Abstract

A novel optical testing method termed the grating-slit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the grating-slit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometrical-optics model for the grating-slit test is presented and the fringe contrast ratio with respect to the slit width and object-grating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio.

© 2007 Optical Society of America

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References

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  1. V. Ronchi, “40 Years of History of Grating Interferometer,” Appl. Opt 3,437–451 (1964).
    [CrossRef]
  2. T. Yatagai, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt 23,3676–3679 (1984).
    [CrossRef] [PubMed]
  3. C.-R. Jorge and S. Jose, Automatic phase-shifting Ronchi tester with a square Ronchi ruling, O. Wolfgang and N. Erik, eds. (SPIE, 2004), pp.199–210.
  4. K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
    [CrossRef]
  5. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
    [CrossRef] [PubMed]
  6. M. M. Gonzalez and N. A. Ochoa, “The Ronchi test with an LCD grating,” Opt. Commun 191,203–207 (2001).
    [CrossRef]
  7. J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt Acta 11,85–88 (1964).
    [CrossRef]
  8. A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop TestingD. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

2001 (1)

M. M. Gonzalez and N. A. Ochoa, “The Ronchi test with an LCD grating,” Opt. Commun 191,203–207 (2001).
[CrossRef]

1997 (1)

K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
[CrossRef]

1992 (1)

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop TestingD. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop TestingD. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

1984 (1)

T. Yatagai, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt 23,3676–3679 (1984).
[CrossRef] [PubMed]

1974 (1)

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

1964 (2)

V. Ronchi, “40 Years of History of Grating Interferometer,” Appl. Opt 3,437–451 (1964).
[CrossRef]

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

Brangaccio, D. J.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Bruning, J. H.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Cornejo-Rodriguez, A.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop TestingD. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

Farrant, D. I.

K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
[CrossRef]

Gallagher, J. E.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Gonzalez, M. M.

M. M. Gonzalez and N. A. Ochoa, “The Ronchi test with an LCD grating,” Opt. Commun 191,203–207 (2001).
[CrossRef]

Herriott, D. R.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Hibino, K.

K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
[CrossRef]

Jorge, C.-R.

C.-R. Jorge and S. Jose, Automatic phase-shifting Ronchi tester with a square Ronchi ruling, O. Wolfgang and N. Erik, eds. (SPIE, 2004), pp.199–210.

Jose, S.

C.-R. Jorge and S. Jose, Automatic phase-shifting Ronchi tester with a square Ronchi ruling, O. Wolfgang and N. Erik, eds. (SPIE, 2004), pp.199–210.

Malacara, D.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop TestingD. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

Ochoa, N. A.

M. M. Gonzalez and N. A. Ochoa, “The Ronchi test with an LCD grating,” Opt. Commun 191,203–207 (2001).
[CrossRef]

Oreb, B. F.

K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
[CrossRef]

Rayces, J. L.

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

Ronchi, V.

V. Ronchi, “40 Years of History of Grating Interferometer,” Appl. Opt 3,437–451 (1964).
[CrossRef]

Rosenfeld, D. P.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Ward, B. K.

K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
[CrossRef]

White, A. D.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Yatagai, T.

T. Yatagai, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt 23,3676–3679 (1984).
[CrossRef] [PubMed]

Appl. Opt (4)

V. Ronchi, “40 Years of History of Grating Interferometer,” Appl. Opt 3,437–451 (1964).
[CrossRef]

T. Yatagai, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt 23,3676–3679 (1984).
[CrossRef] [PubMed]

K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, “Dynamic range of Ronchi test with a phase-shifted sinusoidal grating,” Appl. Opt 36,6178–6189 (1997).
[CrossRef]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt 13,2693–2703 (1974).
[CrossRef] [PubMed]

Opt Acta (1)

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

Opt. Commun (1)

M. M. Gonzalez and N. A. Ochoa, “The Ronchi test with an LCD grating,” Opt. Commun 191,203–207 (2001).
[CrossRef]

Other (2)

C.-R. Jorge and S. Jose, Automatic phase-shifting Ronchi tester with a square Ronchi ruling, O. Wolfgang and N. Erik, eds. (SPIE, 2004), pp.199–210.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop TestingD. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

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Figures (2)

Fig. 1.
Fig. 1.

The relation between the wavefront and the transverse ray aberration at an observation plane.

Fig. 2.
Fig. 2.

3-D view of the grating-slit test method.

Equations (13)

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

W X P Y P Y P = TA Y r W
W X P Y P Y P = TA Y r
FP x ( x A , y A , x P , y P ) = TA x x P y P + mx A d 2
FP x x A y A x P y P = r × W x P y P x P + mx A d 2
r × W x P y P x P mx A
x A = N × P
r × W x P y P x P mN P
r × W x P y P y P mM P
L = L 0 [ 1 + cos ( 2 π P x A ) ]
dI x P y P = L 0 [ 1 + cos ( 2 π pm TA x x P y P ) ] × KdTAx
I x P y P = L 0 K d 2 + d 2 [ 1 + cos ( 2 π pm TAx x P y P ) ] dTAx
I x P y P = L 0 K [ 1 + sin c ( d mp ) × cos ( 2 π pm TAx x P y P ) ]
V = sin c ( d mp )

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