Produce dotted intensity profile from image

I have produced an image that has an intensity profile that decays outwards. I would like to produce a 2D profile across the middle of the image. I have tried using the improfile function but it gives me an extremely noisy and poor output figure. It also gives me a continuous 'jaggy' line whereas I would like a dotted image. Any suggestions on how to approach this? I was thinking about averaging along several y-values but I am not sure how to do so.

I believe I should be able to see a Gaussian/Lorentzian as a result.

Any help would be greatly appreciated.

Thanks,

Jack