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

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

ENHANCED

both sedimentary rocks and volcanic flows

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

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 Spatial frequencies: sinusoidal

grating versus b/w grating

Diffraction Orders

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"

contrast sensitivity function (CSF) for an eye’s visibility

By blurring

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

LOWPASS FILTERFOURIER TRANSFORM

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