Probability, Statistical Optics, and Data Testing: A Problem Solving ApproachSpringer Science & Business Media, 6 déc. 2012 - 404 pages A basic skill in probability is practically demanded nowadays in many bran ches of optics, especially in image science. On the other hand, there is no text presently available that develops probability, and its companion fields stochastic processes and statistics, from the optical perspective. [Short of a book, a chapter was recently written for this purpose; see B. R. Frieden (ed. ): The Computer in Optical Research, Topics in Applied Physics, Vol. 41 (Springer, Berlin, Heidelberg, New York 1980) Chap. 3] Most standard texts either use illustrative examples and problems from electrical engineering or from the life sciences. The present book is meant to remedy this situation, by teaching probability with the specific needs of the optical researcher in mind. Virtually all the illustrative examples and applications of the theory are from image science and other fields of optics. One might say that photons have replaced electrons in nearly all considera tions here. We hope, in this manner, to make the learning of probability a pleasant and absorbing experience for optical workers. Some of the remaining applications are from information theory, a con cept which complements image science in particular. As will be seen, there are numerous tie-ins between the two concepts. Students will be adequately prepared for the material in this book if they have had a course in calculus, and know the basics of matrix manipulation. |
Table des matières
1 | |
2 | |
7 | |
2 | 13 |
2 | 19 |
2 | 25 |
9 | 33 |
Probability Density Function Basic Properties | 37 |
Stochastic Processes | 177 |
7 | 188 |
8 | 197 |
6 | 203 |
12 | 206 |
Estimating the Mean | 233 |
Estimating a Probability Law | 264 |
The ChiSquare Test of Significance | 294 |
10 | 45 |
9 | 52 |
Fourier Methods in Probability | 70 |
16 | 79 |
23 | 85 |
29 | 93 |
Functions of Random Variables | 99 |
7 | 105 |
Physical Layout | 106 |
10 | 112 |
Bernoulli Trials and its Limiting Cases | 134 |
5 | 140 |
8 | 146 |
Producing Random Numbers that Obey a Prescribed | 163 |
The Student tTest on the Mean | 307 |
6 | 314 |
The FTest on Variance | 320 |
1 | 327 |
4 | 333 |
Principal Components Analysis | 350 |
The Controversy Between Bayesians and Classicists 363 | 362 |
Appendix A Error Function and its Derivative 4 12 | 374 |
223 | 378 |
Appendix E A Crib Sheet of Statistical Parameters and their Errors | 382 |
393 | |
394 | |
Autres éditions - Tout afficher
Probability, Statistical Optics, and Data Testing: A Problem Solving Approach B. Roy Frieden Affichage d'extraits - 1983 |
Expressions et termes fréquents
A₁ amplitude aperture assumed average binary binomial central limit theorem characteristic function chi-square coefficients computed constant convolution correlation curve defined definition denote derivation discrete disjoint emulsion equation error estimate event example finite flip fluctuation Fourier transform frequency Gaussian given Hence identity image plane integral intensity interval known large numbers laser law of large lens m₁ maximum entropy median normal Note obeys object observed occur optical optical transfer function outcome output P(ym P₁ parameter partition law phase photon point spread function Poisson position power spectrum principle probability density probability law problem px(x quantity random variable randomly Rect result RV's sample mean Sect shot noise speckle speckle image statistically independent stochastic process Suppose transfer function turbulence variance x₁ y₁ σ²