# A Resolution in single molecule localisation

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1. Apr 2, 2016

### u0362565

Hi all,

If a camera images a fluorescent molecule gaussian function with diameter roughly 300nm and each image pixel represents 160x160nm how could you say with higher precision where the molecule is located within that pixel. For instance if the localisation precision turns out to be 40nm how is it possible to derive this. I know it's to do with counting the number of photons collected and this given an independent measurement of the molecules position but surely only to within the resolution of the pixel size 160x160nm so how is it that the precision of localisation could be 40nm!? This is the basis of single molecule localisation microscopy but I can't figure out between the optics of the microscope & the engineering of the ccd how these resolution figures are possible. I'm really missing something here.

2. Apr 3, 2016

### sandy stone

Well, I know nothing of the field, so this is just a WAG. Is it possible to shift the camera's field of view by, say, 40 nm and measure the change in brightness of adjacent pixels? I think that would give you a clue.

3. Apr 3, 2016

### secur

Someone who knows single molecule localization microscopy can give a detailed answer but I can tell you the basic idea. As long as the molecule is large enough to send photons to multiple pixels you can localize to better than one pixel size.

For a very simple example suppose the "molecule" is a rectangle, 160nm x 240nm. Suppose we have a 1 x 3 pixel grid (wish I had a picture) oriented horizontally, the molecule in the exact center. Suppose we get 1 photon per 1nm x 1nm area and the microscope works perfectly. Then we would get 160^2 = 25,600 photons in the center, and 12,800 on the left and right. Now suppose we shift the molecule to the left 1nm. Then the photon counts change: the left pixel gets 160 more photons, 12,960 and the right, 12,640. Each time you shift by 1nm, either direction, the photon counts change by 160. So in this very simple case, to determine how far (to the right, in nm's) the molecule's center is from the center of the pixel grid, the formula would be

(right pixel photon count) - (left pixel photon count) / 320

You see with these very simple assumptions (especially, no errors of any sort) with enough photons we could determine the molecule's center location to arbitrary precision.

In real life there are plenty of sources of errors and the figure you give for precision, 40nm, sounds believable. Also note the real statistical calculations required would be much more difficult.

If the molecule is very small, we lose this ability and can only localize within one pixel (160nm) because all the photons go to that one. If it's very big it will "swamp" the detector. So you want to arrange it so that the molecule "just fits" within your pixel grid.

4. Apr 3, 2016

### u0362565

Ah ha yes that makes perfect sense to me now! i just couldn't visualise how this was done despite having seen the standard error formula that gives the localisation precision. Thanks for the explanation.