How Can a Cross Mask Transform a Circle of Light into a Square?

[dm9292]

Question
How is a circle of light turned into a square of light using a mask with a cross. This isn't actually my homework but a challenge question.
Solution
I really have no idea I've looked around on the net and looked in the library but I can't find anything relevant. I don't actually understand how the cross manipulates the light to produce a square. I must ask is it even possible using light or do the same limitations experienced when trying to do this geometrically arise?

 

[chaoseverlasting]

I couldn't really understand the problem. Could you elaborate upon it? What do you mean by a cross in a mask?

 

[dm9292]

Well by a cross in a mask I mean you shine light through a square shaped image and then you have metal mask which has a thin cross in it, this is placed after the square image. By doing this the square is now turned into a circle.

 

[gabbagabbahey]

Well by a cross in a mask I mean you shine light through a square shaped image and then you have metal mask which has a thin[/color] cross in it, this is placed after the square image. By doing this the square is now turned into a circle.

Whenever you have light passing through a thin aperture, diffusion should immediately come to mind.

 

[dm9292]

These are the hints i got, but i am not sure where to go from there:

Say your laser has a Gaussian beam profile and you shine it through a hole to yield a Gaussian-Bessel function:
(http://www.copl.ulaval.ca/uploads/pics/Faisceaux_Bessel-Gauss_spatiotemporels_01.JPG).

How does a Fourier transform of the waveform look in 1D (ie taking an arbitrary cross-section slice of the 3D profile)?

From the transform, how do you think you create a 2D square out of it?

I'm still trying understand this and if anyone can help it would be much appreciated.