Abstract

A holographic technique for correcting aberrations in a telescope objective is presented. An image hologram of the aberrations is used as a correction plate to cancel out all the aberrations of the objective. Experimental results demonstrate diffraction-limited performance of the corrected telescope, as well as practical fields of view and a useful bandwidth (≈ 100 nm) for an objective with 10λ aberrations.

© 1989 Optical Society of America

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References

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  1. D. Gabor, “Microscopy by Reconstructed Wavefronts,” Proc. R. Soc. London Ser. A 197, 454 (1949).
    [CrossRef]
  2. E. N. Leith, J. Upatnieks, “Holographic Imagery Through Diffusing Media,” J. Opt. Soc. Am. 56, 523 (1966).
    [CrossRef]
  3. J. Upatnieks, A. VanderLugt, E. Leith, “Correction of Lens Aberrations by Means of Holograms,” Appl. Opt. 5, 589 (1966).
    [CrossRef] [PubMed]
  4. H. Kogelnik, K. S. Pennington, “Holographic Imaging Through a Random Medium,” J. Opt. Soc. Am. 58, 273 (1968).
    [CrossRef]
  5. B. P. Hildebrand, J. D. Trolinger, “Statistical Analysis of a Holographic System Intended for the Space Shuttle,” Appl. Opt. 22, 2124 (1983).
    [CrossRef] [PubMed]
  6. Achromatic 61-cm (24-in.) focal length telescope objectives from A. Jaegers, Lynbrook, NY.
  7. See, for example, P. G. Boj, M. Pardo, J. A. Quintana, “Display of Ordinary Transmission Holograms with a White Light Source,” Appl. Opt. 25, 4146 (1986);I. Weingartner, K. J. Rosenbruch, “Chromatic Correction of Two- and Three-Element Holographic Imaging Systems,” Opt. Acta 29, 519 (1982).
    [CrossRef] [PubMed]

1986 (1)

1983 (1)

1968 (1)

1966 (2)

1949 (1)

D. Gabor, “Microscopy by Reconstructed Wavefronts,” Proc. R. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Boj, P. G.

Gabor, D.

D. Gabor, “Microscopy by Reconstructed Wavefronts,” Proc. R. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Hildebrand, B. P.

Kogelnik, H.

Leith, E.

Leith, E. N.

Pardo, M.

Pennington, K. S.

Quintana, J. A.

Trolinger, J. D.

Upatnieks, J.

VanderLugt, A.

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Figures (11)

Fig. 1
Fig. 1

Schematic of the telescope with an aberrated objective. The eyepiece is used to image the plane of the aberrator onto the plane of the hologram.

Fig. 2
Fig. 2

Experimental arrangement used to demonstrate aberration corrections on a telescope, illustrated for the recording of the hologram. When reconstructing the hologram it is replaced in the exact position of recording. Interferometry is achieved between the original reference beam and the reconstructed reference beam using the aberrated object wave and the hologram. Imaging is achieved by blocking the original reference beam and reimaging the aberrator-free beam reconstructed by the object wave.

Fig. 3
Fig. 3

(A) Interferogram of the aberrator used. (B) Interference pattern created by interfering the corrected, reconstructed beam and the original reference beam, showing perfect aberration correction.

Fig. 4
Fig. 4

Additional lenses were added to the experimental setup in Fig. 2 to place an object at infinity. In actual practice, the resolution chart was slightly displaced from the exact focus to illuminate a small finite and useful part of the resolution chart.

Fig. 5
Fig. 5

Results of the imaging experiments, demonstrating the retrieval of diffraction-limited performance of the aberrated telescope: (A) aberrated and corrected image of the AF resolution chart; (B) perfect image obtained with an unaberrated telescope of the same aperture as the corrected telescope in (A); (C) aberrated and uncorrected image of the AF resolution chart.

Fig. 6
Fig. 6

Geometry of a refractive aberrator of step size δl used to calculate the field of view and chromatic effects; see text.

Fig. 7
Fig. 7

Results demonstrating perfect aberration correction over the entire field of view of the telescope: (A) aberrator used; (B) in line interferogram showing perfect correction (θ = 0°); (C) inclined beam (θ = 0.8° at the objective, 8° at the hologram) showing a small amount of astigmatism; (D) imaging at θ = 0° [corresponding to (B)]; (E) imaging at θ = 0.8° at the objective [corresponding to (C)].

Fig. 8
Fig. 8

Diagram showing how imaging properties of the eyepiece permit the use of a beacon laser close to the objective, necessary for a practical telescope.

Fig. 9
Fig. 9

Experimental arrangement used to test correcting properties of the telescope with a difference in angular subtense of beacon and object waves.

Fig. 10
Fig. 10

Results of the experiments in Fig. 9. (A) Interferogram showing perfect unaberrated rings, demonstrating aberration correction. Rings are formed due to the difference in angular subtense of the original and reconstructed reference beacon, due to an added lens. (B) Diffraction-limited image of the AF resolution chart obtained with the arrangement in Fig. 9.

Fig. 11
Fig. 11

Interferograms and images obtained with the corrected telescope for different wavelengths of reconstruction: (A) interferogram of the aberrator at 588 nm shows >10λ; (B) uncorrected, aberrated image (588 nm); (C),(D) corrected interferogram and diffraction-limited image at a recording wavelength of 588 nm (orange); (E),(F) as above but at λ = 570 nm (yellow); (G),(H) as above but at λ = 562 nm (green); (I),(J) as above but at λ = 633 nm (red); (K) image obtained at λ = 514 nm (dark green); (L) perfect unaberrated telescope.

Equations (2)

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δ ( Δ ϕ ) = 2 π δ l λ θ 2 2 n ,
δ ϕ = 2 π δ l   [ cos θ   ( n 1 λ 2 n 2 λ 1 ) cos θ   ( λ 2 λ 1 ) ] / λ 1 λ 2 .

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