OPTI 509
Log in to D2L for Course Content

Statistical Optics (3 units). Learn the statistical nature of optical fields via concepts like spatial and temporal coherence. The second-order coherency theory of optical fields is crucial to gain a deeper understanding of optical instruments/systems such as interferometers and imaging systems. Students will be able to analyze partial coherence in imaging systems, laser speckle, and propagation in random medium. Prerequisite: OPTI 501, 508 or instructor permission.

Instructor:
Amit Ashok, Ph.D.
Room 421 | ashoka@optics.arizona.edu | 626 4815

Course Objectives:

  1. Become familiar with the statistical nature of optical fields.
  2. Learn to use stochastic processes to represent optical fields.
  3. Understand the concept of temporal coherence and spatial coherence.
  4. Understand the relationship between spatial coherence and source spatial distribution via the Van-Cittert-Zernike theorem.
  5. Understand the relationship between temporal coherence and source spectral distribution via the Weiner-Khinchin theorem.
  6. Learn the propagation of coherence function through free-space and simple optical elements.
  7. Learn to apply second-order coherence theory to real optical systems e.g. stellar interferometers and imaging systems.
Required Textbook:
Goodman, J. (2000). Statistical Optics. Wiley-Interscience.
Supplementary Reading
Papoulis, A. and Pillai, S. (2001). Probability, Random Variables and Stochastic Processes. McGraw-Hill

Mandel, L. and Wolf, E. (2008), Optical Coherence and Quantum Optics . Cambridge University Press.

Wolf, E. (2007). Introduction to Coherence and Polarization of Light. Cambridge University Press.
Course D2L Site
The course’s online component will be conducted via the University of Arizona’s Desire2Learn software system. The D2L can by accessed by this link: www.d2l.arizona.edu

Distance Learning
The class will be offered via distance learning when possible.

Course Outline
2.1 Review of probability and random variables (3 lectures)
  1. Definition of probability and random variables
  2. Distribution and density function
  3. Bivariate and multivariate random variables
  4. Joint, conditional, and marginal densities
  5. Characteristic function, moment generating function
  6. Transformation of random variables
  7. Complex-valued random variables and random phaser sums
2.2 Stochastic processes (5 lectures)
  1. Definition in terms of random variables and ensemble functions
  2. Ergodicity and stationarity
  3. Auto-correlation, cross-correlation, and Wiener-Khinchin theorem
  4. Gaussian and Poisson random processes
  5. Karhunen-Loeve expansion
  6. Linear transformation of stochastic process
2.3 First-order properties of optical waves (4 lectures)
  1. Monochromatic, non-monochromatic and narrowband light
  2. Polarized and unpolarized thermal light
  3. Partially polarized thermal light
  4. Laser light and pseudo-thermal light
2.4 Second-order coherence theory (10 lectures)
  1. Temporal coherence and complex degree of self coherence
  2. Spatial coherence and complex degree of mutual coherence
  3. Cross-spectral purity
  4. Propagation of mutual coherence
  5. The Van Cittert-Zernike theorem
2.5 Applications of second-order coherence theory (10 lectures)
  1. Laser speckle
  2. Stellar interferometry
  3. Fourier transform spectroscopy
  4. Partial coherence in imaging systems
  5. Propagation through random inhomogenous media
Assignments:
The final grade for the class will have following components:
  1. Homework: 25%
  2. Class Project: 20%
  3. Midterm Exam: 25%
  4. Final Exam: 30%
Grades:
The class grades will depend on the class score statistics. However, nominally the following scores ranges will be used to assign grades:
  • 100%-90%: A
  • 75%-89%: B
  • 65%-74%: C
  • 55%-64%: D
  • 0%-54%: E