Abstract

We present the results of the phase-diversity algorithm applied to simulated and laboratory data. We show that the exact amount of defocus distance does not need to be known exactly for the phase-diversity algorithm on extended scene imaging. We determine, through computer simulation, the optimum diversity distance for various scene types. Using laboratory data, we compare the aberrations recovered with the phase-diversity algorithm and those measured with a Fizeau interferometer that uses a He-Ne laser. The two aberration sets agree with a Strehl ratio of over 0.9. The contrast of the recovered object is found to be ten times that of the raw image.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  13. R. D. Fiete, T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574–585 (2001).
    [CrossRef]
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    [CrossRef]

2001

Y. Ohneda, N. Baba, N. Miura, T. Sakurai, “Multiresolution approach to image reconstruction with phase-diversity technique,” Opt. Rev. 8, 32–36 (2001).
[CrossRef]

R. D. Fiete, T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574–585 (2001).
[CrossRef]

1999

1994

M. G. Lofdahl, G. B. Scharmer, “Wave-front sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

1993

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astron. J. 415, 862–874 (1993).
[CrossRef]

1992

R. G. Paxman, T. J. Schultz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. A 9, 1072–1085 (1992).
[CrossRef]

1990

N. Baba, E. Kenmochi, “Wave-front retrieval with use of defocused PSF data,” Optik (Stuttgart) 84, 70–72 (1990).

1988

1982

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

1976

1970

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Ayers, G. R.

Baba, N.

Y. Ohneda, N. Baba, N. Miura, T. Sakurai, “Multiresolution approach to image reconstruction with phase-diversity technique,” Opt. Rev. 8, 32–36 (2001).
[CrossRef]

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

N. Baba, E. Kenmochi, “Wave-front retrieval with use of defocused PSF data,” Optik (Stuttgart) 84, 70–72 (1990).

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1998).

Christou, J. C.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astron. J. 415, 862–874 (1993).
[CrossRef]

Dainty, J. C.

Dolne, J. J.

J. J. Dolne, D. Gerwe, M. M. Johnson, “Performance of three reconstruction methods on blurred and noisy images of extended scenes,” in Digital Image Recovery and Synthesis IV, T. J. Schulz, P. S. Idell, eds., Proc. SPIE3815, 164–175 (1999).
[CrossRef]

Fienup, J. R.

R. G. Paxman, T. J. Schultz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. A 9, 1072–1085 (1992).
[CrossRef]

R. G. Paxman, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
[CrossRef]

Fiete, R. D.

R. D. Fiete, T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574–585 (2001).
[CrossRef]

Gerwe, D.

J. J. Dolne, D. Gerwe, M. M. Johnson, “Performance of three reconstruction methods on blurred and noisy images of extended scenes,” in Digital Image Recovery and Synthesis IV, T. J. Schulz, P. S. Idell, eds., Proc. SPIE3815, 164–175 (1999).
[CrossRef]

Gonsalves, R. A.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Jefferies, S. M.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astron. J. 415, 862–874 (1993).
[CrossRef]

Johnson, M. M.

J. J. Dolne, D. Gerwe, M. M. Johnson, “Performance of three reconstruction methods on blurred and noisy images of extended scenes,” in Digital Image Recovery and Synthesis IV, T. J. Schulz, P. S. Idell, eds., Proc. SPIE3815, 164–175 (1999).
[CrossRef]

Kenmochi, E.

N. Baba, E. Kenmochi, “Wave-front retrieval with use of defocused PSF data,” Optik (Stuttgart) 84, 70–72 (1990).

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lee, D. J.

Lofdahl, M. G.

M. G. Lofdahl, G. B. Scharmer, “Wave-front sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Miura, N.

Y. Ohneda, N. Baba, N. Miura, T. Sakurai, “Multiresolution approach to image reconstruction with phase-diversity technique,” Opt. Rev. 8, 32–36 (2001).
[CrossRef]

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

Noll, R.

Ohneda, Y.

Y. Ohneda, N. Baba, N. Miura, T. Sakurai, “Multiresolution approach to image reconstruction with phase-diversity technique,” Opt. Rev. 8, 32–36 (2001).
[CrossRef]

Paxman, R. G.

R. G. Paxman, T. J. Schultz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. A 9, 1072–1085 (1992).
[CrossRef]

R. G. Paxman, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
[CrossRef]

Roggeman, M.

Sakurai, T.

Y. Ohneda, N. Baba, N. Miura, T. Sakurai, “Multiresolution approach to image reconstruction with phase-diversity technique,” Opt. Rev. 8, 32–36 (2001).
[CrossRef]

Scharmer, G. B.

M. G. Lofdahl, G. B. Scharmer, “Wave-front sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Schultz, T. J.

R. G. Paxman, T. J. Schultz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. A 9, 1072–1085 (1992).
[CrossRef]

Tantalo, T.

R. D. Fiete, T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574–585 (2001).
[CrossRef]

Tsumuraya, F.

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

Welsh, B. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1998).

Astron. Astrophys.

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Astron. Astrophys. Suppl. Ser.

M. G. Lofdahl, G. B. Scharmer, “Wave-front sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Astron. J.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astron. J. 415, 862–874 (1993).
[CrossRef]

J. Opt. Soc. A

R. G. Paxman, T. J. Schultz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. A 9, 1072–1085 (1992).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

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

R. D. Fiete, T. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574–585 (2001).
[CrossRef]

Opt. Lett.

Opt. Rev.

Y. Ohneda, N. Baba, N. Miura, T. Sakurai, “Multiresolution approach to image reconstruction with phase-diversity technique,” Opt. Rev. 8, 32–36 (2001).
[CrossRef]

Optik (Stuttgart)

N. Baba, E. Kenmochi, “Wave-front retrieval with use of defocused PSF data,” Optik (Stuttgart) 84, 70–72 (1990).

Other

J. J. Dolne, D. Gerwe, M. M. Johnson, “Performance of three reconstruction methods on blurred and noisy images of extended scenes,” in Digital Image Recovery and Synthesis IV, T. J. Schulz, P. S. Idell, eds., Proc. SPIE3815, 164–175 (1999).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1998).

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Figures (7)

Fig. 1
Fig. 1

Interferometer system uses a He-Ne laser as the source, and the imaging system uses a fiber-optics bundle as the source. The imaging system lenses have focal lengths of 1 m and clear aperture of 5 cm. The pixels of the Starlight digital camera are 7.4 μm × 7.4 μm in size. ND, neutral density, AF, Air Force.

Fig. 2
Fig. 2

Residual rms error between reconstructed and true wave fronts for various diversity defocus distances.

Fig. 3
Fig. 3

PD recovery for a partially known diversity defocus distance. True defocus is 0.5λ rms. The algorithm assumes that defocus = (0.3 + ∊)λ rms and optimizes with respect to ∊.

Fig. 4
Fig. 4

PD applied to laboratory data. The diversity defocus distance is 0.5λ pv. The optical system has 0.55λ pv of defocus aberration. The aberrations recovered with the PD algorithm and interferometer agree with a Strehl ratio of 0.99.

Fig. 5
Fig. 5

Same as Fig. 4 but with the roles of images reversed; i.e., the in-focus image in Fig. 4 becomes the diversity image in Fig. 5, and the diversity image in Fig. 4 becomes the in-focus image in Fig. 5. The optical system has 1.05λ pv of defocus. The Strehl ratio = 0.99.

Fig. 6
Fig. 6

PD applied to two different sections of the same image. The corresponding diversity images are not shown. Astigmatism is introduced by our tilting the lens. The aberrations recovered by separate use of the different image sections are approximately the same. The Strehl ratios are 0.94 for the top portion and 0.95 for the bottom portion.

Fig. 7
Fig. 7

Typical image profile through slices of the reconstructed object and the detected image. Contrast computed from slices shows a tenfold improvement as compared with contrast from the detected focal-plane image.

Equations (10)

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ix, y=ox, y  hx, y+nx, y,
idx, y=ox, y  hdx, y+ndx, y.
lo, h|i11, 1,, iDX, Y=d=1Dx=1Xy=1Y×12πσ2exp-idx, y-o  hdx, y22σ2.
Ôu, v=Ĥ*u, vIu, v+Ĥd*u, vIdu, v|Ĥu, v|2+|Ĥdu, v|2.
Iu, v=ix, y, Idu, v=idx, y, Ou, v=ox, y, Hu, v=hx, y, Hdu, v=hdx, y, Nu, v=nx, y, Ndu, v=ndx, y.
Hu, v=Pu, vexpi2πΘu, v Pu, vexpi2πΘu, v, Hdu, v=Pu, vexpi2πΘu, v+Φu, v Pu, vexpi2πΘu, v+Φu, v,
E=x,yWix, y-ô  ĥx, y2+idx, y-ô  ĥdx, y2,
Strehl=u,vexpi2πΘˆpdu, v-Θˆintu, v2UV2,
Ax, y=exp-x2+y2/d2,
C=Imax-IminImax+Imin.

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