Find the error in: "We collect photons per localisation event from a molecule imaged…

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Fourier optics and image formation · Fourier optics and image formation

What an Instrument Can See, Ch Seeing what the transfer function forbids: phase contrast and super-resolution

Problem

Find the error in: "We collect N=4000N = 4000 photons per localisation event from a molecule imaged with a point-spread function of σPSF=140\sigma_{\mathrm{PSF}} = 140 nm. Since roughly 80 per cent of the light is lost to background, effectively only N=800N = 800 photons contribute, giving σloc=σPSF/N=140 nm/800≈4.9\sigma_{\mathrm{loc}} = \sigma_{\mathrm{PSF}}/\sqrt{N} = 140\ \mathrm{nm}/\sqrt{800} \approx 4.9 nm. Because 4.9 nm is far smaller than the diffraction-limited resolution of about 200 nm at this numerical aperture and wavelength, our microscope's optical transfer function must now support spatial frequencies far beyond the usual cutoff 2NA/λ2\mathrm{NA}/\lambda: we have improved the classical resolution about forty-fold."

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