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 Testing D. Malacara, ed. (Wiley-Interscience, New York, 1992), p. 321.

2001

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

1997

1984

1974

1964

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

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

Brangaccio, D. J.

Bruning, J. H.

Farrant, D. I.

Gallagher, J. E.

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.

Hibino, K.

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.

Rayces, J. L.

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

Ronchi, V.

Rosenfeld, D. P.

Ward, B. K.

White, A. D.

Yatagai, T.

Appl. Opt.

Opt Acta

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

Opt. Commun.

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

Other

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 Testing D. 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)

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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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