Abstract

We report experimental results for what we believe to be a new technique for estimating aberrations that extends the strength of an aberration that may be sensed with Hartmann sensor technology by means of an algorithm that processes both a Hartmann sensor image and a conventional image formed with the same aberration. We find that the theory and the experiment match well within the experimental error and that strong defocus aberrations can be accurately sensed with this technique.

© 1999 Optical Society of America

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References

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  1. A. Watson, “Hubble successor gathers support,” Science 272, 1735 (1996).
    [CrossRef]
  2. T. Reichhardt, A. Abbott, D. Swinbanks, “What will be the next big thing?” Nature 381, 465 (1996).
    [CrossRef]
  3. R. A. Carerras, D. K. Marker, J. M. Wilkes, “Tunable membrane mirrors used with real time holography,” in Novel Optical Systems and Large-Aperture Imaging, Proc. SPIE3430, 202–208 (1998).
  4. M. C. Roggemann, B. M. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  5. M. C. Roggemann, T. J. Schulz, “Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements,” Appl. Opt. 37, 4321–4329 (1998).
    [CrossRef]
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  7. J. R. Fienup, J. C. Marron, T. J. Schulz, J. H. Seldin, “Hubble space telescope characterized by using phase-retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993).
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  8. A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  10. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  11. D. A. Pierre, Optimization Theory with Applications (Dover, New York, 1986).
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  13. H. D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962).

1998 (1)

1996 (2)

A. Watson, “Hubble successor gathers support,” Science 272, 1735 (1996).
[CrossRef]

T. Reichhardt, A. Abbott, D. Swinbanks, “What will be the next big thing?” Nature 381, 465 (1996).
[CrossRef]

1993 (1)

1982 (1)

1976 (1)

Abbott, A.

T. Reichhardt, A. Abbott, D. Swinbanks, “What will be the next big thing?” Nature 381, 465 (1996).
[CrossRef]

Baird, C.

A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).

Berkopec, T.

A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).

Branch, M. A.

M. A. Branch, A. Grace, MATLAB Optimization Toolbox (Math Works, Natick, Mass., 1996).

Carerras, R. A.

R. A. Carerras, D. K. Marker, J. M. Wilkes, “Tunable membrane mirrors used with real time holography,” in Novel Optical Systems and Large-Aperture Imaging, Proc. SPIE3430, 202–208 (1998).

Fienup, J. R.

Goodman, J. W.

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

Grace, A.

M. A. Branch, A. Grace, MATLAB Optimization Toolbox (Math Works, Natick, Mass., 1996).

Jankevics, A.

A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).

Landers, F.

A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).

Marker, D. K.

R. A. Carerras, D. K. Marker, J. M. Wilkes, “Tunable membrane mirrors used with real time holography,” in Novel Optical Systems and Large-Aperture Imaging, Proc. SPIE3430, 202–208 (1998).

Marron, J. C.

Noll, R. J.

Pierre, D. A.

D. A. Pierre, Optimization Theory with Applications (Dover, New York, 1986).

Reichhardt, T.

T. Reichhardt, A. Abbott, D. Swinbanks, “What will be the next big thing?” Nature 381, 465 (1996).
[CrossRef]

Roggemann, M. C.

Schulz, T. J.

Seldin, J. H.

Swinbanks, D.

T. Reichhardt, A. Abbott, D. Swinbanks, “What will be the next big thing?” Nature 381, 465 (1996).
[CrossRef]

Watson, A.

A. Watson, “Hubble successor gathers support,” Science 272, 1735 (1996).
[CrossRef]

Welsh, B. M.

M. C. Roggemann, B. M. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Wilkes, J. M.

R. A. Carerras, D. K. Marker, J. M. Wilkes, “Tunable membrane mirrors used with real time holography,” in Novel Optical Systems and Large-Aperture Imaging, Proc. SPIE3430, 202–208 (1998).

Wirth, A.

A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).

Young, H. D.

H. D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962).

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Nature (1)

T. Reichhardt, A. Abbott, D. Swinbanks, “What will be the next big thing?” Nature 381, 465 (1996).
[CrossRef]

Science (1)

A. Watson, “Hubble successor gathers support,” Science 272, 1735 (1996).
[CrossRef]

Other (7)

A. Wirth, A. Jankevics, F. Landers, C. Baird, T. Berkopec, “Final report on the testing of the CIRS telescopes using the Hartmann technique,” (Adaptive Optics Associates, 54 CambridgePark Drive, Cambridge, Mass. 02140, 1993).

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

R. A. Carerras, D. K. Marker, J. M. Wilkes, “Tunable membrane mirrors used with real time holography,” in Novel Optical Systems and Large-Aperture Imaging, Proc. SPIE3430, 202–208 (1998).

M. C. Roggemann, B. M. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

D. A. Pierre, Optimization Theory with Applications (Dover, New York, 1986).

M. A. Branch, A. Grace, MATLAB Optimization Toolbox (Math Works, Natick, Mass., 1996).

H. D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962).

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Figures (5)

Fig. 1
Fig. 1

Diagram of the Hartmann sensor concept.

Fig. 2
Fig. 2

Simulated Hartmann sensor image for a strongly aberrated input wave front. The edges of the subapertures have been superimposed on the image, and a negative image is shown for clarity.

Fig. 3
Fig. 3

Functional block diagram of the wave-front sensing concept.

Fig. 4
Fig. 4

Functional block diagram of the wave-front sensing experimental setup.

Fig. 5
Fig. 5

Examples of experimental results for the case of the input aberration α4 = 16.60: (a) the measured conventional image, (b) the measured Hartmann sensor image, and (c) the computed conventional image when the estimated value α̃4 = 17.33 is used.

Tables (1)

Tables Icon

Table 1 Experimental Aberration Sensing Results for Sensing Only Defocus Aberration, Zernike Polynomial 4a

Equations (15)

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tHx=Sexp-j kw2fl|x-xcs|2rectx-xcsd,
Uabx=Pxexpjϕabx,
ULx=UabxtHx.
HAf=expj2π flλ1-λ|f|21/2,
UDxD=-1ULxHAf,
IDxD=|UDxD|2.
UIxi=κUabx,
IIxi=|UIxi|2.
ϕ˜abRxn=k=2K αkZkxn,
Jα¯=xDIDxD1/2-I˜DxD, α¯1/22+xiIIxi1/2-I˜Ixi, α¯1/22,
RC=|fA|+L+d1,
ϕedge=k RI22RC,
α4=ϕedge3.464.
Δα42α4RC2ΔRC2+α4RI2ΔRI2,
Δα42π3.464λ2RI2RC22ΔRC2+4RIRC2ΔRI2,

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