Abstract

Uncoated corner cube retroreflectors (CCRs) operating via total internal reflection (TIR) are less susceptible to internal heating than their metal-coated analogs, lacking an absorber on the rear surface. Even so, environments that induce differential heating within the CCR will result in thermal lensing of the incident wavefront, introducing aberrations that will generally reduce the central irradiance of the polarization-sensitive far-field diffraction pattern (FFDP). In this paper, we characterize the sensitivity of TIR CCRs to axial and radial thermal gradients. We present simulated FFDPs for key input polarizations and incidence angles and provide a generalized analytic model that approximates the behavior of the central irradiance as temperature differences are introduced.

© 2012 Optical Society of America

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  1. T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
    [CrossRef]
  2. A. G. Emslie and P. F. Strong, “Optical distortion caused by a vertical temperature gradient in a retro-reflector,” Apollo Laser Ranging Retro-Reflector Experiment, SO78, final report (1971), pp. 272–286, http://hdl.handle.net/2060/19710011991.
  3. J. E. Faller, “The Apollo retroreflector arrays and a new multi-lensed receiver telescope,” in Space Research XII (Akademie-Verlag, 1972), pp. 235–246.
  4. J. L. Zurasky, “Cube corner retroreflector test and analysis,” Appl. Opt. 15, 445–452 (1976).
    [CrossRef]
  5. D. G. Currie, S. Dell’Agnello, and G. O. Delle Monache, “A lunar laser ranging retroreflector array for the 21st century,” Acta Astronaut. 68, 667–680 (2011).
    [CrossRef]
  6. S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
    [CrossRef]
  7. T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
    [CrossRef]
  8. T. W. Murphy and S. D. Goodrow, “Polarization and far-field diffraction patterns of total internal reflection corner cubes,” Appl. Opt., doc. id 175366 (to be published).
  9. Haraeus Qurzglas, “Quartz glass for optics data and properties,” May2011, http://optics.heraeus-quarzglas.com .
  10. http://physics.ucsd.edu/tmurphy/papers/ccr-sim/ccr-sim.html .

2011 (2)

D. G. Currie, S. Dell’Agnello, and G. O. Delle Monache, “A lunar laser ranging retroreflector array for the 21st century,” Acta Astronaut. 68, 667–680 (2011).
[CrossRef]

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

2010 (1)

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

2008 (1)

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

1976 (1)

Adelberger, E. G.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Alley, C. O.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Arnold, D. A.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Battat, J. B. R.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Berardi, S.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Bianco, G.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Boni, A.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Cantone, C.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Carey, L. N.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Currie, D. G.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

D. G. Currie, S. Dell’Agnello, and G. O. Delle Monache, “A lunar laser ranging retroreflector array for the 21st century,” Acta Astronaut. 68, 667–680 (2011).
[CrossRef]

Dell’Agnello, S.

D. G. Currie, S. Dell’Agnello, and G. O. Delle Monache, “A lunar laser ranging retroreflector array for the 21st century,” Acta Astronaut. 68, 667–680 (2011).
[CrossRef]

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Delle Monache, G. O.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

D. G. Currie, S. Dell’Agnello, and G. O. Delle Monache, “A lunar laser ranging retroreflector array for the 21st century,” Acta Astronaut. 68, 667–680 (2011).
[CrossRef]

Emslie, A. G.

A. G. Emslie and P. F. Strong, “Optical distortion caused by a vertical temperature gradient in a retro-reflector,” Apollo Laser Ranging Retro-Reflector Experiment, SO78, final report (1971), pp. 272–286, http://hdl.handle.net/2060/19710011991.

Faller, J. E.

J. E. Faller, “The Apollo retroreflector arrays and a new multi-lensed receiver telescope,” in Space Research XII (Akademie-Verlag, 1972), pp. 235–246.

Garattini, M.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Goodrow, S. D.

T. W. Murphy and S. D. Goodrow, “Polarization and far-field diffraction patterns of total internal reflection corner cubes,” Appl. Opt., doc. id 175366 (to be published).

Hoyle, C. D.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Intaglietta, N.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

LeBlanc, P.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Lops, C.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Luceri, V.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Maiello, M.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Martini, M.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

McGarry, J. F.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

McMillan, R. J.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

Michelsen, E. L.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Murphy, T. W.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

T. W. Murphy and S. D. Goodrow, “Polarization and far-field diffraction patterns of total internal reflection corner cubes,” Appl. Opt., doc. id 175366 (to be published).

Nordtvedt, K.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Orin, A. E.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Pearlman, M. R.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Porcelli, L.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Samad, R. L.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

Sciarretta, C.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Strasburg, J. D.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Strong, P. F.

A. G. Emslie and P. F. Strong, “Optical distortion caused by a vertical temperature gradient in a retro-reflector,” Apollo Laser Ranging Retro-Reflector Experiment, SO78, final report (1971), pp. 272–286, http://hdl.handle.net/2060/19710011991.

Stubbs, C. W.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Swanson, H. E.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Tauraso, R.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Vittori, R.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Williams, E.

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Zagwodzki, T. W.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Zerbini, S.

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Zurasky, J. L.

Acta Astronaut. (1)

D. G. Currie, S. Dell’Agnello, and G. O. Delle Monache, “A lunar laser ranging retroreflector array for the 21st century,” Acta Astronaut. 68, 667–680 (2011).
[CrossRef]

Adv. Space Res. (1)

S. Dell’Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori, C. Cantone, M. Garattini, A. Boni, M. Martini, C. Lops, N. Intaglietta, R. Tauraso, D. A. Arnold, M. R. Pearlman, G. Bianco, S. Zerbini, M. Maiello, S. Berardi, L. Porcelli, C. O. Alley, J. F. McGarry, C. Sciarretta, V. Luceri, and T. W. Zagwodzki, “Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS,” Adv. Space Res. 47, 822–842 (2011).
[CrossRef]

Appl. Opt. (1)

Icarus (1)

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, C. D. Hoyle, R. J. McMillan, E. L. Michelsen, R. L. Samad, C. W. Stubbs, and H. E. Swanson, “Long-term degradation of optical devices on the Moon,” Icarus 208, 31–35 (2010).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

T. W. Murphy, E. G. Adelberger, J. B. R. Battat, L. N. Carey, C. D. Hoyle, P. LeBlanc, E. L. Michelsen, K. Nordtvedt, A. E. Orin, J. D. Strasburg, C. W. Stubbs, H. E. Swanson, and E. Williams, “The apache point observatory lunar laser-ranging operation: instrument description and first detections,” Publ. Astron. Soc. Pac. 120, 20–37 (2008).
[CrossRef]

Other (5)

T. W. Murphy and S. D. Goodrow, “Polarization and far-field diffraction patterns of total internal reflection corner cubes,” Appl. Opt., doc. id 175366 (to be published).

Haraeus Qurzglas, “Quartz glass for optics data and properties,” May2011, http://optics.heraeus-quarzglas.com .

http://physics.ucsd.edu/tmurphy/papers/ccr-sim/ccr-sim.html .

A. G. Emslie and P. F. Strong, “Optical distortion caused by a vertical temperature gradient in a retro-reflector,” Apollo Laser Ranging Retro-Reflector Experiment, SO78, final report (1971), pp. 272–286, http://hdl.handle.net/2060/19710011991.

J. E. Faller, “The Apollo retroreflector arrays and a new multi-lensed receiver telescope,” in Space Research XII (Akademie-Verlag, 1972), pp. 235–246.

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Figures (9)

Fig. 1.
Fig. 1.

Three-dimensional representations of wavefronts produced by a CCR subject to a thermal gradient at normal incidence. At left is the perfect reflecting (metal-coated) case for an axial thermal gradient, resulting in a perfectly spherical wavefront. At center is the perfect reflector afflicted with a radial thermal gradient. At right is an example TIR case, depicting the combined effects of the TIR phase shifts and the perturbations from an axial thermal gradient. If the wavefront travels upward, all panels correspond to the corner cube being cooler on the front surface or on the periphery, although the results of this paper are insensitive to the sign of the thermal gradient.

Fig. 2.
Fig. 2.

FFDPs produced by a TIR CCR with an axial thermal gradient. Right-handed circular input polarization is at left, followed by horizontal and vertical linear input polarizations. In each grid, the incidence angle increases in 5° steps from left to right. Rows correspond to various front-to-vertex temperature differences, increasing in 1.0 K steps. Each frame is 50λ/7D radians across. Irradiance is normalized to the normal incidence isothermal frame in the top left. All results herein correspond to the behavior of fused silica at a wavelength of 532 nm.

Fig. 3.
Fig. 3.

FFDPs produced by a TIR CCR with a radial thermal gradient. Panels follow the conventions of Fig. 2 with the exception of the center-to-edge temperature difference increasing in steps of 0.5 K.

Fig. 4.
Fig. 4.

Central irradiance of the FFDP as a function of axial temperature difference. The solid curve corresponds to a CCR employing perfectly reflecting (metalized) rear surfaces. For TIR, all rotations of linear input polarization fall within the gray envelope, and the dotted curve corresponds to circular input polarization of either handedness. Incidence angle increases in 5° increments from left to right, and irradiance is normalized to the isothermal case in each panel. At normal incidence, the curves do not deviate from each other.

Fig. 5.
Fig. 5.

Central irradiance of the FFDP as a function of radial temperature difference. Panels follow the conventions of Fig. 4. At normal incidence, the curves do not deviate from each other.

Fig. 6.
Fig. 6.

Central irradiance of the FFDP of a TIR CCR subject to both axial and radial thermal gradients, at normal incidence. As the axial temperature difference increases, the radial temperature difference follows proportionally. Irradiance is normalized to the isothermal case.

Fig. 7.
Fig. 7.

Irradiance profiles of the central lobe of the FFDPs of TIR CCRs subject to thermal gradients at normal incidence. Temperature differences correspond to those required to reduce the central irradiance to half that of the isothermal case. The perfect reflector (metal-coated CCR) is at left, followed by TIR cases given right-handed circular and linear input polarizations. Envelopes encompass maximum variability in horizontal and vertical profiles, and for all rotations of the input polarization in the linear case. The isothermal case in the left panel corresponds to the Airy function.

Fig. 8.
Fig. 8.

Comparison of the central irradiance of simulated FFDPs (points) and the prescribed analytic models (curves), with axial thermal gradients at left and radial thermal gradients at right, for normal incidence. The axial wavefront is modeled as a paraboloid and the radial wavefront is modeled as a cone. Irradiance is normalized to the isothermal case.

Fig. 9.
Fig. 9.

Profiles of the radial thermal gradient phase perturbations and models. The gray envelope encompasses the variability of the wavefront perturbations. The solid line corresponds to the cone whose phase offset is the average of the extrema at the perimeter, and the dashed line represents the cone which equally overestimates and underestimates the area-weighted wavefront.

Equations (14)

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λ¯=λ0n0+βδT¯,
ϕ=2πlλ¯=2πl(1+αδT¯)(n0+βδT¯)λ0.
ϕ=2πlλ0(n0+ηδT¯).
δT¯=ΔThhz¯+ΔTRRr¯.
Δϕ=2πlηΔδT¯λ0.
I(0,0)=|apertureS(r,θ)exp[iϕ(r,θ)]rdrdθ|2.
I(0,0)=|02πdθ0RrdrSnexp(iϕn)exp[iϕΔT(r,θ)]|2.
I(0,0)=|n=16{Snexp(iϕn)π3(n1)π3ndθ0Rrdrexp[iϕΔT(r,θ)]}|2.
I(0,0)=|n=16{Snexp(iϕn)}0π3dθ0Rrdrexp[iϕΔT(r,θ)]|2.
ITIR(0,0)=9.505|0π/3dθ0Rrdrexp[iϕΔT(r,θ)]|2.
ITIR(0,0)=0.528π2R41cos(ϕR)ϕR2.
ITIR(0,0)=1.056π2R4ϕR22cos(ϕR)2sin(ϕR)+2ϕR4.
ϕR=2πηΔThRλ0.
ϕR=3.737πηΔTRRλ0.

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