Microscopy: Deconvolve the PSF and enhance resolution

[eoghan]

Hi all,

In a diffracted limited microscope the resolution has a limit given by the Airy disk and this gives rise to the Rayleigh criteria. But if I deconvolve the observed image removing the psf then I eliminate the diffraction effects and I can resolve any distinct points, whatever close they are. Am I missing something?

 

[eoghan]

Also, another question related to the previous one. In the book Three-dimensional electron microscopy of macromolecular assemblies by Frank, ed 2006 ch 2.5.1 - "Concept of resolution" it is said

"Optical definitions of resolution are based on the ability of an instrument to resolve two points separated by a given distance d. [...] [Another] criticism is that the resolution criterion formulated above does not lend itself to a suitable experiment when applied to high-resolution EM. On the nanometer scale, any test object as well as the support it must be placed on, reveals its atomic makeup."

What does this passage mean? Why cannot have suitable experiments with the Rayleigh resolution criterion?

 

[olivermsun]

In a diffracted limited microscope the resolution has a limit given by the Airy disk and this gives rise to the Rayleigh criteria. But if I deconvolve the observed image removing the psf then I eliminate the diffraction effects and I can resolve any distinct points, whatever close they are. Am I missing something?

The problem is that the deconvolution problem is ill-posed, meaning that a solution may not be unique, or may not even exist, and/or is quickly corrupted by the presence of noise, no matter how tiny.

 

[DrDu]

The problem is that the deconvolution problem is ill-posed, meaning that a solution may not be unique, or may not even exist, and/or is quickly corrupted by the presence of noise, no matter how tiny.

Nevertheless deconvolution is nowadays a standard technique to enhance resolution, though, for the reasons mentioned by you, it has it's own limitations.

 

[olivermsun]

Sure, approximate deconvolution methods are used all the time to improve images. But the mathematics tell us why we can't just eliminate diffraction or aberrations once and for all and be done with it. ;)