# I Resolution when not diffraction limited

Tags:
1. Aug 11, 2016

### Emperor42

Does anyone know if there is a way to determine the resolution of an optics system that is NOT diffraction limited. I know you can calculate the resolution of a diffraction limited system using the Rayleigh criterion, but that assumes the system is diffraction limited. Is there some way using the spot diagrams?

2. Aug 11, 2016

### drvrm

well, can you give some details of spot diagrams?

3. Aug 11, 2016

### Drakkith

Staff Emeritus
You could try comparing the spot diagram of the optical system with that of a perfect system. Try comparing the smallest blur diameter for both systems.

4. Aug 12, 2016

### Emperor42

5. Aug 15, 2016

### Andy Resnick

You have to be more specific.

Near-field imaging systems are not diffraction limited; in NSOM (near field scanning optical microscopy) the resolution is given by the size of the fiber tip. Stimulated emission depletion is also not diffraction-limited, but I'm not sure what the resolution limit is. Other super-resolution techniques involve multiple images and/or computation.

6. Aug 16, 2016

### Emperor42

I think I was not being specific in my question. I am using a conventional optics setup with an object, objective lens and a CCD chip. My question is if the optics system is not perfect so light lies outside the airy disk then what is the resolution then?

Last edited: Aug 16, 2016
7. Aug 16, 2016

### Drakkith

Staff Emeritus
I doubt there's an easy answer. You'd have to evaluate the optical system and the resulting spot diagrams and then do a complicated analysis. Not only does the size of the spot matter, but so does the intensity of the light at different points on the spot, the shape of the spot, and whether the spot is symmetrical or not. I can't say I'm an expert, but I've read a little on this subject, including a book full of spot diagrams of various telescopes and an actual discussion and analysis of resolution in several different contexts. The understanding I came away with was that resolution is complicated to figure out, especially when you have imperfect optics with large, asymmetric aberrations.

8. Aug 16, 2016

### Andy Resnick

Not sure what you mean by 'air disk'. Presumably you mean "airy disk"?

In any case, the word 'resolution' is generally poorly defined. You can compute various system characteristics (spot size, cutoff frequency, etc) and these can vary over the image field. In some cases, there is a simple way to compute the modulation transfer function (or contrast transfer function, for sampled systems such as a CCD), but the more fidelity you try to add (Bayer filter, chromatic aberrations, system noise, etc) the more complex the calculation.

If you have a spot diagram, you can try to compute the two-point separation distance (Rayleigh criterion); just be aware that the calculation is not particularly accurate. In general, it's best to directly measure the system performance rather than try to model it.