Abstract

Recent progress in micro-optics fabrication and optical modeling software opens the opportunity to investigate how microlenslet-array-based compact relay systems can be designed and assessed. We present various optical configurations that include an appropriate baffle computation to eliminate ghost images, followed by an analysis of image quality. The investigation shows the existing trade-off between compactness of the system and a tiling effect observed in the corresponding image, an effect we refer to as lensletization. To yield meaningful optical modeling results, we provide insight into ray-tracing optimization while ensuring a sufficient signal-to-noise ratio. The results show that, given no discernable lensletization, the most compact configuration to image gray-scale images is the 5f-based system. Finally, simulations of the imaging of gray scale and color bitmaps through microlenslet arrays are demonstrated for the first time to our knowledge.

© 2003 Optical Society of America

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References

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  1. V. Shaoulov, J. Rolland, “Compact relay lenses using microlenslet arrays,” in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 74–79 (2002).
    [CrossRef]
  2. J. P. Rolland, H. Hua, V. Shaoulov, “Design of a compact relay lens,” Tech. Rep. TR02-05 (University of Central Florida, Orlando, Fla., 2002).
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    [CrossRef]
  7. J. Mir, “High resolution optical-addressing device and electronic scanner and/or printer apparatus employing such device,” U.S. patent4,377,753 (22March1983).
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    [CrossRef]
  9. H. Hua, A. Girardot, C. Gao, J. P. Rolland, “Engineering of head-mounted projective displays,” Appl. Opt. 39, 3814–3824 (2000).
    [CrossRef]
  10. V. Shaoulov, C. Meyer, Y. Argotti, J. P. Rolland, “Optical phase plates as a creative media for special effects in images,” in Novel Optical Systems Design and Optimization IV, J. M. Sasian, P. K. Manhart, eds., Proc. SPIE4442, 112–118 (2001).
    [CrossRef]
  11. V. Belvard, P. Revy, “Optical zooming lens,” U.S. patent3,970,368 (20July1976).
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    [CrossRef]
  14. ASAP Technical Guide Radiometric Analysis, Breault Research Organization, Tucson, Ariz. (2002), pp. 43–45.

2001

J. P. Rolland, V. Shaoulov, F. J. Gonzalez, “The art of back-of-the-envelope paraxial raytracing,” IEEE Trans. Educ. 44, 365–372 (2001).
[CrossRef]

2000

1996

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

1994

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

1982

1980

1979

Anderson, R. H.

Argotti, Y.

V. Shaoulov, C. Meyer, Y. Argotti, J. P. Rolland, “Optical phase plates as a creative media for special effects in images,” in Novel Optical Systems Design and Optimization IV, J. M. Sasian, P. K. Manhart, eds., Proc. SPIE4442, 112–118 (2001).
[CrossRef]

Belvard, V.

V. Belvard, P. Revy, “Optical zooming lens,” U.S. patent3,970,368 (20July1976).

Brewin, M.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

Dandliker, R.

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

Davies, N.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

Gao, C.

Girardot, A.

Gonzalez, F. J.

J. P. Rolland, V. Shaoulov, F. J. Gonzalez, “The art of back-of-the-envelope paraxial raytracing,” IEEE Trans. Educ. 44, 365–372 (2001).
[CrossRef]

Herzig, H. P.

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

Hua, H.

H. Hua, A. Girardot, C. Gao, J. P. Rolland, “Engineering of head-mounted projective displays,” Appl. Opt. 39, 3814–3824 (2000).
[CrossRef]

J. P. Rolland, H. Hua, V. Shaoulov, “Design of a compact relay lens,” Tech. Rep. TR02-05 (University of Central Florida, Orlando, Fla., 2002).

Hugle, W.

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

Kawazi, M.

Macdonald, J.

P. Mouroulis, J. Macdonald, “Geometrical Optics and Optical Design,” (Oxford U. Press, New York, 1997), pp. 94–108.

McCormick, M.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

Meyer, C.

V. Shaoulov, C. Meyer, Y. Argotti, J. P. Rolland, “Optical phase plates as a creative media for special effects in images,” in Novel Optical Systems Design and Optimization IV, J. M. Sasian, P. K. Manhart, eds., Proc. SPIE4442, 112–118 (2001).
[CrossRef]

Mir, J.

J. Mir, “High resolution optical-addressing device and electronic scanner and/or printer apparatus employing such device,” U.S. patent4,377,753 (22March1983).

Mouroulis, P.

P. Mouroulis, J. Macdonald, “Geometrical Optics and Optical Design,” (Oxford U. Press, New York, 1997), pp. 94–108.

Nussebaum, P.

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

Ogura, Y.

Revy, P.

V. Belvard, P. Revy, “Optical zooming lens,” U.S. patent3,970,368 (20July1976).

Rolland, J.

V. Shaoulov, J. Rolland, “Compact relay lenses using microlenslet arrays,” in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 74–79 (2002).
[CrossRef]

Rolland, J. P.

J. P. Rolland, V. Shaoulov, F. J. Gonzalez, “The art of back-of-the-envelope paraxial raytracing,” IEEE Trans. Educ. 44, 365–372 (2001).
[CrossRef]

H. Hua, A. Girardot, C. Gao, J. P. Rolland, “Engineering of head-mounted projective displays,” Appl. Opt. 39, 3814–3824 (2000).
[CrossRef]

V. Shaoulov, C. Meyer, Y. Argotti, J. P. Rolland, “Optical phase plates as a creative media for special effects in images,” in Novel Optical Systems Design and Optimization IV, J. M. Sasian, P. K. Manhart, eds., Proc. SPIE4442, 112–118 (2001).
[CrossRef]

J. P. Rolland, H. Hua, V. Shaoulov, “Design of a compact relay lens,” Tech. Rep. TR02-05 (University of Central Florida, Orlando, Fla., 2002).

Shaoulov, V.

J. P. Rolland, V. Shaoulov, F. J. Gonzalez, “The art of back-of-the-envelope paraxial raytracing,” IEEE Trans. Educ. 44, 365–372 (2001).
[CrossRef]

V. Shaoulov, C. Meyer, Y. Argotti, J. P. Rolland, “Optical phase plates as a creative media for special effects in images,” in Novel Optical Systems Design and Optimization IV, J. M. Sasian, P. K. Manhart, eds., Proc. SPIE4442, 112–118 (2001).
[CrossRef]

J. P. Rolland, H. Hua, V. Shaoulov, “Design of a compact relay lens,” Tech. Rep. TR02-05 (University of Central Florida, Orlando, Fla., 2002).

V. Shaoulov, J. Rolland, “Compact relay lenses using microlenslet arrays,” in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 74–79 (2002).
[CrossRef]

Takami, M.

Toyama, M.

Volkel, R.

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

Appl. Opt.

IEEE Trans. Educ.

J. P. Rolland, V. Shaoulov, F. J. Gonzalez, “The art of back-of-the-envelope paraxial raytracing,” IEEE Trans. Educ. 44, 365–372 (2001).
[CrossRef]

Opt. Eng.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

R. Volkel, H. P. Herzig, P. Nussebaum, R. Dandliker, W. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35, 3323–3330 (1996).
[CrossRef]

Other

V. Shaoulov, C. Meyer, Y. Argotti, J. P. Rolland, “Optical phase plates as a creative media for special effects in images,” in Novel Optical Systems Design and Optimization IV, J. M. Sasian, P. K. Manhart, eds., Proc. SPIE4442, 112–118 (2001).
[CrossRef]

V. Belvard, P. Revy, “Optical zooming lens,” U.S. patent3,970,368 (20July1976).

P. Mouroulis, J. Macdonald, “Geometrical Optics and Optical Design,” (Oxford U. Press, New York, 1997), pp. 94–108.

J. Mir, “High resolution optical-addressing device and electronic scanner and/or printer apparatus employing such device,” U.S. patent4,377,753 (22March1983).

V. Shaoulov, J. Rolland, “Compact relay lenses using microlenslet arrays,” in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 74–79 (2002).
[CrossRef]

J. P. Rolland, H. Hua, V. Shaoulov, “Design of a compact relay lens,” Tech. Rep. TR02-05 (University of Central Florida, Orlando, Fla., 2002).

ASAP Technical Guide Radiometric Analysis, Breault Research Organization, Tucson, Ariz. (2002), pp. 43–45.

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Figures (10)

Fig. 1
Fig. 1

Paraxial layouts of 1:1 imaging with a single pair of microlenses.

Fig. 2
Fig. 2

Ray sketching illustrating the presence of ghost images for a stack of two microlenslet arrays without baffles.

Fig. 3
Fig. 3

Microlenslet arrays 1:1 imaging 2f system with the appropriate baffle to minimize ghost images.

Fig. 4
Fig. 4

Illustration of the irradiance profiles of an extended object imaged through a (a) 2f- and (b) 3f-system microlenslet array relay lens.

Fig. 5
Fig. 5

ASAP layout of the 2f-system microlenslet-array-based relay system with two 11 by 11 arrays of microlenses and the appropriate baffle. The object to be imaged is not represented in the figure; however, shown from right to left are the baffle, the two microlenslet arrays made of plano-convex square lenses, and the detector upon which an image will be formed given the object in front of the baffle.

Fig. 6
Fig. 6

SNR for the 5f system as a function of the number of rays emitted from the object, obtained with Eq. (3). In this plot N equal 8281 pixels and η equals 34%.

Fig. 7
Fig. 7

Imaging and irradiance distribution of an ellipse: (a) original image; (b) image through the 2f system, (c) image through the 3f system, (d) image through the 4f system, (e) image through the 5f system, (f) image through 6f system, (g) image through the 7f system. For the irradiance distributions, the gray-level value versus the number of pixels in the object is plotted. The autocorrelation functions of the image are plotted in arbitrary units.

Fig. 8
Fig. 8

Imaging and irradiance distribution of a gray-scale bitmap object: (a) original image, (b) image through the 2f system, (c) image through the 3f system, (d) image through the 4f system, (e) image through the 5f system, (f) image through the 6f system, (g) image through the 7f system.

Fig. 9
Fig. 9

Normalized PSF plots for 0%, 70%, 95%, and 100% vignetted subfields of view for a pair of plano-convex lenses.

Fig. 10
Fig. 10

Simulation of the imaging of red-green-blue image through a stack of two microlenslet arrays to qualitatively assess the impact of chromatic aberrations on image formation.

Tables (2)

Tables Icon

Table 1 P-V Error in the Difference of the Normalized Autocorrelation of the Object and the Image

Tables Icon

Table 2 Overall Compactness of the Microlenslet Array Relay Configurations

Equations (4)

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

OAL=2x2|x|-|f|,
FOV=M-1D,
SNRdBx=10 log10xN η.
OAL=2M2M-1 |f|,

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