Abstract

A simple and inexpensive optical setup to phase-shifting interferometry is proposed. This optical setup is based on the Twyman-Green Interferometer where the phase shift is induced by the lateral displacement of the point laser source. A theoretical explanation of the induced phase by this alternative method is given. The experimental results are consistent with the theoretical expectations. Both, the phase shift and the wrapped phase are recovered by a generalized phase-shifting algorithm from two or more interferograms with arbitrary and unknown phase shift. The experimental and theoretical results show the feasibility of this unused phase-shifting technique.

© 2013 OSA

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References

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2013

R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering51, 626–632 (2013).
[CrossRef]

L. Bruno and A. Poggialini, “Phase-shifting interferometry by an open-loop voltage controlled laser diode,” Opt. Commun.290, 118–125 (2013).
[CrossRef]

2011

2010

M. Vannoni, A. Sordini, and G. Molesini, “He-ne laser wavelength-shifting interferometry,” Opt. Commun.283, 5169–5172 (2010).
[CrossRef]

J. Min, B. Yao, P. Gao, R. Guo, J. Zheng, and T. Ye, “Parallel phase-shifting interferometry based on michelson-like architecture,” Appl. Opt.49, 6612–6616 (2010).
[CrossRef] [PubMed]

2008

2007

2005

A. Patil and P. Rastogi, “Approaches in generalized phase shifting interferometry,” Optics and Lasers in Engineering43, 475–490 (2005).
[CrossRef]

1998

C. Tay, C. Quan, and H. Shang, “Shape identification using phase shifting interferometry and liquid-crystal phase modulator,” Optics & Laser Technology30, 545–550 (1998).

1995

T. Pfeifer, R. Tutsch, J. Evertz, and G. Weres, “Generalized aspects of multiple-wavelength techniques in optical metrology,” {CIRP} Annals - Manufacturing Technology44, 493–496 (1995).
[CrossRef]

1991

1987

1985

1974

Absil, E.

Aguilar, L. A.

R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering51, 626–632 (2013).
[CrossRef]

Álvarez Herrero, A.

Atlan, M.

Belenguer, T.

Brangaccio, D. J.

Bruning, J. H.

Bruno, L.

L. Bruno and A. Poggialini, “Phase-shifting interferometry by an open-loop voltage controlled laser diode,” Opt. Commun.290, 118–125 (2013).
[CrossRef]

Cheng, Y.-Y.

Eiju, T.

Evertz, J.

T. Pfeifer, R. Tutsch, J. Evertz, and G. Weres, “Generalized aspects of multiple-wavelength techniques in optical metrology,” {CIRP} Annals - Manufacturing Technology44, 493–496 (1995).
[CrossRef]

Gallagher, J. E.

Gao, P.

Gross, M.

Guerrero-Sanchez, F.

R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering51, 626–632 (2013).
[CrossRef]

Guo, R.

Hariharan, P.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Herriott, D. R.

Juarez-Salazar, R.

R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering51, 626–632 (2013).
[CrossRef]

Lai, G.

Malacara, D.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis Group, 2005).
[CrossRef]

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis Group, 2005).
[CrossRef]

Meneses-Fabian, C.

Min, J.

Molesini, G.

M. Vannoni, A. Sordini, and G. Molesini, “He-ne laser wavelength-shifting interferometry,” Opt. Commun.283, 5169–5172 (2010).
[CrossRef]

Oreb, B. F.

Patil, A.

A. Patil and P. Rastogi, “Approaches in generalized phase shifting interferometry,” Optics and Lasers in Engineering43, 475–490 (2005).
[CrossRef]

Pfeifer, T.

T. Pfeifer, R. Tutsch, J. Evertz, and G. Weres, “Generalized aspects of multiple-wavelength techniques in optical metrology,” {CIRP} Annals - Manufacturing Technology44, 493–496 (1995).
[CrossRef]

Poggialini, A.

L. Bruno and A. Poggialini, “Phase-shifting interferometry by an open-loop voltage controlled laser diode,” Opt. Commun.290, 118–125 (2013).
[CrossRef]

Quan, C.

C. Tay, C. Quan, and H. Shang, “Shape identification using phase shifting interferometry and liquid-crystal phase modulator,” Optics & Laser Technology30, 545–550 (1998).

Quiroga, J. A.

Rastogi, P.

A. Patil and P. Rastogi, “Approaches in generalized phase shifting interferometry,” Optics and Lasers in Engineering43, 475–490 (2005).
[CrossRef]

Rivera-Ortega, U.

Robledo-Sanchez, C.

R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering51, 626–632 (2013).
[CrossRef]

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Rosenfeld, D. P.

Servin, M.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis Group, 2005).
[CrossRef]

Shang, H.

C. Tay, C. Quan, and H. Shang, “Shape identification using phase shifting interferometry and liquid-crystal phase modulator,” Optics & Laser Technology30, 545–550 (1998).

Sordini, A.

M. Vannoni, A. Sordini, and G. Molesini, “He-ne laser wavelength-shifting interferometry,” Opt. Commun.283, 5169–5172 (2010).
[CrossRef]

Tay, C.

C. Tay, C. Quan, and H. Shang, “Shape identification using phase shifting interferometry and liquid-crystal phase modulator,” Optics & Laser Technology30, 545–550 (1998).

Toto-Arellano, N.-I.

Tutsch, R.

T. Pfeifer, R. Tutsch, J. Evertz, and G. Weres, “Generalized aspects of multiple-wavelength techniques in optical metrology,” {CIRP} Annals - Manufacturing Technology44, 493–496 (1995).
[CrossRef]

Vannoni, M.

M. Vannoni, A. Sordini, and G. Molesini, “He-ne laser wavelength-shifting interferometry,” Opt. Commun.283, 5169–5172 (2010).
[CrossRef]

Vargas, J.

Vázquez-Castillo, J. F.

Weres, G.

T. Pfeifer, R. Tutsch, J. Evertz, and G. Weres, “Generalized aspects of multiple-wavelength techniques in optical metrology,” {CIRP} Annals - Manufacturing Technology44, 493–496 (1995).
[CrossRef]

White, A. D.

Wyant, J. C.

Yao, B.

Yatagai, T.

Ye, T.

Zheng, J.

{CIRP} Annals - Manufacturing Technology

T. Pfeifer, R. Tutsch, J. Evertz, and G. Weres, “Generalized aspects of multiple-wavelength techniques in optical metrology,” {CIRP} Annals - Manufacturing Technology44, 493–496 (1995).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

L. Bruno and A. Poggialini, “Phase-shifting interferometry by an open-loop voltage controlled laser diode,” Opt. Commun.290, 118–125 (2013).
[CrossRef]

M. Vannoni, A. Sordini, and G. Molesini, “He-ne laser wavelength-shifting interferometry,” Opt. Commun.283, 5169–5172 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Optics & Laser Technology

C. Tay, C. Quan, and H. Shang, “Shape identification using phase shifting interferometry and liquid-crystal phase modulator,” Optics & Laser Technology30, 545–550 (1998).

Optics and Lasers in Engineering

A. Patil and P. Rastogi, “Approaches in generalized phase shifting interferometry,” Optics and Lasers in Engineering43, 475–490 (2005).
[CrossRef]

R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering51, 626–632 (2013).
[CrossRef]

Other

D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley & Sons, 2007).
[CrossRef]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis Group, 2005).
[CrossRef]

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

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Figures (4)

Fig. 1
Fig. 1

(a) Centered collimating system with a point source. (b) Tilted plane wavefront obtained by a lateral source displacement. (c) Twyman-Green Interferometer illuminated with a tilted plane wavefront. (d) Alternative representation of Fig. 1(c).

Fig. 2
Fig. 2

The fringe-pattern translation and the phase-shifting effects induced by the lateral source displacement.

Fig. 3
Fig. 3

(a) and (b) Two adjacent phase shifted interferograms acquired with the proposed PSI technique. (c) Wrapped phase distribution recovered by processing the two interfero-grams shown in Figs. 3(a) and 3(b) with the suggested GPSI algorithm.

Fig. 4
Fig. 4

(a) Phase shift and (b) image translation measurements versus lateral source displacement. This experiments correspond to the relative distances between the mirrors of (red) D = 3.96 cm, and (blue) D = 7.91 cm.

Equations (10)

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A ( p , d ) = A 0 r exp [ i k r ] ,
A ( p , d ) B 0 exp [ i k 2 f ( p 2 + d 2 2 d . p ) ] ,
B ( p , d ) = B 0 exp [ i k 2 f ( d 2 2 d p ) ] ,
tan θ = d / f ,
I ( p , d ) = | B ( p 2 , d ) + B ˜ ( p 2 , d ) | 2 ,
B ˜ ( p 2 , d ) = B ( p 1 , d ) exp [ i k ρ + i ϕ ( p 0 ) ] ,
B ( p 2 , d ) = B ( p 1 + σ , d ) = B ( p 1 , d ) exp [ i k σ d / f ] .
I ( p , d ) = 2 a + 2 a cos [ ϕ ( p τ ( d ) ) δ ( d ) ] ,
τ ( d ) = ( g + D ) d / f .
δ ( d ) D k ( d / f ) 2 ,

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