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Course Information Summary
1.0
COURSE: OPTICS FOR IMAGING - SIMG xxx
1.1 One-quarter course: Four credit hours.
1.2 Three 50-minute lectures and one 3-hour lab per week.
1.3 Prerequisite: Credit in SPSP-313 (University Physics III)
2.0
COURSE DESCRIPTION
The description of optical imaging systems. Topics include refraction, reflection, imaging with lenses,
stops and pupils, and optical system design using computer software.
3.0
COURSE OBJECTIVES
At the conclusion of the course, the student will be able to:
3.1 Determine locations and sizes of images produced by optical systems with multiple elements
3.2 Understand the concepts of aberrations
3.3 Design, characterize, and optimize simple imaging systems
4.0
COURSE OUTLINE
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
5.0
Wave and ray representation of light
Snell’s law in ray and wave representation
Refractive index, dispersion
Plane and curved mirrors
Thin lenses, combinations
Thick lenses
Stops and pupils, radiometry
Optical raytracing software
Computer-aided optical system design
Aberrations of optical systems
INSTRUCTIONAL TECHNIQUES
5.1
5.2
5.3
5.4
Lectures
Demonstrations
Laboratories
Optical design software
6.0
EVALUATION
6.1 Assigned homework
6.2 Quizzes
6.3 Two or three hour exams
6.4 Comprehensive final exam
7.0
POSSIBLE TEXTS
7.1
7.2
Optics, E. Hecht, Addison-Wesley, 2002.
Seeing the Light, D. Falk, D. Brill, and D. Stork, Harper and Row, 1986.
Course Information Summary
1.0
COURSE: OPTICAL PHYSICS FOR IMAGING II - SIMG yyy, SPSP-455
1.1 One-quarter course: Four credit hours.
1.2 Three 50-minute lectures and one 3-hour lab per week.
1.3 Prerequisites:
Credit in SPSP-313 (University Physics III)
SIMG-??? (Linear Mathematics for Imaging)
2.0
COURSE DESCRIPTION
The principles of wave optics are applied to imaging systems. Topics include propagation of
electromagnetic radiation, the wave equation, diffraction, and interference. Particular emphasis is
placed on the fundamental limitations of the optical system on the resulting image.
3.0
COURSE OBJECTIVES
At the conclusion of the course, the student will be able to:
3.1 Determine the location and size of the image in an optical system with multiple elements
3.2 Understand the physical concepts of light as applied to imaging
3.3 Understand the fundamental limitations on the quality of the image due to the optical system
4.0
COURSE OUTLINE
4.1 Harmonic oscillations, superpositions
4.2 Traveling waves
4.3 Electromagnetic theory
4.3.1
Maxwell’s equations
4.3.2
Electromagnetic waves
4.3.3
Superposition and phasors
4.4 Light at an interface
4.4.1
Huygens Principle
4.4.2
Reflection and refraction
4.4.3
Fresnel equations
4.4.4
Total internal reflection
4.5 Polarization of Light
4.5.1
Malus’ Law
4.5.2
Types of Polarization Mechanisms
4.6 Interference
4.6.1
Young’s experiment
4.6.2
Thin films
4.6.3
Michelson interferometer
4.7 Diffraction
4.7.1
Single slit diffraction
4.7.2
Diffraction gratings
4.7.3
Circular aperture
4.8 Imaging
4.8.1
Diffraction limit to image quality
4.8.2
Modulation transfer functions
4.8.3
Point spread functions, image formation
5.0
INSTRUCTIONAL TECHNIQUES
5.1
5.2
5.3
5.4
Lectures
Demonstrations
Laboratories
Programming Assignment
6.0
EVALUATION
6.1 Assigned homework
6.2 Quizzes
6.3 Two or three hour exams
6.4 Comprehensive final exam
7.0
POSSIBLE TEXTS
7.1
7.2
7.3
7.4
Introduction to Optics, F. Pendrotti and L. Pendrotti, Prentice-Hall 1993
Optics, E. Hecht, Addison-Wesley, 2002.
Seeing the Light, D. Falk, D. Brill, and D. Stork, Harper and Row 1986
Introduction to Modern Optics G. Fowles, Dover, 1975
Course Information Summary
1.0
COURSE: LINEAR MATHEMATICS FOR IMAGING - SIMG xxx
1.1 One-quarter course: Four credit hours.
1.2 Two 100-minute lectures per week.
1.3 Prerequisite: Credit in SMAM-305 (Calculus IV)
1.4 Co-requisites: None
2.0
COURSE DESCRIPTION
This course develops the concepts of complex numbers and linear algebra for describing imaging
systems.
3.0
COURSE OBJECTIVES
3.1
3.2
4.0
To develop the concepts of complex numbers, vectors, and matrices
To introduce the student to alternative representations of discrete models of imaging systems via
the discrete Fourier transform.
COURSE OUTLINE
4.1
Review of complex numbers and their geometric interpretation
4.1.1 arithmetic of complex numbers
4.1.2 Euler relation
4.1.3 Argand diagram
4.1.4 phasors
4.2 Representations of images as vectors
4.2.1 lexicographic ordering
4.3 Projections of vectors onto reference vectors, basis vectors.
4.3.1 scalar product of two vectors
4.3.2 length of vector as scalar product
4.3.3 projection, representation of vector as its projections onto basis vectors
4.3.4 vector spaces
4.3.5 representation of set of basis vectors as matrix
4.3.6 matrix-vector multiplication as set of projections
4.3.7 matrix-matrix multiplication
4.3.8 identity matrix
4.3.9 transpose
4.2.10 inverse
4.4 Rotations of vectors
4.4.1 rotation matrices
4.5 Representations of imaging systems as matrices
4.5.1 linear shift-variant systems as matrices
4.5.2 linear shift invariant systems as circulant matrices
4.6 Eigenvectors and eigenvalues
4.6.1 action of matrix on eigenvector as length change
4.6.2 evaluation of eigenvectors of a matrix
4.6.3 diagonalization
4.6.4 representation of vector as projections onto eigenvectors
4.7 Diagonalization of linear shift-invariant matrices
4.7.1 discrete Fourier transform
4.8 Generalization to continuous coordinates
5.0
INSTRUCTIONAL TECHNIQUES
5.1
5.2
5.3
5.4
6.0
EVALUATION
6.1
6.2
6.3
6.4
6.0
Lectures
Demonstrations
Laboratories
Programming Assignments
Several quizzes
Assigned homework
Two or three hour exams
Comprehensive final exam
POSSIBLE TEXTS
6.1 Linear Mathematics and its Application to Imaging, by R. L. Easton (Cambridge University
Press, 2004).
6.2 Linear Algebra and its Applications, Gilbert Strang, 1988.
Course Information Summary
1.0
COURSE: IMAGING SYSTEMS I -- ANALYSIS - SIMG xxx
1.1 One-quarter course: Four credit hours.
1.2 Three 50-minute lectures and one 3-hour lab per week.
1.3 Prerequisite: Credit in SIMG-xxx (Linear Mathematics for Imaging), SIMG-yyy (Computing for
Imaging)
2.0
COURSE DESCRIPTION
This course introduces the concepts of continuous and discrete linear systems to imaging systems.
Emphasis is placed on understanding the underlying mathematical principles and their connection to
imaging applications. The perspective of a mathematical model of an imaging system is introduced at
the beginning and maintained throughout the course. The concepts of linearity, shift invariance,
convolution, Fourier transforms, the impulse response, and the transfer function are considered.
3.0
COURSE OBJECTIVES
At the conclusion of the course, the student will be able to:
3.1 Use analytical and computational methods to analyze linear and shift invariant imaging system.
3.2 Apply the concept of the impulse response and the transfer function to the study of imaging
systems.
4.0
COURSE OUTLINE
4.1
4.2
4.2
4.3
4.4
4.5
4.6
4.7
Imaging Tasks: direct task, inverse problem, system analysis
One- and two-dimensional special functions used in imaging
Description of continuous systems
4.2.1 linearity
4.2.2 shift variant systems
4.2.3 shift-invariant systems
4.2.4 convolution
4.2.5 impulse responses
1-D and 2-D continuous Fourier transforms
4.3.1 projections of functions onto basis functions
4.3.2 basis functions of linear shift-invariant systems
4.3.3 theorems of continuous Fourier transforms
Imaging systems as filters
4.4.1 classes of filters: lowpass, highpass, bandpass, phase
4.4.2 transfer functions
Sampling
4.5.1 ideal sampling
4.5.2 aliasing
4.5.3 realistic sampling, finite sensor size
Fourier transforms of discrete systems
4.6.1 infinite-support DFT
4.6.2 finite-support DFT, leakage
4.6.3 efficient algorithms, FFT
Application of Fourier analysis to imaging systems
4.7.1 Characterization in space domain: point, line, and edge spread functions
4.7.2 Characterization in frequency domain: transfer functions
4.7.3 Modulation Transfer Function (MTF) as system figure of merit
5.0
INSTRUCTIONAL TECHNIQUES
5.1
5.2
5.3
5.4
Lectures
Demonstrations
Laboratories
Programming Assignment
6.0
EVALUATION
6.1 Assigned homework
6.2 Quizzes
6.3 Lab reports
6.4 Two or three hour exams
6.5 Comprehensive final exam
7.0
POSSIBLE TEXTS
7.1 Linear Systems, Fourier Transforms, and Optics,, J. D. Gaskill, Wiley, 1978.
7.2 Linear Mathematics and its Application to Imaging, by R. L. Easton (Cambridge University
Press, 2004).
Course Information Summary
1.0
COURSE: IMAGING SYSTEMS II -- the MTF- SIMG xyx
1.1 One-quarter course: Four credit hours.
1.2 Three 50-minute lectures and one 3-hour lab per week.
1.3 Prerequisite: Credit in SIMG-xxx (Imaging Systems I -- Analysis), SIMG-yyy (Computing for
Imaging)
2.0
COURSE DESCRIPTION
This course applies the concept of the transfer function to practical imaging tasks. Practical methods to
characterize imaging systems are emphasized.
3.0
COURSE OBJECTIVES
At the conclusion of the course, the student will be able to:
3.1 Use analytical and computational methods to analyze linear and shift invariant imaging system.
3.2 Apply the concept of the impulse response and the transfer function to the study of imaging
systems.
4.0
COURSE OUTLINE
4.1
4.2
4.3
4.4
4.5
5.0
Characterization of imaging systems
MTF as a system metric
4.2.1 limitations of MTF
Applications of MTF
4.3.1 printing
4.3.2 optics
Measurement of system MTF
4.4.1 from point spread function
4.4.2 from line spread function
4.4.3 from edge spread function
Approximations of MTF
INSTRUCTIONAL TECHNIQUES
5.1
5.2
5.3
5.4
Lectures
Demonstrations
Laboratories
Programming Assignments
6.0
EVALUATION
6.1 Assigned homework
6.2 Lab reports
6.3 Two or three hour exams
6.4 Comprehensive final exam
7.0
POSSIBLE TEXTS
7.1 Modulation Transfer Function in Optical and Electro-Optical Systems, G. Boreman, SPIE, 2001.
7.2 Linear Mathematics and its Application to Imaging, by R. L. Easton (Cambridge University
Press, 2004).
Course Information Summary
1.0
COURSE: PROBABILITY AND STATISTICS FOR IMAGING - SIMG zzz
1.1 One-quarter course: Four credit hours.
1.2 Two 100-minute lectures
1.3 Prerequisite: SIMG-??? Linear Mathematics for Imaging
2.0
COURSE DESCRIPTION
The principles of probability and statistical analysis applied to imaging systems. Topics include
probability, mean and variance, continuous and discrete probability distributions in imaging (Bernoulli
trials, binomial, uniform, Gaussian, and Poisson distributions), error propagation, moments of
probability distributions, central limit theorem, Bayesian estimation, linear regression, hypothesis
testing,
3.0
COURSE OBJECTIVES
At the conclusion of the course, the student will:
3.1 Understand the concept of probability
3.2 Understand the concepts of stochastic distributions
3.3 ...
4.0
COURSE OUTLINE
4.1 Probability
4.1.1
Relation to the frequency of occurence
4.1.2
Marginal probability
4.1.3
Law of large numbers
4.1.4
Conditional probability
4.1.5
mean and variance
4.1.6
Information
4.1.7
Bayes’ rule
4.2 Probability distributions in imaging
4.2.1
Bernoulli trials
4.2.2
Binomial distribution
4.2.3
Uniform distribution
4.2.4
Gaussian distribution
4.2.5
Poisson distribution
4.3 Propagation of errors
4.4 Fourier methods in probability
4.4.1
characteristic function
4.4.2
moments
4.4.3
central limit theorem
4.5 Linear Regression
4.6 Hypothesis testing
5.0
INSTRUCTIONAL TECHNIQUES
5.1
5.2
5.3
Lectures
Demonstrations
Prayer
6.0
EVALUATION
6.1 Assigned homework
6.2 Quizzes
6.3 Two or three hour exams
6.4 Comprehensive final exam
7.0
POSSIBLE TEXTS
7.1
TBD