Abstract

The blind spot of automobiles has been a critical issue in driving safety performance. Side mirrors that use an aspheric shape to achieve a wider angle rather than conventional spherical or flat mirrors have been recently permitted from European Union safety regulations. However, these mirrors also cause difficulty in perceiving the speed and distance of an approaching vehicle in the aspheric mirror zones with their decreasing radii of curvature. We demonstrated new side mirrors showing a stable vehicle image by inserting a horizontally progressive zone between the two outer spherical zones used for the far and near views.

© 2013 Optical Society of America

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References

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  1. J. Luoma, M. J. Flannagan, and M. Sivak, Transp. Hum. Factors 2, 279 (2000).
    [CrossRef]
  2. J. F. Morgan and M. Blanco, “Synthesis study of light vehicle non-planar mirror research,” NHTSA DOT HS 811–328, 47 (2010).
  3. R. A. Hicks, Opt. Lett. 33, 1672 (2008).
    [CrossRef]
  4. J. Loos, G. Greiner, and H. Seidel, Comput. Aided Des. 30, 595 (1998).
    [CrossRef]
  5. J. Wang, R. Gulliver, and F. Santosa, SIAM J. Appl. Math. 64, 277 (2003).
    [CrossRef]
  6. D. J. Walton and D. S. Meek, J. Comput. Appl. Math. 72, 85 (1996).
    [CrossRef]
  7. Z. Habib and M. Sakai, Comput. Aided Des. 39, 125 (2007).
    [CrossRef]
  8. L. Piegel and W. Tiller, The Nurbs Book (Springer, 1997).
  9. S. M. O’Day, “Binocular disparity in aspherical mirrors,” SAE Technical Paper 980918 (1998).
  10. “Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 810-959, 33 (2008).

2008

2007

Z. Habib and M. Sakai, Comput. Aided Des. 39, 125 (2007).
[CrossRef]

2003

J. Wang, R. Gulliver, and F. Santosa, SIAM J. Appl. Math. 64, 277 (2003).
[CrossRef]

2000

J. Luoma, M. J. Flannagan, and M. Sivak, Transp. Hum. Factors 2, 279 (2000).
[CrossRef]

1998

J. Loos, G. Greiner, and H. Seidel, Comput. Aided Des. 30, 595 (1998).
[CrossRef]

1996

D. J. Walton and D. S. Meek, J. Comput. Appl. Math. 72, 85 (1996).
[CrossRef]

Blanco, M.

J. F. Morgan and M. Blanco, “Synthesis study of light vehicle non-planar mirror research,” NHTSA DOT HS 811–328, 47 (2010).

Flannagan, M. J.

J. Luoma, M. J. Flannagan, and M. Sivak, Transp. Hum. Factors 2, 279 (2000).
[CrossRef]

Greiner, G.

J. Loos, G. Greiner, and H. Seidel, Comput. Aided Des. 30, 595 (1998).
[CrossRef]

Gulliver, R.

J. Wang, R. Gulliver, and F. Santosa, SIAM J. Appl. Math. 64, 277 (2003).
[CrossRef]

Habib, Z.

Z. Habib and M. Sakai, Comput. Aided Des. 39, 125 (2007).
[CrossRef]

Hicks, R. A.

Loos, J.

J. Loos, G. Greiner, and H. Seidel, Comput. Aided Des. 30, 595 (1998).
[CrossRef]

Luoma, J.

J. Luoma, M. J. Flannagan, and M. Sivak, Transp. Hum. Factors 2, 279 (2000).
[CrossRef]

Meek, D. S.

D. J. Walton and D. S. Meek, J. Comput. Appl. Math. 72, 85 (1996).
[CrossRef]

Morgan, J. F.

J. F. Morgan and M. Blanco, “Synthesis study of light vehicle non-planar mirror research,” NHTSA DOT HS 811–328, 47 (2010).

O’Day, S. M.

S. M. O’Day, “Binocular disparity in aspherical mirrors,” SAE Technical Paper 980918 (1998).

Piegel, L.

L. Piegel and W. Tiller, The Nurbs Book (Springer, 1997).

Sakai, M.

Z. Habib and M. Sakai, Comput. Aided Des. 39, 125 (2007).
[CrossRef]

Santosa, F.

J. Wang, R. Gulliver, and F. Santosa, SIAM J. Appl. Math. 64, 277 (2003).
[CrossRef]

Seidel, H.

J. Loos, G. Greiner, and H. Seidel, Comput. Aided Des. 30, 595 (1998).
[CrossRef]

Sivak, M.

J. Luoma, M. J. Flannagan, and M. Sivak, Transp. Hum. Factors 2, 279 (2000).
[CrossRef]

Tiller, W.

L. Piegel and W. Tiller, The Nurbs Book (Springer, 1997).

Walton, D. J.

D. J. Walton and D. S. Meek, J. Comput. Appl. Math. 72, 85 (1996).
[CrossRef]

Wang, J.

J. Wang, R. Gulliver, and F. Santosa, SIAM J. Appl. Math. 64, 277 (2003).
[CrossRef]

Comput. Aided Des.

J. Loos, G. Greiner, and H. Seidel, Comput. Aided Des. 30, 595 (1998).
[CrossRef]

Z. Habib and M. Sakai, Comput. Aided Des. 39, 125 (2007).
[CrossRef]

J. Comput. Appl. Math.

D. J. Walton and D. S. Meek, J. Comput. Appl. Math. 72, 85 (1996).
[CrossRef]

Opt. Lett.

SIAM J. Appl. Math.

J. Wang, R. Gulliver, and F. Santosa, SIAM J. Appl. Math. 64, 277 (2003).
[CrossRef]

Transp. Hum. Factors

J. Luoma, M. J. Flannagan, and M. Sivak, Transp. Hum. Factors 2, 279 (2000).
[CrossRef]

Other

J. F. Morgan and M. Blanco, “Synthesis study of light vehicle non-planar mirror research,” NHTSA DOT HS 811–328, 47 (2010).

L. Piegel and W. Tiller, The Nurbs Book (Springer, 1997).

S. M. O’Day, “Binocular disparity in aspherical mirrors,” SAE Technical Paper 980918 (1998).

“Study of diver performance/acceptance using aspheric mirrors in light vehicle applications,” NHTSA DOT HS 810-959, 33 (2008).

Supplementary Material (1)

» Media 1: MOV (6831 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Horizontal radius of curvature of the inner zone (far view) and outer zone (near view) are RF and RN, respectively. All the vertical radius of curvature has RF. The vehicle image is reduced only in the progressive zone while the image sizes of the inner and outer zones are not changed.

Fig. 2.
Fig. 2.

Cubic spiral is defined by the control points (P1, P2, P3, P4) and the position CN (a,b), which are the variables that are optimized to obtain G2 continuity at the two connection points. Other values of RF, RN, and CF are fixed in the optimization process.

Fig. 3.
Fig. 3.

Optimized blending generates the surface data for the progressive mirror. (a) Three-dimensional surface map. (b) Contour map. (c) The change of the horizontal radius of curvature. (d) The mean focusing power in the horizontal and the vertical direction are negative to minify the reflective image. The astigmatism is the power difference between the horizontal and vertical directions. (e) Mean power distribution. (f) Astigmatism distribution. The astigmatism in the far view is zero.

Fig. 4.
Fig. 4.

Curvature evaluation of the manufactured progressive mirror. The sampling interval of the measured points is 5 mm. (a) Contour map of the measured data. (b) Mean radius of curvature. The progressive zone is spread as compared with the design configuration from the manufacturing difficulty of the rapid production. The power fluctuation in each zone is tolerable. (c) Mean power distribution. (d) Astigmatism distribution.

Fig. 5.
Fig. 5.

Reflective images of a flat, an aspheric, and a progressive mirror. (a) Aspheric mirror. Blue lines were drawn to indicate the boundary lines. (b) Progressive mirror. (c) Rear view of a flat mirror. (d) Rear view of the progressive mirror. Supplementary video 1 depicts the movements of vehicles equipped with a progressive mirror (Media 1).

Equations (3)

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c(u)=i=1nBi,n(u)Pi,0u1Bi,n(u)=n!i!(ni)!ui(1u)ni,
c(u)=inBi,n(u)Pi=nin1Bi,n1(u)(Pi+1Pi),
J=f(P1,P2,P3,P4,a,b)=f[E1(P1,P2,P3,P4,a,b),E2(P1,P2,P3,P4,a,b)]=(E12+E22),

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