The Course syllabus and Lecture Notes

Chapter 1 Introduction to Statistical Optics and Image Formation

  1.1 Overview of Statistical Optics ( PDF)
  1.2 Overview of Image Formation Process ( PDF)

  You can download this pdf file to learn more about the Fourier transform property with thin lens and this pdf file for the image processing functionality with 4f optical system.

Chapter 2 Introduction to Probability Theory and Random Variables ( PDF - 2.2 MB)

  2.1 Definitions of the Related Terms and Concepts: Random Variables, Marginal and Conditional Probabilities, Bayes rule and Markov Events
  2.2 Continuous Random Variables: Moments of RV and Characteristic Function
  2.3 Some Useful Distribution Laws
  2.4 Fourier's Methods: Characteristic Function, Shift Theorem, Characteristic Functions for Some Probability Laws
  2.5 Probability Law for the Sum of Two Independent Random Variables, Central Limit Theorem, Functions of RV

  Workshop 1a:  Probability distribution function (pdf) is  indispensable for a random variable. Thus, how to deduce the pdf of a random variable with incomplete information becomes a critical issue. This workshop introduces a useful scheme, which combines maximum entropy principle with cvx solver, to determine pdf . This  rar folder contains some m-scripts, which will show how an exponential (maxent_1.m), Gaussian (maxent_2.m), and log-normal (maxent_3.m) pdf emerges from specific constraints.
  Workshop 1b: This workshp offers a tutorial on Bayes theorem and basic practices for performing model fitting tasks. The zip folder contains m-scripts to be used in this workshop.

 Homework Set 1 ---Due: Oct. 28, 2020  Here is the homework 1 for the 2020 class. To answer problem 1(c), you will need this matlab mat file irad.mat, which can be download here. The photon stream data for problem 3 is available here. You may also need some Bayes model fitting techniques detailed in Workshop 1b.

Chapter 3 Stochastic Processes ( PDF - 3.35 MB)

  3.1 Autocorrelation Function and Power Spectrum
  3.2 Fourier Transform Theorem and Transfer Theorem for Power Spectrum
  3.3 Statistical Properties of Photon Noise and Ergodic Property
  3.4 Optimum Restoring Filter

  Workshop 2: This zip folder contains the m scripts and data file needed to perform the following simulations: a) Restore the true object from a blurred and noisy image using a regularized direct inverse filter and Wiener-Helstrom filter assuming that the power spectrum of the true object is known (wienerFilter1.m). b) However, it is highly desirable to design a Wiener-Helstrom filter for restoring the true object (wienerFilter2.m) without knowing its power spectrum. c) You can also apply the Bayesian technique to learn the parameters of the Wiener-Helstrom filter from an image and use the filter to restore the true object (wienerFilter3.m). Here psnr.m can be used to evaluate the performances of the image restoring filters.

Chapter 4 Statistical Properties of Light ( PDF - 2.16 MB)

  4.1 Propagation of Monochromatic Light and Huygens-Fresnel Principle
  4.2 Propagation of Non-monochromatic Light
  4.3 Polarized and Unpolarized Thermal Light
  4.4 Partially Polarized Thermal Light
  4.5 Statistical Properties of Thermal Light and Laser Light

  Workshop 3: Three examples are included in this workshop: 1) First, a set of diffraction patterns of a spherical wave are simulated with this script. The Huygens-Fresnel principle is invoked to model the free-space propagation (propagate.m). 2) This m-script TemporalPartialCoherence.m simulates the interference effect of two beams, which have the same power spectrum, but relatively delay in time.

Chapter 5 Modern Theory of Optical Coherence ( PDF - 5.88 MB)

  5.1 Heuristic Introduction
  5.2 Mathematical Description of Temporal Coherence and Spatial Coherence
  5.3 Power Spectrum of Light Source and Cross-Spectral Purity
  5.4 Propagation Behavior of Mutual Coherence Function
  5.5 The van Cittert-Zernicke Theorem: A brief review on the Huygens-Fresnel principle, optical coherence, and van Citter-Zernike Theorem can also be found here ( PPT - 4.3MB)

  Workshop 4: Two examples will be introduced in this workshop: 1) First, we will use this m-script (Inteference.m) to illustrate the inteference of partially coherent point source. You need this matlab function to run the simulation. 2) Second, we will derive the mutual intensity function for a LED optical system (MutualIntensityPropagation.m). This example demonstrates a simple method to generate partially coherent light field.

  Homework Set 2---Due: Dec. 2, 2020. Here is the homework 2 for the 2020 class. You will need this image file cell1.tif to complete question 3. To evaluate the performance of your Wiener filter algorithm, you also need this original image cell0.tif.

Chapter 6 Image Formation Theory ( PDF - 3.14 MB)

  6.1 Intensity Impulse Response
  6.2 Image Formation Described by the Intensity Transfer Function
  6.3 Image Formation with Coherent Light
  6.4 Coherent Imaging: An Example

  Workshop 5: Useful image formation concepts introduced in this chapter will be demonstrated in a) Coherent Imaging, b) Incoherent Imaging, c) PSF at Focus and d) Extended Depth of Focus. You can use this image file to run a) and b).

Chapter 7 Case Study 1 on Image Retrieval in Optics (PDF - 3.8 MB)

  7.1 Types of Image Blur
  7.2 Image Formation Model: Convolution, Blind vs. Non-blind Deconvolution
  7.3 Deblurring with Blind Deconvolution
  7.4 Probabilistic Model of Image Formation
  7.5 Deconvolution with Bayesian Approach, Likelihood, Image Prior, and Blur Prior
  7.6 Motion Deblurring
  7.7 Framework of Bayes Rule for Image Retrieval Applications
  7.8 Iterated Projection Algorithms for Phase Retrieval

  The two image-deblurring algorithms described in 7.5 and 7.6 were implemented in a matlab code, which can be downloaded from Levin and Fergus.

  Workshop 6: This workshop is designed to introduce hand-on experiences on (1) image retrieval and (2) phase retrieval. This zip file contains the m-scripts to be used to recover an object from a blurred and noisy image. The method is detailed in 7.7, which first converts the retrieval problem into a constraint minimization problem. An ADMM solver was then implemented to yield a solution to the minimization problem by compromizing data constraint (TV) with data fedelity. (2) This zip file contains the m-scripts of hybrid input-output (HIO) algorith, detailed in the lecture note 7.8, to demonstrate a phase retrival application. An optical field is focused by a plano-concex lens. The resulting diffraction pattern is recorded at z=1.2*focal length behind the lens. HIO retrieves the phase profile of the optical field before the focused lens from the recorded diffraction pattern dp.bin.

  Homework Set 3 ---Due: January 6, 2020. This is the homework 3 for the 2019 class. To solve problem 3, you will need the diffraction pattern stored in this binary file. You can use fread(fid, [512, 512], ‘real*4’) to import the data into your script.

Chapter 8 The Effects of Partial Coherence on Imaging Formation: A Rigorous Statistical Analysis ( PDF - 3.8 MB)

  8.1 Preliminary Considerations on
    a) Effects of a thin transparent object on mutual coherence function
    b) Time delays induced by a thin lens
    c) Focal-plane-to-focal-plane coherence relationships
    c) Object-Image Coherence Relations for a Thin Lens
  8.2 Methods for Calculating Image Intensity
    a) Integration over the source
    b) Representation of the source by an incident mutual intensity function
  8.3 Image Formation as an Interference Process
    a) An imaging system is an interferometer
    b) Gathering Image Information with Interferometers
    c) Phase Information and Phase Retrieval Problem
  8.4 The Speckel Effect in Coherent Imaging
    a) First-order statistics of speckle
    b) Ensemble Average Coherence

  Workshop 7: Explore the effects of partial coherence on imaging with the formalism of sum over source.

Chapter 9 Case Study 2 on Imaging Formation through Light Scattering ( PDF - 1.8 MB)

  9.1 Light Propagation in Free Space
  9.2 The First Order Born Approximation of Light Scattering in Inhomogeneous Media
  9.3 Three-Dimensional Diffraction Tomography
  9.4 Multi-Plane Tomographic Phase Retrieval
  9.5 Coherence measurements of scattered incoherent light for lensless identification of an object’s location and size
  9.6 Coherence Properties of Light Propagation Through a Scattering Medium
  9.7 Partially Coherent Lens-free Tomographic Microscopy
  9.8 Imaging through Strongly Scattering Media
  9.9 3D imaging in volumetric scattering media using phase-space

  Workshop 8: This workshop (dpc.zip--13.5 Mb) will reconstruct a 3D profile from a through-focus image stack (img512.tif) as illustrated in section 9.4. The retrieval procedure starts with a design of a CTF mask (CTFmask_generator.m) for the imaging system with the system parameters specified in DPC_SystemSetup.m. The Multi-Plane Tomographic Phase Retrieval is coded in "DPC_3DPrf.m", which generates a phase profile CellPrf.mat. The script "Cal_3DProfile.m" will read in CellPrf.mat and prepares a 3D mesh and smooth patches for a specified isovalue of optical pathlength difference. To prepare the 3D isosurface, two useful scripts "alphavol.m" and "smoothpatch.m" are needed. The generated 3D profile is stored in Cell_3Ddata.mat and can be combined with other volume data for further examination.

Chapter 10 Lightfield Imaging with Partially Coherent Light

  10.1 Propagation of generalized radiance and Wigner distribution function ( PDF1 and PDF2)
  10.2 Wigner-based ray-tracing
  10.3 Phase space tomography
  10.4 Wavefield imaging with partially coherent light via phase modulation diversity
  10.5 Ambiguity function and mutual intensity function of patially coherent light