Convolution Flashcards
1
Q
Single Slit Fourier Transform
A
Ep ∝ A’(ky) = A(y) ( ∫ aperture) exp[-iykᵧ]dy
A’(ky) = a/2 ∫ -a/2 exp[-iykᵧ]dy = asinc(kθᵧα/2)
2
Q
Two narrow slits separated by d
A
A’(kᵧ) = exp[-i(d/2)kᵧ] + exp[-i(d/2)kᵧ] = 2cox(kᵧd/2)
3
Q
Diffraction from a rectangular aperture
A
A’(kx,ky) = ∫ (-inf ∫ inf) A(x,y) exp[-i(xkx+yky)]dxdy
=> I (kx,ky) = Iosinc^2(kx b/2) sinc^2(ky a/2)
4
Q
Diffraction from a circular aperture
A
A’(kx) =(2π ∫ 0) (d ∫ 0) A(r,θ) exp[-i(xkx]rdrdθ
=> I = Io [(2 J1(kx d)^2)/ kx d]^2
J1(kx d) is the Bessel function
the first zero is when kx d = 1.22π
= d 2π/λ sin(θ’)
5
Q
Rayleigh criterian diagram
A
see notes
6
Q
resolving point source diagram
A
see notes
7
Q
Convultion theroem
A
F(f*g) = F(f) * F(g)
8
Q
θy =
y =
A
diffraction angle
distance from optic axis to point P
9
Q
y = 2θy
A
for first zeros
