Abstract

We present a novel method of rapidly convergent phase reconstruction from noisy and high-fringe-density intensity patterns without a priori information. We define an error function that incorporates the measured intensity data to ensure the convergence. The error function is the absolute value of the cosine of the difference of the reconstructed phase and the unknown phase, i.e., a calculated or a synthetic interferogram.

© 1998 Optical Society of America

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References

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  1. D. W. Robinson, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), p. 195.
  2. J. E. Grievenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), p. 501.
  3. G. Páez and M. Strojnik, Opt. Lett. 22, 1669 (1997).
    [CrossRef]

1997 (1)

Bruning, J. H.

J. E. Grievenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), p. 501.

Grievenkamp, J. E.

J. E. Grievenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), p. 501.

Páez, G.

Robinson, D. W.

D. W. Robinson, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), p. 195.

Strojnik, M.

Opt. Lett. (1)

Other (2)

D. W. Robinson, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), p. 195.

J. E. Grievenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), p. 501.

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Figures (7)

Fig. 1
Fig. 1

Block diagram illustrating the principal steps of the phase-reconstruction algorithm by the method of synthetic interferograms.

Fig. 2
Fig. 2

Noisy simulated interferometric pattern featuring high-intensity gradients and decreasing contrast.

Fig. 3
Fig. 3

The correctly reconstructed phase exhibits propagated noise.

Fig. 4
Fig. 4

The first n=1 synthetic interferogram obtained with the phase shown in Fig.  3 and the input interferograms, demonstrating one fringe of error.

Fig. 5
Fig. 5

(a) The second n=2 and (b) the third n=3 synthetic interferograms result in a further decreased fraction of fringe error.

Fig. 6
Fig. 6

The fourth n=4 synthetic interferogram exhibits no fringe error: The intensity pattern is that due to noisy, illuminating intensity.

Fig. 7
Fig. 7

The noise-free phase is reconstructed only after three iterations.

Equations (6)

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Icx, y; ξ=rx, yImx, ycosϕx, y+Ψx, y; ξ+Incx, y,
Isx, y; ξ=rx, yImx, ysinϕx, y+Ψx, y; ξ+Insx, y,
Icnx, y; ξ=rx, yImx, ycosϕx, y-ϕnx, y+Ψx, y; ξ+Incnx, y,
Isnx, y; ξ=rx, yImx, ysinϕx, y-ϕnx, y+Ψx, y; ξ+Insnx, y.
nx, y=ϕx, y-ϕnx, y+Ψx, y; ξ+δnnx, y0+Ψx, y; ξ.
Wx, y=131piston+-6xtilt about y axis+-101-6y2-6x2+6y4+12x2y2+6x4third-order spherical+0.53x-12xy2-12x3+10xy4+20x3y2+10x5higher-order coma.

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