I Diffraction, Amplitude and Phase

1. Mar 27, 2016

LmdL

Hi,
Today I was told that phase and amplitude on the screen in a far field of a mask consisting of hole are more or less the same. So, I wanted to check myself, but didn't find any resource for this. All the resources are, as usual, talk about intensity distribution in the Fourier domain, but not phase.
I'll give an example:
Lets say I have a mask with 1 small hole. The Fourier transform will give me a SINC. So the amplitude is SINC function, but what a phase is? I need both amplitude and phase in order to FFT again and reconstruct the initial image.
Can someone provide me a link or suggest a book, where I can view amplitude and phase after FFT for different masks? Like:
One slit: Amplitude - Sinc(...), Phase - ...
Two slits: Amplitude - Sinc(...)*Cos(...), Phase - ...
Circular aperture: Amplitude - Jinc(...), Phase - ...

Thanks!

2. Mar 27, 2016

blue_leaf77

The FFT of a centered rectangular slit is real because the slit describes an even function. Therefore, the phase of the FFT is either 0 or $\pi$ - it's zero at points where the sinc function is positive, and $\pi$ where the sinc drops below zero.

3. Mar 27, 2016

LmdL

So, for slit amplitude and phase are like this:

Is there any book that lists such amplitude+phase graphs for different masks?

4. Mar 27, 2016

blue_leaf77

May be there are a few out there, but I have never seen myself. If you are familiar with matlab, I suggest that you use this software because you can try whatever function you want.

5. Mar 27, 2016

LmdL

Ok, thanks a lot!

6. Mar 28, 2016

Andy Resnick

It depends- if your mask is amplitude only, then as blue_leaf77 notes, the imaginary component of the Fourier Transform is trivial. However, if your mask has a phase component (constant or otherwise), the amplitude and phase of the far-field diffraction will vary (the intensity pattern may or may not change). Goodman's book "Introduction to Fourier Optics" works out the cases of an amplitude grating and a phase grating to show this.