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Integral imaging with multiple image planes using a uniaxial crystal plate

Jae-Hyeung Park, Sungyong Jung, Heejin Choi, and Byoungho Lee

Open Access Open Access

Abstract

Integral imaging has been attracting considerable attention recently because of its advantages that include full parallax, continuous view-points and real-time full-color operation. However, the thickness of the displayed three-dimensional image is limited to a relatively small value due to the degradation of image resolution. A method is proposed here to provide observers with an enhanced perception of depth without severe degradation of resolution by taking advantage of the birefringence of a uniaxial crystal plate. The proposed integral imaging system can display images integrated around three central depth planes by dynamically altering the polarization and controlling both the elemental images and the dynamic slit array mask accordingly. The principle of the proposed method is described and is then verified experimentally.

©2003 Optical Society of America

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Figures (12)
Fig. 1.
Fig. 1. Basic concept of InIm

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Fig. 2.
Fig. 2. Configuration of the proposed InIm system

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Fig. 3.
Fig. 3. Longitudinal shift caused by the glass plate

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Fig. 4.
Fig. 4. Imaging system consisting of a uniaxial crystal plate and a single lens.

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Fig. 5.
Fig. 5. Propagation of the ray through the uniaxial crystal plate (a) Propagation of the horizontally incident rays (i.e. the plane of incidence is perpendicular to the optic axis of the uniaxial crystal) (b) k-surface for the horizontally incident rays (c) Propagation of the vertically incident rays (i.e., the plane of incidence is parallel to the optic axis of the uniaxial crystal) (d) k-surface for the vertically incident rays

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Fig. 6.
Fig. 6. Imaging properties of the optical system consisting of a uniaxial crystal plate and a single lens

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Fig. 7.
Fig. 7. Configuration for locating a point image at the extraordinary-vertical mode image plane

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Fig. 8.
Fig. 8. Geometry for calculating the horizontal position of the point source for a given image point at the extraordinary-vertical mode image plane

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Fig. 9.
Fig. 9. Integrated images by conventional InIm (a) central depth plane is placed at 9.5 cm from the lens array (b) central depth plane is placed at 21 cm from the lens array

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Fig. 10.
Fig. 10. Integrated images by the proposed method (a) extraordinary-horizontal mode(9.5 cm) (b) ordinary mode(13cm) (c) extraordinary-vertical mode(21 cm)

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Fig. 11.
Fig. 11. Experimental setup used for non-mechanical realization

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Fig. 12.
Fig. 12. Integrated images of different depths. Left apple images are located at 140 mm from the lens array and right apple images are located at 243 mm (a) integrated by the conventional method (b) integrated by the proposed method.

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Tables (1)

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Table 1. Specifications of the experimental setup Setup

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Equations (12)

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Δ z = d ( 1 − cos ⁡ θ i n glass 2 − sin 2 θ i ) ≈ d ( 1 − 1 n glass ) ,
Δ z o = d ( 1 − cos ⁡ θ i n o 2 − sin 2 θ i ) ≈ d ( 1 − 1 n o ) ,
l o = f ( g − Δ z o ) g − Δ z o − f ≈ f [ g n o − d ( n o − 1 ) ] g n o − d ( n o − 1 ) − f n o ,
1 n e 2 ( ϕ ) = cos 2 ϕ n o 2 + sin 2 ϕ n e 2 ,
Δ z eh = d ( 1 − cos ⁡ θ i n e 2 − sin 2 θ i ) ≈ d ( 1 − 1 n e ) ,
l eh = f ( g − Δ z eh ) g − Δ z eh − f ≈ f [ g n e − d ( n e − 1 ) ] g n e − d ( n e − 1 ) − f n e .
tan ⁡ ( θ ev ) = sin 2 θ i n e 2 1 − sin 2 θ i n o 2 .
tan ⁡ ( θ ev ′ ) = n e 2 n o 2 tan ⁡ ( θ ev ) .
Δ z ev = d ( 1 − n e cos ⁡ θ i n o n o 2 − sin 2 θ i ) ≈ d ( 1 − n e n o 2 ) ,
l ev = f ( g − Δ z ev ) g − Δ z ev − f ≈ [ g − d ( 1 − n e n o 2 ) ] f g − d ( 1 − n e n o 2 ) − f .
x v − x h : x h − u = l ev − l eh : l eh ,
x = − g − Δ z eh l eh x h = Δ z eh − g l ev ( x v − u ) + Δ z eh − g + f f u ,
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