Abstract

In this work, we present the design and fabrication of a progressive rear-view mirror for motorcycles. In the context of physiological and physical background knowledge, we first analyze the geometric relationships among the profile of the mirror, the blind spot, the field of view, and the reflected image size. On the basis of Walker’s eye model, the binocular disparity is further calculated according to the image size on each retina. We present the polynomial expansion that specifies our progressive mirror’s profile, as well as the fused deposition modeling process for fabricating physical mirrors. Compared with a conventional aspheric or flat mirror, this progressive mirror can achieve a wider horizontal viewing angle and shows a more stable image, thus enhancing riding safety.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Horizontally progressive mirror for blind spot detection in automobiles

Hocheol Lee, Dohyun Kim, and Sung Yi
Opt. Lett. 38(3) 317-319 (2013)

Photorealistic ray tracing to visualize automobile side mirror reflective scenes

Hocheol Lee, Kyuman Kim, Gang Lee, Sungkoo Lee, and Jingu Kim
Opt. Express 22(21) 25729-25738 (2014)

Three-dimensional simulation method of fish-eye lens distortion for a vehicle backup rear-view camera

Daehee Kim and Joonki Paik
J. Opt. Soc. Am. A 32(7) 1337-1343 (2015)

References

  • View by:
  • |
  • |
  • |

  1. W. W. Wierwille, W. A. Schaudt, J. M. Spaulding, S. K. Gupta, G. M. Fitch, D. M. Wiegand, and R. J. Hanowski, Development of a performance specification for camera/video imaging systems on heavy vehicles. Report no DOT HS 810 960, Virginia Tech Transportation Institute, National Highway Traffic Safety Administration, Washington, United Sates (2008).
  2. H. Kondo, S. Oota, T. Yamada, H. Oota, and H. Kondo, “Automobile mirror assembly,” U.S. Patent 5,793,542 1998).
  3. H. Graff, “Wide-angle mirror for automobiles and the like,” U.S. Patent 4,331,382 (1982).
  4. J. Roger, Goolsby “Blind spot sideview mirrors,” U.S. Patent 6,270,225 B1 (2001).
  5. B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
    [Crossref]
  6. S. Zwick, R. Fessler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20(4), 3642–3653 (2012).
    [Crossref] [PubMed]
  7. S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
    [Crossref]
  8. H. Lee, D. Kim, and S. Yi, “Horizontally progressive mirror for blind spot detection in automobiles,” Opt. Lett. 38(3), 317–319 (2013).
    [Crossref] [PubMed]
  9. http://www.statista.com/statistics/252261/us-motorcycle-salesin-units/ .
  10. D. M. Wiegand and R. J. Hanowski, “Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 33, 810–959 (2008).
  11. L. L. C. Zemax, https://www.zemax.com/ .
  12. E. J. McIsaac, and V. D. Bhise, “Automotive field of view analysis using polar plots,” SAE Technical Paper 950602 (1995).
  13. S. O’Day, “Binocular disparity in aspherical mirrors,” SAE paper No. 980918.
    [Crossref]
  14. B. H. Walker, Optical Design for Visual Systems (SPIE, 2000).
  15. D. Qin, M. Takamatsu, and Y. Nakashima, “Disparity limit for binocular fusion in fovea,” Opt. Rev. 13(1), 34–38 (2006).
    [Crossref]
  16. Chuang qin Co., LTD., http://www.cid.com.tw

2013 (1)

2012 (1)

2009 (1)

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

2008 (1)

D. M. Wiegand and R. J. Hanowski, “Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 33, 810–959 (2008).

2006 (1)

D. Qin, M. Takamatsu, and Y. Nakashima, “Disparity limit for binocular fusion in fovea,” Opt. Rev. 13(1), 34–38 (2006).
[Crossref]

1999 (1)

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Aikio, M.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Fessler, R.

Hanowski, R. J.

D. M. Wiegand and R. J. Hanowski, “Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 33, 810–959 (2008).

Inoguchi, K.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Jegorov, J.

Jin, G.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Kim, D.

Lee, H.

Makinen, J.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Morishima, H.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Nakashima, Y.

D. Qin, M. Takamatsu, and Y. Nakashima, “Disparity limit for binocular fusion in fovea,” Opt. Rev. 13(1), 34–38 (2006).
[Crossref]

Notni, G.

Qin, D.

D. Qin, M. Takamatsu, and Y. Nakashima, “Disparity limit for binocular fusion in fovea,” Opt. Rev. 13(1), 34–38 (2006).
[Crossref]

Saito, Y.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Takamatsu, M.

D. Qin, M. Takamatsu, and Y. Nakashima, “Disparity limit for binocular fusion in fovea,” Opt. Rev. 13(1), 34–38 (2006).
[Crossref]

Taniguchi, N.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Wang, Y.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Wiegand, D. M.

D. M. Wiegand and R. J. Hanowski, “Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 33, 810–959 (2008).

Yamazaki, S.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Yang, B.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Yi, S.

Zwick, S.

NHTSA DOT HS (1)

D. M. Wiegand and R. J. Hanowski, “Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 33, 810–959 (2008).

Opt. Express (1)

Opt. Lett. (1)

Opt. Rev. (1)

D. Qin, M. Takamatsu, and Y. Nakashima, “Disparity limit for binocular fusion in fovea,” Opt. Rev. 13(1), 34–38 (2006).
[Crossref]

Optik (Stuttg.) (1)

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Proc. SPIE (1)

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-formsurface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Other (10)

http://www.statista.com/statistics/252261/us-motorcycle-salesin-units/ .

W. W. Wierwille, W. A. Schaudt, J. M. Spaulding, S. K. Gupta, G. M. Fitch, D. M. Wiegand, and R. J. Hanowski, Development of a performance specification for camera/video imaging systems on heavy vehicles. Report no DOT HS 810 960, Virginia Tech Transportation Institute, National Highway Traffic Safety Administration, Washington, United Sates (2008).

H. Kondo, S. Oota, T. Yamada, H. Oota, and H. Kondo, “Automobile mirror assembly,” U.S. Patent 5,793,542 1998).

H. Graff, “Wide-angle mirror for automobiles and the like,” U.S. Patent 4,331,382 (1982).

J. Roger, Goolsby “Blind spot sideview mirrors,” U.S. Patent 6,270,225 B1 (2001).

Chuang qin Co., LTD., http://www.cid.com.tw

L. L. C. Zemax, https://www.zemax.com/ .

E. J. McIsaac, and V. D. Bhise, “Automotive field of view analysis using polar plots,” SAE Technical Paper 950602 (1995).

S. O’Day, “Binocular disparity in aspherical mirrors,” SAE paper No. 980918.
[Crossref]

B. H. Walker, Optical Design for Visual Systems (SPIE, 2000).

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 (13)

Fig. 1
Fig. 1 Image jump can be observed when the eye sees across the borders between sections with different orientations and curvatures. The borders of (a) a mirror composed of a convex portion and a flat portion and (b) a multiradius mirror.
Fig. 2
Fig. 2 Diagram depicting (a) the FOV of various rear-view mirrors for cars, and (b) the FOV goal of the proposed mirror for motorcycles.
Fig. 3
Fig. 3 Diagram illustrating the subtended angles of virtual images.
Fig. 4
Fig. 4 (a) Rear-view mirror dimension. Dotted line indicates the horizontal line. (b) Design layout.
Fig. 5
Fig. 5 Three viewed targets, which represent far, middle, and near vision conditions.
Fig. 6
Fig. 6 Screenshots of (a) the ZEMAX sequential component editor showing the initial layout and (b) the ZEMAX extra data editor.
Fig. 7
Fig. 7 Screenshot of the ZEMAX Merit Function Editor showing the custom merit function implemented for determining the profile of freeform mirror.
Fig. 8
Fig. 8 Incident beam simulated by ZEMAX for different field angles from far, middle and near views.
Fig. 9
Fig. 9 Overall FOV in the horizontal direction, which is the combination of right and left vision, approaches 52.4°.
Fig. 10
Fig. 10 MTF plots of the far view. MTF plots as (a) the left eye sees through the inner zone (Y ~0 mm, Z = 0 mm) and (b) the right eye sees through the inner zone (Y ~0 mm, Z = 0 mm).
Fig. 11
Fig. 11 Four views of the fabricated object. (a) Top view; (b) perspective view; (c) right view; (d) front view.
Fig. 12
Fig. 12 Optical bench for measuring the overall FOV of the partitioned mirror by the ray-trace method.
Fig. 13
Fig. 13 Reflective images of (a) a flat mirror and (b) a freeform reflector.

Tables (2)

Tables Icon

Table 1 Binocular Disparity of the Freeform Mirror for Each Scenario

Tables Icon

Table 2 Binocular Disparity of a Commercial Mirror for Each Scenario

Equations (5)

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

ω c ω f = R(l+ l f ) 2l l f +R(l+ l f )
ID= l R l L l R
z= c r 2 1+ 1(1+k) c 2 r 2 + i=1 N A i x m y n
z= c r 2 1+ 1(1+k) c 2 r 2 + A 1 y 2 + A 2 y 4 + A 3 y 6
z= 0.01( X 2 + Y 2 ) 1+ 10.000001( X 2 + Y 2 ) +4.3651 ( Y 160 ) 2 +3.485 ( Y 160 ) 4 0.733 ( Y 160 ) 6

Metrics