Aliasing-reduced Fresnel diffraction with scale and shift operations

Abstract

Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT) is widely used in optics, especially computer holography. Fresnel diffraction with FFT cannot set different sampling rates between source and destination planes, while shifted-Fresnel diffraction can set different rates. However, an aliasing error may be incurred in shifted-Fresnel diffraction in a short propagation distance, and the aliasing conditions have not been investigated. In this paper, we investigate the aliasing conditions of shifted-Fresnel diffraction and improve its properties based on the conditions.

54‐3: Lensless Holographic 3D Display based on Fast Calculated Computer‐Generated hologram

“…After that the calculated WRP W(xw, yw) is forcedly re-sampled to an uniform sampled WRP W(xw', yw') with the sampling pitch of du. In the last step of the method, the hologram is obtained by calculating the diffraction from the re-sampled W(xw', yw') employing the ARSS -Fresnel diffraction algorithm [15]. The calculation of the hologram H(x, y) is given by:…”

“…Their detailed expression can be found in Ref. [15]. Figure 1(b) shows the reconstruction of the hologram calculated by the above described method.…”

“…A nonuniform sampled WRP (NS-WRP) is designed and calculated from the object by using the nonuniform fast Fourier transform (NUFFT) algorithm, which allows calculating the WRP in a simple and direct way. Then the CGH is obtained by diffraction calculation from the NS-WRP using ARSS-Fresnel diffraction [15]. The generated CGH can reconstruct high quality 3D object with perceptive depth, zoomable function in lenless holographic 3D display system.…”

Phase retrieval for object and probe in the optical near-field

“…It is in particular problematic, when the aliasing free areas of the chirps are smaller than the support of the complex valued field that should be propagated. Approaches to filter Fresnel-Bluestein propagation can be found in [40,46].…”

P‐99: Method to Reduce Ringing Artifact in Holographic Projection

“…The method can achieve color projection with a single SLM device and have potential in three-dimensional scene projection [3,4]. The lensless holographic projection [5,6] method has been proposed, which uses the aliasing-reduced shifted and scaled (ARSS) Fresnel diffraction algorithm [7] to calculate the diffraction field and uses the virtual convergence light instead of random phase to spread the object light, the scaled holographic projection and speckle noise reduction can be achieved. However, the ringing artifacts are born and affect the quality of the reconstructed image.…”