Abstract

A previous Letter by Pedrini et al. [Opt. Lett. 30, 833 (2005)] proposed an iterative single-beam wavefront reconstruction algorithm that uses a sequence of interferograms recorded at different planes. In this Letter, the use of relaxation and multiresolution strategies is investigated in terms of accuracy and computational effort. It is shown that the convergence rate of the conventional iterative algorithm can be significantly improved with the use of relaxation techniques combined with a hierarchy of downsampled intensities that are used within a preconditioner. These techniques prove to be more robust, to achieve a higher accuracy, and to overcome the stagnation problem met in the iterative wavefront reconstruction.

© 2013 Optical Society of America

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References

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  1. P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, Opt. Lasers Eng. 49, 252 (2011).
    [CrossRef]
  2. G. Pedrini, W. Osten, and Y. Zhang, Opt. Lett. 30, 833 (2005).
    [CrossRef]
  3. P. F. Almoro, L. Waller, M. Agour, C. Falldorf, G. Pedrini, W. Osten, and S. G. Hanson, Opt. Lett. 37, 2088 (2012).
    [CrossRef]
  4. V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).
  5. G. Strang, Computational Science and Engineering(Wellesley-Cambridge, 2007).
  6. T. Kozacki, K. Falaggis, and M. Kujawinska, Appl. Opt. 51, 7080 (2012).
    [CrossRef]

2012 (2)

2011 (1)

P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, Opt. Lasers Eng. 49, 252 (2011).
[CrossRef]

2005 (1)

Agour, M.

Almoro, P. F.

P. F. Almoro, L. Waller, M. Agour, C. Falldorf, G. Pedrini, W. Osten, and S. G. Hanson, Opt. Lett. 37, 2088 (2012).
[CrossRef]

P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, Opt. Lasers Eng. 49, 252 (2011).
[CrossRef]

Falaggis, K.

Falldorf, C.

Gundu, P. N.

P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, Opt. Lasers Eng. 49, 252 (2011).
[CrossRef]

Hanson, S. G.

P. F. Almoro, L. Waller, M. Agour, C. Falldorf, G. Pedrini, W. Osten, and S. G. Hanson, Opt. Lett. 37, 2088 (2012).
[CrossRef]

P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, Opt. Lasers Eng. 49, 252 (2011).
[CrossRef]

Kozacki, T.

Kujawinska, M.

Osten, W.

Pedrini, G.

Soifer, V. A.

V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

Strang, G.

G. Strang, Computational Science and Engineering(Wellesley-Cambridge, 2007).

Waller, L.

Zhang, Y.

Appl. Opt. (1)

Opt. Lasers Eng. (1)

P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, Opt. Lasers Eng. 49, 252 (2011).
[CrossRef]

Opt. Lett. (2)

Other (2)

V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

G. Strang, Computational Science and Engineering(Wellesley-Cambridge, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

RMS error of the R-SBMIR for various values of β using a random phase object with a maximum phase difference of 8π for the case of 25 intensities captured at 6.33 mm with an SNR of 35 dB.

Fig. 2.
Fig. 2.

Comparison of the RMS error of the R-SBMIR for the case of Fig. 1 and various MR strategies with P=4. The plots of Fig. 1 are replotted for comparison.

Fig. 3.
Fig. 3.

RMS error of the L-55-4 algorithm with β=0.25 for various sets of phase objects and SNR. One exemplary phase object for each set is shown.

Equations (2)

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Un+1=(1β)L+{Un}+βAn+1exp[iL+{Un}]}
Un=(1β)L{Un+1}+βAnexp[iL{Un+1}]},

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