Analytical model of a three-dimensional integral image recording system that uses circular- and hexagonal-based spherical surface microlenses

Silvia Manolache; Amar Aggoun; Malcolm McCormick; Neil Davies; S. Y. Kung

doi:10.1364/JOSAA.18.001814

Journal of the Optical Society of America A
Vol. 18,
Issue 8,
pp. 1814-1821
(2001)
•https://doi.org/10.1364/JOSAA.18.001814

Analytical model of a three-dimensional integral image recording system that uses circular- and hexagonal-based spherical surface microlenses

Silvia Manolache, Amar Aggoun, Malcolm McCormick, Neil Davies, and S. Y. Kung

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Silvia Manolache, Amar Aggoun, Malcolm McCormick, Neil Davies, and S. Y. Kung, "Analytical model of a three-dimensional integral image recording system that uses circular- and hexagonal-based spherical surface microlenses," J. Opt. Soc. Am. A 18, 1814-1821 (2001)

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Abstract

A mathematical model for a three-dimensional omnidirectional integral recording camera system that uses either circular- or hexagonal-based spherical surface microlens arrays is derived. The geometry of the image formation and recording process is fully described. Matlab is then used to establish the number of recorded micro-intensity distributions representing a single object point and their dependence on spatial position. The point-spread function for the entire optical process for both close and remote imaging is obtained, and the influence of depth on the point-spread dimensions for each type of microlens and imaging condition is discussed. Comparisons of the two arrangements are made, based on the illustrative numerical results presented.

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Point Depth $\| z \|$ (m)	Spread at Close Imaging (mm)		${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
Point Depth $\| z \|$ (m)	Circular Lens	Hexagonal Lens	${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
0.31	0.0120	0.0126	1.043
0.34	0.0133	0.0140	1.045
0.37	0.0151	0.0158	1.047
0.40	0.0173	0.0182	1.048
0.43	0.0205	0.0216	1.050
0.46	0.0253	0.0266	1.051
0.49	0.0331	0.0348	1.052
0.52	0.0481	0.0507	1.053
0.55	0.0889	0.0937	1.053
0.58	0.0621	0.0655	1.053

Point Depth $\| z \|$ (m)	Spread at Remote Imaging (mm)		${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
Point Depth $\| z \|$ (m)	Circular Lens	Hexagonal Lens	${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
0.36	0.004006	0.00363847	0.908
0.39	0.004007	0.00363848	0.907
0.43	0.004009	0.00363851	0.907
0.46	0.004014	0.00363855	0.906
0.47	0.004016	0.00363857	0.905
0.48	0.004020	0.00363859	0.905
0.49	0.004026	0.00363862	0.903
0.50	0.004035	0.00363867	0.901
0.51	0.004051	0.00363873	0.898
0.52	0.004081	0.00363883	0.891

Point Depth $\| z \|$ (m)	Spread at Close Imaging (mm)		${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
Point Depth $\| z \|$ (m)	Circular Lens	Hexagonal Lens	${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
0.31	0.0120	0.0126	1.043
0.34	0.0133	0.0140	1.045
0.37	0.0151	0.0158	1.047
0.40	0.0173	0.0182	1.048
0.43	0.0205	0.0216	1.050
0.46	0.0253	0.0266	1.051
0.49	0.0331	0.0348	1.052
0.52	0.0481	0.0507	1.053
0.55	0.0889	0.0937	1.053
0.58	0.0621	0.0655	1.053

Point Depth $\| z \|$ (m)	Spread at Remote Imaging (mm)		${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
Point Depth $\| z \|$ (m)	Circular Lens	Hexagonal Lens	${Spread}_{hex}$ / ${Spread}_{circ}$ ^b
0.36	0.004006	0.00363847	0.908
0.39	0.004007	0.00363848	0.907
0.43	0.004009	0.00363851	0.907
0.46	0.004014	0.00363855	0.906
0.47	0.004016	0.00363857	0.905
0.48	0.004020	0.00363859	0.905
0.49	0.004026	0.00363862	0.903
0.50	0.004035	0.00363867	0.901
0.51	0.004051	0.00363873	0.898
0.52	0.004081	0.00363883	0.891

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