Abstract

The imaging properties of a holographically corrected telescope are presented for broadband illumination using a single grating to correct for dispersion. High quality, broadband images approaching the performance of diffraction limited instruments are obtained from severely aberrated refractor and reflector telescope objectives.

© 1990 Optical Society of America

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References

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  1. J. Munch, R. Wuerker, “Holographic Technique for Correcting Aberrations in a Telescope,” Appl. Opt. 28, 1312–1317 (1989).
    [CrossRef] [PubMed]
  2. H. Kogelnik, K. S. Pennington, “Holographic Imaging Through a Random Medium,” J. Opt. Soc. Am. 58, 273–273 (1968).
    [CrossRef]
  3. A. Yariv, T. L. Koch, “One-Way Coherent Imaging through a Distorting Medium using Four-Wave Mixing,” Opt. Lett. 7, 113–115 (1982).
    [CrossRef] [PubMed]
  4. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
    [CrossRef]
  5. O. Ikeda, T. Suzuki, T. Sato, “Image Transmission Through a Turbulent Medium Using a Point Reflector and Four-Wave Mixing in BSO Crystal,” Appl. Opt. 22, 2192–2195 (1983).
    [CrossRef] [PubMed]
  6. K. R. MacDonald, W. R. Tompkin, R. W. Boyd, “Passive One-Way Aberration Correction Using Four-Wave Mixing,” Opt. Lett. 13, 485–487 (1988).
    [CrossRef] [PubMed]
  7. For a comparison of various methods, see E. N. Leith, A. Cunha, “Holographic Methods for Imaging Through an Inhomogeneity,” Opt. Eng. 28, 574–579 (1989).
    [CrossRef]
  8. P. G. Boj, M. Pardo, J. A. Quintana, “Display of Ordinary Transmission Holograms with a White Light Source,” Appl. Opt. 25, 4146–4149 (1986).
    [CrossRef] [PubMed]
  9. I. Weingarter, K. J. Rosenbruch, “Chromatic Corrections of Two and Three Element Holographic Imaging Systems,” Opt. Acta 29, 519–529 (1982).
    [CrossRef]
  10. See, for example, H. M. Smith, Principles of Holography, Section 5.4, pps. 109–117 (Wiley, New York, 1969).
  11. The minimum resolvable distance when using coherent illumination is 1.6 times larger than that for incoherent illumination. See, for example, M. V. Klein, T. E. Furtak, in Optics, Section 7.3, p. 489 (Wiley, New York, 1986).
  12. The film characteristics are shown on a linear scale, adapted from the logarithmic sensitivity curves supplied by Polaroid Corporation.

1989 (2)

J. Munch, R. Wuerker, “Holographic Technique for Correcting Aberrations in a Telescope,” Appl. Opt. 28, 1312–1317 (1989).
[CrossRef] [PubMed]

For a comparison of various methods, see E. N. Leith, A. Cunha, “Holographic Methods for Imaging Through an Inhomogeneity,” Opt. Eng. 28, 574–579 (1989).
[CrossRef]

1988 (1)

1986 (1)

1983 (1)

1982 (3)

I. Weingarter, K. J. Rosenbruch, “Chromatic Corrections of Two and Three Element Holographic Imaging Systems,” Opt. Acta 29, 519–529 (1982).
[CrossRef]

A. Yariv, T. L. Koch, “One-Way Coherent Imaging through a Distorting Medium using Four-Wave Mixing,” Opt. Lett. 7, 113–115 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

1968 (1)

Boj, P. G.

Boyd, R. W.

Cronin-Golomb, M.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

Cunha, A.

For a comparison of various methods, see E. N. Leith, A. Cunha, “Holographic Methods for Imaging Through an Inhomogeneity,” Opt. Eng. 28, 574–579 (1989).
[CrossRef]

Fischer, B.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

Furtak, T. E.

The minimum resolvable distance when using coherent illumination is 1.6 times larger than that for incoherent illumination. See, for example, M. V. Klein, T. E. Furtak, in Optics, Section 7.3, p. 489 (Wiley, New York, 1986).

Ikeda, O.

Klein, M. V.

The minimum resolvable distance when using coherent illumination is 1.6 times larger than that for incoherent illumination. See, for example, M. V. Klein, T. E. Furtak, in Optics, Section 7.3, p. 489 (Wiley, New York, 1986).

Koch, T. L.

Kogelnik, H.

Leith, E. N.

For a comparison of various methods, see E. N. Leith, A. Cunha, “Holographic Methods for Imaging Through an Inhomogeneity,” Opt. Eng. 28, 574–579 (1989).
[CrossRef]

MacDonald, K. R.

Munch, J.

Pardo, M.

Pennington, K. S.

Quintana, J. A.

Rosenbruch, K. J.

I. Weingarter, K. J. Rosenbruch, “Chromatic Corrections of Two and Three Element Holographic Imaging Systems,” Opt. Acta 29, 519–529 (1982).
[CrossRef]

Sato, T.

Smith, H. M.

See, for example, H. M. Smith, Principles of Holography, Section 5.4, pps. 109–117 (Wiley, New York, 1969).

Suzuki, T.

Tompkin, W. R.

Weingarter, I.

I. Weingarter, K. J. Rosenbruch, “Chromatic Corrections of Two and Three Element Holographic Imaging Systems,” Opt. Acta 29, 519–529 (1982).
[CrossRef]

White, J. O.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

Wuerker, R.

Yariv, A.

A. Yariv, T. L. Koch, “One-Way Coherent Imaging through a Distorting Medium using Four-Wave Mixing,” Opt. Lett. 7, 113–115 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-Time Phase Conjugate Windowfor One-Way Optical Field Imaging Through a Distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

I. Weingarter, K. J. Rosenbruch, “Chromatic Corrections of Two and Three Element Holographic Imaging Systems,” Opt. Acta 29, 519–529 (1982).
[CrossRef]

Opt. Eng. (1)

For a comparison of various methods, see E. N. Leith, A. Cunha, “Holographic Methods for Imaging Through an Inhomogeneity,” Opt. Eng. 28, 574–579 (1989).
[CrossRef]

Opt. Lett. (2)

Other (3)

See, for example, H. M. Smith, Principles of Holography, Section 5.4, pps. 109–117 (Wiley, New York, 1969).

The minimum resolvable distance when using coherent illumination is 1.6 times larger than that for incoherent illumination. See, for example, M. V. Klein, T. E. Furtak, in Optics, Section 7.3, p. 489 (Wiley, New York, 1986).

The film characteristics are shown on a linear scale, adapted from the logarithmic sensitivity curves supplied by Polaroid Corporation.

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Figures (9)

Fig. 1
Fig. 1

Schematic of basic concept for holographic correction of a telescope objective. (A) Recording the hologram as an image phase hologram of the aberrator. (B) and (C) Using the hologram as a correcting optical element.

Fig. 2
Fig. 2

Chromatic compensation, using a single grating. For equal hologram and grating ruling spacings, both dispersion and astigmatism will be compensated. The achromat forms a white light image of parallel, dispersed rays. See text.

Fig. 3
Fig. 3

(A) Holographic interferogram of aberrator used. Recorded at 633 nm with plane reference wave. (B) Holographic interferogram of aberrated and corrected telescope output and original reference beam, showing aberration correction to ~λ/10 at 633 nm across aperture.

Fig. 4
Fig. 4

Performance of conventional refracting telescope as an imaging instrument with white light, with and without the aberrator. (A) Aberrated, uncorrected image of resolution chart, column 0. (B) Enlarged section of Fig. 4(A), showing region of columns 2 and 3. (C) Unaberrated, uncorrected image. (D) Enlarged section of Fig. 4(C) showing resolution of column 6, line 1 (15.6 μm) in both directions.

Fig. 5
Fig. 5

Performance of aberrated and corrected refracting telescope. (A) Narrow band at recording wavelength (633 nm). (B) Enlarged section of Fig. 5(A), showing resolution of column 5, line 6 (17.5 μm), degraded by laser speckle. (C) Broadband illumination 610–650 nm. (D) Enlarged section of Fig. 5(C), showing resolution of column 6, line 3 (12.4 μm). (E) Illumination by a white light arc lamp, Δλ > 300 nm, dominated by response of film. (F) Enlarged section of Fig. 5(E) showing resolution to column 4, line 3 (50 μm) in both directions, and column 5, line 6 (17.5 μm) in horizontal direction.

Fig. 6
Fig. 6

Transmission curves for the (A) Wratten No. 29 and (B) No. 55 filters used to characterize broadband behavior of instrument, and (C) linear response of the film used to record images.12

Fig. 7
Fig. 7

Experimental arrangement using an imperfect reflector (M) as an imaging component with aberration correction and dispersion compensation. Either a single pinhole or a resolution chart sandwiched with a ground-glass diffuser can be placed at position O, for primary aberrated imaging at B and corrected, unaberrated imaging at C. Light source (W), eyepiece (E), hologram (H), reference beam (R), grating (G), camera (C).

Fig. 8
Fig. 8

Imaging properties of imperfect concave reflector. (A) Image of resolution chart, illuminated with white light. (B) Minimum image of a 10-μm pinhole placed at A and observed at B in Fig. 7. Scale bar is 1 cm long in plane B. (C) Holographically corrected image of resolution chart at 633 nm (using arrangement in Fig. 7). (D) Enlarged section of Fig. 8(C) showing resolution of column 5, line 2 (28 μm), limited by laser speckle.

Fig. 9
Fig. 9

Performance of holographically corrected reflector using broad band illumination and grating corrector. (A) Broadband 610–650 nm, centered around recording wavelength of 633 nm. (B) Enlarged section of Fig. 9(A) showing resolution of column 6, line 1 (15.6 μm). (C) Broadband, 75 nm FWHM, centered at 520 nm. (D) Enlarged section of D, showing resolution of column 4, line 1 (63 μm). (E) White light Δλ > 300 nm. (F) Enlarged part of Fig. 9 (E) showing resolution of column 5, line 1 (31 μm).

Equations (1)

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F remaining error original aberration = 2 h ( λ 1 - λ 2 ) λ 1 λ 2 · λ 1 2 h = Δ λ λ 2 ,

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