Abstract

We use a square grid in the Ronchi test. This grid allows processing of both the X and the Y directions when calculating optical path difference. We use trapezoidal integration to analyze the new patterns, since it does not have the smoothing drawback at the edges of the wave front.

© 1998 Optical Society of America

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References

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  1. A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 321–365.
  2. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.
  3. A. Cornejo-Rodríguez, D. Malacara, “Wavefront determination using Ronchi and Hartmann tests,” Bol. Inst. Tonantzintla 2, 127–129 (1976).
  4. A. Cordero-Dávila, A. Cornejo-Rodríguez, O. Cardona-Nuñez, “Ronchi and Hartmann tests with the same mathematical theory,” Appl. Opt. 31, 2370–2376 (1992).
    [CrossRef]
  5. C. L. Koliopoulos, “Radial grating lateral shear heterodyne interferometer,” Appl. Opt. 19, 1523–1528 (1980).
    [CrossRef] [PubMed]
  6. J. C. Wyant, “Double frequency grating lateral shear interferometer,” Appl. Opt. 12, 2057–2060 (1973).
    [CrossRef] [PubMed]
  7. M. P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974).
    [CrossRef] [PubMed]
  8. W. S. Meyers, H. Philip Stahl, “Contouring of a free oil surface,” in Interferometry Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds., Proc. SPIE1755, 84–94 (1992).
    [CrossRef]
  9. H. Philip Stahl, “STDCE-2 free surface deformation measurement,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Chad, J. D. Trolinger, eds., Proc. SPIE2546, 167–172 (1995).
    [CrossRef]
  10. K. Stultz, H. Philip Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross grating patterns,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).
    [CrossRef]
  11. A. Cordero, E. Luna, S. Zarate, O. Harris, “Evaluación de la calidad de la imagen del telescopio de 2.1 m,” Reporte Técnico IAUNAM, RT-95-02 (1995).
  12. R. Bruscaglioni, “Sulla forma delle fringe d’interferenza ottenute da onde affette da astigmatismo puro con reticoli ad orientamento qualunque,” Reand. Accad. Naz. Lincei 15, 70–73 (1932).
  13. D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 455–499.
  14. D. Dutton, A. Cornejo, M. Lattas, “A semiautomatic method for interpreting shearing interferograms,” Appl. Opt. 7, 125–131 (1968).
    [CrossRef] [PubMed]
  15. K. R. Freishlad, C. L. Koliopoulos, “Modal estimation of a wave front from difference measurements using the discrete Fourier Transform,” J. Opt. Soc. Am. A 3, 1852–1861 (1986).
    [CrossRef]
  16. J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
    [CrossRef]
  17. G. W. R. Leibbrandt, G. Harbers, P. J. Kunts, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 35, 6151–6161 (1996).
    [CrossRef] [PubMed]
  18. G. Harbers, P. J. Kunts, G. W. R. Leibbrandt, “Analysis of lateral shearing interferograms by use of Zernike polynomials,” Appl. Opt. 35, 6162–6172 (1996).
    [CrossRef] [PubMed]

1996 (2)

1992 (1)

1986 (1)

1980 (1)

1976 (1)

A. Cornejo-Rodríguez, D. Malacara, “Wavefront determination using Ronchi and Hartmann tests,” Bol. Inst. Tonantzintla 2, 127–129 (1976).

1974 (1)

1973 (1)

1968 (1)

1964 (1)

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
[CrossRef]

1932 (1)

R. Bruscaglioni, “Sulla forma delle fringe d’interferenza ottenute da onde affette da astigmatismo puro con reticoli ad orientamento qualunque,” Reand. Accad. Naz. Lincei 15, 70–73 (1932).

Bruscaglioni, R.

R. Bruscaglioni, “Sulla forma delle fringe d’interferenza ottenute da onde affette da astigmatismo puro con reticoli ad orientamento qualunque,” Reand. Accad. Naz. Lincei 15, 70–73 (1932).

Cardona-Nuñez, O.

Cordero, A.

A. Cordero, E. Luna, S. Zarate, O. Harris, “Evaluación de la calidad de la imagen del telescopio de 2.1 m,” Reporte Técnico IAUNAM, RT-95-02 (1995).

Cordero-Dávila, A.

Cornejo, A.

Cornejo-Rodríguez, A.

A. Cordero-Dávila, A. Cornejo-Rodríguez, O. Cardona-Nuñez, “Ronchi and Hartmann tests with the same mathematical theory,” Appl. Opt. 31, 2370–2376 (1992).
[CrossRef]

A. Cornejo-Rodríguez, D. Malacara, “Wavefront determination using Ronchi and Hartmann tests,” Bol. Inst. Tonantzintla 2, 127–129 (1976).

A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 321–365.

DeVore, S. L.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 455–499.

Dutton, D.

Freishlad, K. R.

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

Harbers, G.

Harris, O.

A. Cordero, E. Luna, S. Zarate, O. Harris, “Evaluación de la calidad de la imagen del telescopio de 2.1 m,” Reporte Técnico IAUNAM, RT-95-02 (1995).

Koliopoulos, C. L.

Kunts, P. J.

Lattas, M.

Leibbrandt, G. W. R.

Luna, E.

A. Cordero, E. Luna, S. Zarate, O. Harris, “Evaluación de la calidad de la imagen del telescopio de 2.1 m,” Reporte Técnico IAUNAM, RT-95-02 (1995).

Malacara, D.

A. Cornejo-Rodríguez, D. Malacara, “Wavefront determination using Ronchi and Hartmann tests,” Bol. Inst. Tonantzintla 2, 127–129 (1976).

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 455–499.

Meyers, W. S.

W. S. Meyers, H. Philip Stahl, “Contouring of a free oil surface,” in Interferometry Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds., Proc. SPIE1755, 84–94 (1992).
[CrossRef]

Rayces, J. L.

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
[CrossRef]

Rimmer, M. P.

Stahl, H. Philip

K. Stultz, H. Philip Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross grating patterns,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).
[CrossRef]

W. S. Meyers, H. Philip Stahl, “Contouring of a free oil surface,” in Interferometry Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds., Proc. SPIE1755, 84–94 (1992).
[CrossRef]

H. Philip Stahl, “STDCE-2 free surface deformation measurement,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Chad, J. D. Trolinger, eds., Proc. SPIE2546, 167–172 (1995).
[CrossRef]

Stultz, K.

K. Stultz, H. Philip Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross grating patterns,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).
[CrossRef]

Wyant, J. C.

Zarate, S.

A. Cordero, E. Luna, S. Zarate, O. Harris, “Evaluación de la calidad de la imagen del telescopio de 2.1 m,” Reporte Técnico IAUNAM, RT-95-02 (1995).

Appl. Opt. (7)

Bol. Inst. Tonantzintla (1)

A. Cornejo-Rodríguez, D. Malacara, “Wavefront determination using Ronchi and Hartmann tests,” Bol. Inst. Tonantzintla 2, 127–129 (1976).

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964).
[CrossRef]

Reand. Accad. Naz. Lincei (1)

R. Bruscaglioni, “Sulla forma delle fringe d’interferenza ottenute da onde affette da astigmatismo puro con reticoli ad orientamento qualunque,” Reand. Accad. Naz. Lincei 15, 70–73 (1932).

Other (7)

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 455–499.

A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 321–365.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

W. S. Meyers, H. Philip Stahl, “Contouring of a free oil surface,” in Interferometry Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds., Proc. SPIE1755, 84–94 (1992).
[CrossRef]

H. Philip Stahl, “STDCE-2 free surface deformation measurement,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Chad, J. D. Trolinger, eds., Proc. SPIE2546, 167–172 (1995).
[CrossRef]

K. Stultz, H. Philip Stahl, “A discussion of techniques that separate orthogonal data produced by Ronchi cross grating patterns,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 226–232 (1994).
[CrossRef]

A. Cordero, E. Luna, S. Zarate, O. Harris, “Evaluación de la calidad de la imagen del telescopio de 2.1 m,” Reporte Técnico IAUNAM, RT-95-02 (1995).

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Figures (5)

Fig. 1
Fig. 1

(a) Typical geometry of the Ronchi test for a concave mirror. (b) Detected bironchigram for a parabolic mirror with a 15-cm diameter, a 220-cm paraxial radius of curvature, and a square grid whose spatial frequency is 1.8 line/mm.

Fig. 2
Fig. 2

(a) Experimental setup for testing a reflecting telescope. (b) Detected bironchigram for the 84-cm reflecting telescope.

Fig. 3
Fig. 3

Geometry used for bironchigram processing.

Fig. 4
Fig. 4

Calculated path difference for the 84-cm reflecting telescope. Orders of (a) 4, (b) 6, and (c) 8 for the fitted polynomials.

Fig. 5
Fig. 5

Optical path differences obtained with trapezoidal integration.

Equations (9)

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D i = X i ,   Y i ,   M xi ,   M yi i = 1 ,   2 ,   N ,
X hi ,   Y hi = p M xi ,   M yi i = 1 ,   2 ,   N ,
pM X = - R   i = 0 k - 1 j = 0 i   C ij X j Y i - j ,
pM y = - R   i = 0 k - 1 j = 0 i   D ij X j Y i - j .
W X ,   Y = i = 0 k j = 0 i   B ij X j Y i - j .
T xi ,   T yi = X i d / R + pM xi ,   Y i d / R + pM yi .
Tx ,   Ty = - R w x ,   w y ,
W b - W a = - 1 R a b   T x d x + t y d ys ,
W b - W a = - T Xb - T Xa X b - X a + T Yb - T Ya X b - X a 2 R ,

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