Assume that an objective with numerical aperture n a = 1.4 is used to image an in-focus GFP molecule which has an emission wavelength of λ = 520 nm. At a minimum, how many photons on average need to...

Assume that an objective with numerical aperture n_a
= 1.4 is used to image an in-focus GFP molecule which has an emission wavelength of λ = 520 nm. At a minimum, how many photons on average need to be detected in an image in order to potentially determine the location of the molecule with a standard deviation as small as 50 nm? Assume that images of the molecule are acquired under the fundamental data scenario in which the detector has an infinitely large photon detection area. Also assume that the image of the molecule is described by the Airy image function. Perform the same calculation for standard deviations of 25 nm, 5 nm, and 1 nm.