Probability, Statistical Optics, and Data Testing

Scientists in optics are increasingly confronted with problems that are of a random nature and that require a working knowledge of probability and statistics for their solution. This textbook develops these subjects within the context of optics using a problem-solving approach. All methods are explicitly derived and can be traced back to three simple axioms given at the outset. Students with some previous exposure to Fourier optics or linear theory will find the material particularly absorbing and easy to understand.
This third edition contains many new applications to optical and physical phenomena. This includes a method of estimating probability laws exactly, by regarding them as laws of physics to be determined using a new variational principle.

Texte du rabat

Scientists and engineers in optics are increasingly confronted with problems that are of a random nature and that require a working knowledge of probability and statistics for their solution. This book develops these subjects within the context of optics, using a problem-solving approach. All methods are explicitly derived and can be traced back to three simple axioms given at the outset. This third edition contains many new applications to optical and physical phenomena, including a method of exactly estimating probability laws.

Contenu

1. Introduction.- 2. The Axiomatic Approach.- 3. Continuous Random Variables.- 4. Fourier Methods in Probability.- 5. Functions of Random Variables.- 6. Bernoulli Trials and Limiting Cases.- 7. The Monte Carlo Calculation.- 8. Stochastic Processes.- 9. Introduction to Statistical Methods: Estimating the Mean, Median, Variance, S/N, and Simple Probability.- 10. Introduction to Estimating Probability Laws.- 11. The Chi-Square Test of Significance.- 12. The Student t-Test on the Mean.- 13. The F-Test on Variance.- 14. Least-Squares Curve Fitting - Regression Analysis.- 15. Principal Components Analysis.- 16. The Controversy Between Bayesians and Classicists.- 17. Introduction to Estimation Methods.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- Appendix E.- Appendix F.- Appendix G.- References.