Wigner inverse transform based computer generated hologram for large object at far field from its perspective light field

1 . A hologram synthesis method, comprising:

a) obtaining perspective views for a three dimensional object at a distance by capturing light field data at spatial coordinates and angular coordinates expressed as spatial frequencies of light ray angles in a front focal plane at a focal length in front of a lens;

b) synthesizing an intermediate hologram comprising:

using the perspective views as an orthographic view array in a back focal plane at the focal length behind the lens;

performing a Wigner inverse Fourier transform on the orthographic view array to obtain an orthographic light field;

multiplying the orthographic light field with a carrier wave; and

accumulating the multiplied orthographic light field at shifted spatial coordinates to form the intermediate hologram; and

c) synthesizing a final hologram in the front focal plane by performing a Fourier transform using a spatial frequency for the synthesized intermediate hologram.

2 . The hologram synthesis method of claim 1 , wherein the carrier wave comprises a random phase distribution to obtain a wide viewing angle and natural blur of an unfocused object.

3 . The hologram synthesis method of claim 1 , wherein the carrier wave comprises a uniform, linear, spherical, or arbitrary wave for illuminating the object.

4 . A hologram synthesis method, comprising:

a) obtaining perspective views P tx,ty (u, v) for a three dimensional object by capturing light field data at spatial coordinates along (tx, ty) axes and angular coordinates expressed as spatial frequencies (u, v) of light ray angles (θ x , θ y ) in a front focal plane at a focal length (f) in front of a lens;

b) synthesizing an intermediate hologram by using the obtained perspective views P tx,ty (u,v) as an orthographic view array O u′,v′ (t′x, t′y) in a back focal plane at the focal length (f) behind the lens and performing a Wigner inverse Fourier transform on the orthographic view array,

wherein u=sin θ x /λ and v=sin θ y /λ,

wherein u′=−tx/λf and v′=−ty/λf,

wherein t′x=uλf and t′y=vλf, and

wherein λ is a wavelength; and

c) synthesizing a final hologram in the front focal plane by performing a Fourier transform of the synthesized intermediate hologram with spatial frequencies x/λf and y/λf.

5 . The hologram synthesis method of claim 4 , wherein the synthesizing an intermediate hologram comprises:

using the perspective views P tx,ty (u, v) as the orthographic array O u′,v′ (t′x, t′y);

performing a Wigner inverse Fourier transform on the orthographic view array to obtain an orthographic light field;

multiplying the orthographic light field with a carrier wave; and

accumulating the multiplied orthographic light field at shifted spatial coordinates to form the intermediate hologram.

6 . The hologram synthesis method of claim 5 , wherein the carrier wave comprises an arbitrary complex field for illuminating the object.

7 . The hologram synthesis method of claim 5 , wherein the carrier wave comprises a random phase distribution to obtain a wide viewing angle and natural blur of an unfocused object.

8 . The hologram synthesis method of claim 5 , wherein the carrier wave comprises a uniform, linear, spherical, or arbitrary wave for illuminating the object.

9 . The hologram synthesis method of claim 4 , wherein obtaining the perspective views is by using a camera array.

10 . A hologram synthesis system, comprising:

a collecting unit configured to collect perspective views in a front focal plane; and

a hologram synthesizing unit configured to:

obtain perspective views for a three dimensional object at a distance by capturing light field data at spatial coordinates and angular coordinates expressed as spatial frequencies of light ray angles in a front focal plane at a focal length in front of a lens;

synthesize an intermediate hologram by using the obtained perspective views as an orthographic view array in a back focal plane at the focal length behind the lens and performing in a Wigner inverse Fourier transform on the orthographic view array to obtain an orthographic light field; and

synthesize a final hologram in the front focal plane by performing a Fourier transform using a spatial frequency for the synthesized intermediate hologram.