goodman傅里叶光学习题解答.pdf

Introduction to Fourier Optics Third Edition Problem Solutions Joseph W. Goodman Stanford University Copyright Joseph W. Goodman, all rights reserved. September 22, 2005 Preface Doing problems is an essential part of the learning process for any scientific or technical subject. This is particularly true for subjects that are highly mathematical, as is the subject of Introduction to Fourier Optics . However, there are many different types of problems that one could imagine. Some involve straightforward substitution into equations that have been established in the text; such problems are useful in so far as they relate an abstract mathematical result to a real situation, with physical numbers that might be encountered in practice. Other problems may ask students to apply methods similar to those used in the text, but to apply them to a problem that is different in some significant aspect from the one they have already encountered. By far the best problems are those that leave the student feeling that he or she has learned something new from the exercise. With the above in mind, I would like to mention some of my favorite problems from this text, with some indication as to why they are especially valuable: • Problem 2-4 introduces the student to the idea that a sequence of two Fourier transforms, perhaps with different scaling factors, results in an “image” with magnification or demagnification. • Problem 2-8, which explores the conditions under which a cosinusoidal object results in a cosinusoidal image, is highly instructive. • Problem 2-14 introduces the student to the Wigner distribution, a valuable concept which they will encounter nowhere else in the book. • Problem 3-6 shows how the diffraction integrals for monochromatic light can be generalized to