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ECE Course Syllabus

ECE6501 Course Syllabus


Fourier Optics and Holography (3-0-0-3)

Lab Hours
0 supervised lab hours and 0 unsupervised lab hours

Technical Interest
Optics and Photonics

Course Coordinator
Gaylord,Thomas K



Catalog Description
Applications of the Fourier transform and linear systems theory to the analysis of optical propagation, diffraction, imaging, holography, wavefront modulation, and signal processing.

Goodman, Introduction to Fourier Optics (3rd edition), Robert & Company Publishers, 2004. ISBN 9780974707723 (required)

Indicators (SPIs)
SPIs are a subset of the abilities a student will be able to demonstrate upon successfully completing the course.

Outcome 1 (Students will demonstrate expertise in a subfield of study chosen from the fields of electrical engineering or computer engineering):
1.	Explain interference of point sources and plane waves based on the wave equation and the Huygens-Fresnel Principle.
2.      Explain one-dimensional and two-dimensional diffraction based on their Fourier transform representations.  
3.      Explain near-field diffraction of representative slits and apertures.

Outcome 2 (Students will demonstrate the ability to identify and formulate advanced problems and apply knowledge of mathematics and science to solve those problems):
1.	Predict interference patterns produced by arbitrary combinations of plane, cylindrical, and spherical wavefronts.
2.      Analyze interferometric conditions required for specified accuracy levels of phase measurements.
3.      Analyze the operation and accuracy of a Fourier transform spectrometer.    

Outcome 3 (Students will demonstrate the ability to utilize current knowledge, technology, or techniques within their chosen subfield):
1.	Analyze and design holographic configurations for applications such as sensing and data storage.
2.      Analyze and design quantitative phase measurement systems for imaging and wavefront measurement. 

Topical Outline
 1. Two-dimensional functions and transforms
 2. Optical wave fields and their representation
    a. Monochromatic waves, Plane and Spherical Waves
    b. Wave intensity and interference
    c. Optical transmittance functions
    d. Non-monochromatic waves and coherence 
    e. Complex wave amplitude transmittance
 3. Propagation of waves - diffraction
    a. The angular spectrum
    b. Propagation in the Fresnel regime and in the Fraunhofer regime
    c. Inverse propagation
    d. Non-monochromatic wave propagation, quasimonochromatic condition
 4. Lenses and their properties
    a. Ray optics modeling, Wave optics modeling
    b. Fourier transform property - various configurations
 5. Image formation - monochromatic object distributions
    a. Imaging with Fourier transform modules
    b. Coherent impulse response and coherent transfer function
    c. General framework for analyzing coherent imaging systems
    d. Non-monochromatic coherent image formation
    e. Resolution in coherent imaging
 6. Imaging spatially incoherent objects
    a. General analysis and the intensity point spread function
    b. The optical transfer function
    c. Pinhole masks and the OTF
    d. Resolution and the Rayleigh criterion
 7. Imaging transparent objects
    a. Coherent and incoherent limits
    b. Practical configurations
    c. Modifications for microscopy - phase contrast and dark ground methods
    d. Differences between coherent and incoherent imaging
 8. Wavefront modulation 
    a. Photographic film
    b. Spatial light modulators
    c. Diffractive optical elements
 9. Holography
    a. The Gabor hologram, Off-axis reference wave hologram
    b. Display holograms
10. Coherent optical spectrum analysis
    a. Spectral resolution
    b. Practical lens systems
    c. Space-bandwidth product and dynamic range
    d. Channelized and falling-raster analysis methods
11. Coherent spatial filtering: convolvers and correlators
    a. Binary spatial filtering
    b. Vander Lugt and joint-transform correlators
12. Incoherent spatial filtering
    a. Shadow-casting
    b. Diffraction-based systems