Abstract

A detailed analysis of corner cube array (CCA) structure is carried out using the commercially available ray-tracing software ZEMAX. The retroreflective properties of CCA for short-range and long-range propagation are compared. An improved CCA structure with a relatively low structural depth (compared with rectangular CCA) is designed and analyzed. Higher retroreflectance (compared with triangular CCA) at a specific incident angle is proved by ray tracing. Two kinds of CCA structures, including the improved CCA, have been fabricated using laser direct writing technology. The fabrication results are qualified by three-dimensional shape measurement and ray tracing.

© 2010 Optical Society of America

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  1. K. S. J. Pister, D. S. Gunawan, and L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A Phys. 47, 580–583 (1995).
    [CrossRef]
  2. K. Hyyppa, “Signal response of a laser beam scanner,” Opt. Eng. 33, 2770–2776 (1994).
    [CrossRef]
  3. O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
    [CrossRef]
  4. B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” Proc. SPIE 1947, 198–208 (1993).
    [CrossRef]
  5. R. A. Chipman, J. Shamir, H. J. Caulfield, and Q. Zhou, “Wavefront correcting properties of corner-cube arrays,” Appl. Opt. 27, 3203–3209 (1988).
    [CrossRef] [PubMed]
  6. J. Fergason, “Optical system for head mounted display using retroreflector and method of displaying an image,” U.S. patent 5,621,572 (15 April 1997).
  7. R. Kijima and T. Ojika, “Transition between virtual environment and workstation environment with projective head-mounted display,” in IEEE 1997 Virtual Reality Annual International Symposium (IEEE, 1997), pp. 130–137.
    [CrossRef]
  8. M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.
  9. H. Hua, C. Gao, F. Biocca, and J. P. Rolland, “An ultra-light and compact design and implementation of head-mounted projective displays,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2001), pp. 175–182.
  10. H. Hua, L. Brown, and C. Gao, “SCAPE: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graphics Appl. 24, 66–75 (2004).
    [CrossRef]
  11. ASTM International, “Standard specification for retroreflective sheeting for traffic control,” Tech. Rep. ASTM D 4956-0 (2001).
  12. 3M Traffic Control Materials Division, “Product catalog for traffic control materials,” (2003), http://www.3M.com/tcm.
  13. T. L. Hoopman, “Cube-corner retroreflective articles having wide angularity in multiple viewing planes,” U.S. patent 4,588,258 (13 May 1986).
  14. D. C. O’Brien, G. E. Faulkner, and D. J. Edwards, “Optical properties of a retroreflecting sheet,” Appl. Opt. 38, 4137–4144 (1999).
    [CrossRef]
  15. H. D. Eckhardt, “Simple model of corner reflector phenomena,” Appl. Opt. 10, 1559–1566 (1971).
    [CrossRef] [PubMed]
  16. X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
    [CrossRef]
  17. W. H. Venable Jr. and N. L. Johnson, “Unified coordinate system for retroreflectance measurements,” Appl. Opt. 19, 1236–1241 (1980).
    [CrossRef] [PubMed]
  18. J. J. Rennilson, “Retroreflection measurements: a review,” Appl. Opt. 19, 1234–1235 (1980).
    [CrossRef] [PubMed]
  19. G. H. Seward and P. S. Cort, “Measurement and characterization of angular reflectance for cube-corners and microspheres,” Opt. Eng. 38, 164–169 (1999).
    [CrossRef]
  20. J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
    [CrossRef]
  21. H. Kim and B. Lee, “Optimal design of retroreflection corner cube sheets by geometric optics analysis,” Opt. Eng. 46, 094002 (2007).
    [CrossRef]
  22. H. Kim, S.-W. Min, and B. Lee, “Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method,” Appl. Opt. 47, 6453–6469 (2008).
    [CrossRef] [PubMed]
  23. E. Brinksmeier, R. Gläbe, and C. Flucke, “Manufacturing of molds for replication of micro cube corner retroreflectors,” Prod. Eng. Res. Devel. 2, 33–38 (2008).
    [CrossRef]
  24. K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
    [CrossRef]
  25. H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
    [CrossRef]
  26. K. I. Jolic, M. K. Ghantasala, and E. C. Harvey, “Excimer laser machining of corner cube structures,” J. Micromech. Microeng. 14, 388–397 (2004).
    [CrossRef]
  27. P. K. Weng and J. Shie, “A revolving retroreflective marker for an optical tachometer,” Sens. Actuators A Phys. 24, 203–207 (1990).
    [CrossRef]
  28. G. W. Neudeck, J. Spitz, J. C. H. Chang, J. P. Denton, and N. Gallagher, “Precision crystal corner cube arrays for optical gratings formed by (100) silicon planes with selective epitaxial growth,” Appl. Opt. 35, 3466–3470 (1996).
    [CrossRef] [PubMed]
  29. M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
    [CrossRef]
  30. K. Zimmer, D. Hirsch, and F. Big, “Excimer laser machining for the fabrication of analogous microstructures,” Appl. Surf. Sci. 96–98, 425–429 (1996).
    [CrossRef]

2008

E. Brinksmeier, R. Gläbe, and C. Flucke, “Manufacturing of molds for replication of micro cube corner retroreflectors,” Prod. Eng. Res. Devel. 2, 33–38 (2008).
[CrossRef]

H. Kim, S.-W. Min, and B. Lee, “Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method,” Appl. Opt. 47, 6453–6469 (2008).
[CrossRef] [PubMed]

2007

H. Kim and B. Lee, “Optimal design of retroreflection corner cube sheets by geometric optics analysis,” Opt. Eng. 46, 094002 (2007).
[CrossRef]

2005

H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
[CrossRef]

2004

K. I. Jolic, M. K. Ghantasala, and E. C. Harvey, “Excimer laser machining of corner cube structures,” J. Micromech. Microeng. 14, 388–397 (2004).
[CrossRef]

H. Hua, L. Brown, and C. Gao, “SCAPE: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graphics Appl. 24, 66–75 (2004).
[CrossRef]

2002

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
[CrossRef]

1999

G. H. Seward and P. S. Cort, “Measurement and characterization of angular reflectance for cube-corners and microspheres,” Opt. Eng. 38, 164–169 (1999).
[CrossRef]

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

D. C. O’Brien, G. E. Faulkner, and D. J. Edwards, “Optical properties of a retroreflecting sheet,” Appl. Opt. 38, 4137–4144 (1999).
[CrossRef]

1996

1995

K. S. J. Pister, D. S. Gunawan, and L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A Phys. 47, 580–583 (1995).
[CrossRef]

1994

K. Hyyppa, “Signal response of a laser beam scanner,” Opt. Eng. 33, 2770–2776 (1994).
[CrossRef]

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

1993

B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” Proc. SPIE 1947, 198–208 (1993).
[CrossRef]

1990

P. K. Weng and J. Shie, “A revolving retroreflective marker for an optical tachometer,” Sens. Actuators A Phys. 24, 203–207 (1990).
[CrossRef]

1988

1980

1971

Big, F.

K. Zimmer, D. Hirsch, and F. Big, “Excimer laser machining for the fabrication of analogous microstructures,” Appl. Surf. Sci. 96–98, 425–429 (1996).
[CrossRef]

Biocca, F.

H. Hua, C. Gao, F. Biocca, and J. P. Rolland, “An ultra-light and compact design and implementation of head-mounted projective displays,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2001), pp. 175–182.

Brinksmeier, E.

E. Brinksmeier, R. Gläbe, and C. Flucke, “Manufacturing of molds for replication of micro cube corner retroreflectors,” Prod. Eng. Res. Devel. 2, 33–38 (2008).
[CrossRef]

Brown, L.

H. Hua, L. Brown, and C. Gao, “SCAPE: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graphics Appl. 24, 66–75 (2004).
[CrossRef]

Caulfield, H. J.

Chang, J. C. H.

Chang, S.

J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
[CrossRef]

Chipman, R. A.

Cort, P. S.

G. H. Seward and P. S. Cort, “Measurement and characterization of angular reflectance for cube-corners and microspheres,” Opt. Eng. 38, 164–169 (1999).
[CrossRef]

Denton, J. P.

Eckhardt, H. D.

Edwards, D. J.

Engelke, R.

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

Faulkner, G. E.

Fergason, J.

J. Fergason, “Optical system for head mounted display using retroreflector and method of displaying an image,” U.S. patent 5,621,572 (15 April 1997).

Flucke, C.

E. Brinksmeier, R. Gläbe, and C. Flucke, “Manufacturing of molds for replication of micro cube corner retroreflectors,” Prod. Eng. Res. Devel. 2, 33–38 (2008).
[CrossRef]

Gale, M. T.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Gallagher, N.

Gao, C.

H. Hua, L. Brown, and C. Gao, “SCAPE: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graphics Appl. 24, 66–75 (2004).
[CrossRef]

H. Hua, C. Gao, F. Biocca, and J. P. Rolland, “An ultra-light and compact design and implementation of head-mounted projective displays,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2001), pp. 175–182.

Ghantasala, M. K.

K. I. Jolic, M. K. Ghantasala, and E. C. Harvey, “Excimer laser machining of corner cube structures,” J. Micromech. Microeng. 14, 388–397 (2004).
[CrossRef]

Gläbe, R.

E. Brinksmeier, R. Gläbe, and C. Flucke, “Manufacturing of molds for replication of micro cube corner retroreflectors,” Prod. Eng. Res. Devel. 2, 33–38 (2008).
[CrossRef]

Goto, M.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Gunawan, D. S.

K. S. J. Pister, D. S. Gunawan, and L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A Phys. 47, 580–583 (1995).
[CrossRef]

Harvey, E. C.

K. I. Jolic, M. K. Ghantasala, and E. C. Harvey, “Excimer laser machining of corner cube structures,” J. Micromech. Microeng. 14, 388–397 (2004).
[CrossRef]

Hines, B. E.

B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” Proc. SPIE 1947, 198–208 (1993).
[CrossRef]

Hirsch, D.

K. Zimmer, D. Hirsch, and F. Big, “Excimer laser machining for the fabrication of analogous microstructures,” Appl. Surf. Sci. 96–98, 425–429 (1996).
[CrossRef]

Hockel, H.

H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
[CrossRef]

Hofmann, U.

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

Hoopman, T. L.

T. L. Hoopman, “Cube-corner retroreflective articles having wide angularity in multiple viewing planes,” U.S. patent 4,588,258 (13 May 1986).

Hsu, V. S.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

Hua, H.

H. Hua, L. Brown, and C. Gao, “SCAPE: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graphics Appl. 24, 66–75 (2004).
[CrossRef]

H. Hua, C. Gao, F. Biocca, and J. P. Rolland, “An ultra-light and compact design and implementation of head-mounted projective displays,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2001), pp. 175–182.

Hyyppa, K.

K. Hyyppa, “Signal response of a laser beam scanner,” Opt. Eng. 33, 2770–2776 (1994).
[CrossRef]

Inami, M.

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

Johnson, E. G.

H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
[CrossRef]

Johnson, N. L.

Jolic, K. I.

K. I. Jolic, M. K. Ghantasala, and E. C. Harvey, “Excimer laser machining of corner cube structures,” J. Micromech. Microeng. 14, 388–397 (2004).
[CrossRef]

Kahn, J. M.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

Kawakami, N.

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

Kijima, R.

R. Kijima and T. Ojika, “Transition between virtual environment and workstation environment with projective head-mounted display,” in IEEE 1997 Virtual Reality Annual International Symposium (IEEE, 1997), pp. 130–137.
[CrossRef]

Kim, H.

Kohlmann-von Platen, K. T.

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

Kurosawa, T.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Lee, B.

Li, S.

J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
[CrossRef]

Lin, L.

K. S. J. Pister, D. S. Gunawan, and L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A Phys. 47, 580–583 (1995).
[CrossRef]

Maeda, T.

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

Martins, R.

H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
[CrossRef]

Merz, P.

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

Min, S.-W.

Nakamara, O.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Nakamata, T.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Neudeck, G. W.

O’Brien, D. C.

Ojika, T.

R. Kijima and T. Ojika, “Transition between virtual environment and workstation environment with projective head-mounted display,” in IEEE 1997 Virtual Reality Annual International Symposium (IEEE, 1997), pp. 130–137.
[CrossRef]

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Pister, K. S. J.

K. S. J. Pister, D. S. Gunawan, and L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A Phys. 47, 580–583 (1995).
[CrossRef]

Reimer, K.

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

Rennilson, J. J.

Rolland, J. P.

H. Hua, C. Gao, F. Biocca, and J. P. Rolland, “An ultra-light and compact design and implementation of head-mounted projective displays,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2001), pp. 175–182.

Rossi, M.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Schulz, H.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Sekiguchi, D.

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

Seward, G. H.

G. H. Seward and P. S. Cort, “Measurement and characterization of angular reflectance for cube-corners and microspheres,” Opt. Eng. 38, 164–169 (1999).
[CrossRef]

Shamir, J.

Shie, J.

P. K. Weng and J. Shie, “A revolving retroreflective marker for an optical tachometer,” Sens. Actuators A Phys. 24, 203–207 (1990).
[CrossRef]

Spitz, J.

Sung, J.

H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
[CrossRef]

Tachi, S.

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

Takai, N.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Toyoda, K.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Venable, W. H.

Wagner, B.

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

Weng, P. K.

P. K. Weng and J. Shie, “A revolving retroreflective marker for an optical tachometer,” Sens. Actuators A Phys. 24, 203–207 (1990).
[CrossRef]

Yanagida, Y.

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

Yuan, J.

J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
[CrossRef]

Zhang, Y.

J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
[CrossRef]

Zhou, Q.

Zhu, X.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

Zimmer, K.

K. Zimmer, D. Hirsch, and F. Big, “Excimer laser machining for the fabrication of analogous microstructures,” Appl. Surf. Sci. 96–98, 425–429 (1996).
[CrossRef]

Appl. Opt.

Appl. Surf. Sci.

K. Zimmer, D. Hirsch, and F. Big, “Excimer laser machining for the fabrication of analogous microstructures,” Appl. Surf. Sci. 96–98, 425–429 (1996).
[CrossRef]

IEEE Comput. Graphics Appl.

H. Hua, L. Brown, and C. Gao, “SCAPE: supporting stereoscopic collaboration in augmented and projective environments,” IEEE Comput. Graphics Appl. 24, 66–75 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

J. Micromech. Microeng.

K. I. Jolic, M. K. Ghantasala, and E. C. Harvey, “Excimer laser machining of corner cube structures,” J. Micromech. Microeng. 14, 388–397 (2004).
[CrossRef]

Opt. Commun.

J. Yuan, S. Chang, S. Li, and Y. Zhang, “Design and fabrication of micro-cube-corner array retroreflectors,” Opt. Commun. 209, 75–83 (2002).
[CrossRef]

Opt. Eng.

H. Kim and B. Lee, “Optimal design of retroreflection corner cube sheets by geometric optics analysis,” Opt. Eng. 46, 094002 (2007).
[CrossRef]

K. Hyyppa, “Signal response of a laser beam scanner,” Opt. Eng. 33, 2770–2776 (1994).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schulz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

G. H. Seward and P. S. Cort, “Measurement and characterization of angular reflectance for cube-corners and microspheres,” Opt. Eng. 38, 164–169 (1999).
[CrossRef]

Proc. SPIE

B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” Proc. SPIE 1947, 198–208 (1993).
[CrossRef]

Proc. SPIE

K. Reimer, R. Engelke, U. Hofmann, P. Merz, K. T. Kohlmann-von Platen, and B. Wagner, “Progress in gray-tone lithography and replication techniques for different materials,” Proc. SPIE 3879, 98–108 (1999).
[CrossRef]

H. Hockel, R. Martins, J. Sung, and E. G. Johnson, “Design and fabrication of trihedral corner-cube arrays using analog exposure based on phase masks,” Proc. SPIE 5720, 78–85 (2005).
[CrossRef]

Prod. Eng. Res. Devel.

E. Brinksmeier, R. Gläbe, and C. Flucke, “Manufacturing of molds for replication of micro cube corner retroreflectors,” Prod. Eng. Res. Devel. 2, 33–38 (2008).
[CrossRef]

Rev. Sci. Instrum.

O. Nakamara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, and T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retroreflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
[CrossRef]

Sens. Actuators A Phys.

K. S. J. Pister, D. S. Gunawan, and L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A Phys. 47, 580–583 (1995).
[CrossRef]

P. K. Weng and J. Shie, “A revolving retroreflective marker for an optical tachometer,” Sens. Actuators A Phys. 24, 203–207 (1990).
[CrossRef]

Other

ASTM International, “Standard specification for retroreflective sheeting for traffic control,” Tech. Rep. ASTM D 4956-0 (2001).

3M Traffic Control Materials Division, “Product catalog for traffic control materials,” (2003), http://www.3M.com/tcm.

T. L. Hoopman, “Cube-corner retroreflective articles having wide angularity in multiple viewing planes,” U.S. patent 4,588,258 (13 May 1986).

J. Fergason, “Optical system for head mounted display using retroreflector and method of displaying an image,” U.S. patent 5,621,572 (15 April 1997).

R. Kijima and T. Ojika, “Transition between virtual environment and workstation environment with projective head-mounted display,” in IEEE 1997 Virtual Reality Annual International Symposium (IEEE, 1997), pp. 130–137.
[CrossRef]

M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, “Visuo-haptic display using head-mounted projector,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2000), pp. 233–240.

H. Hua, C. Gao, F. Biocca, and J. P. Rolland, “An ultra-light and compact design and implementation of head-mounted projective displays,” in IEEE 2000 Virtual Reality Annual International Symposium (IEEE, 2001), pp. 175–182.

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Figures (10)

Fig. 1
Fig. 1

Geometrical structures of two basic types of CCA: (a) perspective view of one triangular corner cube, top view and side view of TCCA structure; (b) perspective view of one rectangular corner cube, top view and side view of RCCA structure.

Fig. 2
Fig. 2

Retroreflectance measurement setup modeled in ZEMAX.

Fig. 3
Fig. 3

Ray-tracing results of retroreflected energy pattern recorded by the detector when β = 0 : (a) energy distribution retroreflected by the TCCA, (b) energy distribution retroreflected by the RCCA.

Fig. 4
Fig. 4

Retroreflectance at different incident angles for TCCA and RCCA: (a) retroreflectance calculated by Eckhardt’s model; (b) retroreflectance calculated by ray tracing.

Fig. 5
Fig. 5

Geometrical structure of PCCA: perspective view of one pentagonal corner cube, top view and side view of PCCA structure.

Fig. 6
Fig. 6

Retroreflectance at different incident angles for PCCA and TCCA: (a) retroreflectance of PCCA calculated by Eckhardt’s model; (b) retroreflectance of PCCA and TCCA calculated by ray tracing.

Fig. 7
Fig. 7

Transverse coordinates of one CCA cell at different depth: (a) cross sections of TCCA; (b) cross sections of PCCA.

Fig. 8
Fig. 8

Fabrication results: (a) SEM image of TCCA; (b) SEM image of PCCA.

Fig. 9
Fig. 9

Three-dimensional data of the CCA structure: (a) three-dimensional view of the TCCA and PCCA; (b) profile data of TCCA for different angles.

Fig. 10
Fig. 10

Decline in retroreflectance for the imperfect PCCA.

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