Can Diffraction Effects be Removed with an Interferometer?

[BigTanker22]

Diffraction is obviously a limiting constraint on high-precision imaging instruments. But is it possible, given a known aperture shape, to remove the diffraction caused by that aperture?

At this point, I know that the diffraction pattern of an aperture or slide film brought to rear focus is the Fourier transform of that object (assuming uniform illumination). My problem is that a Fourier transform consists of both real and imaginary components, but image intensity is the mod-squared of the electric field (I = |E|²), so only amplitudes are measured.

If I'm somehow able to record the phase information (Im(E)²) of the diffraction pattern, then I should be able to reconstruct the electric field at the Fraunhoffer plane according to: Re(E) = sqrt(|E|² - Im(E)²) .

Can this be done somehow with an interferometer?

 

[Andy Resnick]

ITYM 'deconvolution'.

http://en.wikipedia.org/wiki/Deconvolution

There's also apodization of the entrance pupil to generate 'super resolution':

http://ultra.bu.edu/papers/Bryn_opticsExp_2004_Pupilfilters.PDF

"structured illumination" has been proposed to do almost excatly what you are think of:

http://cbst.ucdavis.edu/publications/gustafsson.pdf/view