Rochester, New York, EE. UU. 8-12 de Octubre, OFMC9, 1-3 (2006).
    [PubMed]
  9. W. Rasban, National Institutes of Health, USA. ImageJ V. 1.312u, Image Processing and Analysis in Java, http://rsb.info.nih.gov/ij/.
  10. L. Carmona-Paredes and R. Díaz-Uribe, "Geometric analysis of the null screens used for testing convex optical surfaces," Rev. Mex. Fís. 53, 421-430 (2007).
  11. R. Bolado-Gómez, "Prueba de un espejo elipsoidal cóncavo en eje (F/0.273) por medio de una pantalla nula cilíndrica," Tesis de Licenciatura, Facultad de Ciencias (Universidad Nacional Autónoma de México, 2005).
  12. R. Díaz-Uribe, "Medium-precision null-screen testing of off-axis parabolic mirrors for segmented primary telescope optics: the large millimeter telescope," Appl. Opt. 39, 2790-2804 (2000).
    [CrossRef]
  13. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).
  14. O. Vladimirovna and M. F. González-Cardel, Métodos Numéricos (Ediciones Instituto de Investigación de Tecnología Educativa de la Universidad Tecnológica de México, 2002).
  15. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992), pp. 161-166.
  16. M. Campos-García, R. Bolado-Gómez, and R. Díaz-Uribe, "Testing fast aspheric. concave surfaces with a cylindrical null screen," Appl. Opt. , Doc. ID 87342 (posted 1/8/2008 in press).
    [PubMed]

2007 (1)

L. Carmona-Paredes and R. Díaz-Uribe, "Geometric analysis of the null screens used for testing convex optical surfaces," Rev. Mex. Fís. 53, 421-430 (2007).

2006 (1)

R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
[CrossRef]

2005 (1)

2004 (1)

2000 (2)

Avendaño-Alejo, M.

R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
[CrossRef]

M. Avendaño-Alejo, M. Campos-García, and R. Díaz-Uribe, "Tilted null screens with drop shaped spots: radial and square arrays," in Proceedings of Frontiers in Optics 2006 90th Annual Meeting, Optical Fabrication and Testing, Topical Meeting, Rochester, New York, EE. UU. 8-12 de Octubre, OFMC9, 1-3 (2006).
[PubMed]

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992), pp. 161-166.

Bolado-Gomez, R.

R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
[CrossRef]

Bolado-Gómez, R.

R. Bolado-Gómez, "Prueba de un espejo elipsoidal cóncavo en eje (F/0.273) por medio de una pantalla nula cilíndrica," Tesis de Licenciatura, Facultad de Ciencias (Universidad Nacional Autónoma de México, 2005).

M. Campos-García, R. Bolado-Gómez, and R. Díaz-Uribe, "Testing fast aspheric. concave surfaces with a cylindrical null screen," Appl. Opt. , Doc. ID 87342 (posted 1/8/2008 in press).
[PubMed]

Campos-García, M.

R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
[CrossRef]

M. Avendaño-Alejo, M. Campos-García, and R. Díaz-Uribe, "Tilted null screens with drop shaped spots: radial and square arrays," in Proceedings of Frontiers in Optics 2006 90th Annual Meeting, Optical Fabrication and Testing, Topical Meeting, Rochester, New York, EE. UU. 8-12 de Octubre, OFMC9, 1-3 (2006).
[PubMed]

M. Campos-García, R. Bolado-Gómez, and R. Díaz-Uribe, "Testing fast aspheric. concave surfaces with a cylindrical null screen," Appl. Opt. , Doc. ID 87342 (posted 1/8/2008 in press).
[PubMed]

Campos-García, Manuel

Carmona-Paredes, L.

L. Carmona-Paredes and R. Díaz-Uribe, "Geometric analysis of the null screens used for testing convex optical surfaces," Rev. Mex. Fís. 53, 421-430 (2007).

Díaz-Uribe, R.

L. Carmona-Paredes and R. Díaz-Uribe, "Geometric analysis of the null screens used for testing convex optical surfaces," Rev. Mex. Fís. 53, 421-430 (2007).

R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
[CrossRef]

Campos-García, R. Díaz-Uribe, and F. S. Granados-Agustin, "Testing fast aspheric surfaces with a linear array of sources," Appl. Opt. 43, 6255-6264 (2004).
[CrossRef] [PubMed]

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

R. Díaz-Uribe, "Medium-precision null-screen testing of off-axis parabolic mirrors for segmented primary telescope optics: the large millimeter telescope," Appl. Opt. 39, 2790-2804 (2000).
[CrossRef]

M. Campos-García, R. Bolado-Gómez, and R. Díaz-Uribe, "Testing fast aspheric. concave surfaces with a cylindrical null screen," Appl. Opt. , Doc. ID 87342 (posted 1/8/2008 in press).
[PubMed]

M. Avendaño-Alejo, M. Campos-García, and R. Díaz-Uribe, "Tilted null screens with drop shaped spots: radial and square arrays," in Proceedings of Frontiers in Optics 2006 90th Annual Meeting, Optical Fabrication and Testing, Topical Meeting, Rochester, New York, EE. UU. 8-12 de Octubre, OFMC9, 1-3 (2006).
[PubMed]

Dorn, W. S.

D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, 1964), Chap. 6, pp. 178-183.

Durán-Ramírez, V. M.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).

Ghozeil, E.

E. Ghozeil, "Hartmann and other screen tests," in Optical Shop Testing, 2nd ed., D.Malacara, ed. (Wiley, 1992), pp. 367-396.

González-Cardel, M. F.

O. Vladimirovna and M. F. González-Cardel, Métodos Numéricos (Ediciones Instituto de Investigación de Tecnología Educativa de la Universidad Tecnológica de México, 2002).

Granados-Agustin, F. S.

Malacara-Doblado, D.

Malacara-Hernández, D.

McCracken, D. D.

D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, 1964), Chap. 6, pp. 178-183.

Paredes, L. Carmona

L. Carmona Paredes, "Imágenes de aberturas elípticas en la prueba de superficies convexas con pantallas nulas," Tesis de Maestría, Posgrado en Ciencias Físicas (Universidad Nacional Autónoma de México, 2005).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).

Rasban, W.

W. Rasban, National Institutes of Health, USA. ImageJ V. 1.312u, Image Processing and Analysis in Java, http://rsb.info.nih.gov/ij/.

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992), pp. 161-166.

Salas-Peimbert, D. P.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).

Trujillo-Schiaffino, G.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).

Vladimirovna, O.

O. Vladimirovna and M. F. González-Cardel, Métodos Numéricos (Ediciones Instituto de Investigación de Tecnología Educativa de la Universidad Tecnológica de México, 2002).

Appl. Opt. (5)

Proc. SPIE (1)

R. Díaz-Uribe, R. Bolado-Gomez, M. Campos-García, and M. Avendaño-Alejo, "Medium precision optical testing of a fast concave elliptical mirror by a cylindrical null screen," in Optical Design and Fabrication, J. Breckinridge and Y. Wang, eds., Proc. SPIE 6034, 60340Y (2006).
[CrossRef]

Rev. Mex. Fís. (1)

L. Carmona-Paredes and R. Díaz-Uribe, "Geometric analysis of the null screens used for testing convex optical surfaces," Rev. Mex. Fís. 53, 421-430 (2007).

Other (9)

R. Bolado-Gómez, "Prueba de un espejo elipsoidal cóncavo en eje (F/0.273) por medio de una pantalla nula cilíndrica," Tesis de Licenciatura, Facultad de Ciencias (Universidad Nacional Autónoma de México, 2005).

E. Ghozeil, "Hartmann and other screen tests," in Optical Shop Testing, 2nd ed., D.Malacara, ed. (Wiley, 1992), pp. 367-396.

D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, 1964), Chap. 6, pp. 178-183.

L. Carmona Paredes, "Imágenes de aberturas elípticas en la prueba de superficies convexas con pantallas nulas," Tesis de Maestría, Posgrado en Ciencias Físicas (Universidad Nacional Autónoma de México, 2005).

M. Avendaño-Alejo, M. Campos-García, and R. Díaz-Uribe, "Tilted null screens with drop shaped spots: radial and square arrays," in Proceedings of Frontiers in Optics 2006 90th Annual Meeting, Optical Fabrication and Testing, Topical Meeting, Rochester, New York, EE. UU. 8-12 de Octubre, OFMC9, 1-3 (2006).
[PubMed]

W. Rasban, National Institutes of Health, USA. ImageJ V. 1.312u, Image Processing and Analysis in Java, http://rsb.info.nih.gov/ij/.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).

O. Vladimirovna and M. F. González-Cardel, Métodos Numéricos (Ediciones Instituto de Investigación de Tecnología Educativa de la Universidad Tecnológica de México, 2002).

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992), pp. 161-166.

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Figures (10)

Fig. 1
Fig. 1

(a) Setup used for the PSM with cylindrical null screen and design variables, (b) flat-printed null screen to be used in the testing of the concave ellipsoidal surface.

Fig. 2
Fig. 2

Evolution of the image spots on the test surface by displacing the null screen along the optical axis a distance Δ z : (a) Δ z = 0   mm , (b) Δ z = 1.524   mm , (c) Δ z = 2.667   mm , (d) Δ z = 3.81   mm .

Fig. 3
Fig. 3

(a) Plot of the positions of the spots centroids for the ten images captured by displacement of the cylindrical null screen, (b) zoom from a section image.

Fig. 4
Fig. 4

Image position for nine spots and their respective shift from 0 to 3.81   mm (∗ initials spots). These points belong to the selected region on Fig. 3.

Fig. 5
Fig. 5

Integration paths. (a) Single image of 428 spots, (b) PSM (11 images, 4708 spots).

Fig. 6
Fig. 6

(a) Closed integration path selected of the centroids for the ten images captured by displacement of the cylindrical null screen, (b) detail of the integration path compared to the same path with point shifting and without point shifting.

Fig. 7
Fig. 7

(a) Closed path selected on the points of a single image, (b) closed path selected with more points with the use of the PSM.

Fig. 8
Fig. 8

Reconstruction of the differences in sagitta between the measured surface and the best fitting conic: (a) single image; (b) with PSM.

Fig. 9
Fig. 9

Profile of the step of the differences between the experimental data and the best fit of the conic surface without the use of the PSM compared to the same points with the PSM.

Fig. 10
Fig. 10

Measure of the step height for different y positions, with and without PSM.

Tables (2)

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Table 1 Setup Parameters Used for the Design of the Cylindrical Null Screen

Tables Icon

Table 2 Parameters of the Best Fit Conic Surface

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ρ 2 = a ( r Q b ) [ a 2 r 2 + ρ 1 2 b ( Q b 2 r ) ] 1 / 2 a 2 Q + ρ 1 2 ρ 1 ,
z 2 = ρ 2 ρ 1 a + b .
ρ 3 = R ,
z 3 = a ρ 2 2 + a ( Q z 2 r ) 2 + 2 ρ 1 ρ 2 ( Q z 2 r ) ρ 1 ρ 2 2 ρ 1 ( Q z 2 r ) 2 + 2 a ρ 2 ( Q z 2 r ) × ( R ρ 2 ) + z 2 ,
z m z 1 = P 1 P ( n x n z d x + n y n z d y ) ,
z m = i = 1 m 1 { ( n x i n z i + n x i + 1 n z i + 1 ) ( x i + 1 x i ) 2 + ( n y i n z i + n y i + 1 n z i + 1 ) ( y i + 1 y i ) 2 } + z 1 ,
z = r { r 2 ( k + 1 ) [ ( x x 0 ) 2 + ( y y 0 ) 2 ] } 1 / 2 k + 1 + z 0 + A x + B y ,

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