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Phase retrieval is a powerful numerical method that can be used to determine the wavefront of laser beams based only on intensity measurements, without the use of expensive, low-resolution specialized wavefront sensors such as Shack-Hartmann sensors. However, phase retrieval techniques generally suffer from poor convergence and fidelity when the input measurements contain electronic or optical ...

The phase retrieval is formulated as an inverse problem, where the forward propagation is defined by Discrete Diffraction Transform (DDT) [1], [2]. This propagation model is precise and aliasing free for pixelwise invariant (pixelated) wave field distributions in the sensor and object planes. Because of finite size of sensors DDT can be illconditioned and the regularization is an important comp...

What we believe to be a new technique, based on a modified Gerchberg-Saxton algorithm (MGSA) and a phase modulation scheme in the Fresnel-transform domain, is proposed to reduce cross talks existing in multiple-image encryption and multiplexing. First, each plain image is encoded and multiplexed into a phase function by using the MGSA and a different wavelength/position parameter. Then all the ...

Optics has provided a promising means for the development of information hiding in recent years. However, conventional optical systems can only hide limited number images, and implementation complexity is usually high methods. In this paper, we propose new scheme to implement based on single-input multiple-output (SIMO) binary amplitude-only holograms (AOHs) using modified Gerchberg-Saxton algo...

In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, the spirit of so-called transference principles extremal combinatorics, that if a given algebraic hypergraph “dense” certain sense, then generic low-dimensional subset its vertices induces subhypergraph also “dense.” (For technical reasons, only consider subsets are parameterized by rational func...

A classical theorem of Simonovits from the 1980s asserts that every graph $G$ satisfying ${e(G) \gg v(G)^{1+1/k}}$ must contain $\gtrsim \left(\frac{e(G)}{v(G)}\right)^{2k}$ copies $C_{2k}$. Recently, Morris and Saxton established a balanced version Simonovits' theorem, showing such has $C_{2k}$, which are `uniformly distributed' over edges $G$. Moreover, they used this result to obtain sharp b...

Visual cryptography (VC) is developed to be a promising approach encoding secret information using pixel expansion rules. The useful can directly rendered based on human vision without the usage of decryption algorithms. However, many VC schemes cannot withstand occlusion attacks. In this paper, new scheme proposed binary amplitude-only holograms (AOHs) generated by modified Gerchberg-Saxton al...

We report on the development of a doubly weighted Gerchberg-Saxton algorithm (DWGS) to enable generation of uniform beamlet arrays with a spatial light modulator (SLM) for use in multiphoton multifocal imaging applications. The algorithm incorporates the WGS algorithm as well as feedback of fluorescence signals from the sample measured with a single-photon avalanche diode (SPAD) detector array....