Abstract

This paper reports on the realization of a type of micromachined retroreflecting sheeting material. The geometry presented has high reflection efficiency even at large incident angles, and it can be manufactured through polymer replication techniques. The paper consists of two parts: A theoretical section outlining the design parameters and their impact on the optical performance, and secondly, an experimental part comprising both manufacturing and optical evaluation for a candidate retroreflecting sheet material in traffic control devices. Experimental data show that the retroreflecting properties are promising. The retroreflector consists of a front layer of densely packed spherical microlenses, a back surface of densely packed spherical micromirrors, and a transparent spacer layer. The thickness of the spacer layer determines in part the optical characteristics of the retroreflector.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. T. W. Liepmann, �??How retroreflectors bring the light back,�?? Laser Focus World 30, 129-132 (1994).
  2. R. Beer and D. Marjaniemi, �??Wavefronts and construction tolerances for a cat's-eye retroreflector,�?? Appl. Opt. 5, 1191-1197 (1966).
    [CrossRef] [PubMed]
  3. J. J. Snyder, �??Paraxial ray analysis of a cat�??s eye retroreflector,�?? Appl. Opt. 14, 1825-1828 (1975).
    [CrossRef] [PubMed]
  4. J. L. Zurasky, �??Cube corner retroreflector test and analysis,�?? Appl. Opt. 15, 445-452 (1976).
    [CrossRef] [PubMed]
  5. D. C. O�??Brien, G. E. Faulkner, and D. J. Edwards, �??Optical properties of a retroreflecting sheet�??, Appl. Opt. 38, 4137-4144 (1999).
    [CrossRef]
  6. 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]
  7. Corning SMILE�?� Lens Array (Corning Incorporated Photonic Materials, Corning, NY, 2003) <a href="http://www.corning.com/photonicmaterials">http://www.corning.com/photonicmaterials</a>.
  8. Publication CIE 54.2-2001, Retroreflection: Definition and measurement, ISBN 3 900 734 992 (Commission Internationale de L�??Eclairage, 2001).
  9. L. Danielsson and S. Niemann, �??Optical microrelief retroreflector�??, International Publication Number WO 95/34006, Dec. 14, 1995.
  10. E. Hecht, Optics, 4th Edition, (Addison Wesley Longman Inc., Reading, MA, 2002), Ch. 5 and 11.
  11. Software OSLO Rev. 6.1 (Lambda Research Corp., Littleton, MA, 2003), <a href="http://www.sinopt.com">http://www.sinopt.com</a>.
  12. Publication CIE 72-1987, Guide to the properties and uses of retroreflectors at night, ISBN 3 900 734 089 (Commission Internationale de L�??Eclairage , 1987).
  13. O. �?hman, H. Sjödin, B. Ekström, and G. Jacobsson, �??Microfluidic structure and process for its manufacture,�?? International Publication Number WO 91/16966, Nov. 14, 1991, and U.S. Patent 5 376 252, Dec. 27, 1994.
  14. O. Rötting, W. Röpke, H. Becker, and C. Gärtner, �??Polymer microfabrication technologies,�?? Microsystem Technologies 8, 32-36 (2002).
    [CrossRef]
  15. D. Daly, R.F. Stevens, M.C. Hutley, and N. Davies, �??The manufacture of microlenses by melting photoresist,�?? IOP Short Meetings 30, 23-34 (1991).
  16. T. R. Jay, M. B. Stern, and R. E. Knowlden, �??Effect of refractive microlens array fabrication parameters on optical quality,�?? in Miniature and Micro-Optics: Fabrication and System Applications II, C Roychoudhuri and W B Veldkamp, Eds., Proc. SPIE 1751, 236-245 (1992).
  17. CIE Standard Illuminants for Colorimetry, joint ISO 10526:1999 / CIE S005/E-1998 standard.
  18. Product Catalog for Traffic Control Materials (3M Traffic Control Materials Division, St. Paul, MN, 2003), <a href="http://www.3M.com/tcm">http://www.3M.com/tcm</a>.
  19. Publication CIE 15.2-1986, Colorimetry, 2nd Edition, ISBN 3 900 734 00 3 (Commission Internationale de L�??Eclairage, 1986).
  20. M. Rossi and I. Kallioniemi, "Micro-optical modules fabricated by high-precision replication processes", in Diffractive Optics and Micro-Optics, Vol. 75 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 2002), pp. 108-110.

Appl. Opt.

Diffractive Optics and Micro-Optics

M. Rossi and I. Kallioniemi, "Micro-optical modules fabricated by high-precision replication processes", in Diffractive Optics and Micro-Optics, Vol. 75 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 2002), pp. 108-110.

IOP Short Meetings

D. Daly, R.F. Stevens, M.C. Hutley, and N. Davies, �??The manufacture of microlenses by melting photoresist,�?? IOP Short Meetings 30, 23-34 (1991).

Laser Focus World

T. W. Liepmann, �??How retroreflectors bring the light back,�?? Laser Focus World 30, 129-132 (1994).

Microsystem Technologies

O. Rötting, W. Röpke, H. Becker, and C. Gärtner, �??Polymer microfabrication technologies,�?? Microsystem Technologies 8, 32-36 (2002).
[CrossRef]

Opt. Eng.

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

T. R. Jay, M. B. Stern, and R. E. Knowlden, �??Effect of refractive microlens array fabrication parameters on optical quality,�?? in Miniature and Micro-Optics: Fabrication and System Applications II, C Roychoudhuri and W B Veldkamp, Eds., Proc. SPIE 1751, 236-245 (1992).

Other

CIE Standard Illuminants for Colorimetry, joint ISO 10526:1999 / CIE S005/E-1998 standard.

Product Catalog for Traffic Control Materials (3M Traffic Control Materials Division, St. Paul, MN, 2003), <a href="http://www.3M.com/tcm">http://www.3M.com/tcm</a>.

Publication CIE 15.2-1986, Colorimetry, 2nd Edition, ISBN 3 900 734 00 3 (Commission Internationale de L�??Eclairage, 1986).

Corning SMILE�?� Lens Array (Corning Incorporated Photonic Materials, Corning, NY, 2003) <a href="http://www.corning.com/photonicmaterials">http://www.corning.com/photonicmaterials</a>.

Publication CIE 54.2-2001, Retroreflection: Definition and measurement, ISBN 3 900 734 992 (Commission Internationale de L�??Eclairage, 2001).

L. Danielsson and S. Niemann, �??Optical microrelief retroreflector�??, International Publication Number WO 95/34006, Dec. 14, 1995.

E. Hecht, Optics, 4th Edition, (Addison Wesley Longman Inc., Reading, MA, 2002), Ch. 5 and 11.

Software OSLO Rev. 6.1 (Lambda Research Corp., Littleton, MA, 2003), <a href="http://www.sinopt.com">http://www.sinopt.com</a>.

Publication CIE 72-1987, Guide to the properties and uses of retroreflectors at night, ISBN 3 900 734 089 (Commission Internationale de L�??Eclairage , 1987).

O. �?hman, H. Sjödin, B. Ekström, and G. Jacobsson, �??Microfluidic structure and process for its manufacture,�?? International Publication Number WO 91/16966, Nov. 14, 1991, and U.S. Patent 5 376 252, Dec. 27, 1994.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Illustration of the properties retroreflection, brilliancy, and divergence. Retroreflectance R is defined as the ratio of the reflected luminous flux to the incident flux within the narrow confines of incident and reflected geometrical conditions. Brilliancy is the term used for the reflected flux at certain observation angles, e.g. 0.2°, and it is normally given by the coefficient of retroreflection RA (cd/lux/m2), while the divergence is a measure of the maximum angular distribution of the reflected flux.

Fig. 2.
Fig. 2.

Working principle of the sheeting material. The left part of the cross-section shows how the two spheres have a common center of curvature. The right part exemplifies the ray path through an element. Rl denotes the radius of curvature for the lens, Rm is the radius of curvature for the mirror, d is the aperture diameter, t is the total thickness, n is the refractive index of the spacer material, and β is the incidence angle of the light. It is assumed that n>1.

Fig. 3.
Fig. 3.

Different designs with respect to the ratio t/d give the elements different retroreflective properties. This theoretical figure depicts the change in retroreflectance R with less than 2° divergence (open circles) for white light at 0° entrance angle, as well as change in maximum divergence in degrees (closed circles), when the ratio t/d is varied. Also, corresponding maximum entrance angle β for retroreflection is plotted for completeness. The inserted figures show a geometrical picture of the different designs. The maximum entrance angle β occurs when the paraxial focus strikes the edge of the spherical mirror. Note that when translating the maximum entrance angle (top x-axis) into corresponding t/d ratio (bottom x-axis), these values are plotted as categories rather than actual numbers. Hence, the distance between the scale marks on the bottom x-axis is not equidistant in terms of t/d values.

Fig. 4.
Fig. 4.

Theoretical knife edge distribution curves depicting the relative energy for white light along the x- and y-axis as a function of position (in degrees) for a design with t/d=1.32. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. The retroreflectance R is about 1.0 (all of the light entering the lens is retroreflected back) for entrance angle β of 5°, and about 0.8 for entrance angle of 37°.

Fig. 5.
Fig. 5.

Theoretical knife edge distribution curves depicting the relative energy for white light along the x- and y-axis as a function of position (in degrees) for a design with t/d=3.13. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. The entrance angle β is 5° and 15°. Notice that the retroreflectance R for the two cases 5° and 15° are not the same: the ratio of light entering and leaving the lens is drastically reduced at 15°.

Fig. 6.
Fig. 6.

Theoretical knife edge distribution curves depicting the relative energy along the x- and y-axis as a function of position (in degrees) for a design with t/d=3.13. The optical system is described in a right-handed coordinate system in which the incident light is traveling along the positive z-axis. The entrance angle β is 5°. Illumination with light of two different wavelengths (405 nm and 546 nm) gives rise to different divergence properties. The retroreflectance R is about the same for the two wavelengths.

Fig. 7.
Fig. 7.

The casting set-up including the mould inserts and the spacer-ring. The casting was performed using a thermosetting epoxy that was injected into the cavity by the help of syringes. The two mould inserts are respectively fixated by steering pins, and the steel plates are equipped with a vacuum pumping capacity pressing the mould inserts flat.

Fig. 8.
Fig. 8.

Scanning electron micrographs for the lens side of the epoxy retroreflector. The lens aperture diameter is 600 µm, and the sag height 183 µm. The length of the scale bar is 1000 µm.

Fig. 9.
Fig. 9.

Scanning electron micrographs for the mirror side of the epoxy retroreflector. The lens aperture diameter is 610 µm, and the sag height 92 µm. The length of the scale bar is 300 µm.

Fig. 10.
Fig. 10.

Experimental coefficient of retroreflection RA for two different samples as a function of entrance angle β (in degrees). Sample A is ~1020 µm thick and sample B is ~1080 µm thick. The observation angle α is 0.2°.

Fig. 11.
Fig. 11.

Experimental coefficient of retroreflection RA as a function of observation angle α (in degrees) for a set of entrance angles β (5°, 10°, 20°, 30°) for sample A where t ~1020 µm.

Fig. 12.
Fig. 12.

Experimental coefficient of retroreflection RA as a function of observation angle α (in degrees) for a set of entrance angles β (5°, 10°, 20°, 30°) for sample B where t ~1080 µm.

Equations (3)

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

t = n R l ( n 1 ) .
R m = t R l .
R l R m = n 1 .

Metrics