# What exactly is deconvolution doing?

The widely recognized theory for the detected image in microscope (I believe) is calculated by taking the convolution of the object and a point spread function (PSF). Deconvolution tries to reverse this operation to get back the original object. This explanation sounds easy and intuitive but after some digging, I found that I don't understand what deconvolution is doing anymore.

So this PSF is actually made up of two components: detection (PSF_det) and illumination PSF (PSF_ill). If we talk about widefield microscopy, illumination is constant so PSF_ill=1 which means the PSF in the original theory is just PSF_det. This is still ok but a quick question will be why doesn't this operation return the image of the object (image with infinite resolution)?

If we talk about confocal microscopy, PSF_ill is not 1 and we can basically approximate to PSF_det giving PSF=PSF_det^2. So we can see that the convolution with this PSF actually gives higher resolution. My main question with this is what happens if I deconvolve this image? Am I removing the effect of PSF_det? If so, do I end up with PSF=PSF_det (without the square) which has lower resolution then I started with?

• Can you explain what PSF_ill and PSF_det are? They are not generally known terms, and may be specific to the kind of microscopy you are doing. Jun 14 at 10:58
• @garyp Are you questioning the abbreviations, which literally follow the full text phrase? Or do you mean the actual PSFs used for each? Jun 14 at 21:40
• The PSFs. Why are two needed, and what do they represent. I suspect my issue is ignorance of the application. I also suspect that I'm not the only ignoramous. Jun 15 at 12:56
• Usually only 1 PSF is used in image formation theory for widefield microscopy since the illumination is constant. However in confocal microscope, the illumination is localized so it is represented by a PSF (which is what almost every single text I read talks about: resolution is not infinite because of diffraction limit). If it helps, we can use the idea used in Image Scanning Microscopy (PRL 104, 198101 (2010)) to think about the PSF. Illumination PSF describes the probability portion of the sample is illuminated while detection PSF is detection probability by detector from a point source. Jun 15 at 13:37