Abstract

A design of a large-numerical-aperture aspherical singlet for three-dimensional (3-D) sensor applications is presented. This lens can be used to generate a homogenous irradiance on the target in a 3-D sensor, which is based on the principle of time of flight and uses an LED as light source. A numerical method was used in the design. The designed planoaspherical singlet has a numerical aperture of 0.67, low refractive index, and moderate surface shape for easy fabrication. The simulation results revealed that the irradiance deviation within 97% of the designed area is less than 5% and that the transmittance of the lens is greater than 90.5%. The results from a Lambertian source were compared with those from a point source.

© 2000 Optical Society of America

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References

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1999 (1)

1998 (4)

G. Andersen, R. J. Knize, “A high resolution, holographically corrected microscope with a Fresnel lens objective at large working distances,” Opt. Exp. 2, 546–551 (1998).

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

N. C. Evans, D. L. Shealy, “Design and optimization of an irradiance profile-shaping system with a genetic algorithm method,” Appl. Opt. 37, 5216–5221 (1998).
[CrossRef]

J. M. Gordon, A. Rabl, “Reflectors for uniform far-field irradiance: fundamental limits and example of an axisymmetric solution,” Appl. Opt. 37, 44–47 (1998).
[CrossRef]

1997 (1)

1993 (1)

1989 (1)

1986 (1)

1982 (2)

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
[CrossRef]

W. B. Veldkamp, “Technique for generating focal-plane flattop laser-beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

1975 (2)

1949 (1)

G. D. Wassermann, E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62, 2–8 (1949).
[CrossRef]

Andersen, G.

G. Andersen, R. J. Knize, “A high resolution, holographically corrected microscope with a Fresnel lens objective at large working distances,” Opt. Exp. 2, 546–551 (1998).

Barnoski, M. K.

M. K. Barnoski, “Coupling components for optical waveguides,” in M. K. Barnoski, ed., Fundamentals of Optical Fiber Communications (Academic, New York, 1976), pp. 83–105.

Bundschuh, B.

B. Bundschuh, Laseroptische 3D-Konturerfassung (Vieweg Verlag, Braunschweig, Germany, 1991), pp. 60–62.

Burkhard, D. G.

Buxbaum, B.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

Chen, Z.

Deng, X.

Elmer, W. B.

W. B. Elmer, The Optical Design of Reflectors (Wiley, New York, 1980).

Etten, V.

V. Etten, V. D. Plaats, Fundamentals of Optical Fiber Communications (Prentice Hall, Cambridge, 1991), pp. 139–147.

Evans, N. C.

Gordon, J. M.

Hartmann, K.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

R. Schwarte, H. Heinol, Z. Xu, K. Hartmann, “A new active 3D-vision system based on rf-modulation interferometry of incoherent light,” Intelligent Robots and Computer Vision XIV: Algorithms, Techniques, Active Vision, and Materials Handling, D. P. Casasent, ed., Proc. SPIE2588, 126–134 (1995).

Hayashi, S.

Heinol, H.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

R. Schwarte, H. Heinol, Z. Xu, K. Hartmann, “A new active 3D-vision system based on rf-modulation interferometry of incoherent light,” Intelligent Robots and Computer Vision XIV: Algorithms, Techniques, Active Vision, and Materials Handling, D. P. Casasent, ed., Proc. SPIE2588, 126–134 (1995).

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

Ichimura, I.

Kino, G. S.

Kleuver, W.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

Knize, R. J.

G. Andersen, R. J. Knize, “A high resolution, holographically corrected microscope with a Fresnel lens objective at large working distances,” Opt. Exp. 2, 546–551 (1998).

Leger, J. R.

J. R. Leger, “Laser beam shaping,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 223–257.

Liang, X.

Luan, X.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

Ma, R.

Mansuripur, M.

Plaats, V. D.

V. Etten, V. D. Plaats, Fundamentals of Optical Fiber Communications (Prentice Hall, Cambridge, 1991), pp. 139–147.

Rabl, A.

Ries, H.

Ringbeck, T.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

Roberts, N. C.

Sasián, J. M.

Schwarte, R.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

R. Schwarte, H. Heinol, Z. Xu, K. Hartmann, “A new active 3D-vision system based on rf-modulation interferometry of incoherent light,” Intelligent Robots and Computer Vision XIV: Algorithms, Techniques, Active Vision, and Materials Handling, D. P. Casasent, ed., Proc. SPIE2588, 126–134 (1995).

Shafer, D.

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
[CrossRef]

Shealy, D. L.

Tai, W.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

Veldkamp, W. B.

W. B. Veldkamp, “Technique for generating focal-plane flattop laser-beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

Wassermann, G. D.

G. D. Wassermann, E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62, 2–8 (1949).
[CrossRef]

Winston, R.

Wolf, E.

G. D. Wassermann, E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62, 2–8 (1949).
[CrossRef]

Xu, Z.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

R. Schwarte, H. Heinol, Z. Xu, K. Hartmann, “A new active 3D-vision system based on rf-modulation interferometry of incoherent light,” Intelligent Robots and Computer Vision XIV: Algorithms, Techniques, Active Vision, and Materials Handling, D. P. Casasent, ed., Proc. SPIE2588, 126–134 (1995).

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

Yu, W.

Zhang, Z.

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

Appl. Opt. (8)

J. Opt. Soc. Am. A (1)

Opt. Exp. (1)

G. Andersen, R. J. Knize, “A high resolution, holographically corrected microscope with a Fresnel lens objective at large working distances,” Opt. Exp. 2, 546–551 (1998).

Opt. Laser Technol. (1)

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
[CrossRef]

Proc. Phys. Soc. B (1)

G. D. Wassermann, E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62, 2–8 (1949).
[CrossRef]

Rev. Sci. Instrum. (1)

W. B. Veldkamp, “Technique for generating focal-plane flattop laser-beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

Tech. Messen (1)

R. Schwarte, H. Heinol, B. Buxbaum, Z. Xu, T. Ringbeck, Z. Zhang, W. Tai, K. Hartmann, W. Kleuver, X. Luan, “Neuartige 3D-Visionssysteme auf der Basis Layout-optimierter PMD-Strukturen,” Tech. Messen 7–8, 264–271 (1998).

Other (7)

R. Schwarte, H. Heinol, B. Buxbaum, T. Ringbeck, Z. Xu, K. Hartmann, “Principles of three-dimensional imaging techniques,” in Computer Vision and Applications. 1. Sensors and Imaging, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic, Boston, 1999), pp. 463–484.

R. Schwarte, H. Heinol, Z. Xu, K. Hartmann, “A new active 3D-vision system based on rf-modulation interferometry of incoherent light,” Intelligent Robots and Computer Vision XIV: Algorithms, Techniques, Active Vision, and Materials Handling, D. P. Casasent, ed., Proc. SPIE2588, 126–134 (1995).

M. K. Barnoski, “Coupling components for optical waveguides,” in M. K. Barnoski, ed., Fundamentals of Optical Fiber Communications (Academic, New York, 1976), pp. 83–105.

V. Etten, V. D. Plaats, Fundamentals of Optical Fiber Communications (Prentice Hall, Cambridge, 1991), pp. 139–147.

B. Bundschuh, Laseroptische 3D-Konturerfassung (Vieweg Verlag, Braunschweig, Germany, 1991), pp. 60–62.

W. B. Elmer, The Optical Design of Reflectors (Wiley, New York, 1980).

J. R. Leger, “Laser beam shaping,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 223–257.

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Figures (5)

Fig. 1
Fig. 1

Basic setup for translating a small extended source S through desired aspherical singlet AL to target T of radius R max at distance L. The second surface of the lens is an aspherical surface.

Fig. 2
Fig. 2

(a) Surface profile of the designed planoaspherical lens; maximal sag is 5.5 mm at a clear aperture 20.5 mm. (b) Plot of the radius of curvature of the surface with aperture height. The minimal radius of curvature is 11.1 mm.

Fig. 3
Fig. 3

Simulated irradiance distribution on target of 2-m distance. (a) Three-dimensional display of the irradiance distribution. The source is a circular disk of diameter 100 µm. (b) Irradiance scans across the center of the target. Solid curve with error bars, with a circular disk source of diameter 100 µm; dashed curve, with a rectangular source of size 500 µm × 500 µm. The ripples are the characteristic of the statistical accuracy of our simulation. The inset in (b) shows the details of the irradiance variation.

Fig. 4
Fig. 4

Transmittance of the aspherical lens. In the whole clear aperture the transmittance is larger than 90.5%.

Fig. 5
Fig. 5

Irradiance distribution from a point source with the same lens.

Equations (15)

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

0Ω BA cos θdΩ=0y Ey2πydy,
E0=BA sin2 θmaxRmax2.
y=Rmaxsin θmaxsin θ.
sin θ1=1/nsin θ,
dy2dz2=-n cos θ1-cos u2n sin θ1-sin u2,
y2=L1 tan θ+d+z2tan θ1,
tan u2=y-y2L-z2.
tan u2=sin θL-z2Rmaxsin θmax-L1cos θ-d+z2n2-sin2 θ1/2.
dy2dθ=L1cos2 θ+d+z2cos2 θ1dθ1dθ+tan θ1 dz2dθ.
dθ1dθ=cos θn cos θ1=cos θn2-sin2 θ1/2.
dz2dθ=-L1cos2 θ+n2d+z2cos θn2-sin2 θ3/2n2-sin2 θ1/2-cos u2sin θ-sin u2+sin θn2-sin2 θ1/2,
z2=0  at θ=0.
z2=cy221+1-c2y221/2+i=18 aiy22i,
c=-8.409849×10-2,
a1=-3.024942×10-3, a2=3.278520×10-5, a3=-9.433133×10-7, a4=3.729810×10-8, a5=-6.968223×10-10, a6=7.935733×10-12, a7=-4.798852×10-14, a8=1.259980×10-16.

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