# Optical filters: What is the difference between Free Spectral Range (FSR) and the resolution based on (FWHM)

I have a question regarding the Free Spectral Range (FSR) and resolution based on (FWHM) of optical filters like based on Fabry-Perot-Interferometers.

As of now, I always thought of the resolution as the minimum spacing between two spectral peaks an optical filter can separate (see my crappy paint picture).

But somehow there is also the free spectral range, which is mostly mentioned as the spacing between two peaks (minimal step in wavelength to achieve the next constructive interference(=transmission of light)) in literature and online powerpoints, which I thought of would be the resolution. Also, it's mentioned, that the FSR decreases when you try to increase the resolution and that the FSR always need to be bigger than resolution.

Could someone explain me on how these two relate to each other and if I am correct in my understanding based on the resolution?

EDIT: So on this page under "Finesse and Mode Width (Resolution)" there is the correlation between FSR and Resolution (9). ->>> https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=9021

So I can improve resolution by having a higher finesse or by lowering the free spectral range, easy to understand.

But still I don't get the Free Spectral Range, when there are optical sensors that can basically be driven to nearly every specific wavelength, see page 5 ->> https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/ssd/c13272-02_kacc1250e.pdf (Minimal distance there would be the resolution mentioned on graph "spectral resolution vs. peak transmission wavelength" on page 3).

Should I imagine resolution and free spectral range like this? ->> https://i.stack.imgur.com/vOcmZ.jpg

$$\FSR = λ/4\$$ is the resolution due to wavelength
$$\ FWHM = H^4/R^3\$$ is the range due to spacing of 2 narrow spectrum with interference patterns.