Week 8 Diffraction

Question 1

what would the fourier transform of something small and spikey generally look like

Answer 1

the corresponding fourier transform is broad and smooth

Question 2

give four common fourier transforms

Answer 2

top hat –> Sinc
Gaussian –> Gaussian
Constant –> Delta Function
2 Delta Functions –> Cos

Question 3

when is Fraunhofer diffraction applied

Answer 3

in the far field scenario

Question 4

what is the fraunhofer diffraction intensity equation

Answer 4

I = E0^2 [sinc(πasinθ/λ)]^2

Question 5

what are the four fraunhofer diffraction assumptions

Answer 5

phase varies linearly across the aperture
amplitude is same from all parts of the aperture
ignored obliquity factor
distance between source and aperture is big

Question 6

what are the two convolution equations

Answer 6

h(x) = ∫ f(x')g(x-x')dx'
H(x) = F(x)G(x)

Question 7

what is the intensity equation of a two wide slit grating

Answer 7

I = I0[sinc(πasinθ/λ)]^2[cos(πdsinθ/λ)]^2

where a is slit width and d is slit separation

Question 8

what is the intensity equation for a diffraction grating of N narrow slits

Answer 8

I = E0^2[sinc(πasinθ/λ)]^2 {[sin(Nπdsinθ/λ)]^2 / [sin(πdsinθ/λ)]^2}

Question 9

what is the diffraction spectrometry resolution equation

Answer 9

δλ = λ/Nm