Abstract

The Fresnel Interferometric Imager is a space-based astronomical telescope project yielding milli- arcsecond angular resolution and high contrast images with loose manufacturing constraints. This optical concept involves diffractive focusing and formation flying: a first “primary optics” space module holds a large binary Fresnel array, and a second “focal module” holds optical elements and focal instruments that allow for chromatic dispersion correction. We have designed a reduced-size Fresnel Interferometric Imager prototype and made optical tests in our laboratory in order to validate the concept for future space missions. The primary module of this prototype consists of a square, 8cm side, 23m focal length Fresnel array. The focal module is composed of a diaphragmed small telescope used as “field lens,” a small cophased diverging Fresnel zone lens that cancels the dispersion, and a detector. An additional module collimates the artificial targets of various shapes, sizes, and dynamic ranges to be imaged. We describe the experimental setup, different designs of the primary Fresnel array, and the cophased Fresnel zone lens that achieves rigorous chromatic correction. We give quantitative measurements of the diffraction limited performances and dynamic range on double sources. The tests have been performed in the visible domain, λ=400700nm. In addition, we present computer simulations of the prototype optics based on Fresnel propagation that corroborate the optical tests. This numerical tool has been used to simulate the large aperture Fresnel arrays that could be sent to space with diameters of 3 to 30m, foreseen to operate from Lyman α (121nm) to mid IR (25μm).

© 2009 Optical Society of America

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References

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  1. A. Baez, “A self-supporting metal Fresnel zone-plate to focus extreme ultra-violet and soft x-rays,” Nature 186, 958 (1960).
    [CrossRef]
  2. A. Baez, “Fresnel zone plate for optical image formation using extreme ultraviolet and soft X radiation,” J. Opt. Soc. Am. 51, 405-412 (1961).
    [CrossRef]
  3. Y. M. Chesnokov, “A space-based very high angular resolution telescope,” Space Bulletin 1(2), 18-21 (1993).
  4. Roderick A. Hyde, “Eyeglass. 1. Very large aperture diffractive telescopes,” Appl. Opt. 38, 4198-4212 (1999).
    [CrossRef]
  5. D. Massonnet, “Un nouveau type de télescope spatial-,” Brevet CNES-Ref. 03.13403 (2003).
  6. L. Koechlin, D. Serre, and P. Duchon, “High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection,” Astron. Astrophys. 443, 709-720(2005).
    [CrossRef]
  7. D. Faklis and G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592-598 (1989).
  8. L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
    [CrossRef]
  9. D. Serre, L. Koechlin, and P. Deba, “Fresnel interferometric arrays for space-based imaging: testbed results,” Proc. SPIE 6687, 66870I (2007).
    [CrossRef]
  10. P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201-L205 (2001).
    [CrossRef]
  11. O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379-387 (2003).
    [CrossRef]
  12. J. L. Soret, “Sur les phénomènes de diffraction produits par les réseaux circulaires,” Arch. Sci. Phys. Nat. 52, 320-337(1875).
  13. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
    [CrossRef] [PubMed]
  14. L. Schupmann, Die Medial-Fernrohre. Eine neue Konstruktion für grosse astronomische Instrumente (B. G. Teubner, 1899).
  15. D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462-2468 (1995).
    [CrossRef] [PubMed]
  16. G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605-608(1989).
  17. E. Hasman, N. Davidson, and A. A. Friesem, “Efficient multilevel phase holograms for CO2 lasers,” Opt. Lett. 16, 423-425 (1991).
    [CrossRef] [PubMed]
  18. U. Levy, D. Mendlovic, and E. Marom, “Efficiency analysis of diffractive lenses,” J. Opt. Soc. Am. A 18, 86-93 (2001).
    [CrossRef]

2009 (1)

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

2007 (1)

D. Serre, L. Koechlin, and P. Deba, “Fresnel interferometric arrays for space-based imaging: testbed results,” Proc. SPIE 6687, 66870I (2007).
[CrossRef]

2005 (1)

L. Koechlin, D. Serre, and P. Duchon, “High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection,” Astron. Astrophys. 443, 709-720(2005).
[CrossRef]

2003 (1)

O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379-387 (2003).
[CrossRef]

2001 (3)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

U. Levy, D. Mendlovic, and E. Marom, “Efficiency analysis of diffractive lenses,” J. Opt. Soc. Am. A 18, 86-93 (2001).
[CrossRef]

P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201-L205 (2001).
[CrossRef]

1999 (1)

1995 (1)

1993 (1)

Y. M. Chesnokov, “A space-based very high angular resolution telescope,” Space Bulletin 1(2), 18-21 (1993).

1991 (1)

1989 (2)

G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605-608(1989).

D. Faklis and G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592-598 (1989).

1961 (1)

1960 (1)

A. Baez, “A self-supporting metal Fresnel zone-plate to focus extreme ultra-violet and soft x-rays,” Nature 186, 958 (1960).
[CrossRef]

1875 (1)

J. L. Soret, “Sur les phénomènes de diffraction produits par les réseaux circulaires,” Arch. Sci. Phys. Nat. 52, 320-337(1875).

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Baez, A.

A. Baez, “Fresnel zone plate for optical image formation using extreme ultraviolet and soft X radiation,” J. Opt. Soc. Am. 51, 405-412 (1961).
[CrossRef]

A. Baez, “A self-supporting metal Fresnel zone-plate to focus extreme ultra-violet and soft x-rays,” Nature 186, 958 (1960).
[CrossRef]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Chesnokov, Y. M.

Y. M. Chesnokov, “A space-based very high angular resolution telescope,” Space Bulletin 1(2), 18-21 (1993).

Davidson, N.

Deba, P.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

D. Serre, L. Koechlin, and P. Deba, “Fresnel interferometric arrays for space-based imaging: testbed results,” Proc. SPIE 6687, 66870I (2007).
[CrossRef]

Désert, J.-M.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Duchon, P.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

L. Koechlin, D. Serre, and P. Duchon, “High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection,” Astron. Astrophys. 443, 709-720(2005).
[CrossRef]

Ehrenreich, D.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Faklis, D.

D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462-2468 (1995).
[CrossRef] [PubMed]

D. Faklis and G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592-598 (1989).

Ferlet, R.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Friesem, A. A.

Gomez de Castro, A. I.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Guyon, O.

O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379-387 (2003).
[CrossRef]

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Hasman, E.

Hebrard, G.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Hyde, Roderick A.

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Karovska, M.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Koechlin, L.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

D. Serre, L. Koechlin, and P. Deba, “Fresnel interferometric arrays for space-based imaging: testbed results,” Proc. SPIE 6687, 66870I (2007).
[CrossRef]

L. Koechlin, D. Serre, and P. Duchon, “High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection,” Astron. Astrophys. 443, 709-720(2005).
[CrossRef]

Lecavelier Des Etangs, A.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Levy, U.

Marom, E.

Massonnet, D.

D. Massonnet, “Un nouveau type de télescope spatial-,” Brevet CNES-Ref. 03.13403 (2003).

Mendlovic, D.

Morris, G. M.

D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462-2468 (1995).
[CrossRef] [PubMed]

D. Faklis and G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592-598 (1989).

Nisenson, P.

P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201-L205 (2001).
[CrossRef]

Papaliolios, C.

P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201-L205 (2001).
[CrossRef]

Peillon, C.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Pelló, R.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Schupmann, L

L. Schupmann, Die Medial-Fernrohre. Eine neue Konstruktion für grosse astronomische Instrumente (B. G. Teubner, 1899).

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Serre, D.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

D. Serre, L. Koechlin, and P. Deba, “Fresnel interferometric arrays for space-based imaging: testbed results,” Proc. SPIE 6687, 66870I (2007).
[CrossRef]

L. Koechlin, D. Serre, and P. Duchon, “High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection,” Astron. Astrophys. 443, 709-720(2005).
[CrossRef]

Sing, D.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Soret, J. L.

J. L. Soret, “Sur les phénomènes de diffraction produits par les réseaux circulaires,” Arch. Sci. Phys. Nat. 52, 320-337(1875).

Swanson, G. J.

G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605-608(1989).

Veldkamp, W. B.

G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605-608(1989).

Vidal-Madjar, A.

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

Appl. Opt. (2)

Arch. Sci. Phys. Nat. (1)

J. L. Soret, “Sur les phénomènes de diffraction produits par les réseaux circulaires,” Arch. Sci. Phys. Nat. 52, 320-337(1875).

Astron. Astrophys. (2)

O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379-387 (2003).
[CrossRef]

L. Koechlin, D. Serre, and P. Duchon, “High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection,” Astron. Astrophys. 443, 709-720(2005).
[CrossRef]

Astrophys. J. (1)

P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201-L205 (2001).
[CrossRef]

Exper. Astron. (1)

L. Koechlin, D. Serre, P. Deba, R. Pelló, C. Peillon, P. Duchon, A. I. Gomez de Castro, M. Karovska, J.-M. Désert, D. Ehrenreich, G. Hebrard, A. Lecavelier Des Etangs, R. Ferlet, D. Sing, and A. Vidal-Madjar, “The fresnel interferometric imager,” Exper. Astron. 23, 379-402(2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (2)

A. Baez, “A self-supporting metal Fresnel zone-plate to focus extreme ultra-violet and soft x-rays,” Nature 186, 958 (1960).
[CrossRef]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Opt. Eng. (2)

G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605-608(1989).

D. Faklis and G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592-598 (1989).

Opt. Lett. (1)

Proc. SPIE (1)

D. Serre, L. Koechlin, and P. Deba, “Fresnel interferometric arrays for space-based imaging: testbed results,” Proc. SPIE 6687, 66870I (2007).
[CrossRef]

Space Bulletin (1)

Y. M. Chesnokov, “A space-based very high angular resolution telescope,” Space Bulletin 1(2), 18-21 (1993).

Other (2)

D. Massonnet, “Un nouveau type de télescope spatial-,” Brevet CNES-Ref. 03.13403 (2003).

L. Schupmann, Die Medial-Fernrohre. Eine neue Konstruktion für grosse astronomische Instrumente (B. G. Teubner, 1899).

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Figures (13)

Fig. 1
Fig. 1

In this two-module configuration, a binary diffracting mask (Fresnel array), related to a Fresnel zone plate, is placed on plane (1) and is used at its first order of interference. From a source at infinity, different wavelengths (dashed and dotted lines) are focused at different distances. In the second module, field optics (2) form a pupil plane (3), where a diverging cophased Fresnel zone lens (FZL) is placed. Theoretically, the emerging beam is perfectly achromatic (Faklis and Morris 1989 [7]), but divergent. A lens (4) is placed to make it converge. The final achromatic image is formed onto plane (5).

Fig. 2
Fig. 2

Orthogonal Fresnel array, 8 cm side to side, 116 Fresnel zones in the diagonal direction (26680 subapertures) yielding a 23 m focal length at 600 nm , carved by a UV laser beam in a 80 μm thick stainless steel foil. The smallest patterns (located on the periphery of the array) are 140 μm squares. On the right part of the figure can be seen a zoom on these patterns, on the Autocad file generated to carve the array.

Fig. 3
Fig. 3

Left: Phase map as seen from the focus in a void element in the orthogonal development of a Fresnel array. Right: Phase map as seen from the focus in a void element in the multispider circular development of a Fresnel array. P x and P y are the x and y pseudoperiod of the local Fresnel zone.

Fig. 4
Fig. 4

Optimized Fresnel array. One can see the source collimator on the background, behind, and through the array. The size, number of Fresnel zones, and focal length are same as in Fig. 3, but a Soret pattern held with a multispider enhances transmission by a factor 1.6 and dynamic range by a factor 2 compared to the purely orthogonal design. On the right can be seen a zoom on the patterns closest to the periphery of the array (Autocad file generated), which can be compared to the orthogonal case in Fig. 3.

Fig. 5
Fig. 5

Focal module is composed of a Maksutov telescope used as a field lens, a cophased diverging Fresnel diffractive lens situated in the pupil plane, and an achromatic doublet next to that pupil plane. The Maksutov telescope is diaphragmed to a 3.1 cm diameter, resulting in Δ λ / λ = 0.4 for a nondiaphragmed 200 arc sec field of view [Eq. (12)]. The achromatic image plane can be sent either onto a CCD or an eyepiece for control. A small mask is placed at the focal plane of the “field telescope,” eliminating residual light from the 0 and 1 diffraction orders of the Fresnel array located 23 m upstream.

Fig. 6
Fig. 6

Optical element placed in A 2 (power P 2 ) will correct the chromatism induced by the Fresnel array placed in A 1 (power P 1 ), using an optical device characterized by its principal planes H o and H i (power P H o H i ).

Fig. 7
Fig. 7

Optical paths in a blazed diverging FZL illustrated for three zones. At the uncorrected focus of the Fresnel array, simply reimaged by the field optics, the wavefronts at different wavelengths converge on the optical axis at different positions A 0 , λ 1 , A 0 , λ 2 , etc. The diverging FZL, having the same number of zones as the Fresnel array, is placed in the pupil plane and is used at its order 1 . The “reverse” chromaticity of the FZL results in all the A 0 , λ becoming conjugate with a unique point E 0 , therefore achieving chromatic correction of the emerging beam. I and H are respectively the entrance and exit points of a wavefront sample into (out of) the Fresnel lens. C is the intersection of the emerging wavefront samples with a spherical surface centered on E 0 . Indices 0 are for on-axis points.

Fig. 8
Fig. 8

Left: Three-dimensional view of the five central zones of a diverging FZL. The vertical scale is highly exaggerated, as the depth of the slopes is 1.31 μm , whereas the radius of the central zone is 600 μm . The discretized number of levels cannot be seen at the scale of this print. Right: Photograph of the manufactured cophased diverging FZL; 16.054 mm in effective diameter, 116 zones.

Fig. 9
Fig. 9

Numerically simulated efficiency as a function of wavelength for a fused silica cophased FZL, optimized for λ = 600 nm . The three different curves are for lenses with a continuuous profile, with a profile sampled onto 32 levels (these two efficiencies not distinguishable at this scale), and a profile sampled onto 8 levels (top to bottom curves). Our lens (Fig. 8), discretized with 128 depth levels, has an efficiency not distinguishable, on the display scale, from that of a continuous profile lens. More than 90% efficiency is available through a Δ λ / λ = 0.3 bandpass.

Fig. 10
Fig. 10

Microscopic 72 arc sec , galaxy-shaped target, laser carved into a metal foil, is illuminated with a halogen source and collimated. It is then imaged by the Fresnel imager prototype. The cutting irregularities and metal bubbles that can be seen are real and not due to imaging. The faint horizontal and vertical lines are the two orthogonal diffraction spikes due to the Fresnel array.

Fig. 11
Fig. 11

Standard USAF test target is placed at the focal plane of the collimator, illuminated with a white LED and imaged by the Fresnel imager prototype. The 6 group number associated to the 4 element number results in a number of line pairs per mm corresponding to the diffraction limit of our prototype. This image is a raw exposure, simply dark-subtracted. As this target is an extended source and is convoluted with the spikes of the PSF, high dynamic range imaging cannot be achieved in this case. However, very high dynamic range is achievable for sparse fields.

Fig. 12
Fig. 12

Angular resolution measurements at four wavelengths: 550, 600, 650, and 700 nm . In each graph, the theoretical profile (dashed curve) is the convolution of a uniform disk source size ( 0.77 arc sec ) with a diffraction limited PSF. It is compared with the measured profile (solid curve) sampled from the interpolated measurements points (circles), which represent the brightness of the camera pixels. The prototype reaches limit by diffraction for all these wavelengths, confirming the efficiency of the chromatic correction and the blazed diverging Fresnel zone lens design. Scattered light near central peak can be attributed to air turbulence observed in the clean room.

Fig. 13
Fig. 13

PSF on the left has been obtained with our prototype, using a Luxeon LED with peak emission at 630 nm illuminating a monomode fiber. This image has simply been dark-subtracted. The PSF on the right is from our computer simulation, taking all the optical elements and the spectrum of the source into account. The computer simulation considers perfect optical elements, except the FZL for which the commissioned jigsaw profile is used, and does not model the air turbulence. The two images are highly saturated, with the same thresholds, in order to show the faint levels of the PSF. The dynamic range is slightly better in the theoretical case than in the measured one ( 1 × 10 6 in the square delimitation shown on the right figure, 2 × 10 6 on the corresponding one on the real measurement). The slight shadow at the bottom of the left image is due to the secondary mirror of the Maksutov telescope used as a field lens. This comparison validates the numerical simulation tools, which can be used to predict what can be expected with larger arrays.

Tables (1)

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Table 1 Comparison of Efficiencies at First Order ( λ blaze ) Computed with Eq. (15), and the Theoretical Limits Calculated in [17]

Equations (15)

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OPD ( x ) = x 2 + f 2 f .
T o ( x , y ) = h ( x ) g ( y ) + g ( x ) h ( y )
T c ( x , y ) = h ( x ) h ( y ) + g ( x ) g ( y ) .
[ T ] = [ T 1 , 1 T 1 , 2 T 2 , 1 T 2 , 2 ] = [ 1 0 P 2 1 ] [ 1 C 0 1 ] [ 1 0 P H o H i 1 ] [ 1 B 0 1 ] [ 1 0 P 1 1 ] .
T 1 , 1 = 1 C P H o H i ( B + C ) α λ + B C α λ P H o H i , T 2 , 2 = 1 B P H o H i ( B + C ) β λ + B C β λ P H o H i , T 1 , 2 = B + C P H o H i B C .
P = T 2 , 1 = P H o H i λ [ β + β P H o H i C α + α P H o H i B ] λ 2 α β ( B + C P H o H i B C ) .
B + C P H o H i B C = 0 ,
B C = P H o H i B 1 , C B = P H o H i C 1.
β α = B 2 C 2 .
P 1 = α λ = 8 N 1 λ m 1 D 1 2 , P 2 = β λ = 8 N 2 λ m 2 D 2 2 ,
B 2 C 2 = N 2 N 1 D 1 2 D 2 2 m 2 m 1 .
Δ λ λ = 2 × f ield   o ptics   diameter n 2 D 8 N D ,
Δ λ λ = 2 × f ield   o ptics   diameter n 1.22 D 8 N D ,
A 0 , λ I + k λ + n λ I H E 0 H = cs t λ ,
A 0 , λ I + k λ + n λ I H E 0 H = optical path .

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