(a) A microscope objective has and the imaging wavelength is . A microscopist wants…

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

What an Instrument Can See, Ch Spatial coherence and the van Cittert-Zernike theorem

Problem

(a) A microscope objective has

\mathrm{NA}_{\text{obj}} = 0.90

and the imaging wavelength is

\lambda = 550\,\text{nm}

. A microscopist wants the highest transmitted spatial frequency to be

2.6

cycles per micrometre. Using the coherence-parameter model

\sigma_{\mathrm{c}} = \mathrm{NA}_{\text{cond}}/\mathrm{NA}_{\text{obj}}

and the cutoff

(1+\sigma_{\mathrm{c}})\mathrm{NA}_{\text{obj}}/\lambda

(valid for

\sigma_{\mathrm{c}}\le1

), find the condenser numerical aperture

\mathrm{NA}_{\text{cond}}

and the resulting value of

\sigma_{\mathrm{c}}

that are needed. (b) The same laboratory later measures the visibility of an interferometer observing a red giant star at

\lambda = 550\,\text{nm}

and finds the first visibility null at a baseline of

B_0 = 5.4\,\text{m}

. Assuming a uniform-disc brightness model, find the fitted angular diameter of the star in milliarcseconds, and state, without recomputing, how a limb-darkened model would change this figure.

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