Two pinholes of unequal size are illuminated by the same quasi-monochromatic

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Coherence and statistical optics · Coherence and statistical optics

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

Problem

Two pinholes of unequal size are illuminated by the same quasi-monochromatic, spatially partially coherent field. Because the pinholes differ in area, the light passing through them has irradiances

I_1 = 3.0

(arbitrary units) and

I_2 = 1.0

(same units) at the observation screen when only one hole is open at a time. With both holes open, the fringe pattern on a distant screen shows

I_{\max} = 6.08

and

I_{\min} = 1.92

(same units). ((a)) Write the two-beam irradiance formula in terms of

I_1

I_2

and the complex coherence factor

\mu_{12}

. ((b)) Use the measured

I_{\max}

and

I_{\min}

to find

|\mu_{12}|

. ((c)) Check your result against

I_{\max}+I_{\min}

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