An oil-immersion fluorescence objective ( ) images a specimen incoherently at

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Fourier optics and image formation · Fourier optics and image formation

What an Instrument Can See, Ch The transfer function of an imaging system

Problem

An oil-immersion fluorescence objective (

\mathrm{NA}=1.30

) images a specimen incoherently at

\lambda = 520\ \mathrm{nm}

. Consider a spatial-frequency component of full modulation (

m=1

), close to the objective's cutoff; the several pixels that together span one period of it receive an average optical power of

1.5\ \mathrm{pW}

while the shutter is open for

20\ \mathrm{ms}

. ((a)) Estimate the total number of photons those pixels collect during the exposure. (Recall the energy of one photon at this wavelength.) ((b)) This component is transferred by the objective's OTF at

\mathcal{H}=0.06

. Estimate its signal-to-noise ratio, using the shot-noise result

\mathrm{SNR}=m\mathcal{H}\sqrt{N/2}

. ((c)) State whether this component is usably resolved, taking

\mathrm{SNR}\approx3

as the practical threshold.

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