Abstract

We present a technique for the measurement of longitudinal displacement using a lateral shearing cyclic path optical configuration (CPOC) setup and phase shifting interferometry. In the technique, a plane mirror mounted on a linear translation stage, placed slightly away from the focal plane of a lens, introduces a longitudinal focal shift to the incident focusing beam. The resulting spherical wavefront emerging from the lens is sheared into two orthogonally polarized beams using the CPOC setup. By applying polarization phase shifting interferometry (PPSI), the longitudinal focal shift of the beam focus is calculated by determining the slope of the optical path difference variation between the sheared beams. Similarly, the additional focal shift introduced due to longitudinal translation of the mirror, by an unknown amount, is determined using PPSI. Half of the difference between the two longitudinal focal shifts measured gives the longitudinal displacement of the mirror. The technique can be used for an extended range of distance measurement. The novelty of the technique is the introduction of CPOC for the distance measurement. The advantages of the technique compared to other related methods are discussed.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010 (1)

2009 (1)

2007 (1)

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

2005 (1)

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

1998 (2)

L. Rovati, U. Minoni, M. Bonardi, and F. Docchi, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29, 121–127 (1998).
[CrossRef]

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

1988 (3)

1987 (2)

1986 (1)

M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Bechstein, K. H.

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Bhaduri, B.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Bonardi, M.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchi, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29, 121–127 (1998).
[CrossRef]

Cassaing, F.

Chatterjee, S.

Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49, 6552–6557 (2010).
[CrossRef] [PubMed]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Creath, K.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1998), Vol.  26, pp. 349–393.
[CrossRef]

Docchi, F.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchi, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29, 121–127 (1998).
[CrossRef]

Eiju, T.

Faridi, M. S.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

Fuchs, W.

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Grindel, M.

M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Hariharan, P.

Hausler, G.

Herrmann, J. M.

Houairi, K.

Hutflees, J.

Kothial, M. P.

M. P. Kothial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Kubota, T.

Kumar, Y. P.

Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49, 6552–6557 (2010).
[CrossRef] [PubMed]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).
[CrossRef]

Maul, M.

Mehta, D. S.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

Minoni, U.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchi, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29, 121–127 (1998).
[CrossRef]

Mirza, S.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

Nara, M.

Oreb, B. F.

Rosenbruch, K. J.

M. P. Kothial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Rovati, L.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchi, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29, 121–127 (1998).
[CrossRef]

Shakher, C.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

Singh, P.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

Sirohi, R. S.

M. P. Kothial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

R. S. Sirohi, Wave Optics and Its Applications (Orient Longman, 1993)

Weissmann, H.

Yoshino, T.

Appl. Opt. (4)

J. Opt. (2)

L. Rovati, U. Minoni, M. Bonardi, and F. Docchi, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29, 121–127 (1998).
[CrossRef]

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, and C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 063602 (2005).
[CrossRef]

Opt. Laser Technol. (2)

M. P. Kothial, R. S. Sirohi, and K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting interferometer,” Opt. Laser Technol. 39, 268–274 (2007).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Other (3)

D. Malacara, Optical Shop Testing (Wiley, 2007).
[CrossRef]

R. S. Sirohi, Wave Optics and Its Applications (Orient Longman, 1993)

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1998), Vol.  26, pp. 349–393.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Shear fringes produced due to initial positioning of MR between P and L.

Fig. 3
Fig. 3

Least square fit to the OPD variation of the shear fringes for the initial position of MR.

Fig. 4
Fig. 4

Shear fringes produced due to longitudinal displacement of MR by 0.27 m m from the initial position.

Fig. 5
Fig. 5

Least square fit to the OPD variation of the shear fringes for the final position of MR.

Equations (11)

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Δ f = f 2 R .
R 1 = S d 1 λ - D + K
R 1 = S θ 1 D + K ,
Δ f 1 = f 2 R 1 .
R 2 = S θ 2 D + K ,
Δ f 2 = f 2 R 2 .
x = Δ f 2 - Δ f 1 2 .
α = π 2 2 γ ,
I ( x , y ) = I 0 ( x , y ) { 1 + V ( x , y ) cos [ Φ ( x , y ) + α i ] ,
Φ = tan 1 [ 2 ( I 2 I 4 ) 2 I 3 I 1 I 5 ] .
OPD = ( λ 2 π ) Φ .

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