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?