Spatial Filtering and the Abbe Theory of Imaging

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

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

APPLICATIONS OF SPATIAL FILTERING ØDetecting and sharpening boundary discontinuities (fingerprints, geography remote sensing images) ENHANCED both sedimentary rocks volcanic flows ØRemoving unwanted noise from a laser Beam ENHANCED ØIdentifying faults in the masks used to make integrated circuits miscolored check ØRemoving unwanted features from photographs and

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

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

SPATIAL FILTERING Ø Optical Fourier analysis: • Use fine, square mesh form a twodimensional 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 Ø Spatial filtering: modify image by filtering the spatial frequencies contained Optical Fourier analysis

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

EXAMPLE IN MASKING: Ø Ø By blurring contrast sensitivity function (CSF) for an eye’s visibility 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"

EXPERIMENT PROCEDURE Ø Ø Ø 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 FOURIER TRANSFORM BANDPASS FILTER LOWPASS FILTER

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

RESULTS FOR REAL IMAGE ACTUAL IMAGE LOWPASS FILTER BANDPASS FILTER

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

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