DISCUSSION ON THE RELATIONSHIP BETWEEN DISPLACEMENT AND FREQUENCY SHIFTING CHARACTERISTICS IN COMPUTER-GENERATED HOLOGRAPHY AND ITS APPLICATIONS

The displacement theorem and frequency shifting theorem are not only important concepts in information optics, but they can also provide specific control over the spectrum of a hologram and the spatial position of the reconstructed image. In this paper, the differing relationships of the displacement and frequency shifting characteristics in space and frequency domains of the computer-generated holography (CGH) are discussed in detail based on Fresnel diffraction. Their intrinsic connection and effects on the holographic light field are explained and analyzed. Furthermore, by combining these two operations, it is possible to arbitrarily manipulate the hologram spectrum without affecting the position of reconstructed images, which facilitates functions such as diffraction order filtering of holograms and frequency division multiplexing. It can be demonstrated that the fundamental concepts have practical applications in addressing practical advanced research problems. The above discussion also deepens the understanding of the tangible concepts to the displacement theorem and frequency shifting theorem in Fourier transforms during diffraction propagation.