Objective:

Students will gain a physical understanding of optical processing. They will learn how manipulation of the pattern in the frequency plane affects the image in the image plane.  Students are expected to study the material presented in the textbook and the Web material.

Web Material:

Additional Material: Hecht, chapter 11, chapter 7.4.4

Excel and the Fourier transform

See Fourier Transform Optics for details about the spreadsheet.

Excel and the convolution (Fourier transform)

In this spreadsheet the response function is normalized.  You can pick different object functions and different response functions.  The input range for the spreadsheet contains 1024 values.  Since Excel's Fourier transform tool assumes periodic data starting at x = 0, the data corresponding to the negative x-values are in the second half of the range.

[For the spreadsheets to work the "Add-Ins" Analysis ToolPak and Analysis ToolPak-VBA have to be installed and checked.  The spreadsheet contains macros for the FFT and the inverse FFT.  If macros are enabled, you can just click the appropriate button to calculate the FFT and the inverse FFT. If the macros do not run on your computer, click Tools, Macro, Visual Basic Editor.  In the editor check that funcres.xla, procdb.xla, and atpvbaen.xla are loaded.  Click Tools, Preferences, and browse for the missing files on your hard disk.  You should find them in a directory with a name similar C:\Program Files\Microsoft Office\Office10\Library\Analysis.]

Excel and the convolution (Overlapp)

In this spreadsheet the convolution of various functions is represented as the overlap of the two functions as one is shifted over the other.

Assignment: