Abstract

A lateral shear interferometer using Ronchi rulings, spatial filtering, and moire technique is described. Two gratings of different spatial frequency are placed on opposite sides of the focus of the beam under test. First diffraction orders of the first grid after being diffracted at the second grating and subsequent spatial filtering form the carrier frequency lateral shear interferogram. It is visualized using the moire fringe technique which simultaneously provides arbitrary reference fringe orientation and number. The experimental verification of principles is given.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Ronchi, “Forty Years of History of a Grating Interferometer,” Appl. Opt. 3, 437 (1964).
    [CrossRef]
  2. M. V. R. K. Murty, A. Cornejo, “Sharpening the Fringes in the Ronchi Test,” Appl. Opt. 12, 2230 (1973).
  3. K. Patorski, “Heuristic Explanation of Grating Shearing Interferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
    [CrossRef]
  4. A. W. Lohmann, O. Bryngdahl, “A Lateral Wavefront Shearing Interferometer with Variable Shear,” Appl. Opt. 6, 1934 (1967).
    [CrossRef] [PubMed]
  5. J. Schwider, “Single Sideband Ronchi Test,” Appl. Opt. 20, 2635 (1981).
    [CrossRef] [PubMed]
  6. N. M. Spornik, V. I. Yanichkin, “Grating Interferometer with Variable Shearing of Wavefronts and Arbitrary Fringe Detection,” Sov. J. Opt. Technol. 38, 487 (1971).
  7. J. C. Wyant, “Double Frequency Grating Lateral Shear Interferometer,” Appl. Opt. 12, 2057 (1973).
    [CrossRef] [PubMed]
  8. P. Hariharan, W. H. Steel, J. C. Wyant, “Double Grating Interferometer with Variable Lateral Shear,” Opt. Commun. 11, 317 (1974).
    [CrossRef]
  9. M. P. Rimmer, J. C. Wyant, “Evaluation of Large Aberrations Using a Lateral-Shear Interferometer Having Variable Shear,” Appl. Opt. 14, 142 (1975).
    [PubMed]
  10. P. Hariharan, Z. S. Hegedus, “Double Grating Interferometers. II. Application to Collimated Beams,” Opt. Commun. 14, 148 (1975).
    [CrossRef]
  11. J. D. Briers, “Ronchi Test Formulae. 1. Theory,” Opt. Laser Technol. 11, 189 (1979).
    [CrossRef]

1984 (1)

K. Patorski, “Heuristic Explanation of Grating Shearing Interferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
[CrossRef]

1981 (1)

1979 (1)

J. D. Briers, “Ronchi Test Formulae. 1. Theory,” Opt. Laser Technol. 11, 189 (1979).
[CrossRef]

1975 (2)

M. P. Rimmer, J. C. Wyant, “Evaluation of Large Aberrations Using a Lateral-Shear Interferometer Having Variable Shear,” Appl. Opt. 14, 142 (1975).
[PubMed]

P. Hariharan, Z. S. Hegedus, “Double Grating Interferometers. II. Application to Collimated Beams,” Opt. Commun. 14, 148 (1975).
[CrossRef]

1974 (1)

P. Hariharan, W. H. Steel, J. C. Wyant, “Double Grating Interferometer with Variable Lateral Shear,” Opt. Commun. 11, 317 (1974).
[CrossRef]

1973 (2)

1971 (1)

N. M. Spornik, V. I. Yanichkin, “Grating Interferometer with Variable Shearing of Wavefronts and Arbitrary Fringe Detection,” Sov. J. Opt. Technol. 38, 487 (1971).

1967 (1)

1964 (1)

Briers, J. D.

J. D. Briers, “Ronchi Test Formulae. 1. Theory,” Opt. Laser Technol. 11, 189 (1979).
[CrossRef]

Bryngdahl, O.

Cornejo, A.

Hariharan, P.

P. Hariharan, Z. S. Hegedus, “Double Grating Interferometers. II. Application to Collimated Beams,” Opt. Commun. 14, 148 (1975).
[CrossRef]

P. Hariharan, W. H. Steel, J. C. Wyant, “Double Grating Interferometer with Variable Lateral Shear,” Opt. Commun. 11, 317 (1974).
[CrossRef]

Hegedus, Z. S.

P. Hariharan, Z. S. Hegedus, “Double Grating Interferometers. II. Application to Collimated Beams,” Opt. Commun. 14, 148 (1975).
[CrossRef]

Lohmann, A. W.

Murty, M. V. R. K.

Patorski, K.

K. Patorski, “Heuristic Explanation of Grating Shearing Interferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
[CrossRef]

Rimmer, M. P.

Ronchi, V.

Schwider, J.

Spornik, N. M.

N. M. Spornik, V. I. Yanichkin, “Grating Interferometer with Variable Shearing of Wavefronts and Arbitrary Fringe Detection,” Sov. J. Opt. Technol. 38, 487 (1971).

Steel, W. H.

P. Hariharan, W. H. Steel, J. C. Wyant, “Double Grating Interferometer with Variable Lateral Shear,” Opt. Commun. 11, 317 (1974).
[CrossRef]

Wyant, J. C.

Yanichkin, V. I.

N. M. Spornik, V. I. Yanichkin, “Grating Interferometer with Variable Shearing of Wavefronts and Arbitrary Fringe Detection,” Sov. J. Opt. Technol. 38, 487 (1971).

Appl. Opt. (6)

Opt. Acta (1)

K. Patorski, “Heuristic Explanation of Grating Shearing Interferometry Using Incoherent Illumination,” Opt. Acta 31, 33 (1984).
[CrossRef]

Opt. Commun. (2)

P. Hariharan, Z. S. Hegedus, “Double Grating Interferometers. II. Application to Collimated Beams,” Opt. Commun. 14, 148 (1975).
[CrossRef]

P. Hariharan, W. H. Steel, J. C. Wyant, “Double Grating Interferometer with Variable Lateral Shear,” Opt. Commun. 11, 317 (1974).
[CrossRef]

Opt. Laser Technol. (1)

J. D. Briers, “Ronchi Test Formulae. 1. Theory,” Opt. Laser Technol. 11, 189 (1979).
[CrossRef]

Sov. J. Opt. Technol. (1)

N. M. Spornik, V. I. Yanichkin, “Grating Interferometer with Variable Shearing of Wavefronts and Arbitrary Fringe Detection,” Sov. J. Opt. Technol. 38, 487 (1971).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Double grating interferometer adjusted for zero shear: O, phase object; L1–L2 and L3–L4, afocal imaging systems; G1 and G2, identical diffraction gratings; F1 and F2, spatial filters; OP1, intermediate interference plane; OP2, observation plane including detecting grating G3; γ, tilt angle between interfering beams (+1,−1) and (−1,+1).

Fig. 2
Fig. 2

Geometry for calculating shear and tilt between the double diffraction orders (+1,−1) and (−1,+1). The propagation directions of the beams are indicated by the lines corresponding to the principal rays. The geometry shown corresponds to grating G2 of lower spatial frequency compared with the frequency of G1.

Fig. 3
Fig. 3

Lateral shearing interference fringes of the wavefront with spherical aberration. The shear amount Δ is equal to (a) 0 mm, (b) 2.3 mm, (c) 4.3 mm. Photographs on the left- and right-hand sides correspond to the display mode with α-type and β-type tilt reference fringes, respectively.

Fig. 4
Fig. 4

Fringe patterns for (a) Δ = 6.9 mm, (b) Δ = 9.2 mm, (c) Δ = 11.2 mm.

Fig. 5
Fig. 5

Fringe patterns for (a) Δ = 13.9 mm, (b) Δ = 15.7 mm, (c) Δ = 16.6 mm.

Equations (4)

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

γ = 2 arctan { ( z 1 + z 2 ) tan [ arcsin ( λ / d ) ] / f } ,
d f = λ / 2 sin ( γ / 2 ) .
Δ = 2 f tan [ | arcsin ( λ d 1 - λ d 2 ) | ] = 2 f tan δ + 1 , - 1 ,
γ = 2 arctan ( { ( z 1 + z 2 ) tan [ arcsin ( λ / d 1 ) ] - z 2 tan δ + 1 , - 1 } / f ) .

Metrics