Abstract

We describe a method of absolute distance measurement based on the lateral shearing interferometry of point-diffracted spherical waves. A unique feature is that the distance measurement is not confined only along a single line of the optical axis, but the target is allowed to take movement freely within a volumetric measurement space formed by the aperture angle of point-diffraction. Detailed measurement theory is explained along with experimental verification.

© 2006 Optical Society of America

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References

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  1. P. de Groot, "Grating interferometer for flatness testing," Opt. Lett. 21, 228-230 (1996).
    [CrossRef] [PubMed]
  2. R. Dändliker, R. Thalmann, and D. Prongué, "Two-wavelength laser interferometry using superheterodyne detection," Opt. Lett. 13, 339-341 (1988).
    [CrossRef] [PubMed]
  3. F. Bien, M. Camac, H. J. Caulfield, and S. Ezekiel, "Absolute distance measurements by variable wavelength interferometry," Appl. Opt. 20, 400-403 (1981).
    [CrossRef] [PubMed]
  4. H. Kikuta, K. Iwata, and R. Nagata, "Distance measurement by the wavelength shift of laser diode light," Appl. Opt. 25, 2976-2980 (1986).
    [CrossRef] [PubMed]
  5. U. Schnell, R. Dändliker, and S. Gray, "Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target," Opt. Lett. 21, 528-530 (1996).
    [CrossRef] [PubMed]
  6. H.-G. Rhee and S.-W. Kim, "Absolute distance measurement by two-point-diffraction interferometry," Appl. Opt. 41, 5921-5928 (2002).
    [CrossRef] [PubMed]
  7. M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, and E. A. Swanson, "Femtosecond transillumination optical coherence tomography," Opt. Lett. 18, 950-951 (1993).
    [CrossRef] [PubMed]
  8. K. Minoshima and H. Matsumoto, "High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser," Appl. Opt. 39, 5512-5517 (2000).
    [CrossRef]
  9. J. Ye, "Absolute measurement of a long, arbitrary distance to less than an optical fringe," Opt. Lett. 29, 1153-1155 (2004).
    [CrossRef] [PubMed]
  10. H. Kihm and S.-W. Kim, "Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers," Opt. Lett. 29, 2366-2368 (2004).
    [CrossRef] [PubMed]
  11. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
    [CrossRef]
  12. M. P. Rimmer and J. C. Wyant, "Evaluation of large aberrations using a Lateral Shear Interferometer having variable shear," Appl. Opt. 14, 142-150 (1975).
    [PubMed]

2004 (2)

2002 (1)

2000 (1)

1996 (2)

1993 (1)

1988 (1)

1986 (1)

1982 (1)

1981 (1)

1975 (1)

Bien, F.

Camac, M.

Caulfield, H. J.

Dändliker, R.

de Groot, P.

Ezekiel, S.

Fujimoto, J. G.

Gray, S.

Hee, M. R.

Ina, H.

Iwata, K.

Izatt, J. A.

Jacobson, J. M.

Kihm, H.

Kikuta, H.

Kim, S.-W.

Kobayashi, S.

Matsumoto, H.

Minoshima, K.

Nagata, R.

Prongué, D.

Rhee, H.-G.

Rimmer, M. P.

Schnell, U.

Swanson, E. A.

Takeda, M.

Thalmann, R.

Wyant, J. C.

Ye, J.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Lett. (6)

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Figures (4)

Fig. 1.
Fig. 1.

System configuration for absolute distance measurement using lateral shearing interferometry of spherical waves. The inlet in top left shows the cross-sectional view of the transmitter, and the inlet in top right illustrates the two shearing interferograms being generated.

Fig. 2.
Fig. 2.

Four boundaries specifying the overall measurement range; D: receiver global size, d: receiver resolution, θ: transmitter aperture angle, S: lateral offset.

Fig. 3.
Fig. 3.

Reconstruction of the master wavefront W(x,y) by Fourier-transform technique; (a) Lateral shearing interferogram sampled at (xc, yc, zc)=(0,0,700) mm, S=2 mm, D=9 mm, (b) Frequency spectrum obtained by Fourier-transform, (c) Phase determination of ΔWx and ΔWy, (d) Reconstructed master wavefront W(x,y).

Fig. 4.
Fig. 4.

Measurement results of R; (a) moving along z axis from 400 m to 1200 mm at xc=yc=~30 mm (b) moving along y axis from-50 mm to 50 mm at xc=~30 mm and zc=~1000 mm,

Tables (1)

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Table 1. Zernike coefficients for a spherical wavefront in terms of its source coordinates.

Equations (8)

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Δ W x = W ( x + S 2 , y ) W ( x S 2 , y ) = n = 0 k 1 m = 0 n C nm x m y n m
where C nm = j = 1 ( k n + 1 ) 2 2 ( 2 j 1 + m 2 j 1 ) ( S 2 ) 2 j 1 B 2 j 1 + n , 2 j 1 + m
Δ W y = W ( x , y + S 2 ) W ( x , y S 2 ) = n = 0 k 1 m = 0 n D nm x m y n m
where D nm = j = 1 ( k n + 1 ) 2 2 ( 2 j 1 + n m 2 j 1 ) ( S 2 ) 2 j 1 B 2 j 1 + n , m
W ( x , y ) = ( x c x ) 2 + ( y c y ) 2 + z c 2 + p
W ( x , y ) = R 1 + H + p R ( 1 + H 2 H 2 8 ) + p
where H = ( 2 x c x 2 y c y + x 2 + y 2 ) R 2
R = 1 ( 4 A 5 + 2 A 4 2 + A 6 2 )

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