Conventional optical synthesis, the manipulation of phase and amplitude spectral components to produce an pulse in different temporal modes, is revolutionizing ultrafast science metrology. These technologies rely on Fourier transform light fields between time frequency domains one-dimensional space. However, within this treatment it impossible incorporate quantum correlation among photons. Here...

Leaf identification is a challenging research. So far, many approaches have been proposed. In this paper, an approach that combines Fourier descriptors with other shape features was investigated to identify 100 hundred kinds of leaves. The result shows that the combination of Fourier descriptors and several other shape features can be used to identify leaves with the accuracy rate of 88%. This ...

The fractional Fourier transform (FRT) is shown to be of potential use in analyzing the motion of a surface by use of holographic interferometry. The extra degree of freedom made available by the use of the FRT allows information regarding both translational and tilting motion to be obtained in an efficient manner.

We show an accurate procedure to obtain a Fourier transform (FT) with no dc term using a commercial twisted-nematic liquid-crystal display. We focus on the application to holographic storage of binary data pages, where a drastic decrease of the dc term in the FT is highly desirable. Two different codification schemes are considered: binary pi radians phase modulation and hybrid ternary modulati...

We describe our new method for watermarking digital images. Our work is motivated by the study of phase only filters in Fourier optics. In this paper we concentrate on greyscale images, even though our method works for color also. We take the discrete Fourier transform of an image and determine a signature based upon a binary phase-only filter (BPOF). We replace certain frequency magnitudes wit...

J. R. Fienup Environmental Research Institute of Michigan P.O. Box 8618 Ann Arbor, Michigan 48107 Abstract. This paper reviews the GerchbergSaxton algorithm and variations thereof that have been used to solve a number of difficult reconstruction and synthesis problems in optics and related fields. It can be used on any problem in which only partial information (including both measurements and c...

The ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order fractional Fourier transform is equal to the ordinary Fourier transform. This paper discusses the relationship of the fractional Fourier transform to harmonic oscillation; both co...

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher information capacity and noise-resilience. However, schemes to generate the resources required for computing have so far been lacking linear optics. Here, we show how GHZ states arbitrary dimensions numbers photons using optical circuits described by Fourier transform matrices. Combi...

The Truncated Fourier Transform (tft) is a variation of the Discrete Fourier Transform (dft/fft) that allows for input vectors that do not have length 2 n for n a positive integer. We present the univariate version of the tft, originally due to Joris van der Hoeven, heavily illustrating the presentation in order to make these methods accessible to a broader audience.