Abstract

We have developed what we believe is a new technique for obtaining a whole-field image representing the deforming amounts of a diffuse object. The object is supposedly continuously deforming and does not stop deforming during the measurement. This technique uses arccosine operations to extract the absolute, not signed, value of the phase. We assume that a right-phase change retains almost the same value in a small local area. This retention determines the sign of the phase and consequently the value of the phase change. The deformation phase during any term of the deforming process is shown as a map through the temporal-phase unwrapping of the calculated phase.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2000 (1)

1997 (1)

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in ESPI using one speckle interferometry of a deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

1996 (1)

A. Davila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

1995 (1)

1994 (2)

1990 (1)

1985 (1)

1982 (1)

Adachi, M.

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in ESPI using one speckle interferometry of a deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Carlsson, T. E.

Creath, K.

Davila, A.

A. Davila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

Frankena, H. J.

Grant, I.

Haasteven, A. J. P.

Ina, H.

Inabe, K.

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in ESPI using one speckle interferometry of a deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Kaufmann, G. H.

A. Davila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

Kerr, D.

A. Davila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

Kobayashi, S.

Pedrini, G.

Takeda, M.

Tiziani, H. J.

Ueyama, Y.

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in ESPI using one speckle interferometry of a deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Vikhagen, E.

Wang, J.

Wei, A.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. Davila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

Opt. Rev. (1)

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in ESPI using one speckle interferometry of a deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Optical layout of a DSPI, which is also used in our experiment.

Fig. 2
Fig. 2

Light-intensity change on the pixel of a CCD camera due to deformation of the object.

Fig. 3
Fig. 3

Complex plane plotting of exp[iδ kl (r)] in a local area (3 × 3 pixels) where δ kl (r) is given by Eq. (3). The number of points is 36 and some overlap.

Fig. 4
Fig. 4

Upper half complex plane plot of Z = [I max(r) - I min(r)]exp[iδ kl (r)]. Δψ is the phase of the average value for [I max(r) - I min(r)]{exp[iδ kl (r)] - (2/π)i}. The number of points is 18, and one point overlaps.

Fig. 5
Fig. 5

Change in Δψ(r, t) in Fig. 4 concerning the continuously deforming object.

Fig. 6
Fig. 6

Complex plane plotting of cos[ψ(r, t 0)]sin[Δψ(r, t k - t 0)] + isin[ψ(r, t 0)]sin[Δψ(r, t k - t 0)], where t k is from t 0 to t j .

Fig. 7
Fig. 7

(a) Complex plane plot of values calculated by [I max(r) - I min(r)]exp[iδ′(r, t)]. (b) Complex plane plot of the values that are selected from the points shown in Fig. 7(a).

Fig. 8
Fig. 8

Time dependencies of deformation phases about points B and C in Fig. 1: solid curves, dependence obtained by using a local area of 3 × 3 pixels; broken curves, that of 5 × 5 pixels.

Fig. 9
Fig. 9

Whole-field images of the deformation phase where a local area of 5 × 5 pixels and a median filter (5 × 5) were used. (a) From the capturing start t 0 to t 20 (20th-frame capturing moment); (b) from the capturing start t 0 to t 200.

Fig. 10
Fig. 10

Whole-field images of the deformation phase from the capturing start t 0 to t 200, where a local area of 3 × 3 pixels and a median filter of 3 × 3 pixels were used.

Equations (10)

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Ir, t=ODr+OALTrcosψr, t,
|ψr, tk|=cos-1Ir, tk-Imaxr+Iminr2Imaxr-Iminr2.
δklr=±|ψr, tl|-±|ψr, tk|
cosψr, t0+Δψr, tj-t0=cosψr, t0cosΔψr, tj-t0-sinψr, t0×sinΔψr, tj-t0.
sinψr, t0sinΔψr, tj-t0=cosψr, t0cosΔψr, tj-t0-cosψr, t0+Δψr, tj-t0=cosψr, t0cosΔψr, tj-t0-cosψr, tj.
ψr, t0=argcosψr, t0sinΔψr, tj-t0+isinψr, t0sinΔψr, tj-t0.
δr, t=±|ψr, t|-ψr, t0,
Δψr, t=argCrr, t+iCir, t.
Δψr, tn=l=1l=nargexp iΔψr, tl-Δψr, tl-1.
ϕr, tq-tp=Δψr, tq-Δψr, tp.

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