Spatial Filtering and the Abbe Theory of Imaging Presented By : Ajit Balagopal Karunanand Ogirala Hui Shen

OUTLINE Applications, experiment purposes Introduction Spatial frequencies Spatial filtering Experiment procedure Result Summary

APPLICATIONS OF SPATIAL FILTERING ENHANCED Detecting and sharpening boundary discontinuities (fingerprints, geography remote sensing images) Removing unwanted noise from a laser Beam Identifying faults in the masks used to make integrated circuits Removing unwanted features from photographs both sedimentary rocks and volcanic flows ENHANCED Figure 1 shows a checkerboard that is similar to the one displayed in Figure 5.3 in your textbook. One of the checks is colored incorrectly, but it is difficult to see. In this case the target -- the miscolored check -- is being camaflouged by a mask (ie., the other checks). The reduced visibility of the target is an example of masking. Figure 2 shows the same pattern after it has been blurred. Surprisingly, blurring the pattern makes the target easier to see! miscolored check

EXPERIMENT PURPOSES We need to understand Abbe theory of image formation : What are spatial frequencies? How does spatial filtering effect image formation? This is just the topic we talk about!

INTRODUCTION -SPATIAL FREQUENCIES Grating equation: sinθm= mλ/d (m = an integer) Variation of signals in space can be expressed as spatial frequencies Higher spatial frequencies give better spatial resolution Sharp, crisp images require low as well as high spatial frequencies Diffraction Orders Spatial frequencies: sinusoidal grating versus b/w grating

Optical Fourier analysis SPATIAL FILTERING Optical Fourier analysis: • Use fine, square mesh form a two-dimensional grid of points • Orders representing frequency components in the filter • Low spatial frequencies: close to optical axis • High spatial frequencies: further from the optical axis Spatial filtering: modify image by filtering the spatial frequencies contained Optical Fourier analysis

FILTER DESCRIPTION High pass filter (blocking D.C.) : Glass plate with small inkdot Soft images Low pass filter (blocking A.C.): Pin hole Sharp images Band pass filter: transparent circle on dark plate allowing specific frequency When vertical slit is placed, vertical frequency variations are passed and horizontal frequency variations are blocked.

EXAMPLE IN MASKING: target low spatial frequencies (weak) mask high spatial frequencies (sharp) removing high spatial frequencies increases the visibility of the target By blurring, some of the mask frequencies are now outside the "window of visibility" By blurring contrast sensitivity function (CSF) for an eye’s visibility

EXPERIMENT PROCEDURE The basic setup for the experiment is as shown in the diagram. We need a beam collimator, we used a colimator with magnification 8. The laser beam must be horizontal and parallel to the edges of the breadboard. The image should be separated at focal length t the transform lens. Now observe the images on target by placing filters back of the transform lens at focal length

RESULTS FOR MESH ACTUAL IMAGE HORIZONTAL SLIT VERTICAL SLIT HIGHPASS FILTER

RESULTS FOR MESH ACTUAL IMAGE BANDPASS FILTER FOURIER TRANSFORM LOWPASS FILTER

RESULTS FOR REAL IMAGE ACTUAL IMAGE HORIZONTAL SLIT HIGHPASS FILTER VERTICAL SLIT

RESULTS FOR REAL IMAGE ACTUAL IMAGE LOWPASS FILTER BANDPASS FILTER

SUMMARY The application of image formation by spatial filtering Introduction to spatial frequencies and spatial filtering Verifying Abbe theory of imaging

REFERENCES http://rst.gsfc.nasa.gov http://www.eneate.freeserve.co.uk