A microscope objective has numerical aperture and is used at (a He-Ne laser line)

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

A microscope objective has numerical aperture

\mathrm{NA} = 1.05

and is used at

\lambda = 633\ \mathrm{nm}

(a He-Ne laser line). The same amplitude step edge is imaged once under fully coherent illumination and once under fully incoherent illumination, using the generic 10 to 90 per cent rise figures this chapter derived for a clear circular pupil,

\Delta x_{\mathrm{coh}} \approx 0.354\,\lambda/\mathrm{NA}

and

\Delta x_{\mathrm{inc}} \approx 0.666\,\lambda/\mathrm{NA}

. ((a)) A colleague argues that, since the incoherent cutoff frequency is exactly twice the coherent one, the incoherent edge must rise in exactly half the distance the coherent edge takes. Compute

\Delta x_{\mathrm{coh}}

and

\Delta x_{\mathrm{inc}}

for this objective and wavelength, and state the actual ratio

\Delta x_{\mathrm{inc}}/\Delta x_{\mathrm{coh}}

. ((b)) Explain in one or two sentences why doubling a cutoff frequency does not halve an edge-rise distance.

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