Abstract

Applications of optical systems, including depth by focus and three-dimensional metrology, have been developed recently in which the image is characterized over a range of object depths simultaneously and in which the focus of the systems is also varied. Important to such applications is the variation of image magnification with focus. A general understanding of this phenomenon is developed, and two new and useful concepts associated with the variation of the magnification of an image are introduced. Errors and oversights in the existing literature are explained and corrected, and the requirements for an optical system to exhibit the magnification properties desired in such applications are identified. It is shown that not all telecentric systems have these properties and that there exist practical and attractive nontelecentric systems that do exhibit them.

© 2002 Optical Society of America

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References

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  1. T. Darrell, K. Wohn, “Pyramid based depth from focus,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 504–509.
    [CrossRef]
  2. M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 1360–1365 (1997).
    [CrossRef]
  3. D. F. Schaack, “Making accurate three-dimensional measurements through a standard borescope,” in Nondestructive Evaluation of Aging Aircraft, Airports, and Aerospace Hardware II, G. A. Geithman, G. E. Georgeson, eds., Proc. SPIE3397, 264–276 (1998).
    [CrossRef]
  4. D. F. Schaack, “Apparatus and method for making accurate three-dimensional size measurements of inaccessible objects,” U.S. patent6,009,189 (28December1999).
  5. P. T. Quinn, “Focus size compensation,” U.S. patent4,083,057 (4April1978).
  6. R. G. Willson, S. A. Shafer, “Active lens control for high precision computer imaging,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 2063–2070.
  7. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 131.
  8. P. J. Scott, “The pupil in perspective,” Photogramm. Rec. 9, 83–92 (1977).
    [CrossRef]
  9. R. Howell, “Method and apparatus for viewing and measuring damage in an inaccessible area,” U.S. patent4,078,864 (14March1978).
  10. A. Dianna, J. Costello, “Digitally measuring scopes using a high resolution encoder,” U.S. patent5,573,492 (12November1996).
  11. P. Luo, Y. Chao, M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
    [CrossRef]
  12. W. Wallin, “A note on apparent magnification in out-of-focus images,” J. Opt. Soc. Am. 43, 60–61 (1953).
    [CrossRef]
  13. M. Yasukuni, T. Ogura, T. Omaki, M. Tanaka, “Zoom lens system capable of constant magnification photography,” U.S. patent4,193,667 (18March1980).
  14. C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. London Sect. B 65, 429–437 (1952).
    [CrossRef]
  15. D. F. Schaak, “Focusing systems for perspective dimensional measurements and optical metrology, U.S. patent application (filed 24July1998).

1997

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 1360–1365 (1997).
[CrossRef]

1994

P. Luo, Y. Chao, M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

1977

P. J. Scott, “The pupil in perspective,” Photogramm. Rec. 9, 83–92 (1977).
[CrossRef]

1953

1952

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. London Sect. B 65, 429–437 (1952).
[CrossRef]

Chao, Y.

P. Luo, Y. Chao, M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Costello, J.

A. Dianna, J. Costello, “Digitally measuring scopes using a high resolution encoder,” U.S. patent5,573,492 (12November1996).

Darrell, T.

T. Darrell, K. Wohn, “Pyramid based depth from focus,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 504–509.
[CrossRef]

Dianna, A.

A. Dianna, J. Costello, “Digitally measuring scopes using a high resolution encoder,” U.S. patent5,573,492 (12November1996).

Howell, R.

R. Howell, “Method and apparatus for viewing and measuring damage in an inaccessible area,” U.S. patent4,078,864 (14March1978).

Luo, P.

P. Luo, Y. Chao, M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Nayar, S. K.

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 1360–1365 (1997).
[CrossRef]

Ogura, T.

M. Yasukuni, T. Ogura, T. Omaki, M. Tanaka, “Zoom lens system capable of constant magnification photography,” U.S. patent4,193,667 (18March1980).

Omaki, T.

M. Yasukuni, T. Ogura, T. Omaki, M. Tanaka, “Zoom lens system capable of constant magnification photography,” U.S. patent4,193,667 (18March1980).

Quinn, P. T.

P. T. Quinn, “Focus size compensation,” U.S. patent4,083,057 (4April1978).

Schaack, D. F.

D. F. Schaack, “Making accurate three-dimensional measurements through a standard borescope,” in Nondestructive Evaluation of Aging Aircraft, Airports, and Aerospace Hardware II, G. A. Geithman, G. E. Georgeson, eds., Proc. SPIE3397, 264–276 (1998).
[CrossRef]

D. F. Schaack, “Apparatus and method for making accurate three-dimensional size measurements of inaccessible objects,” U.S. patent6,009,189 (28December1999).

Schaak, D. F.

D. F. Schaak, “Focusing systems for perspective dimensional measurements and optical metrology, U.S. patent application (filed 24July1998).

Scott, P. J.

P. J. Scott, “The pupil in perspective,” Photogramm. Rec. 9, 83–92 (1977).
[CrossRef]

Shafer, S. A.

R. G. Willson, S. A. Shafer, “Active lens control for high precision computer imaging,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 2063–2070.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 131.

Sutton, M.

P. Luo, Y. Chao, M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Tanaka, M.

M. Yasukuni, T. Ogura, T. Omaki, M. Tanaka, “Zoom lens system capable of constant magnification photography,” U.S. patent4,193,667 (18March1980).

Wallin, W.

Watanabe, M.

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 1360–1365 (1997).
[CrossRef]

Willson, R. G.

R. G. Willson, S. A. Shafer, “Active lens control for high precision computer imaging,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 2063–2070.

Wohn, K.

T. Darrell, K. Wohn, “Pyramid based depth from focus,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 504–509.
[CrossRef]

Wynne, C. G.

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. London Sect. B 65, 429–437 (1952).
[CrossRef]

Yasukuni, M.

M. Yasukuni, T. Ogura, T. Omaki, M. Tanaka, “Zoom lens system capable of constant magnification photography,” U.S. patent4,193,667 (18March1980).

IEEE Trans. Pattern Anal. Mach. Intell.

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 1360–1365 (1997).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

P. Luo, Y. Chao, M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Photogramm. Rec.

P. J. Scott, “The pupil in perspective,” Photogramm. Rec. 9, 83–92 (1977).
[CrossRef]

Proc. Phys. Soc. London Sect. B

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. London Sect. B 65, 429–437 (1952).
[CrossRef]

Other

D. F. Schaak, “Focusing systems for perspective dimensional measurements and optical metrology, U.S. patent application (filed 24July1998).

T. Darrell, K. Wohn, “Pyramid based depth from focus,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 504–509.
[CrossRef]

R. Howell, “Method and apparatus for viewing and measuring damage in an inaccessible area,” U.S. patent4,078,864 (14March1978).

A. Dianna, J. Costello, “Digitally measuring scopes using a high resolution encoder,” U.S. patent5,573,492 (12November1996).

M. Yasukuni, T. Ogura, T. Omaki, M. Tanaka, “Zoom lens system capable of constant magnification photography,” U.S. patent4,193,667 (18March1980).

D. F. Schaack, “Making accurate three-dimensional measurements through a standard borescope,” in Nondestructive Evaluation of Aging Aircraft, Airports, and Aerospace Hardware II, G. A. Geithman, G. E. Georgeson, eds., Proc. SPIE3397, 264–276 (1998).
[CrossRef]

D. F. Schaack, “Apparatus and method for making accurate three-dimensional size measurements of inaccessible objects,” U.S. patent6,009,189 (28December1999).

P. T. Quinn, “Focus size compensation,” U.S. patent4,083,057 (4April1978).

R. G. Willson, S. A. Shafer, “Active lens control for high precision computer imaging,” in Proceedings of IEEE International Conference on Robotics and Automation (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 2063–2070.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 131.

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Figures (3)

Fig. 1
Fig. 1

Tracing the chief ray and two marginal rays through an optical system consisting of an entrance pupil (EntP), first and second principal planes (PP1 and PP2), and an image viewing plane (IVP). The chief ray marks the centroid of an unvignetted bundle of rays at the IVP.

Fig. 2
Fig. 2

First example of a system exhibiting constant relative magnification. The system consists of two thin lenses, L1 and L2, and an IVP. The focal length of L1 is negative, and the focal length of L2 is positive. The aperture stop S is located at L2. (a) Overall view of the system viewing a point on a nearby object; the focal state of the system is set for a range larger than that of the object. (b) Detailed view of the situation shown in (a); the system is focused at infinity. Rays from a second object point symmetrically located about the optical axis were added to allow visualization of the position of the entrance pupil. Because S is located at L2, the entrance pupil EntP is located between L1 and L2. The principal planes of the system PP1 and PP2 are located behind L2. IVP is located at the rear focal point of system, FP2, when the system is focused at infinity. (c) View of the system when it is refocused on the nearby object at constant relative magnification; the height of the image of the object point on the IVP remains unchanged. L1 moves toward the object and L2 moves away from the object to keep EntP at an unchanged position along the optical axis with respect to the object. The IVP moves away from the object. The fact that FP2 moves only slightly during this particular focusing operation is a coincidence.

Fig. 3
Fig. 3

Second example of a system exhibiting constant relative magnification. (a) Overall layout of the system. The system consists of three lens groups, L1, L2, and L3, drawn as thin lenses. The stop S is located at the front focal plane of L1, and the IVP is located at the rear focal plane of L3. The position of L2 is variable and serves to adjust the focal state of the system. The rays are drawn from an object at infinity. (b) Detail view of the rear portion of the system when it is focused at infinity and it is viewing a nearby object plane. The image is out of focus at IVP. (c) Detail view of the rear portion of the system when it is focused on the nearby object plane. L2 has moved a distance d i between panels (b) and (c), and the image height remains unchanged as this focusing operation proceeds.

Equations (12)

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

M=MF, R,
M=M1FM2R.
Me=hicrhocr=-1zEntp-zozPP1-zEntp+1-zPP1-zEntpf×zIVP-zPP2.
Me=-fzEntp-zo.
Mαf=-fzEntp-zmin-f-f-fα-1+αf=-α-1α-12-1
MαfM-111000.
zPP1+1-zPP1fzIVP-zPP2=K,
1zPP1-zf+1zIVP-zPP2=1f.
K=fzff+zf-zPP1,
zIVP=zff+zPP2+fzPP1-zPP2-zPP1zPP2f+zf-zPP1.
zL1=zf-4+-3zf1/216-3zf1/23, zL2=zf-5+31/23zf2-25zf+483-zf1/216-3zf1/2, zIVP=-316-3zf1/2-zf3/2-6-zf1/216-3zf1/2+331/2zf2-3431/2zf+9631/23-zf1/216-3zf1/2,
Me=-f1f3zof2,

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