The assignment is attached, please show working.1. (5 marks) Determine the functional form of the...

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The assignment is attached, please show working.

1. (5 marks) Determine the functional form of the Fraunhofer diffraction pattern of apertures which have the following transmission functions (partially transmitting):(a) f x e?( 2 / 2 ) ( ) ? x ?2 (a Gaussian transmission function)(b) f(x) is a series of N (where N is very large) symmetric grating steps with triangular transmission function with base width a, spaced by 2a, and with peak transmission of 1. (Hint: make use of the convolution theorem to simplify the problem).
see attached for the rest
Thank you

Robert · Accepted Answer

SOLUTION 2: 
a) If the width of the bars nu the aperture is halved, the angle subtended by the 
diffraction patterns gets doubled and the pattern emerges in a narrow manner. 
b) For triangular apertures the function is written as: 
         , 2 3 3 1 3 1t x y y x y x y          
When the length of the bars gets doubled, the pattern will emerge the same but with 
angles of the pattern in more acute manner. 
c) The circular edge inside the triangle will double the streaks in the pattern and the 
width of the streaks will depend on the radius of the circle. 
SOLUTION 3: 
The expression for the limit of resolution can be written as: 
0Ly
d

  
The distance strands can be calculated by substituting, 20L m , 0 600nm   and 0.12y m  
Thus, 410d m . 
SOLUTION 4: 
We substitute 2 id   and 02L  . 
See the image below:
Given that the aperture is square and has a square central obstruction. 
Thus,

The assignment is attached, please show working. 1. (5 marks) Determine the functional form of the Fraunhofer diffraction pattern of apertures which have the following transmission functions...

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