Abstract

The Talbot interferometer using different self-imaging structures is studied and applied for laser beam collimation. A circular–linear grating pair enables visual dynamic detection and computer moirégram analysis. Automatic single-frame processing is performed using a 2D continuous wavelet transform. Conducting moirégram imaging in the Fresnel field of a double-diffraction system is brought up to avoid using distortion-free objectives and simplify the experimental setup. Simulation and experimental results document the method properties and provide beautiful exemplification of the double-grating Fresnel diffraction theory developed earlier.

© 2014 Optical Society of America

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References

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2013

2011

2010

2008

2006

Z. Wang and H. Ma, Opt. Eng. 45, 045601 (2006).
[CrossRef]

2001

1994

1991

1989

1988

1987

1985

P. Szwaykowski and K. Patorski, J. Opt. 16, 95 (1985).
[CrossRef]

1976

1975

S. Yokozeki, K. Patorski, and K. Ohnishi, Opt. Commun. 14, 401 (1975).
[CrossRef]

1972

A. Lohmann and D. Silva, Opt. Commun. 4, 326 (1972).
[CrossRef]

1971

Bernabeu, E.

Chang, C. W.

Dhanotia, J.

Huang, L.

Jimenez-Castillo, I.

Kothiyal, M. P.

Kumar, R.

Lohmann, A.

A. Lohmann and D. Silva, Opt. Commun. 4, 326 (1972).
[CrossRef]

A. Lohmann and D. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

Ma, H.

Z. Wang and H. Ma, Opt. Eng. 45, 045601 (2006).
[CrossRef]

Malacara, D.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Morlanes, T.

Nand, D.

Ohnishi, K.

S. Yokozeki, K. Patorski, and K. Ohnishi, Opt. Commun. 14, 401 (1975).
[CrossRef]

Patorski, K.

K. Pokorski and K. Patorski, Opt. Express 21, 22596 (2013).
[CrossRef]

P. Szwaykowski and K. Patorski, Appl. Opt. 28, 4679 (1989).
[CrossRef]

P. Szwaykowski and K. Patorski, J. Opt. 16, 95 (1985).
[CrossRef]

K. Patorski, S. Yokozeki, and T. Suzuki, Appl. Opt. 15, 1234 (1976).
[CrossRef]

S. Yokozeki, K. Patorski, and K. Ohnishi, Opt. Commun. 14, 401 (1975).
[CrossRef]

K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1–108.

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).

Pokorski, K.

Prakash, S.

Rana, S.

Reid, G.

D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics, 1993).

Robinson, D. W.

D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics, 1993).

Salgado-Remacha, F. J.

Sanchez-Brea, L. M.

Sasaki, O.

Servin, M.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Shakher, C.

Silva, D.

A. Lohmann and D. Silva, Opt. Commun. 4, 326 (1972).
[CrossRef]

A. Lohmann and D. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

Silva, D. E.

Sirohi, R. S.

Sriram, K. V.

Su, D. C.

Su, X.

Suzuki, T.

Szwaykowski, P.

Theocaris, P. S.

P. S. Theocaris, Moire Fringes in Strain Analysis (Pergamon, 1969).

Torcal-Milla, F. J.

Wang, Z.

Z. Wang and H. Ma, Opt. Eng. 45, 045601 (2006).
[CrossRef]

Wen, J.

Xiao, M.

Yokozeki, S.

Zhang, Y.

Adv. Opt. Photon.

Appl. Opt.

J. Opt.

P. Szwaykowski and K. Patorski, J. Opt. 16, 95 (1985).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. Yokozeki, K. Patorski, and K. Ohnishi, Opt. Commun. 14, 401 (1975).
[CrossRef]

A. Lohmann and D. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

A. Lohmann and D. Silva, Opt. Commun. 4, 326 (1972).
[CrossRef]

Opt. Eng.

Z. Wang and H. Ma, Opt. Eng. 45, 045601 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Other

K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1–108.

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).

P. S. Theocaris, Moire Fringes in Strain Analysis (Pergamon, 1969).

D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics, 1993).

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Supplementary Material (1)

» Media 1: AVI (3751 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the circular–linear grating Talbot interferometer with defocused detection plane.

Fig. 2.
Fig. 2.

Moiré patterns generated by multiplicative superimposition of circular and linear gratings with spatial periods d1 and d2, respectively (Media 1). (a) d1>d2, (b) d1<d2, (c) and (d) d1=d2.

Fig. 3.
Fig. 3.

Moirégrams recorded in the Fresnel diffraction field behind detecting grating G2. See the text for an explanation of axial separation distances, z1 and z2.

Fig. 4.
Fig. 4.

Slope of the axial cross section of the moirégram phase versus lens axial position. The position with a zero slope value corresponds to a collimated beam. In the proximity of the collimation position, 20 μm lens shift corresponds to a 7×104 divergence/convergence angle change (for the lens diameter of approximately 40 mm).

Equations (3)

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

(d22d12)x2±2d12d2px+d22y2=d12d22p2,
p=h±k
φ(x,y)=2πd1(x2+y2)2πd2x.

Metrics