Abstract

A method is presented to sense the wave front at the exit of an optical surface. This method uses a set of diffracted rays generated when a He-Ne laser impinges on a rectangular diffraction grating. The grating was placed near the curvature center of the surface to be tested. After they are reflected in the test surface, the diffracted rays have the information of the slopes of the wave front, like in the Hartmann test. The Hartmann pattern was registered near the curvature center and captured with a CCD camera. The slopes for each ray are measured from the experimental pattern, and they are compared with the ideal ones simulated in a computer. The evaluation was carried out by use of Seidel polynomials to obtain the information of the aberrations of a mirror 53 cm in diameter.

© 2003 Optical Society of America

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References

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  1. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.
  2. A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 321–365.
  3. R. G. Lane, M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt. 31, 6902–6910 (1992).
    [Crossref] [PubMed]
  4. R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing method for optical testing,” Opt. Lett. 24, 951–953 (1999).
    [Crossref]
  5. E. Hecht, Optics (Addison-Wesley Iberoamericana, Madrid, 2000), Chap. 4, pp. 146–147.
  6. D. Malacara, “Appendix 1. An optical surface and its characteristics,” in Optical Shop Testing (Wiley, New York, 1992), pp. 743–744.
  7. E. Luna-Aguilar, A. Cornejo-Rodríguez, A. Cordero Dávila, “Prueba nula de Ronchi-Hartmann,” Rev. Mex. Fís. 38, 150–161 (1992).
  8. A. Morales, D. Malacara, “Geometrical parameters in the Hartmann test of aspherical mirrors,” Appl. Opt. 22, 3957–3959 (1983).
    [Crossref] [PubMed]
  9. J. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap. 2, pp. 14–15.
  10. C. Robledo-Sánchez, G. Camacho-Basilio, A. Jaramillo-Nuñez, David Gale, “Aberration extraction in the Hartmann test by use of spatial filters,” Appl. Opt. 38, 3483–3489 (1999).
    [Crossref]

1999 (2)

1992 (2)

R. G. Lane, M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt. 31, 6902–6910 (1992).
[Crossref] [PubMed]

E. Luna-Aguilar, A. Cornejo-Rodríguez, A. Cordero Dávila, “Prueba nula de Ronchi-Hartmann,” Rev. Mex. Fís. 38, 150–161 (1992).

1983 (1)

Camacho-Basilio, G.

Cordero Dávila, A.

E. Luna-Aguilar, A. Cornejo-Rodríguez, A. Cordero Dávila, “Prueba nula de Ronchi-Hartmann,” Rev. Mex. Fís. 38, 150–161 (1992).

Cornejo-Rodríguez, A.

E. Luna-Aguilar, A. Cornejo-Rodríguez, A. Cordero Dávila, “Prueba nula de Ronchi-Hartmann,” Rev. Mex. Fís. 38, 150–161 (1992).

A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 321–365.

Gale, David

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

Goodmann, J. W.

J. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap. 2, pp. 14–15.

Hecht, E.

E. Hecht, Optics (Addison-Wesley Iberoamericana, Madrid, 2000), Chap. 4, pp. 146–147.

Jaramillo-Nuñez, A.

Lane, R. G.

Luna-Aguilar, E.

E. Luna-Aguilar, A. Cornejo-Rodríguez, A. Cordero Dávila, “Prueba nula de Ronchi-Hartmann,” Rev. Mex. Fís. 38, 150–161 (1992).

Malacara, D.

A. Morales, D. Malacara, “Geometrical parameters in the Hartmann test of aspherical mirrors,” Appl. Opt. 22, 3957–3959 (1983).
[Crossref] [PubMed]

D. Malacara, “Appendix 1. An optical surface and its characteristics,” in Optical Shop Testing (Wiley, New York, 1992), pp. 743–744.

Morales, A.

Moreno-Barriuso, E.

Navarro, R.

Robledo-Sánchez, C.

Tallon, M.

Appl. Opt. (3)

Opt. Lett. (1)

Rev. Mex. Fís. (1)

E. Luna-Aguilar, A. Cornejo-Rodríguez, A. Cordero Dávila, “Prueba nula de Ronchi-Hartmann,” Rev. Mex. Fís. 38, 150–161 (1992).

Other (5)

E. Hecht, Optics (Addison-Wesley Iberoamericana, Madrid, 2000), Chap. 4, pp. 146–147.

D. Malacara, “Appendix 1. An optical surface and its characteristics,” in Optical Shop Testing (Wiley, New York, 1992), pp. 743–744.

J. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap. 2, pp. 14–15.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 321–365.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for sensing the wave front by use of a set of diffracted rays. ST is the surface under test; DG is the diffraction grating plane, illuminated by the He-Ne laser. At the plane, containing point P p , the complete observed Hartmanngram is registered.

Fig. 2
Fig. 2

Liquid-crystal display from a slide projector used as a diffraction grating.

Fig. 3
Fig. 3

Set of rays that impinge the surface under test.

Fig. 4
Fig. 4

Set of diffracted rays that produce the Hartmanngram.

Fig. 5
Fig. 5

Diagram that shows the angular resolution in two tests T 1 and T 2, are tangent to TS.

Tables (3)

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Table 1 Functions Uj and Their Derivatives

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Table 2 Coordinates of Points P and Pp

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Table 3 Coefficients of the Aberrations in Seidel Polynomials

Equations (8)

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

Xp=X0-z-ZpS2xS2z,
Yp=Y0-z-ZpS2yS2z,
S2=S1-2S1·NN,
N=-z/x, -z/y, 1z/x2+z/y2+11/2,
z=1k+1R-R2-K+1X02+Y021/2.
WX0, Y0=j=1k wjUjX0, Y0,
Fj=UjX0, UjY0.
T=j=1k wjFj.

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