Abstract

The power reflection and polarization properties of a close-packed array of retroreflectors are modeled, and a commercially available sheet is measured to verify the predictions. The modeling technique is conceptually simple and applicable to a wide range of structures of this type. The close-packed sheet retroreflects over a range of angles of incidence of approximately -40 to 40 deg in both directions and returns the polarization that illuminates it largely unchanged. Predictions of returned power are within 10% for light incident within 15 deg of normal and within 20% for angles less than 20 deg. Angles of polarization rotation are predicted to within 10 deg over a similar range of input angles. The model predicts the angular aperture of the sheet and the major features of the angular response. Future research will focus on design of structures with wider angles of acceptance and responses optimized for specific applications.

© 1999 Optical Society of America

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References

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  1. K. Hyyppa, “Signal response of a laser beam scanner,” Opt. Eng. 33, 2770–2776 (1994).
    [CrossRef]
  2. O. Nakumara, M. Goto, K. Toyoda, N. Takai, T. Kurosawa, T. Nakamata, “A laser tracking robot-performance calibration system using ball-seated bearing mechanisms and a spherically shaped cat’s eye retro-reflector,” Rev. Sci. Instrum. 65, 1006–1011 (1994).
    [CrossRef]
  3. B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” in Spaceborne Interferometry, R. D. Reasenberg, ed., Proc. SPIE1947, 198–208 (1993).
    [CrossRef]
  4. C. K. Carniglia, “Tolerancing an extended corner cube for HABE tracking and pointing applications,” in Acquisition, Tracking and Pointing VIII, M. K. Masten, L. A. Stockum, M. M. Birnhaum, G. E. Sevaston, eds., Proc. SPIE2221, 676–685 (1994).
    [CrossRef]
  5. A. Minato, N. Sugimoto, “Method of measuring dihedral angles of a cube-corner retroreflector having curved mirror surfaces,” Opt. Eng. 33, 1187–1192 (1994).
    [CrossRef]
  6. K. S. J. Pister, D. S. Gunawan, L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A 46–47, 580–583 (1995).
  7. G. W. Neudeck, J. Spitz, J. C. H. Chang, J. P. Denton, N. Gallagher, “Precision corner cube arrays for optical gratings formed by (100) silicon planes with selective epitaxial growth,” Appl. Opt. 35, 3466–3470 (1996).
    [CrossRef] [PubMed]
  8. R. A. Chipman, J. Shamir, H. J. Caulfield, Q. Zhou, “Wavefront correcting properties of corner-cube arrays,” Appl. Opt. 27, 3203–3209 (1988).
    [CrossRef] [PubMed]
  9. Reflexite UK Ltd, Unit 10, 23 Armstrong Way, Great Western Industrial Park, Southall, Middlesex, UB2 4SD; www.reflexite.com .
  10. OTO87 corner cube, Fresnel Optics, 1300 Mt. Read Blvd., Rochester, N.Y. 14606.
  11. R. R. Hodgson, R. A. Chipman, “Measurement of corner cube polarization,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 436–447 (1990).
  12. R. M. A. Azzam, J. Liu, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36, 1553–1559 (1997).
    [CrossRef] [PubMed]
  13. M. S. Scholl, “Ray trace through a corner-cube retroreflector with complex reflection coefficients,” J. Opt. Soc. Am. A 12, 1589–1592 (1995).
    [CrossRef]
  14. J. W. Morris, C. H. An, “Polarization properties of non-symmetric retroreflectors,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 333–345 (1990).
  15. E. Wolf, M. Born, Principles of Optics, 6th ed. (Pergamon, N.Y., 1993), pp. 628–632.

1997

1996

1995

M. S. Scholl, “Ray trace through a corner-cube retroreflector with complex reflection coefficients,” J. Opt. Soc. Am. A 12, 1589–1592 (1995).
[CrossRef]

K. S. J. Pister, D. S. Gunawan, L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A 46–47, 580–583 (1995).

1994

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

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

A. Minato, N. Sugimoto, “Method of measuring dihedral angles of a cube-corner retroreflector having curved mirror surfaces,” Opt. Eng. 33, 1187–1192 (1994).
[CrossRef]

1988

An, C. H.

J. W. Morris, C. H. An, “Polarization properties of non-symmetric retroreflectors,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 333–345 (1990).

Azzam, R. M. A.

Born, M.

E. Wolf, M. Born, Principles of Optics, 6th ed. (Pergamon, N.Y., 1993), pp. 628–632.

Carniglia, C. K.

C. K. Carniglia, “Tolerancing an extended corner cube for HABE tracking and pointing applications,” in Acquisition, Tracking and Pointing VIII, M. K. Masten, L. A. Stockum, M. M. Birnhaum, G. E. Sevaston, eds., Proc. SPIE2221, 676–685 (1994).
[CrossRef]

Caulfield, H. J.

Chang, J. C. H.

Chipman, R. A.

R. A. Chipman, J. Shamir, H. J. Caulfield, Q. Zhou, “Wavefront correcting properties of corner-cube arrays,” Appl. Opt. 27, 3203–3209 (1988).
[CrossRef] [PubMed]

R. R. Hodgson, R. A. Chipman, “Measurement of corner cube polarization,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 436–447 (1990).

Denton, J. P.

Gallagher, N.

Goto, M.

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

Gunawan, D. S.

K. S. J. Pister, D. S. Gunawan, L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A 46–47, 580–583 (1995).

Hines, B. E.

B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” in Spaceborne Interferometry, R. D. Reasenberg, ed., Proc. SPIE1947, 198–208 (1993).
[CrossRef]

Hodgson, R. R.

R. R. Hodgson, R. A. Chipman, “Measurement of corner cube polarization,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 436–447 (1990).

Hyyppa, K.

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

Kurosawa, T.

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

Lin, L.

K. S. J. Pister, D. S. Gunawan, L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A 46–47, 580–583 (1995).

Liu, J.

Minato, A.

A. Minato, N. Sugimoto, “Method of measuring dihedral angles of a cube-corner retroreflector having curved mirror surfaces,” Opt. Eng. 33, 1187–1192 (1994).
[CrossRef]

Morris, J. W.

J. W. Morris, C. H. An, “Polarization properties of non-symmetric retroreflectors,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 333–345 (1990).

Nakamata, T.

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

Nakumara, O.

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

Neudeck, G. W.

Pister, K. S. J.

K. S. J. Pister, D. S. Gunawan, L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A 46–47, 580–583 (1995).

Scholl, M. S.

Shamir, J.

Spitz, J.

Sugimoto, N.

A. Minato, N. Sugimoto, “Method of measuring dihedral angles of a cube-corner retroreflector having curved mirror surfaces,” Opt. Eng. 33, 1187–1192 (1994).
[CrossRef]

Takai, N.

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

Toyoda, K.

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

Wolf, E.

E. Wolf, M. Born, Principles of Optics, 6th ed. (Pergamon, N.Y., 1993), pp. 628–632.

Zhou, Q.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

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

A. Minato, N. Sugimoto, “Method of measuring dihedral angles of a cube-corner retroreflector having curved mirror surfaces,” Opt. Eng. 33, 1187–1192 (1994).
[CrossRef]

Rev. Sci. Instrum.

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

Sens. Actuators A

K. S. J. Pister, D. S. Gunawan, L. Lin, “Micromachined corner cube reflectors as a communication link,” Sens. Actuators A 46–47, 580–583 (1995).

Other

Reflexite UK Ltd, Unit 10, 23 Armstrong Way, Great Western Industrial Park, Southall, Middlesex, UB2 4SD; www.reflexite.com .

OTO87 corner cube, Fresnel Optics, 1300 Mt. Read Blvd., Rochester, N.Y. 14606.

R. R. Hodgson, R. A. Chipman, “Measurement of corner cube polarization,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 436–447 (1990).

J. W. Morris, C. H. An, “Polarization properties of non-symmetric retroreflectors,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet and X-Ray, J. W. Morris, R. A. Chipman, eds., Proc. SPIE1317, 333–345 (1990).

E. Wolf, M. Born, Principles of Optics, 6th ed. (Pergamon, N.Y., 1993), pp. 628–632.

B. E. Hines, “Optical truss and retroreflector modeling for picometer laser metrology,” in Spaceborne Interferometry, R. D. Reasenberg, ed., Proc. SPIE1947, 198–208 (1993).
[CrossRef]

C. K. Carniglia, “Tolerancing an extended corner cube for HABE tracking and pointing applications,” in Acquisition, Tracking and Pointing VIII, M. K. Masten, L. A. Stockum, M. M. Birnhaum, G. E. Sevaston, eds., Proc. SPIE2221, 676–685 (1994).
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

Retroreflecting sheet.

Fig. 2
Fig. 2

Corner-cube retroreflector.

Fig. 3
Fig. 3

Apertures for paths through retroreflector for (a) normal incidence and (b) 15-deg angle of incidence.

Fig. 4
Fig. 4

Simulated intensity of returned vertical polarization versus angle of incidence for ideal retroreflector illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 5
Fig. 5

Simulated intensity of returned vertical polarization versus angle of incidence for realistic retroreflector illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 6
Fig. 6

Simulated intensity of returned horizontal polarization versus angle of incidence for realistic retroreflector illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 7
Fig. 7

Simulated returned polarization ellipse angle versus angle of incidence for realistic retroreflector illuminated with vertically polarized light. Contours are in degrees of rotation relative to vertical direction.

Fig. 8
Fig. 8

Simulated intensity of returned vertical polarization versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 9
Fig. 9

Simulated intensity of returned horizontal polarization versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 10
Fig. 10

Simulated returned polarization ellipse angle versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light. Contours are in degrees of rotation relative to vertical direction.

Fig. 11
Fig. 11

Measurement rig for retroreflecting sheet evaluation.

Fig. 12
Fig. 12

Measured intensity of returned vertical polarization versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 13
Fig. 13

False-color map of the measured intensity of returned vertical polarization versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light.

Fig. 14
Fig. 14

Measured intensity of returned horizontal polarization versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light. Contours are in decibels relative to maximum intensity.

Fig. 15
Fig. 15

Returned polarization ellipse angle versus angle of incidence for retroreflecting sheet illuminated with vertically polarized light. Contours are in degrees of rotation relative to vertical direction.

Fig. 16
Fig. 16

Measured intensity of returned vertical polarization versus angle of incidence for retroreflecting sheet illuminated with horizontally polarized light. Contours are in decibels relative to maximum intensity.

Fig. 17
Fig. 17

Measured intensity of returned horizontal polarization versus angle of incidence for retroreflecting sheet illuminated with horizontally polarized light. Contours are in decibels relative to maximum intensity.

Fig. 18
Fig. 18

Returned polarization ellipse angle versus angle of incidence for retroreflecting sheet illuminated with horizontally polarized light. Contours are in degrees of rotation relative to vertical direction.

Tables (1)

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Table 1 Inequalities Defining the Input Apertures for Potential Paths through the Retroreflector

Equations (17)

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kˆi=-αnˆ1, βnˆ2, γnˆ3.
kˆ12=kˆi+2αnˆ1.
kˆ23=kˆi+2αnˆ1+2βnˆ2.
kˆ0=kˆi+2αnˆ1+2βnˆ2+2γnˆ3.
kˆ0=kˆi-2kˆi,
sˆm=nˆm×kˆm|nˆm×kˆm|,
pˆm=kˆm×sˆm|kˆm×sˆm|,
y1+z11,
y10,
z10.
x2+z21,
x20,
z20,
x3+y31,
x30,
z30.
ϕ=arctanIhIv,

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