Abstract

The orientation of remote objects can be easily measured optically and very accurately using optical technologies. In this paper, we address the accuracy of a roll angle estimation technique that is based on the estimation of the polarization of a retroreflected beam and is applied in a long-range measurement task. Over long transmission ranges, the optical power decreases significantly leading to severe SNR deterioration. As a result, the measurement accuracy decreases. In this study, the estimation is carried out using a maximum-likelihood estimator and its performance is evaluated using the analytical Cramer–Rao bound.

© 2013 Optical Society of America

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References

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  1. P. Besl, “Active, optical range imaging sensors,” Mach. Vision Appl. 1, 127–152 (1988).
    [CrossRef]
  2. J. Kahn and J. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
    [CrossRef]
  3. G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.
  4. I. Rahneberg, H. Büchner, and G. Jäger, “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).
    [CrossRef]
  5. Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44, 839–843 (2012).
    [CrossRef]
  6. E. Shi, J. Guo, Z. Jia, and Y. Huang, “Theoretic study on new method for roll angle measurement of machines,” in IEEE International Conference on Automation and Logistics (IEEE, 2008), pp. 2722–2726.
  7. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2001).
  8. W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
    [CrossRef]
  9. S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).
  10. S. Lambert and W. Casey, Laser Communications in Space (Artech House, 1995).
  11. B. Porat, Digital Processing of Random Signals: Theory and Methods (Prentice-Hall, 1994), Chap. 3.
  12. S. Kay, Fundamentals of Statistical Signal Processing, Volume II: Detection Theory (Prentice-Hall, 1998).
  13. S. Arnon, “Lunar optical wireless communication and navigation network for robotic and human exploration,” Proc. SPIE 8162, 816202 (2011).
    [CrossRef]

2012 (1)

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44, 839–843 (2012).
[CrossRef]

2011 (1)

S. Arnon, “Lunar optical wireless communication and navigation network for robotic and human exploration,” Proc. SPIE 8162, 816202 (2011).
[CrossRef]

2010 (1)

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

2009 (1)

I. Rahneberg, H. Büchner, and G. Jäger, “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).
[CrossRef]

1997 (1)

J. Kahn and J. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

1988 (1)

P. Besl, “Active, optical range imaging sensors,” Mach. Vision Appl. 1, 127–152 (1988).
[CrossRef]

Arnon, S.

S. Arnon, “Lunar optical wireless communication and navigation network for robotic and human exploration,” Proc. SPIE 8162, 816202 (2011).
[CrossRef]

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).

Barry, J.

J. Kahn and J. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).

Besl, P.

P. Besl, “Active, optical range imaging sensors,” Mach. Vision Appl. 1, 127–152 (1988).
[CrossRef]

Binari, S.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Büchner, H.

I. Rahneberg, H. Büchner, and G. Jäger, “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).
[CrossRef]

Burris, H. R.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Casey, W.

S. Lambert and W. Casey, Laser Communications in Space (Artech House, 1995).

Creamer, N.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Feng, Q.

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44, 839–843 (2012).
[CrossRef]

Ferraro, M. S.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Font, C.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Frawley, S.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Freeman, W. T.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Gilbreath, G.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Gilbreath, G. C.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Goetz, P.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Goetz, P. G.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Guo, J.

E. Shi, J. Guo, Z. Jia, and Y. Huang, “Theoretic study on new method for roll angle measurement of machines,” in IEEE International Conference on Automation and Logistics (IEEE, 2008), pp. 2722–2726.

Hacker, K.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2001).

Huang, Y.

E. Shi, J. Guo, Z. Jia, and Y. Huang, “Theoretic study on new method for roll angle measurement of machines,” in IEEE International Conference on Automation and Logistics (IEEE, 2008), pp. 2722–2726.

Jäger, G.

I. Rahneberg, H. Büchner, and G. Jäger, “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).
[CrossRef]

Jia, Z.

E. Shi, J. Guo, Z. Jia, and Y. Huang, “Theoretic study on new method for roll angle measurement of machines,” in IEEE International Conference on Automation and Logistics (IEEE, 2008), pp. 2722–2726.

Kahn, J.

J. Kahn and J. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Karagiannidis, G.

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing, Volume II: Detection Theory (Prentice-Hall, 1998).

Lambert, S.

S. Lambert and W. Casey, Laser Communications in Space (Artech House, 1995).

Mahon, R.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Meehan, T.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Moore, C. I.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Mozersky, S.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Murphy, J. L.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Oh, E.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Porat, B.

B. Porat, Digital Processing of Random Signals: Theory and Methods (Prentice-Hall, 1994), Chap. 3.

Rabinovich, W.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Rabinovich, W. S.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Rahneberg, I.

I. Rahneberg, H. Büchner, and G. Jäger, “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).
[CrossRef]

Reese, S.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Saint-Georges, E.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Schober, R.

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).

Sender, J.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Shi, E.

E. Shi, J. Guo, Z. Jia, and Y. Huang, “Theoretic study on new method for roll angle measurement of machines,” in IEEE International Conference on Automation and Logistics (IEEE, 2008), pp. 2722–2726.

Suite, M. R.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Thomas, L. M.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Uecke, S.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Uysal, M.

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).

Vasquez, J.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Vilcheck, M.

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

Xu, B.

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

Zhai, Y.

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44, 839–843 (2012).
[CrossRef]

Zhang, B.

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44, 839–843 (2012).
[CrossRef]

Mach. Vision Appl. (1)

P. Besl, “Active, optical range imaging sensors,” Mach. Vision Appl. 1, 127–152 (1988).
[CrossRef]

Opt. Laser Technol. (1)

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44, 839–843 (2012).
[CrossRef]

Proc. IEEE (1)

J. Kahn and J. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Proc. SPIE (3)

W. S. Rabinovich, C. I. Moore, H. R. Burris, J. L. Murphy, M. R. Suite, R. Mahon, M. S. Ferraro, P. G. Goetz, L. M. Thomas, C. Font, G. C. Gilbreath, B. Xu, S. Binari, K. Hacker, S. Reese, W. T. Freeman, S. Frawley, E. Saint-Georges, S. Uecke, and J. Sender, “Free space optical communications research at the U.S. Naval Research Laboratory,” Proc. SPIE 7587, 758702 (2010).
[CrossRef]

I. Rahneberg, H. Büchner, and G. Jäger, “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).
[CrossRef]

S. Arnon, “Lunar optical wireless communication and navigation network for robotic and human exploration,” Proc. SPIE 8162, 816202 (2011).
[CrossRef]

Other (7)

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).

S. Lambert and W. Casey, Laser Communications in Space (Artech House, 1995).

B. Porat, Digital Processing of Random Signals: Theory and Methods (Prentice-Hall, 1994), Chap. 3.

S. Kay, Fundamentals of Statistical Signal Processing, Volume II: Detection Theory (Prentice-Hall, 1998).

G. Gilbreath, N. Creamer, W. Rabinovich, T. Meehan, M. Vilcheck, J. Vasquez, R. Mahon, E. Oh, P. Goetz, and S. Mozersky, “Modulating retro-reflectors for space, tracking, acquisition, and ranging using multiple quantum-well technology,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), pp. 494–507.

E. Shi, J. Guo, Z. Jia, and Y. Huang, “Theoretic study on new method for roll angle measurement of machines,” in IEEE International Conference on Automation and Logistics (IEEE, 2008), pp. 2722–2726.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

Different DOF.

Fig. 2.
Fig. 2.

Roll angle measurement system overview. System parts are: laser source, half-wave plate (HWP), retroreflector (RR), polarizing beam splitter (PBS), and photodiodes (PDs) s and p.

Fig. 3.
Fig. 3.

Standard deviation of the proposed MLE, std(θ^ML), (measured in [mrad]), as function of θ is compared to the CRB for different SNR values. The edges are better than the CRB because of nonnegative signal restriction.

Fig. 4.
Fig. 4.

Bias of the MLE, θ^ML, as a function of θ for different SNR values. This figure accompanies the std versus CRB graph in Fig. 3.

Fig. 5.
Fig. 5.

Standard deviation of the MLE, std(θ^ML), for two different angle values compared to the CRB for two different SNR values. The smaller angle and higher SNR have the lowest std.

Fig. 6.
Fig. 6.

Bias of the MLE θ^ML, for two different angle values and two different SNR values. This figure accompanies the std versus CRB graph in Fig. 5.

Tables (1)

Tables Icon

Table 1. Parameters Used for Simulations

Equations (32)

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

Is=isigcos2(π/4+4θ)Ip=isigsin2(π/4+4θ),
isig=RPR,
PRPTGTLTLFSTatmGRRLRRLFSTatmGRLR,
GRR(πDRRλ)4S,
LFS=(λ4πD)2,
LRR=LRRLHWPLPBS,
s=Is+nsp=Ip+np,
σ2=σth2+σsh2+σDC2,
σ2σth2=(4KBTB)/RSh,
fs(s|θ,isig,σ2)N(isigcos2(4θ+π/4),σ2)fp(p|θ,isig,σ2)N(isigsin2(4θ+π/4),σ2).
fs,p(s,p|θ,isig,σ2)=i=1Nfs(si|)fp(pi|)=1(2πσ2)Nexp(12σ2i=1N(sμs)2+(pμp)2),
μs=isigcos2(4θ+π/4),μp=isigsin2(4θ+π/4).
L(θ,isig|s,p)=lnfs,p(s,p|θ,isig,σ2)
ϑ^ML=argmaxϑL(Jϑ|s,p),
Lϑ=0
i^sigML=s¯+p¯,
s¯=E[s],p¯=E[p]
θ^ML=18arcsin[p¯s¯p¯+s¯]
limNs¯=μs,limNp¯=μp
limNE[θ^ML]18arcsin[μpμsμp+μs]=θ
I(ϑ)=1σ2[μ(ϑ)ϑ]T[μ(ϑ)ϑ]
[μ(ϑ)ϑ]T=[cos2(4θ+π/4)sin2(4θ+π/4)4isigcos(8θ)4isigcos(8θ)],
I=1σ2[14(3cos(16θ))2isigsin(16θ)2isigsin(16θ)32isig2cos(8θ)].
I1=σ2N[2tan(8θ)4isigtan(8θ)4isig3cos(16θ)32isig2(cos(16θ)+1)].
CRB(θ^|θ,isig,N,σ2)=σ2isig2N3cos(16θ)32(cos(16θ)+1),
SNRisig2σ2
H0:{ns,np}H1:{s,p},
LRT=lnfs,p(s,p|θ^ML,i^sigML,σ2)fs,p(s,p|isig=0,σ2)=N2σ2(s¯2+p¯2)thr,
s¯={s¯s¯>0εs¯0,p¯={p¯p¯>0εp¯0
θ^ML=18arcsin[p¯s¯i^sig].
s=isigcos2(4θ+π/4)+nsp=κisigsin2(4θ+π/4)+np,
θ^ML=18arcsin[pκsp+κs]

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