Abstract

The performance of wide-field multiple-aperture imaging systems is dominated by easily understood, low-order errors. Each aperture produces an individual image, each pair of apertures produces a set of fringes under a diffraction envelope, and the system bandwidth produces a coherence envelope. For wide-field imaging, each of these elements must be coincident in the image plane as the field angle changes. We explore the causes of image degradation, derive first-order rules for preserving image quality across field, and give an example design that enforces some of the rules to achieve a relatively wide-field interferometric imaging telescope.

© 2006 Optical Society of America

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  1. J. E. Harvey and R. A. Rockwell, "Performance characteristics of phased array and thinned-aperture optical telescopes," Opt. Eng. 27, 762-768 (1988).
  2. R. V. Shack, J. D. Rancout, and H. Morrow, "Effects of dilution on a six-element synthetic aperture," Appl. Opt. 10, 257-259 (1971).
    [CrossRef] [PubMed]
  3. M. J. E. Golay, "Point arrays having compact, nonredundant autocorrelations," J. Opt. Soc. Am. 61, 272-273 (1971).
  4. T. J. Cornwell, "A novel principle for optimization of the instantaneous Fourier plane coverage of correlation arrays," IEEE Trans. Antennas Propag. 36, 1165-1167 (1988).
    [CrossRef]
  5. A. B. Meinel, "Aperture synthesis using independent telescopes," Appl. Opt. 9, 2501-2504 (1970).
    [CrossRef] [PubMed]
  6. W. A. Traub, "Combining beams from separated telescopes," Appl. Opt. 25, 528-532 (1986).
    [CrossRef] [PubMed]
  7. R. R. Butts, "Effects of piston and tilt errors on the performance of multiple mirror telescopes," in Wavefront Distortions in Power Optics, C. A. Klein, ed., Proc. SPIE 293, 85-89 (1981).
  8. R. V. Shack, "Aberration limitations on optical array telescopes," J. Opt. Soc. Am. 68, 1361 (1978).
  9. R. L. Lucke, "Influence of seidel distortion on combining beams from a phased telescope array," Appl. Opt. 38, 4776-4783 (1999).
    [CrossRef]
  10. R. D. Sigler and A. L. Palmer, "Increasing the phased field of view of large distributed aperture telescope arrays," in Current Developments in Lens Design and Optical Engineering II, R. E. Fischer, B. Johnson, and W. Smith, eds., Proc. SPIE 4441, 60-71 (2001).
    [CrossRef]
  11. J. E. Harvey, A. B. Wissinger, and A. N. Bunner, "A parametric study of various synthetic aperture telescope configurations for coherent imaging applications," in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 194-207 (1986).
  12. J. E. Harvey and C. Ftaclas, "Field of view limitations of phased telescope arrays," Appl. Opt. 34, 5787-5798 (1995).
    [CrossRef] [PubMed]
  13. L. D. Weaver, J. S. Fender, and C. R. DeHainaut, "Design considerations for multiple telescope imaging arrays," Opt. Eng. 27, 730-735 (1988).
  14. J. S. Fender, "Phased array optical systems," in Infrared, Adaptive, and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 122-128 (1986).
  15. N. V. Ryabova and D. N. Eskov, Multiaperture synthesis telescope systems with direct image formation," Sov. J. Opt. Technol. 60, 507-521 (1993).
  16. C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).
  17. E. Hege, J. Beckers, P. Strittmatter, and D. McCarthy, "Multiple mirror telescope as a phased array telescope," Appl. Opt. 24, 2565-2576 (1985).
    [CrossRef] [PubMed]
  18. P. Salinari, "The Large Binocular Telescope," in 18th Congress of the International Comission for Optics, A. J. Glass, J. W. Goodman, A. H. Guenther, and T. Asakura, eds., Proc. SPIE , 3749, 691-692 (1999).
    [CrossRef]
  19. J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley 1978), see especially pp. 72, 200, 328-329.
  20. R. Kingslake, Lens Design Fundamentals (Academic, 1978).
  21. A. B. Meinel, "Aperture synthesis using independent telescopes," Appl. Opt. 9, 2501-2504 (1970).
    [CrossRef] [PubMed]
  22. J. C. Wyant and K. Creath, "Basic wavefront aberration theory for optical metrology," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1992), Vol. 11.
  23. H. M. Merklinger, "Scheimpflug's patent," in Photo Techniques, November-December 1996.

2001 (1)

R. D. Sigler and A. L. Palmer, "Increasing the phased field of view of large distributed aperture telescope arrays," in Current Developments in Lens Design and Optical Engineering II, R. E. Fischer, B. Johnson, and W. Smith, eds., Proc. SPIE 4441, 60-71 (2001).
[CrossRef]

1999 (2)

P. Salinari, "The Large Binocular Telescope," in 18th Congress of the International Comission for Optics, A. J. Glass, J. W. Goodman, A. H. Guenther, and T. Asakura, eds., Proc. SPIE , 3749, 691-692 (1999).
[CrossRef]

R. L. Lucke, "Influence of seidel distortion on combining beams from a phased telescope array," Appl. Opt. 38, 4776-4783 (1999).
[CrossRef]

1995 (1)

1988 (4)

C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).

L. D. Weaver, J. S. Fender, and C. R. DeHainaut, "Design considerations for multiple telescope imaging arrays," Opt. Eng. 27, 730-735 (1988).

J. E. Harvey and R. A. Rockwell, "Performance characteristics of phased array and thinned-aperture optical telescopes," Opt. Eng. 27, 762-768 (1988).

T. J. Cornwell, "A novel principle for optimization of the instantaneous Fourier plane coverage of correlation arrays," IEEE Trans. Antennas Propag. 36, 1165-1167 (1988).
[CrossRef]

1986 (3)

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, "A parametric study of various synthetic aperture telescope configurations for coherent imaging applications," in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 194-207 (1986).

J. S. Fender, "Phased array optical systems," in Infrared, Adaptive, and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 122-128 (1986).

W. A. Traub, "Combining beams from separated telescopes," Appl. Opt. 25, 528-532 (1986).
[CrossRef] [PubMed]

1985 (1)

1981 (1)

R. R. Butts, "Effects of piston and tilt errors on the performance of multiple mirror telescopes," in Wavefront Distortions in Power Optics, C. A. Klein, ed., Proc. SPIE 293, 85-89 (1981).

1971 (1)

1970 (2)

Beckers, J.

Bunner, A. N.

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, "A parametric study of various synthetic aperture telescope configurations for coherent imaging applications," in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 194-207 (1986).

Butts, R. R.

R. R. Butts, "Effects of piston and tilt errors on the performance of multiple mirror telescopes," in Wavefront Distortions in Power Optics, C. A. Klein, ed., Proc. SPIE 293, 85-89 (1981).

Cornwell, T. J.

T. J. Cornwell, "A novel principle for optimization of the instantaneous Fourier plane coverage of correlation arrays," IEEE Trans. Antennas Propag. 36, 1165-1167 (1988).
[CrossRef]

Creath, K.

J. C. Wyant and K. Creath, "Basic wavefront aberration theory for optical metrology," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1992), Vol. 11.

DeHainault, C. R.

C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).

DeHainaut, C. R.

L. D. Weaver, J. S. Fender, and C. R. DeHainaut, "Design considerations for multiple telescope imaging arrays," Opt. Eng. 27, 730-735 (1988).

Eskov, D. N.

N. V. Ryabova and D. N. Eskov, Multiaperture synthesis telescope systems with direct image formation," Sov. J. Opt. Technol. 60, 507-521 (1993).

Fender, J. S.

L. D. Weaver, J. S. Fender, and C. R. DeHainaut, "Design considerations for multiple telescope imaging arrays," Opt. Eng. 27, 730-735 (1988).

J. S. Fender, "Phased array optical systems," in Infrared, Adaptive, and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 122-128 (1986).

Ftaclas, C.

Gaskill, J.

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley 1978), see especially pp. 72, 200, 328-329.

Golay, M. J. E.

Gonglewski, J. D.

C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).

Harvey, J. E.

J. E. Harvey and C. Ftaclas, "Field of view limitations of phased telescope arrays," Appl. Opt. 34, 5787-5798 (1995).
[CrossRef] [PubMed]

J. E. Harvey and R. A. Rockwell, "Performance characteristics of phased array and thinned-aperture optical telescopes," Opt. Eng. 27, 762-768 (1988).

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, "A parametric study of various synthetic aperture telescope configurations for coherent imaging applications," in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 194-207 (1986).

Hege, E.

Henta, K. P.

C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, 1978).

Lucke, R. L.

McCarthy, D.

Meinel, A. B.

Merklinger, H. M.

H. M. Merklinger, "Scheimpflug's patent," in Photo Techniques, November-December 1996.

Morrow, H.

Palmer, A. L.

R. D. Sigler and A. L. Palmer, "Increasing the phased field of view of large distributed aperture telescope arrays," in Current Developments in Lens Design and Optical Engineering II, R. E. Fischer, B. Johnson, and W. Smith, eds., Proc. SPIE 4441, 60-71 (2001).
[CrossRef]

Rancout, J. D.

Rockwell, R. A.

J. E. Harvey and R. A. Rockwell, "Performance characteristics of phased array and thinned-aperture optical telescopes," Opt. Eng. 27, 762-768 (1988).

Ryabova, N. V.

N. V. Ryabova and D. N. Eskov, Multiaperture synthesis telescope systems with direct image formation," Sov. J. Opt. Technol. 60, 507-521 (1993).

Salinari, P.

P. Salinari, "The Large Binocular Telescope," in 18th Congress of the International Comission for Optics, A. J. Glass, J. W. Goodman, A. H. Guenther, and T. Asakura, eds., Proc. SPIE , 3749, 691-692 (1999).
[CrossRef]

Shack, R. V.

R. V. Shack, J. D. Rancout, and H. Morrow, "Effects of dilution on a six-element synthetic aperture," Appl. Opt. 10, 257-259 (1971).
[CrossRef] [PubMed]

R. V. Shack, "Aberration limitations on optical array telescopes," J. Opt. Soc. Am. 68, 1361 (1978).

Sigler, R. D.

R. D. Sigler and A. L. Palmer, "Increasing the phased field of view of large distributed aperture telescope arrays," in Current Developments in Lens Design and Optical Engineering II, R. E. Fischer, B. Johnson, and W. Smith, eds., Proc. SPIE 4441, 60-71 (2001).
[CrossRef]

Strittmatter, P.

Traub, W. A.

Waver, L. D.

C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).

Weaver, L. D.

L. D. Weaver, J. S. Fender, and C. R. DeHainaut, "Design considerations for multiple telescope imaging arrays," Opt. Eng. 27, 730-735 (1988).

Wissinger, A. B.

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, "A parametric study of various synthetic aperture telescope configurations for coherent imaging applications," in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 194-207 (1986).

Wyant, J. C.

J. C. Wyant and K. Creath, "Basic wavefront aberration theory for optical metrology," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1992), Vol. 11.

Appl. Opt. (7)

IEEE Trans. Antennas Propag. (1)

T. J. Cornwell, "A novel principle for optimization of the instantaneous Fourier plane coverage of correlation arrays," IEEE Trans. Antennas Propag. 36, 1165-1167 (1988).
[CrossRef]

J. Opt. Soc. Am. (2)

R. V. Shack, "Aberration limitations on optical array telescopes," J. Opt. Soc. Am. 68, 1361 (1978).

M. J. E. Golay, "Point arrays having compact, nonredundant autocorrelations," J. Opt. Soc. Am. 61, 272-273 (1971).

Opt. Eng. (3)

L. D. Weaver, J. S. Fender, and C. R. DeHainaut, "Design considerations for multiple telescope imaging arrays," Opt. Eng. 27, 730-735 (1988).

J. E. Harvey and R. A. Rockwell, "Performance characteristics of phased array and thinned-aperture optical telescopes," Opt. Eng. 27, 762-768 (1988).

C. R. DeHainault, K. P. Henta, L. D. Waver, and J. D. Gonglewski, "Design of a wide field of view phased array telescope," Opt. Eng. 27, 762-768 (1988).

Proc. SPIE (2)

P. Salinari, "The Large Binocular Telescope," in 18th Congress of the International Comission for Optics, A. J. Glass, J. W. Goodman, A. H. Guenther, and T. Asakura, eds., Proc. SPIE , 3749, 691-692 (1999).
[CrossRef]

R. D. Sigler and A. L. Palmer, "Increasing the phased field of view of large distributed aperture telescope arrays," in Current Developments in Lens Design and Optical Engineering II, R. E. Fischer, B. Johnson, and W. Smith, eds., Proc. SPIE 4441, 60-71 (2001).
[CrossRef]

Sov. J. Opt. Technol. (1)

N. V. Ryabova and D. N. Eskov, Multiaperture synthesis telescope systems with direct image formation," Sov. J. Opt. Technol. 60, 507-521 (1993).

Other (7)

J. S. Fender, "Phased array optical systems," in Infrared, Adaptive, and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 122-128 (1986).

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, "A parametric study of various synthetic aperture telescope configurations for coherent imaging applications," in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, ed., Proc. SPIE 643, 194-207 (1986).

R. R. Butts, "Effects of piston and tilt errors on the performance of multiple mirror telescopes," in Wavefront Distortions in Power Optics, C. A. Klein, ed., Proc. SPIE 293, 85-89 (1981).

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley 1978), see especially pp. 72, 200, 328-329.

R. Kingslake, Lens Design Fundamentals (Academic, 1978).

J. C. Wyant and K. Creath, "Basic wavefront aberration theory for optical metrology," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1992), Vol. 11.

H. M. Merklinger, "Scheimpflug's patent," in Photo Techniques, November-December 1996.

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Figures (15)

Fig. 1
Fig. 1

Optical schematic of the LBT, including an enlarged view of the beam combiner.

Fig. 2
Fig. 2

Entrance pupil and PSF for a two-aperture system with large apertures on a relatively short baseline.

Fig. 3
Fig. 3

(a) For perfect beam combining, the images from each aperture and the fringe center must be coincident in the image plane of the system. (b) The only errors that can occur during beam combining are lateral and longitudinal separation of the images, fringes that shift away from the images, and aberrated wavefronts in any of the subapertures of the system.

Fig. 4
Fig. 4

(a) On-axis wave fan for a three-aperture imaging interferometer whose beam combiner has not been corrected for low-order beam combining errors. (b), (c) Wave fans for an imaging interferometer whose beam combiner has not been corrected for low-order beam combining errors show power, tilt, and piston errors at (b) a 2 arcmin and (c) a 4 arcmin field angle.

Fig. 5
Fig. 5

Cross sections of the monochromatic PSF from a two-aperture system with piston errors of (a) δ = 0 waves, (b) δ = 0.15 waves, (c) δ = 0.4 waves. For Eq. (6) D = 1   m , λ = 0.5   μm , f = 10   m , and Δ = 1.5   m .

Fig. 6
Fig. 6

Monochromatic PSF recovers every time the piston passes through π, so that a cosine fringe is centered under the Somb envelope, but the more realistic polychromatic PSF continues to degrade because of the addition of the coherence envelope.

Fig. 7
Fig. 7

PSFs of a two-aperture system with increasing piston errors. The system consisted of two 8   m apertures on a 14   m baseline. The center wavelength was 4 .8   μm with a bandwidth of 1 .2   μm .

Fig. 8
Fig. 8

Linear piston errors in a multiple-aperture system can be viewed as coma in the parent system and can be eliminated by satisfying the Abbe sine condition for the axial rays in each arm of the interferometer.

Fig. 9
Fig. 9

Parameters used in Eq. (9) to correct linear piston errors.

Fig. 10
Fig. 10

(a) Wave fans before the sine condition is applied to the LBT beam-combiner design. Field angles of 0, 1∕4, and 1∕2 arcmin are shown. (b) Wave fans after the sine condition is applied to the LBT beam-combiner design. (Note the 10× scale change between (a) and (b).

Fig. 11
Fig. 11

Spot diagrams and cross sections of the PSFs (a) before and (b) after correction of linear piston errors in the LBT beam combiner. The PSFs were calculated for a rectangular spectrum of width 0 .8   μm centered at 2 .2   μm .

Fig. 12
Fig. 12

Both single- and dual-arm models of the system show that the linear piston has been corrected and only higher-order piston errors remain in the LBT beam combiner.

Fig. 13
Fig. 13

Constant and linear image separations have been corrected in the LBT beam combiner. Quadratic image separations remain but do not dominate the system performance.

Fig. 14
Fig. 14

Scheimpflug condition states that the object and image planes must intersect in the system's principal planes.

Fig. 15
Fig. 15

Linear defocus errors remain in the LBT beam combiner but do not dominate the system's performance.

Tables (1)

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Table 1 Correction Methods for Low-Order Beam-Combining Errors

Equations (15)

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A ( x , y ) = Cyl ( 1 D 1 [ ( x x 1 ) 2 + ( y y 1 ) 2 ] 1 / 2 ) + Cyl ( 1 D 2 [ ( x x 2 ) 2 + ( y y 2 ) 2 ] 1 / 2 ) ,
Cyl ( r ) = { 1 r < 1 / 2 0 r > 1 / 2 .
I ( x , y ) = ( 1 λ f ) 2 { ( π D 1     2 4 ) 2 Somb 2 ( D 1 λ f r ) + ( π D 2     2 4 ) 2 Somb 2 ( D 2 λ f r ) + 2 ( π D 1 D 2 4 ) 2 Somb ( D 1 λ f r ) Somb ( D 2 λ f r ) ×  cos [ 2 π λ f ( x 1 x 2 ) x + 2 π λ f ( y 1 y 2 ) y ] } ,
A ( x , y ) = Cyl ( 1 D [ ( x Δ 2 ) 2 + y 2 ] 1 / 2 ) + Cyl ( 1 D [ ( x + Δ 2 ) 2 + y 2 ] 1 / 2 ) ,
I ( x , y ) = ( π D 2 2 λ f ) 2 Somb 2 ( D λ f r ) cos 2 ( 2 π λ f Δ 2 x ) .
A ( x , y ) = Cyl ( 1 D [ ( x Δ 2 ) 2 + y 2 ] 1 / 2 ) + exp ( i π δ ) Cyl ( 1 D [ ( x + Δ 2 ) 2 + y 2 ] 1 / 2 ) .
I ( x , y ) = ( π D 2 4 λ f ) 2 Somb 2 ( D λ f r ) + ( π D 2 4 λ f ) 2 Somb 2 ( D λ f r ) + 2 ( π D 2 4 λ f ) 2 Somb 2 ( D λ f r ) cos ( 2 π Δ λ f x + π δ ) .
m = sin u / sin u ,
h = a sin u ,
h / sin u = Δ y / α ,
A ( x , y ) = Cyl ( 1 D ( x Δ 2 ) 2 + y 2 ) + exp [ i 4 π ξ D ( x Δ 2 ) ] × Cyl ( 1 D ( x + Δ 2 ) 2 + y 2 )
I ( x , y ) = ( π D 2 4 λ f ) 2 [ Somb 2 ( D λ f r ) + Somb 2 ( D λ f ( x - 2 ξ D ) 2 + y 2 ) + 2 Somb ( D λ f r ) Somb ( D λ f ( x 2 ξ D ) 2 + y 2 ) × cos ( 2 π Δ ( x λ f ξ D ) ) ] .
W tilt = ( 1 / λ ) ( D / 2 ) ( Δ y / f ) ,
A ( x , y ) = Cyl ( 1 D [ ( x Δ 2 ) 2 + y 2 ] 1 / 2 ) +  exp { i 2 π β 4 D 2 [ ( x Δ 2 ) 2 + y 2 ] } ×  Cyl ( 1 D [ ( x + Δ 2 ) 2 + y 2 ] 1 / 2 ) .
δ z / λ = 8 ( f - number ) 2 W 020 ,

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