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Is it possible to find out coordinates of slits by interference image?

Actually I have several questions. Assume my friend gave me a stripe which shows interference picture of light (like in a diffraction experiement with slits). I know wavelength and I know that there are several slits, but I don't where they are. Can I compute coordinates of slits? Can I compute thickness of slits (if they have various thickness)? Is it possible in 2D case, I mean light pass through some mask (plate with slits and holes), and I want to find out slits and holes in the mask?

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    $\begingroup$ yes, to some extent and it is done by high resolution radar imaging of scattering objects. Since only the far-field of the scatterer is observed from a narrow angular position much detail is lost but not all wavelength size detail. Alternatively, the so-called near-field antenna measurement to characterize the EM radiation does a very-detailed reconstruction of the diffraction effects within and from the emitting antenna. $\endgroup$
    – hyportnex
    Mar 2 at 14:02
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    $\begingroup$ If you dont know distance to target then its complicated. Just imagine the dual slit experiment, the distance between fringes is dependent on the distance between fringes and screen. But in general yes, what you describe is called diffraction imaging and it is used to image whole planes and even some depth information. It is an active field of research using XUV and x-rays to be able to image nano objects. $\endgroup$ Mar 10 at 20:03

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If the screen is far from the slits, the fringe pattern is the Fourier transform of the slit pattern. If you know the amplitude and phase at each point on the screen you can do a Fourier transform to get the slit pattern. But from just a screen image you don’t have phase information to do that. But you do know that the slit pattern is entirely real-valued, so you can use inverse methods to find a slit pattern which would produce the observed screen image. These methods work by making a guess of the slit pattern, calculating the screen image, then gradually making changes to the slit pattern until the calculated screen image matches the observed image.

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