Abstract

Traditional microscopes have limitations in obtaining true 3D (three-dimensional) stereovision. Although some optical microscopes have been developed for 3D vision, many of them are complex, expensive, or limited to transparent samples. In this research, a freeform optical prism array was designed and fabricated to achieve 3D stereo imaging capability for microscope and machine vision applications. To form clear stereo images from multiple directions simultaneously, freeform optical surface design was applied to the prisms. In a ray tracing operation to determine the optical performance of the freeform prisms, Taylor series was used to calculate the surface shape. The virtual image spot diagrams were generated by using ray tracing methods for both the freeform prisms and the regular prisms. The results showed that all the light rays can be traced back to a single point for the freeform prism, and aberration was much smaller than that of the regular prism. The ray spots formed by the freeform prisms were adequate for image formation. Furthermore, the freeform prism array was fabricated by using a combined ultraprecision diamond turning and slow tool servo broaching process in a single, uninterrupted operation. The slow tool servo process ensured that the relative tolerance among prisms is guaranteed by the precision of the ultraprecision machine without the need for assembly. Finally 3D imaging tests were conducted to verify the freeform prism array’s optical performance. The principle of the freeform prism array investigated in this research can be applied to microscopy, machine vision, robotic sensing, and many other areas.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. D. Cheng, Y. Wang, H. Hua, M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48, 2655–2668 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. C. N. Huang, L. Li, A. Y. Yi, “Design and fabrication of a micro alvarez lens array with a variable focal length,” Microsyst. Technol. 15, 559–563 (2009).
    [CrossRef]
  20. A. Y. Yi, C. N. Huang, F. Klocke, C. Brecher, M. Winterschladen, G. Pongs, “Compression molding of freeform glass optics,” Appl. Opt. 45, 6511–6518 (2006).
    [CrossRef] [PubMed]

2010

L. Li, S. A. Collins, A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” ASME J. Manuf. Sci. Eng. 132, 021002 (2010).
[CrossRef]

L. Li, A. Y. Yi, “Development of a 3D artificial compound eye,” Opt. Express 18, 18125–18137 (2010).
[CrossRef] [PubMed]

2009

D. Cheng, Y. Wang, H. Hua, M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48, 2655–2668 (2009).
[CrossRef] [PubMed]

C. N. Huang, L. Li, A. Y. Yi, “Design and fabrication of a micro alvarez lens array with a variable focal length,” Microsyst. Technol. 15, 559–563 (2009).
[CrossRef]

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

M. Levoy, Z. Zhang, I. Mcdowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), p 144–61 (2009).
[CrossRef] [PubMed]

2008

J. Rosen, G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[CrossRef]

X. Hao, Z. Zheng, X. Liu, P. Gu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
[CrossRef]

C. Y. Chen, T. T. Yang, W. S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16, 15495–15505 (2008).
[CrossRef] [PubMed]

2007

Y. Xiao, K. B. Lim, “A prism-based single-lens stereovision system: From trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

2006

2002

2000

D. H. Lee, I. S. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Rob. Autom. 16, 528–541 (2000).
[CrossRef]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” ACM Trans. Graphics 25, 924–34 (2006).
[CrossRef]

Aikio, M.

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

Bergmann, L.

L. Bergmann, Optics of Waves and Particles (Walter de Gruyter, 1999).

Brecher, C.

Brooker, G.

J. Rosen, G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[CrossRef]

Chen, C. Y.

Cheng, D.

Collins, S. A.

L. Li, S. A. Collins, A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” ASME J. Manuf. Sci. Eng. 132, 021002 (2010).
[CrossRef]

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” ACM Trans. Graphics 25, 924–34 (2006).
[CrossRef]

Gu, P.

X. Hao, Z. Zheng, X. Liu, P. Gu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
[CrossRef]

Hao, X.

X. Hao, Z. Zheng, X. Liu, P. Gu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
[CrossRef]

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” ACM Trans. Graphics 25, 924–34 (2006).
[CrossRef]

Hua, H.

Huang, C. N.

C. N. Huang, L. Li, A. Y. Yi, “Design and fabrication of a micro alvarez lens array with a variable focal length,” Microsyst. Technol. 15, 559–563 (2009).
[CrossRef]

A. Y. Yi, C. N. Huang, F. Klocke, C. Brecher, M. Winterschladen, G. Pongs, “Compression molding of freeform glass optics,” Appl. Opt. 45, 6511–6518 (2006).
[CrossRef] [PubMed]

Jin, G.

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

Klocke, F.

Kweon, I. S.

D. H. Lee, I. S. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Rob. Autom. 16, 528–541 (2000).
[CrossRef]

Lee, D. H.

D. H. Lee, I. S. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Rob. Autom. 16, 528–541 (2000).
[CrossRef]

Levoy, M.

M. Levoy, Z. Zhang, I. Mcdowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), p 144–61 (2009).
[CrossRef] [PubMed]

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” ACM Trans. Graphics 25, 924–34 (2006).
[CrossRef]

Li, L.

L. Li, A. Y. Yi, “Development of a 3D artificial compound eye,” Opt. Express 18, 18125–18137 (2010).
[CrossRef] [PubMed]

L. Li, S. A. Collins, A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” ASME J. Manuf. Sci. Eng. 132, 021002 (2010).
[CrossRef]

C. N. Huang, L. Li, A. Y. Yi, “Design and fabrication of a micro alvarez lens array with a variable focal length,” Microsyst. Technol. 15, 559–563 (2009).
[CrossRef]

Lim, K. B.

Y. Xiao, K. B. Lim, “A prism-based single-lens stereovision system: From trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

Liu, X.

X. Hao, Z. Zheng, X. Liu, P. Gu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
[CrossRef]

Makinen, J. T.

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

Mcdowall, I.

M. Levoy, Z. Zhang, I. Mcdowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), p 144–61 (2009).
[CrossRef] [PubMed]

Muschaweck, J.

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” ACM Trans. Graphics 25, 924–34 (2006).
[CrossRef]

Pongs, G.

Ries, H.

Rochow, T. G.

T. G. Rochow, P. A. Tucker, Introduction to Microscopy by Means of Light, Electrons, X Rays, or Acoustics (Plenum, 1994).

Rosen, J.

J. Rosen, G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[CrossRef]

Sun, W. S.

Talha, M. M.

Tucker, P. A.

T. G. Rochow, P. A. Tucker, Introduction to Microscopy by Means of Light, Electrons, X Rays, or Acoustics (Plenum, 1994).

Wang, Y.

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

D. Cheng, Y. Wang, H. Hua, M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48, 2655–2668 (2009).
[CrossRef] [PubMed]

Winterschladen, M.

Xiao, Y.

Y. Xiao, K. B. Lim, “A prism-based single-lens stereovision system: From trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

Yang, B.

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

Yang, T. T.

Yi, A. Y.

L. Li, S. A. Collins, A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” ASME J. Manuf. Sci. Eng. 132, 021002 (2010).
[CrossRef]

L. Li, A. Y. Yi, “Development of a 3D artificial compound eye,” Opt. Express 18, 18125–18137 (2010).
[CrossRef] [PubMed]

C. N. Huang, L. Li, A. Y. Yi, “Design and fabrication of a micro alvarez lens array with a variable focal length,” Microsyst. Technol. 15, 559–563 (2009).
[CrossRef]

A. Y. Yi, C. N. Huang, F. Klocke, C. Brecher, M. Winterschladen, G. Pongs, “Compression molding of freeform glass optics,” Appl. Opt. 45, 6511–6518 (2006).
[CrossRef] [PubMed]

Zhang, Z.

M. Levoy, Z. Zhang, I. Mcdowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), p 144–61 (2009).
[CrossRef] [PubMed]

Zheng, Z.

X. Hao, Z. Zheng, X. Liu, P. Gu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
[CrossRef]

ACM Trans. Graphics

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” ACM Trans. Graphics 25, 924–34 (2006).
[CrossRef]

Appl. Opt.

ASME J. Manuf. Sci. Eng.

L. Li, S. A. Collins, A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” ASME J. Manuf. Sci. Eng. 132, 021002 (2010).
[CrossRef]

IEEE Trans. Rob. Autom.

D. H. Lee, I. S. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Rob. Autom. 16, 528–541 (2000).
[CrossRef]

Image Vis. Comput.

Y. Xiao, K. B. Lim, “A prism-based single-lens stereovision system: From trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

J. Microsc.

M. Levoy, Z. Zhang, I. Mcdowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), p 144–61 (2009).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt.

X. Hao, Z. Zheng, X. Liu, P. Gu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Microsyst. Technol.

C. N. Huang, L. Li, A. Y. Yi, “Design and fabrication of a micro alvarez lens array with a variable focal length,” Microsyst. Technol. 15, 559–563 (2009).
[CrossRef]

Nat. Photonics

J. Rosen, G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[CrossRef]

Opt. Express

Optik

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

Other

S. Kasap and P. Capper, eds., Springer Handbook of Electronic and Photonic Materials (Springer, 2007).
[CrossRef]

L. Bergmann, Optics of Waves and Particles (Walter de Gruyter, 1999).

http://www.hirox-usa.com/products/microscope/kh7700_03.html.

http://www.waltrontech.com/EN/index.asp.

http://www.digitalmicroscope.com/feature/multi_viewer.php.

T. G. Rochow, P. A. Tucker, Introduction to Microscopy by Means of Light, Electrons, X Rays, or Acoustics (Plenum, 1994).

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Figures (13)

Fig. 1
Fig. 1

Principles for 3D vision. (a) By combining three prisms and a viewing lens, three images can be formed for one object. The object planes P1, P2, and P3 for the three images are tilted because of the prisms. Such a setup is equivalent to a system consisting of three individual lenses viewing from three directions (b).

Fig. 2
Fig. 2

Schematic of a ray path through a prism.

Fig. 3
Fig. 3

(a) Cross sectional view and (b) isometric view of the prism array (unit, mm).

Fig. 4
Fig. 4

Schematic showing virtual images formed by the prisms. V1, V2, and V3 are the three virtual images formed by the prisms; these virtual images become the virtual objects for the viewing lens.

Fig. 5
Fig. 5

Virtual image formed by the parallel plate and one of the surrounding prisms. The center parallel plate will form a virtual image right above the object, while the surrounding prisms cannot form a good quality virtual image because of very large aberrations.

Fig. 6
Fig. 6

Ray tracing of a freeform prism. Ray coming from the object point (O) will refract at the bottom (1) and top (2) surfaces of a prism; virtual image point (V) is on the ray that is back traced from the top surface of the prism.

Fig. 7
Fig. 7

(a) Surface profile of the freeform prism. (b) The difference of the freeform prism from the prism designed in Section 2.

Fig. 8
Fig. 8

Effect of the step size in calculating the freeform surface.

Fig. 9
Fig. 9

(a) 3D ray tracing for a freeform prism. (b) Spot diagram of the freeform prism; inset plot shows the enlarged spot diagram.

Fig. 10
Fig. 10

(a) 3D ray tracing for a regular prism with flat surfaces. (b) Spot diagram of the regular prism.

Fig. 11
Fig. 11

Tool path for slow tool servo broaching of the freeform prism obtained by compensating the cutting tool shape using the surface profile and the normal vector of the freeform prism.

Fig. 12
Fig. 12

3D stereo views by using the freeform prism array and a zoom lens system: (a) ballpoint pen tip; (b) 0.2 mm diameter micro drill bit.

Fig. 13
Fig. 13

Enlarged view of the 0.2 mm micro drill bit at 4.5 × magnification: (a) viewing through one of the freeform prisms; (b) viewing without using the freeform prism but with the object at a tilted position.

Equations (13)

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

δ = I 1 I 1 + I 2 I 2 = I 1 + I 2 A .
A = I 1 + I 2 .
A = I 1 + I 2 = sin 1 ( 1 n sin I 1 ) + sin 1 ( 1 n sin I 2 ) = sin 1 ( 1 n sin K K ) + sin 1 ( 1 n sin A ) .
sin I 1 = n sin I 1 .
N 1 ( O A × A B ) = 0 .
cos I 1 = O A N 1 | O A | | N 1 | ,
cos I 1 = A B N 1 | A B | | N 1 | .
n sin I 2 = sin I 2 ,
N 2 ( A B × B C ) = 0 ,
cos I 2 = A B N 2 | A B | | N 2 | ,
cos I 2 = B C N 2 | B C | | N 2 | .
| Z ( X B , Y B ) | B ( n + 1 ) | Z ( X B , Y B ) | B ( n ) + Δ X | f X B | X B n + Δ Y | f Y B | X B n + 1 2 ! [ Δ X 2 | 2 f X B X B | X B n + 2 Δ X Δ Y | 2 f X B Y B | X B n + Δ Y 2 | 2 f Y B Y B | X B n ] + .
| Z ( X B , Y B ) | B ( n + 1 ) | Z ( X B , Y B ) | B ( n ) + Δ X | f X B | X B n + Δ Y | f Y B | X B n .

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