Abstract

Some high-performance imaging systems, including wide angle “monocentric” lenses made of concentric spherical shells, form a deeply curved image surface coupled to focal plane sensors by optical fiber bundles with a curved input and flat output face. However, refraction at the angled input facet limits the range of input angles, even for fiber bundles with numerical aperture 1. Here we investigate using a curved beam deflector near the focal surface to increase the field of view and improve spatial resolution at the edges of the field of view. We show the field of view of such an imager can be increased from approximately 60° (full width at half maximum intensity) to over 90° using an embossed refractive microprism array, where the prism angle varies across the aperture to maintain coupling. We describe a proof-of-principle experiment using a f = 17.8mm fiber-coupled monocentric singlet lens, and show that a local region of microprisms embossed into a thin layer of SU-8 photopolymer can increase the field of view by 50%.

© 2015 Optical Society of America

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References

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2014 (2)

2013 (1)

2012 (1)

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

2009 (1)

1997 (1)

W. Y. Lau, C. K. Leow, and A. K. C. Li, “History of endoscope and laparoscopic Surgery,” World of Surgery 21(4Issue 4), 444–453 (1997).
[Crossref]

1995 (1)

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

1975 (1)

Abashin, M.

Agurok, I. P.

Arianpour, A.

Burden, A. R.

Cozannet, A.

Di Falco, A.

Fainman, Y.

Ford, J. E.

Freeman, L.

Hills, R.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Jing, L.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Johnson, A. R.

Johnson, R. W.

Karr, M. E.

Kordas, J. F.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Krauss, T.

Lau, W. Y.

W. Y. Lau, C. K. Leow, and A. K. C. Li, “History of endoscope and laparoscopic Surgery,” World of Surgery 21(4Issue 4), 444–453 (1997).
[Crossref]

Ledebuhr, A. G.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Leow, C. K.

W. Y. Lau, C. K. Leow, and A. K. C. Li, “History of endoscope and laparoscopic Surgery,” World of Surgery 21(4Issue 4), 444–453 (1997).
[Crossref]

Lewis, I. T.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Li, A. K. C.

W. Y. Lau, C. K. Leow, and A. K. C. Li, “History of endoscope and laparoscopic Surgery,” World of Surgery 21(4Issue 4), 444–453 (1997).
[Crossref]

Liu, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Lu, Z.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Morrison, R. L.

Nielsen, D. P.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Olivas, S. J.

Pang, L.

Park, H. S.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Pleasance, L. D.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Priest, R. E.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Reardon, C.

Shannon, M. J.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Shields, J. E.

Smolyaninov, A.

Stack, R. A.

Stamenov, I.

Treheux, M.

Wang, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Welna, K.

Wilson, B. A.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

Wu, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Xu, J.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Zhao, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Appl. Opt. (2)

Int. J. Photoenergy (1)

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Xu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 1 (2012).
[Crossref]

Opt. Express (3)

Proc. SPIE (1)

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. S. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70–83 (1995).
[Crossref]

World of Surgery (1)

W. Y. Lau, C. K. Leow, and A. K. C. Li, “History of endoscope and laparoscopic Surgery,” World of Surgery 21(4Issue 4), 444–453 (1997).
[Crossref]

Other (5)

J. A. Waidelich, Jr., “Spherical lens imaging device,” U.S. patent 3,166,623 (19. January 1965).

R. Kingslake, A History of the Photographic Lens (Academic, 1989), pp. 49–67.

T. S. Axelrod, N. J. Colella, and A. G. Ledebuhr, “The wide-field-of-view camera,” in Energy and Technology Review (Lawrence Livermore National Laboratory, 1988).

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled Monocentric Lens Imaging,” in Imaging and Applied Optics, OSA Technical Digest (2013).

J. J. Hancock, The Design, Fabrication, and Calibration of a Fiber Filter Spectrometer. Doctoral dissertation. University of Arizona, Tucson, 2012.

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Figures (16)

Fig. 1
Fig. 1 a) 3-D geometrical schematic of monocentric fiber coupled imager, b) shows how an off-axis focusing beam would couple into a fiber bundle with a planar face, while c) shows how the locally angled input face of the curved-face fiber bundle interferes with signal coupling, and limits the maximum angle achievable with a simple straight fiber bundle.
Fig. 2
Fig. 2 FRED simulation of coupling efficiency of an F/2 nearly diffraction limited monocentric lens with 2.5µm pitch fibers. The power drops off dramatically as the field approaches the 35°, the complement to the critical angle of the fiber bundle.
Fig. 3
Fig. 3 Illustration of light coupling into fibers at various angles for a) bare curved-face fiber bundle, b) surface-enhanced curved-face fiber bundle, and c) enlarged view of a scattering facet surface and a beam deflective structure modifying the focusing beam to enhance coupling in an angled facet.
Fig. 4
Fig. 4 FRED 2-dimensional simulation of laser (532nm) incident at 0°, 15°, 30°, 45° incident on a) flat bundle (NA = 1) and b) curved-face bundle (NA = 1) and exiting in air (n = 1).
Fig. 5
Fig. 5 Experimental demonstration of a 1mm spot size laser incident at angles of 0°, 15°, 30°, 45° on a) flat fiber bundle, b) curved-face fiber bundle. The contrast of these images have been inverted to show the regions of the dark rings where the intensity is greatest. The exit angles are measured by examining the peak relative intensities for their respective graphs below.
Fig. 6
Fig. 6 FRED Simulation of fiber coupled monocentric imager’s output response when coupled to a sensor with a 3.3µm pitch and 10µm glue thickness. The irradiance drops as a function of angle, and at 45° a negligible amount of energy is transmitted to the sensor.
Fig. 7
Fig. 7 Illustration of the cross-section of the radial microprism array and fiber bundle in conjunction with the monocentric lens, and a ray optics schematic of propagation of light through micro-prism array and fiber.
Fig. 8
Fig. 8 Illustration of a focused beam incident on a micro-prism array molded on the a) polished input surface of the fiber bundle, b) micro-prism array molded with a non-zero thickness onto the polished fiber bundle. Colored fibers signify coupling from the focusing beam.
Fig. 9
Fig. 9 a) 2-dimensional facet efficiency color plot as a function of field angle and tolerance angle, b) chosen facet efficiency for micro-prism array, c) blaze angle of prism array with respect to the field angle.
Fig. 10
Fig. 10 a) Schematic of ball lens system with an embossed micro-prism array on the input surface of the fiber bundle, b) region with no prisms, c, d) regions with micro-prism array. The microprism array has a thickness of 390µm.
Fig. 11
Fig. 11 a,b) Cross section of a 3-D FRED simulation of the micro-prism array increasing coupling efficiency at a field angle (45°) larger than the axial critical angle, c) polychromatic MTF calculation of signal beam on surface of fiber bundle, d) irradiance plot on a pixel array.
Fig. 12
Fig. 12 Irradiance spread function at 45° on surface of the a) polished input fiber bundle, b) input surface of the fiber bundle after being deflected by the prism array.
Fig. 13
Fig. 13 FRED calculation of signal-to-noise ratio of the input and release facet beams incident on groups of 3x3 fibers.
Fig. 14
Fig. 14 a) F/# 4.3 BK7 ball lens, b) curved-face fiber bundle with microprism array, c) close up of microprism array, d) microscope image of fiber, e) top view of molded micro-prism array structure, f) cross-section of Vikuiti BEF II 90/24 microprism array, g) ball lens and fiber bundle in 3D printed mount.
Fig. 15
Fig. 15 a) Photograph of image transferred through fiber bundle both with a smooth spherical surface (upper half) and with a molded prism (lower half) over the region from 27° to 52° field angle. The prism array extends the field of view where the polished bundle no longer transmits a significant signal. b,c) Slant edge chart MTF measurements at on-axis and 45° off axis.
Fig. 16
Fig. 16 Stitched image of prism array molded bundle with a diffusive output surface. The image was stitched from several images at a constant 1 sec exposure and ISO 400.

Equations (8)

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

n 1 sin(θf+θb)= n 2 sin(θg)
n 2 sin(θg'+θf)= n 3 sin(θfθt)
θg'= sin 1 n 3 sin(θfθt) n 2 θf
n 1 sin(θf+θb)= n 2 sin(θg'+θb)
n 1 sin(θf)cos(θb)+ n 1 cos(θf)sin(θb)= n 2 sin(θg')cos(θb)+ n 2 cos(θg')sin(θb)
n 1 sin(θf)+ n 2 sin(θg')=tanθb( n 2 cos(θg') n 1 cos(θf))
θb= tan 1 n 1 sinθf+ n 2 cosθg' n 2 cosθg' n 1 cosθf
η= P in P in + P rel

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