Abstract

We test the statistical properties of static, atmospherelike wave fronts in glass that allow repeatable testing of astronomical adaptive optics instrumentation. The technology is mask-structured ion exchange (MSI) in glass and has significant advantages over other transmissive technologies. The screens are easy to clean, are insensitive to ambient temperature changes, and have high optical-to-near-infrared transmission. However, the effective coherence length (r 0) on each of the fabricated screens is systematically too large or, equivalently, the fabricated aberrations are too weak. Despite this strong caveat, the screens appear to be quite useful: Long-exposure point-spread functions have realistic shapes, and power spectrum indices closely match those of the computer-generated wave fronts. Most significant, stacking screens with similar r 0 values reduced r 0 by the amount predicted by turbulence theory. The refractivity of MSI screens remains unmeasured. Finally, we present our design of an optical system that emulates the key characteristics of the Very Large Telescope, made to contain glass phase screens and to mimic an array of stars for multiconjugate adaptive optics system testing.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. In the present paper a pixel is defined as the smallest area with a single phase value.
  26. The sampling of r0 on the upper-altitude screen was originally chosen with scintillation tests in mind and to have a convenient round number of pixels on each axis. For the present paper the pertinent point is that r0 is not undersampled on either screen.
  27. J. Kolb, European Southern Observatory Garching bei München, Germany (personal communication, 2004).
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  29. For comparison, we note that, because of differences in dry air at a given temperature in the same wavelength range, expected changes are very small (of the order of 1 × 10-6), with weak dependence on pressure.
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    [CrossRef]
  31. Taken as 100% × [n(0.55 μm) - n(0.8 μm)]/[n(0.55 μm) - 1.0].
  32. Taken as 100% × [FWHM(0.633 μm) - FWHM(0.831 μm)]/FWHM(0.633 μm).
  33. R. Conan, “MAPS for MAD,” available from the author, European Southern Observatory, Garching bei München, Germany (personal communication, 2001).
  34. W. Xu, W. Seifert, “Optical glasses with high IR transmission,” in Specialized Optical Developments in Astronomy, E. Atad-Ettedgui, S. D’Odorico, eds., Proc. SPIE4842, 402–408 (2002).
    [CrossRef]

2002 (1)

A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
[CrossRef]

2001 (1)

2000 (3)

1998 (2)

M. A. A. Neil, M. J. Booth, T. Wilson, “Dynamic wave-front generation for the testing and optimization of optical systems,” Appl. Opt. 23, 1849–1851 (1998).

D. J. Cho, S. T. Thurman, J. T. Donner, G. M. Morris, “Characteristics of a 128 × 128 liquid-crystal spatial light modulator for wave-front generation,” Opt. Lett. 23, 969–971 (1998).
[CrossRef]

1997 (3)

1996 (1)

1995 (1)

1994 (1)

1993 (1)

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

1992 (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolgomorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

1985 (1)

R. Foy, A. Laberie, “Feasibility of adaptive optics with a laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

1977 (1)

J. W. Hardy, J. E. Lefebvre, C. L. Loliopoulis, “Real-time atmospheric compensation,” J. Opt. Soc. Am. 67, 460–369 (1977).
[CrossRef]

1976 (1)

1975 (1)

1965 (1)

Agabi, A.

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

Angel, J. R. P.

Bähr, J.

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Index-distributed planar microlenses for three dimensional micro-optics fabricated by silver-sodium ion exchange in BGG 335 substrates,” Appl. Opt. 33, 5919–5924 (1994).
[CrossRef] [PubMed]

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

Bell, K.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Booth, M. J.

M. A. A. Neil, M. J. Booth, T. Wilson, “Dynamic wave-front generation for the testing and optimization of optical systems,” Appl. Opt. 23, 1849–1851 (1998).

Borgnino, J.

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

A. Ziad, R. Conan, A. Tokovinen, F. Martin, J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5425 (2000).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Brenner, K.-H.

Buscher, D. F.

Butler, D. J.

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

Champagne, F. H.

Cho, D. J.

Clark, P.

Conan, R.

A. Ziad, R. Conan, A. Tokovinen, F. Martin, J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5425 (2000).
[CrossRef]

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

R. Conan, “MAPS for MAD,” available from the author, European Southern Observatory, Garching bei München, Germany (personal communication, 2001).

Crampton, D.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Dainty, J. C.

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolgomorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Donner, J. T.

Dreyer, G. F.

Dunlop, C. N.

Fitzsimmons, J.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Foy, R.

R. Foy, A. Laberie, “Feasibility of adaptive optics with a laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Fried, D. L.

Friehe, C. A.

Fuchs, A.

Gibson, C. H.

Glindemann, A.

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolgomorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Hardy, J. W.

J. W. Hardy, J. E. Lefebvre, C. L. Loliopoulis, “Real-time atmospheric compensation,” J. Opt. Soc. Am. 67, 460–369 (1977).
[CrossRef]

Herriot, G.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Hippler, S.

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

Jolissaint, L.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Kasper, M.

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

Kelly, T.-L.

Kolb, J.

J. Kolb, European Southern Observatory Garching bei München, Germany (personal communication, 2004).

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynold’s numbers,” in Turbulence, Classic Papers on Statistical Theory, S. K. Fredlander, L. Topper, eds. (Wiley-Interscience, New York, 1961), pp. 151–155.

La Rue, J. C.

Laberie, A.

R. Foy, A. Laberie, “Feasibility of adaptive optics with a laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Lane, R. G.

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolgomorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Lee, B.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Lefebvre, J. E.

J. W. Hardy, J. E. Lefebvre, C. L. Loliopoulis, “Real-time atmospheric compensation,” J. Opt. Soc. Am. 67, 460–369 (1977).
[CrossRef]

Loliopoulis, C. L.

J. W. Hardy, J. E. Lefebvre, C. L. Loliopoulis, “Real-time atmospheric compensation,” J. Opt. Soc. Am. 67, 460–369 (1977).
[CrossRef]

Love, G. D.

Marchetti, E.

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

Martin, F.

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

A. Ziad, R. Conan, A. Tokovinen, F. Martin, J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5425 (2000).
[CrossRef]

Masciadri, E.

Miller, J. J.

R. G. Paxman, B. J. Thelen, J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, R. G. Paxman, eds., Proc. SPIE3763, 2–10 (1999).
[CrossRef]

Morris, G. M.

Motera, D.

Myers, R. M.

Neil, M. A. A.

M. A. A. Neil, M. J. Booth, T. Wilson, “Dynamic wave-front generation for the testing and optimization of optical systems,” Appl. Opt. 23, 1849–1851 (1998).

Noll, R. J.

Paxman, R. G.

R. G. Paxman, B. J. Thelen, J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, R. G. Paxman, eds., Proc. SPIE3763, 2–10 (1999).
[CrossRef]

Rhoadarmer, T. A.

Rhodarmer, T. A.

Richardson, H.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.
[CrossRef]

Roggemann, M. C.

Saarinen, J.

Salmio, R.-P.

Sarazin, M.

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

Seifert, W.

W. Xu, W. Seifert, “Optical glasses with high IR transmission,” in Specialized Optical Developments in Astronomy, E. Atad-Ettedgui, S. D’Odorico, eds., Proc. SPIE4842, 402–408 (2002).
[CrossRef]

Sharf, I.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Sharples, R. M.

Sinzinger, S.

Spick, T.

Tallon, M.

Tervonen, A.

Testorf, M.

Thelen, B. J.

R. G. Paxman, B. J. Thelen, J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, R. G. Paxman, eds., Proc. SPIE3763, 2–10 (1999).
[CrossRef]

Thurman, S. T.

Tokovinen, A.

Tokovinin, A.

A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
[CrossRef]

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

Trinquet, H.

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

Turunen, J.

van der Kamp, D.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Vernan, J. P.

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, J. P. Vernan, “Design of the dual-conjugate adaptive optics test-bed,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds. ESO Conference and Workshop Proceedings58, 383–389 (2001).

Vernin, J.

Vernin, J. P.

Welsh, B. M.

Wilson, T.

M. A. A. Neil, M. J. Booth, T. Wilson, “Dynamic wave-front generation for the testing and optimization of optical systems,” Appl. Opt. 23, 1849–1851 (1998).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Xu, W.

W. Xu, W. Seifert, “Optical glasses with high IR transmission,” in Specialized Optical Developments in Astronomy, E. Atad-Ettedgui, S. D’Odorico, eds., Proc. SPIE4842, 402–408 (2002).
[CrossRef]

D. J. Butler, E. Marchetti, J. Bähr, W. Xu, S. Hippler, M. Kasper, R. Conan, “Phase screens for astronomical multi-conjugate adaptive optics: application to MAPS,” in Adaptive Optics Systems and Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 623–634 (2002).
[CrossRef]

Zadrozny, A.

Ziad, A.

A. Ziad, R. Conan, A. Tokovinen, F. Martin, J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5425 (2000).
[CrossRef]

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

Am. Astron. Soc. (1)

F. Martin, R. Conan, A. Tokovinin, A. Ziad, H. Trinquet, J. Borgnino, A. Agabi, M. Sarazin, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Am. Astron. Soc. 144, 39–44 (2000).

Appl. Opt. (9)

A. Ziad, R. Conan, A. Tokovinen, F. Martin, J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5425 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, T. Wilson, “Dynamic wave-front generation for the testing and optimization of optical systems,” Appl. Opt. 23, 1849–1851 (1998).

A. Fuchs, J. P. Vernin, M. Tallon, “Laboratory simulation of a turbulent layer: optical and in situ characterisation,” Appl. Opt. 35, 1751–1755 (1996).
[CrossRef] [PubMed]

E. Masciadri, J. Vernin, “Optical technique for inner-scale measurement: possible astronomical applications,” Appl. Opt. 36, 1320–1327 (1997).
[CrossRef] [PubMed]

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For comparison, we note that, because of differences in dry air at a given temperature in the same wavelength range, expected changes are very small (of the order of 1 × 10-6), with weak dependence on pressure.

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Taken as 100% × [n(0.55 μm) - n(0.8 μm)]/[n(0.55 μm) - 1.0].

Taken as 100% × [FWHM(0.633 μm) - FWHM(0.831 μm)]/FWHM(0.633 μm).

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In the present paper a pixel is defined as the smallest area with a single phase value.

The sampling of r0 on the upper-altitude screen was originally chosen with scintillation tests in mind and to have a convenient round number of pixels on each axis. For the present paper the pertinent point is that r0 is not undersampled on either screen.

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Figures (9)

Fig. 1
Fig. 1

Inverted gray-scale image of a 0.7 mm × 0.53 mm section of an MSI mask with 1.8-μm-diameter apertures. Because the aperture density is correlated with phase shift, the pattern corresponds to a phase-shift step (left-hand side) and a steady decrease to smaller phase-shift values (i.e., decreasing aperture density) toward the right-hand side.

Fig. 2
Fig. 2

Measured power spectra of phase fluctuations for screens 1 and 2 at two different wavelengths are given as examples (top), along with spectra for the computer-generated phase screens (bottom). For the sake of clarity, the linear fit is excluded for the fabricated screens. For further explanation, see Sections 5 and 8.

Fig. 3
Fig. 3

Image of the annular computer-generated phase wave front (top) used for screen 1 (left-hand side) and screen 2 (right-hand side) and pictures of the fabricated screens (bottom). See Table 1 for further information.

Fig. 4
Fig. 4

Transmission of pure HOYA SLW glass (solid curve) and the MSI-processed glass screens 1, 3, and 4 (dashed curve) and screen 2 (dotted curve), showing surface reflection losses of ∼8%. The uncertainty in individual curves is ∼2%. Glass thickness was approximately 1.6 mm. See Section 6 for further details.

Fig. 5
Fig. 5

Long-exposure point-spread function images for screen 1 (top), screen 2 (bottom) at 0.633 μm (left-hand side) and 0.831 μm (right-hand side). The field of view is the same in each image. The relative sizes of the left and right hand-side panels are consistent with the change in wavelength. It can be seen that each screen produces its own characteristic PSF (speckle) structure.

Fig. 6
Fig. 6

PSF FWHM plotted as a function of the aperture size (for each screen) at 0.633 μm (left-hand side) and 0.831 μm (right-hand side) as an example.

Fig. 7
Fig. 7

Long-exposure OTFs and long-exposure radial profiles for screen 1 (top four) and screen 2 (bottom four) at 0.633 μm (right-hand side) and 0.831 μm (left-hand side) are given as examples. The truncation of the PSF wings for screen 2 is caused by the CCD edges. r 0 was determined by matching the optical transfer curves at the 1/e point.

Fig. 8
Fig. 8

Refractive index of HOYA SLW glass plotted as a function of wavelength, together with the curves for three arbitrary optical glasses for comparison.

Fig. 9
Fig. 9

Three-dimensional layout of the turbulence generator, including three phase screens and plates. The pupil mask is placed ∼0.7 mm from the ground-layer phase screen. The darkly shaded lenses are BaF2, and the others are N-SF6. The total length, from input to output focus, is 0.78 m. Each glass phase screen has a diameter of 10 cm.

Tables (4)

Tables Icon

Table 1 Geometrical Size and P–V Phase Shift for Each Computer-Generated (CG) Phase Screena

Tables Icon

Table 2 Size of r0 on Each Fabricated and Computer-Generated (CG) Phase Screen as Judged by Different Tests

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Table 3 Power Spectrum Slopes for Fabricated and Computer-Generated (CG) Screens

Tables Icon

Table 4 Ratio of r0 (0.633 μm) to r0 (0.831 μm) for Computer-Generated (CG) and Fabricated Screensa

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

r0=0.98 λ/FWHM,
Φk=0.023r0-5/3k-11/3,
Dϕ,hx=ϕhx-ϕhx+x2,
OTFhx=exp-0.5Dϕ,hx.
OTFLE,hν=exp-3.44λFνr05/3,
r0,eff=r0,a-5/3+r0,b-5/3-3/5.
Footprint size=d+2×dh×tan Θ,

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