All Questions
30
questions
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96
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How to compute the diffraction efficiency of a thin phase grating with arbitrary groove shape?
From Magnusson and Gaylord (1978), the wave amplitudes, $S_i(z)$, of $p$-polarized light for a thin, arbitrary phase grating are given by the equation
$$
\frac{\partial S_i}{\partial z} + \gamma \sum_{...
- 123
1
vote
0
answers
27
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Fraunhofer temporal far-field condition for dispersive Fourier transform (DFT) technique
I am trying to understand the dispersive Fourier transform (DFT) technique for spectral characterization of pulses. In the literature, I found this far-field condition from Fraunhofer approximation in ...
- 11
1
vote
0
answers
25
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Fraunhofer diffraction from composite apertures
I'm trying to calculate the fraunhofer diffraction pattern from a aperture composed of multiple simple shapes, but I've ran into some trouble when trying to simulate the results and I really dont ...
0
votes
0
answers
35
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How do I compute the diffraction efficiency of the orders of an arbitrary grating in the Fraunhofer regime?
Suppose I have an arbitrary grating and it has some transmission profile $t(x)$. I want to compute the diffraction efficiency of the grating's $n^{th}$ order in the Fraunhofer regime. Let the spatial ...
0
votes
0
answers
27
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How to solve Fresnel diffraction integral of vortex beam
Solving Fresnel integral for vortex beam diffraction is necessary and difficult. Without the necessary integral formula, this isn't easy to derive. Therefore, I need some means to calculate it ...
- 11
1
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0
answers
64
views
Intuition behind the math of Diffraction
Is there an intuitive way to understand why the diffraction patterns arising from an arbitrary aperture is Mathematically the Fourier Transform of this aperture function?
- 329
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votes
1
answer
131
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What's the diffraction pattern for free-space propagation plus a thin lens at arbitrary distances?
I am trying to analytically solve the light propagation for the following case:
Starting complex field $E_0$
Fresnel ropagation for a distance $d$ to a lens
Lens applies phase modulation with focal ...
- 93
1
vote
2
answers
189
views
Diffraction limit PSF and angular spectrum method?
I know from the angular spectrum method that given a field $U$ with a wavelength $\lambda$, we can decompose it with Fourier transform.
\begin{equation}
U(x, y,0) = \int \int {\tilde{U}_0(f_x,f_y)} ...
- 444
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votes
1
answer
30
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Evanescent field, condition of $z$ component of $k$?
I am studying evanescent field and diffraction limit and I have one question.
Given a field $ U(x,y,0)$ we can decompose into 2D plane waves.
$U(x,y,0)= \int \int dk_x dk_y \tilde{U}(k_x,k_y) e^{+i(...
- 444
4
votes
1
answer
373
views
Interpretation Fourier Diffraction
I got familiar with interference and now want to understand it with the help of Fourier optics, as it is called.
For the derivation of the diffraction integral the following setup is to consider:
...
- 462
1
vote
1
answer
168
views
Fraunhofer diffraction validity and application in the far field
This question is about the Fraunhofer diffraction and the assumptions under which it is valid. My understanding is that given the complex amplitude of an electric field $E_{z=0}(x,y)$ in the $(z=0)$ ...
- 65
1
vote
1
answer
798
views
Does a lens always act as a Fourier transform?
I understand that putting a lens behind an aperture at the distance 1f, it will "get" the diffraction pattern to appear in the back focal plane. In this case the FT of the aperture plane ...
- 143
1
vote
2
answers
370
views
Fourier Optics: Far Field Image
I have a question about computing the far field diffraction pattern of a laser beam:
If $L_{1}$ is large enough, then at $z=L_{1}$ we see the Fourier transform of the input $f(x, y)$. If $L_{2}$ is ...
- 51
0
votes
1
answer
213
views
Fourier transform of a Bessel function multiplied by a Gaussian
I am computing the diffraction pattern of some specific grating. I end up with the following integral
$$I = \int dx\, J_m(x)e^{-ax^2}e^{-ikx}$$
which is the Fourier transform of the Bessel function of ...
- 1
0
votes
2
answers
1k
views
Fourier Optics - application of the 4f correlator experiment
I am in high-school and planning on basing a research essay on the topic of Fourier Optics. I was looking at the derivations behind the Fourier transform and the fact that the Fourier transform of the ...
