Use of Fourier Transform in Optics

1.Single Slit Diffraction Pattern:

The spreading out of a wave when it passes through a narrow opening is known as the phenomenon of diffraction and the intensity distribution on the screen is called the diffraction pattern. In fresnel diffraction,the screen or the source (or both) are at finite distances from the aperture i.e slit ,then the diffraction pattern corresponds to the fresnel class.In fraunhofer diffraction both the source and the screen are at infinity.




A slit can be represented by a function where the value of the function represents the illumination. Let the slit width be a. Then the illumination will be constant on each point on the slit. Let constant illumination be h.

Then x(t) = h - a / 2 <= t <= +a / 2

The properties of the above function(i.e the pattern of intensity maxima and minima) agree very well with that of the diffraction pattern that one observes due to the single slit.