mathematical methods for optical physics bookfi org

[...]... Fresnel transform 12.2 Linear canonical transforms 12.3 The Laplace transform 12.4 Fractional Fourier transform 12.5 Mixed domain transforms 12.6 The wavelet transform 12.7 The Wigner transform 12.8 Focus: the Radon transform and computed axial tomography (CAT) 12.9 Additional reading 12.10 Exercises 13 Discrete transforms 13.1 Introduction: the sampling theorem 13.2 Sampling and the Poisson sum formula... attention on methods directly related to optical science Here again the standard texts became a problem, as there is not a perfect overlap between important methods for general physics and important methods for optics For example, group theory is not commonly used among most optics researchers, and Fourier transforms, essential to the optics researcher, are not used as much by the rest of the general physics. .. such programs and optical researchers in general seems to have the potential to be a popular resource My goal, then, was to write a textbook on mathematical methods for physics and optical science, with an emphasis on those techniques relevant to optical scientists and engineers The level of the book is intended for an advanced undergraduate or beginning graduate level class on math methods One of my... Preface Why another textbook on Mathematical Methods for Scientists? Certainly there are quite a few good, indeed classic texts on the subject What can another text add that these others have not already done? I began to ponder these questions, and my answers to them, over the past several years while teaching a graduate course on Mathematical Methods for Physics and Optical Science at the University... Fourier transform and its inverse 11.3 Examples of Fourier transforms 11.4 Mathematical properties of the Fourier transform 11.5 Physical properties of the Fourier transform 11.6 Eigenfunctions of the Fourier operator 11.7 Higher-dimensional transforms 11.8 Focus: spatial filtering 11.9 Focus: angular spectrum representation 11.10 Additional reading 11.11 Exercises 12 Other integral transforms 12.1 Introduction:... differential equations, sequences and series, matrices, and this part of the book might be used for any math methods for physics course Later chapters concentrate on techniques significant to optics, including Fourier analysis, asymptotic methods, Green’s functions, and more general types of integral transform A book of this sort requires a lot of help, and I have sought plenty of insight from colleagues... arrow indicates the direction of the vector Examples of vectors in elementary physics include displacement, velocity, force, momentum, and angular momentum, though the concept can be extended to more complicated and abstract systems Algebraically, we will usually represent vectors by boldface characters, i.e F for force, v for velocity, and so on It is worth noting at this point that the word “vector”... properly, we need to formulate mathematically this concept of coordinate system invariance Furthermore, it is not uncommon to require, in the solution of a physical problem, the transformation from one coordinate system to another We therefore take some time to study the mathematics relating to the behavior of a vector under a change of coordinates The simplest coordinate transformation is a change... there exists a generalized form of multiplication for vectors, as well; with three components for each vector, however, there are a large number of possibilities for what we might call “vector multiplication” Just as vectors themselves are invariant under a change of coordinates, any vector multiplication should also be invariant under a change of coordinates It turns out that for three-dimensional vectors... her own difficulties in learning mathematical techniques, a few problems amongst the students have remained common and constant The foremost among these is the “wall” between the mathematics the students learn in math class and the applications they study in other classes The Fourier transform learned in math class is internally treated differently than the Fourier transform used in, say, Fraunhofer diffraction . blank MATHEMATICAL METHODS FOR OPTICAL PHYSICS AND ENGINEERING The first textbook on mathematical methods focusing on techniques for optical science and engineering, this textbook is ideal for advanced. transforms 386 12.1 Introduction: the Fresnel transform 386 12.2 Linear canonical transforms 391 12.3 The Laplace transform 395 12.4 Fractional Fourier transform 400 12.5 Mixed domain transforms. for optics for the past five years and a course on advanced physical optics for two years. MATHEMATICAL METHODS FOR OPTICAL PHYSICS AND ENGINEERING GREGORY J. GBUR University of North Carolina CAMBRIDGE