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

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

3. 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

4. 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!

5. 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

6. 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

7. 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.

8. 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

9. 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

10. RESULTS FOR MESH ACTUAL IMAGE HORIZONTAL SLIT VERTICAL SLIT
HIGHPASS FILTER

11. RESULTS FOR MESH ACTUAL IMAGE BANDPASS FILTER FOURIER TRANSFORM
LOWPASS FILTER

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

13. RESULTS FOR REAL IMAGE
ACTUAL IMAGE
LOWPASS FILTER
BANDPASS FILTER

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

15. REFERENCES