Abstract

In this paper, we report an automated technique for collimation testing by incorporating Fourier fringe analysis of the recorded interferograms in Talbot interferometry. The triangular profile of Talbot interferometric fringes has been recorded using a CCD and computer system. The interferograms corresponding to the in-focus, at-focus, and out-of-focus positions of the collimating lens have been recorded. Direct phase measurement using the Fourier transform method has been used for detection of collimation positions. Good accuracy and precision in measurement have been achieved.

© 2011 Optical Society of America

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References

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  1. K. Patorski, “The self imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1989), Vol.  27, pp. 1–108.
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  6. D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474(1998).
    [Crossref]
  7. C. Shakher, S. Prakash, D. Nand, and R. Kumar, “Collimation testing with circular gratings,” Appl. Opt. 40, 1175–1179 (2001).
    [Crossref]
  8. L. M. S. Bera, F. J. T. Milla, F. J. S. Remacha, T. Morlanes, I. J. Castillo, and E. Bernabeu, “Collimation method using a double grating system,” Appl. Opt. 49, 3363–3368(2010).
    [Crossref]
  9. S. Prakash, S. Rana, S. Prakash, and O. Sasaki, “Automated collimation testing using a temporal phase shifting technique in Talbot interferometry,” Appl. Opt. 47, 5938–5943 (2008).
    [Crossref]
  10. S. Rana, S. Prakash, and S. Prakash, “Automated collimation testing in Lau interferometry using phase shifting technique,” Opt. Lasers Eng. 47, 656–661 (2009).
    [Crossref]
  11. B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
    [Crossref]
  12. T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

2010 (1)

2009 (1)

S. Rana, S. Prakash, and S. Prakash, “Automated collimation testing in Lau interferometry using phase shifting technique,” Opt. Lasers Eng. 47, 656–661 (2009).
[Crossref]

2008 (1)

2001 (1)

1999 (1)

B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
[Crossref]

1998 (1)

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474(1998).
[Crossref]

1995 (1)

T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

1994 (1)

1991 (1)

1987 (1)

1971 (1)

Bera, L. M. S.

Bernabeu, E.

Castillo, I. J.

Chang, C. W.

Evertz, J.

T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

Kandpal, H. C.

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474(1998).
[Crossref]

Kothiyal, M. P.

Kumar, R.

Luo, X.

B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
[Crossref]

Mehta, D. S.

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474(1998).
[Crossref]

Milla, F. J. T.

Mischo, H.

B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
[Crossref]

Morlanes, T.

Nand, D.

Patorski, K.

K. Patorski, “The self imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1989), Vol.  27, pp. 1–108.
[Crossref]

Pfeifer, T.

B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
[Crossref]

T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

Prakash, S.

Rana, S.

S. Rana, S. Prakash, and S. Prakash, “Automated collimation testing in Lau interferometry using phase shifting technique,” Opt. Lasers Eng. 47, 656–661 (2009).
[Crossref]

S. Prakash, S. Rana, S. Prakash, and O. Sasaki, “Automated collimation testing using a temporal phase shifting technique in Talbot interferometry,” Appl. Opt. 47, 5938–5943 (2008).
[Crossref]

Remacha, F. J. S.

Sasaki, O.

Shakher, C.

Silva, D. E.

Sirohi, R. S.

Sriram, K. V.

Su, D. C.

Tutsch, R.

T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

Wang, B.

B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
[Crossref]

T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

Appl. Opt. (6)

Measurement (1)

B. Wang, X. Luo, T. Pfeifer, and H. Mischo, “Moiré deflectometry based on Fourier-transform analysis,” Measurement 25, 249–253 (1999).
[Crossref]

Opt. Laser Technol. (1)

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–474(1998).
[Crossref]

Opt. Lasers Eng. (1)

S. Rana, S. Prakash, and S. Prakash, “Automated collimation testing in Lau interferometry using phase shifting technique,” Opt. Lasers Eng. 47, 656–661 (2009).
[Crossref]

Opt. Lett. (1)

Optik (1)

T. Pfeifer, B. Wang, J. Evertz, and R. Tutsch, “Phase-shifting moire deflectometry,” Optik 98, 158–162 (1995).

Other (1)

K. Patorski, “The self imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1989), Vol.  27, pp. 1–108.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental arrangement for testing the collimation of an optical beam using Talbot interferometry and the Fourier transform method.

Fig. 2
Fig. 2

Fringe pattern recorded (when grating lines are inclined with equal and opposite angles to each other) using a CCD camera at the (a) in-focus, (b) at-focus, and (c) out-of-focus positions of the collimating lens of focal length 250 mm .

Fig. 3
Fig. 3

Flow chart for the Fourier transform algorithm used to process fringes.

Fig. 4
Fig. 4

Fourier spectrum of recorded images at the (a) in-focus, (b) at-focus, and (c) out-of-focus positions.

Fig. 5
Fig. 5

Unwrapped phase map for a fringe patterns corresponding to the (a) in-focus ( Δ f = 20 μm ), (b) at-focus, and (c) out-of-focus ( Δ f = 15 μm ) positions of the collimating lens of focal length 250 mm .

Fig. 6
Fig. 6

Variation of phase with respect to the x axis for the fringe patterns corresponding to the (a) in-focus ( Δ f = 20 μm ), (b) at-focus, and (c) out-of-focus ( Δ f = 15 μm ) positions of the collimating lens of focal length 250 mm .

Equations (11)

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d = 2 p 2 m λ ,
I y ( x , y ) = 1 4 + 2 π 2 n = 0 cos [ π ( 2 n + 1 ) 2 d / ( p 2 / λ ) ] ( 2 n + 1 ) 2 × cos [ 2 π ( 2 n + 1 ) ( χ p + y θ p + Φ ( x , y ) d p + s p ) ] ,
I ( x , y ) 1 4 + 2 π 2 cos ( l π ) cos [ 2 π ( χ p + y θ p + Φ ( x , y ) d p + s p ) ] .
I ( x , y ) = A + B cos [ ψ ( x , y ) + α ( x , y ) ] ,
A = 1 4 , B = 2 π 2 cos ( l π ) , ψ ( x , y ) = 2 π [ Φ ( x , y ) d p + y θ p ] , α ( x , y ) = 2 π ( χ p + s p ) .
I ( x , y ) = A + B cos [ ψ ( x , y ) ] .
I ( u , v ) = A ( u , v ) + C ( u , v ) + C * ( u , v ) ,
C ( x , y ) = 1 2 B ( x , y ) exp [ j ψ ( x , y ) ] ,
C ( x , y ) = Re [ C ( x , y ) ] + Im [ C ( x , y ) ] ,
ψ ( x , y ) = tan 1 [ Im ( C ( x , y ) ) Re ( C ( x , y ) ) ] .
Φ ( x , y ) = p 2 π d ψ ( x , y ) .

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