Abstract

We describe a novel wave-front sensor comprising a distorted diffraction grating, simple optics, and a single camera. A noniterative phase-diversity algorithm is used for wave-front reconstruction. The sensor concept and practical implementation are described in detail, and performance is validated against different Zernike modes and a representative atmospheric phase map.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. M. Blanchard, A. H. Greenaway, “Simultaneous multiplane imaging with a distorted diffraction grating,” Appl. Opt. 38, 6692–6699 (1999).
    [CrossRef]
  2. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
    [CrossRef]
  3. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  4. D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics,” J. Phys. D 6, 2200–2225 (1973).
    [CrossRef]
  5. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983).
    [CrossRef]
  6. C. Roddier, F. Roddier, “Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes,” J. Opt. Soc. Am. A 10, 2277–2287 (1993).
    [CrossRef]
  7. M. A. A. Neil, M. J. Booth, T. Wilson, “Dynamic wave-front generation for the characterization and testing of optical surfaces,” Opt. Lett. 23, 1849–1851 (1998).
    [CrossRef]
  8. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).
  9. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]

1999

1998

1993

1983

1982

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

1973

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics,” J. Phys. D 6, 2200–2225 (1973).
[CrossRef]

1972

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1966

Blanchard, P. M.

Booth, M. J.

Fried, D. L.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

Greenaway, A. H.

Misell, D. L.

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics,” J. Phys. D 6, 2200–2225 (1973).
[CrossRef]

Neil, M. A. A.

Roddier, C.

Roddier, F.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

Teague, M. R.

Wilson, T.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics,” J. Phys. D 6, 2200–2225 (1973).
[CrossRef]

Opt. Eng.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

Opt. Lett.

Optik (Stuttgart)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Other

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Use of a qd-grating and lens combination for imaging multiple object planes onto a single image plane.

Fig. 2
Fig. 2

Schematic diagram of the optical system used for wave-front sensing and an example image recorded during the observation of a well-focused point source at infinity.

Fig. 3
Fig. 3

Schematic showing the basic steps for extraction of the wave-front profile by use of phase-diversity wave-front sensing implemented with a qd grating. -ve, negative.

Fig. 4
Fig. 4

Examples of the grating wave-front modulators used to generate known wave fronts, each encoded with a single Zernike mode: (a) n 2 = 3, (b) n 3 = 3, (c) n 4 = 3, (d) n 5 = 3.

Fig. 5
Fig. 5

Experimental setup for validation of phase-diversity wave-front sensing.

Fig. 6
Fig. 6

Experimental phase-diversity images taken with a grating wave-front modulator encoded with five waves of defocus.

Fig. 7
Fig. 7

Experimental phase-diversity images corresponding to different aberration types and the different images used as input to the phase-diversity algorithm for (a) defocus, (b) astigmatism, (c) coma, (d) trefoil, and (e) spherical aberration.

Fig. 8
Fig. 8

Phase-diversity wave-front measurement with different levels of defocus, showing raw data (open squares) and data corrected with zero-order measurements (solid squares).

Fig. 9
Fig. 9

Zero-order-corrected phase-diversity measurements with different levels of defocus, astigmatism, coma, trefoil, and spherical aberration. The aberration range is from -5λ to 5λ for all except spherical aberration, which is from -2λ to 2λ. Each data set was offset along the vertical axis to separate the points but passes close to the origin without this offset.

Fig. 10
Fig. 10

Applied (open symbols) and measured (solid symbols) levels of different wave-front modes with ten grating wave-front modulators containing mixtures of defocus, coma, and astigmatism.

Fig. 11
Fig. 11

Simulation of atmospheric turbulence. (a) Phase map of a wave-front generated and (b) the corresponding grating wave-front modulator.

Fig. 12
Fig. 12

Experimental phase-diversity image taken with the grating wave-front modulator shown in Fig. 11(b).

Fig. 13
Fig. 13

Phase maps of the wave front measured with (a) the interferometer and (b) phase diversity by use of the data in Fig. 12.

Tables (1)

Tables Icon

Table 1 Measurement Accuracy

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Mm=M0+2mνW20R2,
zm=R22mW20
Mm=2mfW20R2.
ϕwf=π2n1r2+n2r2 sin2θ+n33r3-2rsinθ+n4r3 sin3θ+43 n51-6r2+6r4,
T=1,0<modϕg+ϕwf, 2ππ0,π<modϕg+ϕwf, 2π2π,

Metrics