The linear canonical transform (LCT), is the name of a parameterized continuum of transforms which include, as particular cases, the most widely used linear transforms and operators in engineering and physics such as the Fourier transform, fractional Fourier transform (FRFT), Fresnel transform (FRST), time scaling, chirping, and others. Therefore the LCT provides a unified framework for studyin...

We propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the ray’s 2×2 matrix operators should be right-acting, so that the matrix product succession would go with light’s left-to-right propagation. We express the propagation and refraction operators as a sum of a unit matrix and an imaginary matrix proportional ...

We have designed and constructed a Fourier Transform Spectrometer (FTS) for the study of submillimeter-wave mixers and optical components. The FTS has a large aperture (up to 25.4 cm) and small focal ratio (as fast as f/2.5) to achieve a large throughput. It operates in the 100-3750 GHz (3.3125 cm 1) frequency range with a resolution of up to 75 MHz (0.0025 cm ). Here we discuss the design goal...

1. Everything is number 2. Ancient Astronomy 3. Optics and statics 4. The middle ages and the renaissance 5. Mechanics of motion 6. Newtonian mechanics 7. Early differential equations 8. The Brachistochrone 9. Early methods of solutionLinear differential equations 10 Newton’s second law as a differential equationThe method of perturbations 11. The vibrating stringPartial differential equations ...

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...

This paper discuss about FPGA implementation of radix-4 FFT algorithm, which is simulated ,synthesized, and downloaded on xcv1000 FPGA, which gives the operating speed of 52.3 MHz. Fourier transform play an important role in many digital signal processing applications including acoustics, optics, telecommunications, speech, signal and image processing. However, their wide use makes their comput...

A simple implementation of the full-vectorial plane wave method is presented for modeling photonic crystals with regular ‘atoms’ using MATLAB. We calculate the analytical Fourier transform for an atom and use the shift property to obtain the Fourier transform for any arbitrary supercell consisting of a finite number of atoms, including the quasiperiodic case. MATLAB source code for the implemen...

Natalia A. Schmid, Yoram Bresler, and Pierre Moulin University of Illinois at Urbana-Champaign Coordinated Science Laboratory, 1308 West Main, Urbana, IL 61801 nschmid ifp.uiuc.edu, ybresler uiuc.edu, moulin ifp.uiuc.edu ABSTRACT We consider the estimation of an unknown arbitrary 2D object shape from sparse noisy samples of its Fourier transform. The estimate of the closed boundary curve is par...