Abstract

We present a design methodology for volume hologram filters (VHFs) with telephoto objectives to improve contrast of solar–illuminated artificial satellites observed with a ground–based optical telescope and camera system operating in daytime. VHFs provide the ability to selectively suppress incoming light based on the range to the source, and are used to suppress the daylight background noise since signal (satellite) and noise (daylight scatterers) are located at different altitudes. We derive the overall signal–to–noise ratio (SNR) enhancement as the system metric, and balance main design parameters over two key performance considerations – daylight attenuation and spectral bandwidth – to optimize the functioning of VHFs. Overall SNR enhancement of 7.5 has been achieved. Usage of multi–pixel cameras can potentially further refine this system.

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  1. J. Hughes, “Sky brightness as a function of altitude,” Appl. Opt.3, 1135–1138 (1964).
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  2. R. Anthony, “Observation of non–Rayleigh scattering in the spectrum of the day sky in the region 0.56 to 2.2 microns,” J. Meteor.10, 60–63 (1953).
    [CrossRef]
  3. D. Psaltis, “Coherent optical information systems,” Science298, 1359 (2002).
    [CrossRef] [PubMed]
  4. G. Barbastathis and D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE87, 2098–2120 (1999).
    [CrossRef]
  5. H.-Y. S. Li and D. Psaltis, “Three–dimensional holographic disks,” Appl. Opt.33, 3764–3774 (1994).
    [CrossRef] [PubMed]
  6. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science265, 749–752 (1994).
    [CrossRef] [PubMed]
  7. Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser–induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial–spectral imaging system,” Opt. Lett.33, 2098–2100 (2008).
    [CrossRef] [PubMed]
  8. A. Sinha, W. Sun, T. Shih, and G. Barbastathis, “Volume holographic imaging in transmission geometry,” Appl. Opt.43, 1533–1551 (2004).
    [CrossRef] [PubMed]
  9. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1999).
  10. J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.
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    [CrossRef]
  12. A. Berk, L. S. Bernstein, and D.C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7”, (Spectral Sciences Inc., Burlington MA, 1989)
  13. J. M. Russo and R. K. Kostuk, “Temperature dependence properties of holographic gratings in phenanthrenquinone doped poly(methyl methacrylate) photopolymers,” Appl. Opt.46, 7494–7499 (2007).
    [CrossRef] [PubMed]
  14. Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).
  15. Y. Luo, P. J. Gelsinger, J. K. Barton, G. Barbastathis, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ–PMMA for spectral–spatial imaging filters,” Opt. Lett.33, 566–568 (2008).
    [CrossRef] [PubMed]

2011 (1)

Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).

2008 (2)

2007 (1)

2004 (1)

2002 (1)

D. Psaltis, “Coherent optical information systems,” Science298, 1359 (2002).
[CrossRef] [PubMed]

2000 (1)

G. Barbastathis and D. Psaltis, “Volume holographic multiplexing methods,” Holographic data storage, Springer Series in Optical Sciences76, 21–62 (2000).
[CrossRef]

1999 (1)

G. Barbastathis and D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE87, 2098–2120 (1999).
[CrossRef]

1994 (2)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science265, 749–752 (1994).
[CrossRef] [PubMed]

H.-Y. S. Li and D. Psaltis, “Three–dimensional holographic disks,” Appl. Opt.33, 3764–3774 (1994).
[CrossRef] [PubMed]

1964 (1)

1953 (1)

R. Anthony, “Observation of non–Rayleigh scattering in the spectrum of the day sky in the region 0.56 to 2.2 microns,” J. Meteor.10, 60–63 (1953).
[CrossRef]

Anthony, R.

R. Anthony, “Observation of non–Rayleigh scattering in the spectrum of the day sky in the region 0.56 to 2.2 microns,” J. Meteor.10, 60–63 (1953).
[CrossRef]

Barbastathis, G.

Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).

Y. Luo, P. J. Gelsinger, J. K. Barton, G. Barbastathis, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ–PMMA for spectral–spatial imaging filters,” Opt. Lett.33, 566–568 (2008).
[CrossRef] [PubMed]

Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser–induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial–spectral imaging system,” Opt. Lett.33, 2098–2100 (2008).
[CrossRef] [PubMed]

A. Sinha, W. Sun, T. Shih, and G. Barbastathis, “Volume holographic imaging in transmission geometry,” Appl. Opt.43, 1533–1551 (2004).
[CrossRef] [PubMed]

G. Barbastathis and D. Psaltis, “Volume holographic multiplexing methods,” Holographic data storage, Springer Series in Optical Sciences76, 21–62 (2000).
[CrossRef]

G. Barbastathis and D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE87, 2098–2120 (1999).
[CrossRef]

J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.

Barton, J. K.

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science265, 749–752 (1994).
[CrossRef] [PubMed]

Berk, A.

A. Berk, L. S. Bernstein, and D.C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7”, (Spectral Sciences Inc., Burlington MA, 1989)

Bernstein, L. S.

A. Berk, L. S. Bernstein, and D.C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7”, (Spectral Sciences Inc., Burlington MA, 1989)

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1999).

Brady, D. J.

G. Barbastathis and D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE87, 2098–2120 (1999).
[CrossRef]

Gelsinger, P. J.

Gelsinger-Austin, P. J.

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science265, 749–752 (1994).
[CrossRef] [PubMed]

Hesselink, L.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science265, 749–752 (1994).
[CrossRef] [PubMed]

Hughes, J.

Kamm, R. D.

Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).

Kostuk, R. K.

Li, H.-Y. S.

Luo, Y.

Oh, S. B.

Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).

J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.

Psaltis, D.

D. Psaltis, “Coherent optical information systems,” Science298, 1359 (2002).
[CrossRef] [PubMed]

G. Barbastathis and D. Psaltis, “Volume holographic multiplexing methods,” Holographic data storage, Springer Series in Optical Sciences76, 21–62 (2000).
[CrossRef]

H.-Y. S. Li and D. Psaltis, “Three–dimensional holographic disks,” Appl. Opt.33, 3764–3774 (1994).
[CrossRef] [PubMed]

Robertson, D.C.

A. Berk, L. S. Bernstein, and D.C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7”, (Spectral Sciences Inc., Burlington MA, 1989)

Russo, J. M.

Shih, T.

Sinha, A.

Stenner, M.

J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.

Sun, W.

Watson, J. M.

Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser–induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial–spectral imaging system,” Opt. Lett.33, 2098–2100 (2008).
[CrossRef] [PubMed]

J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.

Wissmann, P.

J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1999).

Zervantonakis, I. K.

Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).

Appl. Opt. (4)

Holographic data storage, Springer Series in Optical Sciences (1)

G. Barbastathis and D. Psaltis, “Volume holographic multiplexing methods,” Holographic data storage, Springer Series in Optical Sciences76, 21–62 (2000).
[CrossRef]

J. Biomed. Eng. (1)

Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Eng.16, 096015 (2011).

J. Meteor. (1)

R. Anthony, “Observation of non–Rayleigh scattering in the spectrum of the day sky in the region 0.56 to 2.2 microns,” J. Meteor.10, 60–63 (1953).
[CrossRef]

Opt. Lett. (2)

Proc. IEEE (1)

G. Barbastathis and D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE87, 2098–2120 (1999).
[CrossRef]

Science (2)

D. Psaltis, “Coherent optical information systems,” Science298, 1359 (2002).
[CrossRef] [PubMed]

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science265, 749–752 (1994).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1999).

J. M. Watson, P. Wissmann, S. B. Oh, M. Stenner, and G. Barbastathis, “Computational optimization of volume holographic imaging systems” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), Paper CMD3.

A. Berk, L. S. Bernstein, and D.C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN7”, (Spectral Sciences Inc., Burlington MA, 1989)

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Figures (7)

Fig. 1
Fig. 1

VHF design setup. As an example, this VHF is assumed to be used for Iridium satellite detection. Inset: a typical diffraction efficiency plot with respect to longitudinal defocus δ.

Fig. 2
Fig. 2

(top) VHF setup using a telephoto as objective, and (bottom) its effective configuration. PP1: first principal plane.

Fig. 3
Fig. 3

Diffraction efficiency of atmospheric scatterers (daylight) for our VHF setup, calculated using (a) analytical method and (b) MATLAB+ZEMAX method. The following parameters are used: λf = 632.8 nm, L = 1.0 mm, a = 1.0 m, θs = 5°, f1 = 2.5 m, f2 = −2.5 mm, FFL = 780 km, EFL = 780 m. Note that these parameters are generic and have not yet been optimized.

Fig. 4
Fig. 4

Multispectral performance of the VHF system for probe source at different altitudes, calculated using (a) analytical method and (b) MATLAB+ZEMAX method, for the VHF setup shown in Fig. 3.

Fig. 5
Fig. 5

(a) Radiance of daylight scattering at different altitudes, (b) spectral radiance of the sky background at ground level, and (c) solar spectral irradiance. All figures are calculated using MODTRAN 4 [12] assuming 23 km ground visibility and rural extinction haze model. The angle was 10 degrees east of zenith at 3:00 PM local time on June 21 at 45 degrees latitude (mid–latitude summer atmospheric model).

Fig. 6
Fig. 6

(a) Signal diffraction efficiency, (b) noise diffraction efficiency, and (c) total system SNR enhancement with respect to hologram thicknesses and recording angles.

Fig. 7
Fig. 7

(a) Diffraction efficiency for satellites at different altitudes, when the system is solely designed for detection of Iridium satellites. Diffraction efficiency (Id/I0) is normalized to the readout intensity when the hologram is probed by Iridium satellites. (b) Turbulence–free point spread functions at multi–pixel cameras for satellites at different orbit heights. From left to right, top to bottom: Sputnik-1 (215 km), International Space Station (340 km), Hubble Space Telescope (595 km), and Iridium (780 km). Color shading denotes the normalized intensity. Note that different axes are used for these four pattern plots.

Tables (1)

Tables Icon

Table 1 Requirements on design parameters for better system performance.

Equations (10)

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I d I 0 = 1 π 0 2 π d ϕ 0 1 d ρ ρ sinc 2 ( a L θ s δ n λ f f 2 ρ sin ϕ ) ,
Δ z FWHM = G λ f f 2 a L ,
r a = EFL FFL ,
Δ z FWHM = G λ f ( EFL ) 2 r L = G λ f f 2 a L EFL FFL .
I d I 0 = 1 π 0 2 π d ϕ 0 1 d ρ ρ sinc 2 ( L θ s n λ f [ ( μ 2 1 2 ) θ s ] ) ,
SNR ( λ ) = λ h c S 0 satellite ( λ ) N 0 daylight ( λ ) ,
SNR ( λ ) = λ h c η s ( λ ) S 0 satellite ( λ ) η n ( λ ) N 0 daylight ( λ ) .
η s = visible q satellite ( λ ) p sun ( λ ) d λ visible p sun ( λ ) d λ .
η n = 0 30 km q daylight ( z ) r daylight ( z ) d z 0 30 km r daylight ( z ) d z .
η n = 0 30 km visible q daylight ( λ , z ) p daylight ( λ ) d λ r daylight ( z ) d z 0 30 km visible p daylight ( λ ) d λ r daylight ( z ) d z .

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