# What is the point spread function and optical transfer function and what uses are they in image processing

So I seem to really be struggling with the concepts of the point spread function (PSF) and optical transfer function (OTF) and what they are used for in image processing.

Everything I seem to google on the concepts seems to come back with telescopes and microscopes or I seem to get information about Delta functions and impulse response of a system and how this relates to convolution, but nothing seems to tell me about what PSF or OTF actually do or measure.

From what I have gathered so far is the following.

1. You start with a linear time invariant (LTI) system you then apply a signal which can be broken down into Diracdelta functions ($$\delta(x)$$), aka the impulse. The (LTI) then outputs a response aka the impulse response ($$h(x)$$) and according to some web sites this is the PSF. Now I can follow the maths to a degree and see how the convolution between the impulse and the impulse response, but what I can wrap my head around is what the PSF is actually useful for.

2. Why is it useful for imaging systems? From a video that I glimpsed at on you tube the PSF spreads the Dirac delta function so in terms of image processing is this effectively telling us how much blur will be in the image itself? Is the the only thing the PSF tells us?

3. Moving on to the OTF, so this is the Fourier transform of the PSF and that as far as I have gotten, as I don't fully understand what the PSF dose for an imaging system. I really cant figure what the OTF does for an imaging system.

4. What's more confusing is now, I keep thinking of the OTF as a kinda of filter function when I see the convolution equation in the frequency domain, dose the OTF itself play a role in frequency filtering if so how?

Fundamentally could someone explain the concepts of PSF and OTF and what they actually tell me about the system in terms of image processing.