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Spatiotemporal multiplexing for holographic display with multiple planar aligned spatial-light-modulators

Dongdong Teng, Lilin Liu, Yueli Zhang, Zhiyong Pang, Shengqian Chang, Jincheng Zhang, and Biao Wang

Open Access Open Access

Abstract

A holographic display system combining the spatial- and time-multiplexing together in one system is proposed. The system is constructed by multiple planar aligned spatial-light-modulators (SLMs). A shiftable cylindrical lens is introduced in to build up an “equivalent SLM” by seamlessly linked horizontal images of the SLMs, which are tiled in a time-sequential manner. The proposed system can realize wide horizontal-viewing-angle holographic three-dimensional (3D) display through the “equivalent SLM”, but bear with low requirements on the number and frame rate of SLMs, and the numerical aperture of the optical system. In the proposed system, only one parallel incident beam is needed, leading to a simplified optical structure. Using two 60Hz phase SLMs, a 3D display with a horizontal viewing angle (VA) of 27.5° is implemented experimentally.

© 2014 Optical Society of America

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Figures (12)
Fig. 1
Fig. 1 The FOVs for (a) a single SLM, (b) multiple SLMs in a planar configuration, (c) multiple SLMs in a planar configuration with a Fourier-transform optical structure, (d) multiple SLMs in a circular configuration, (e) the proposed spatiotemporal multiplexing technology with an “equivalent SLM” which is built up by the SLM’ images in a time-sequential manner.

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Fig. 2
Fig. 2 Schematic optical diagram of the proposed time-multiplexing technology with a shiftable cylindrical lens (DL).

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Fig. 3
Fig. 3 The scheme of the algorithm processes of obtaining the correct CGHs to make the refracted IMs have the same intensity distributions as the target object.

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Fig. 4
Fig. 4 Schematic optical diagram of the proposed display system.

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Fig. 5
Fig. 5 Image pre-processing to generate slices with a larger resolution based on the interpolation method.

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Fig. 6
Fig. 6 Schematic drawing of the experimental setup.

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Fig. 7
Fig. 7 Geometric relationship between the partial cylindrical lenses and the mother DL.

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Fig. 8
Fig. 8 Photograph of the experimental display system.

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Fig. 9
Fig. 9 Captured image when the the 1st layer, the 2nd layer and the 3rd layer are on focus in a sequence.

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Fig. 10
Fig. 10 Captured images when the HHD system works: the model of the teapot consisting of a group of slices and sequential views of the object captured with angular step of 2.7° from −13.5° to 13.5°.

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Fig. 11
Fig. 11 Geometrical diagram showing the deviation distance of the point on the refracted sub-image when the cylindrical lens deviating from the correct position.

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Fig. 12
Fig. 12 Geometrical diagram showing the deviation of the partial cylindrical lens from the correct spatial position when it rotates around the optical axis during the exposure process.

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Equations (11)

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Δd=( f 2 / f 1 ) D 1 ,
θ A =∠Q'A P 1 '+∠ Q 2 'AP'=∠Q'A Q 2 '+∠ Q 2 'AP'=∠Q'AP'.
U P 0 ( x P 0 , y P 0 ) = A ( x P 0 , y P 0 ) exp [ i φ ( x P 0 , y P 0 ) ] = exp [ − i π ( x P 0 − x D L L ) / λ f 2 ] { F − 1 { i λ f U S L M ( x S L M , y S L M ) } } | x P 0 λ f 1 , y P 0 λ f 1
U P k ( x P k , y P k ) = A ( x P k , y P k ) exp ( i φ ( x P k , y P k ) ) = F − 1 { exp ( − j 2 π δ 1 − ( λ f x ) 2 − ( λ f y ) 2 / λ ) F [ U P k − 1 ( x P k − 1 , y P k − 1 ) ] }
A FL =3 D 1 +λ f 1 /Δp
A DL =5( f 2 / f 1 ) D 1 +λ f 1 /Δp
N A FL = A FL / f 1 =λ/Δp+3 D 1 / f 1
N A DL = A DL / f 2 =( λ/Δp )( f 2 / f 1 )+5 D 1 / f 1
N A PLANAR ==λ/Δp+8 D 1 / f 1
| Δ H | = | | v / u | h − | v / u | ( h − d e ) − d e | = | ( | v / u | − 1 ) d e | = | d e u / ( f 2 − u ) | .
d e =a'' a e =a' a e −a''a'=( l/2 )tan θ e −( d/2 )( 1−cos θ e )/cos θ e
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