Past exam of the optics and electrodynamics course of the University of Cambridge / 2016 / Paper 1 / 1 / b / Solution

The transverse spatial coherence width is much larger than the longitudinal coherence length. The longitudinal scale is controlled by spectral bandwidth:For broad, unfiltered visible sunlight it is of order a wavelength to a few wavelengths, roughly $10^{-6}\mathrm{m}$. This is an order-of-magnitude scale, not a uniquely defined solar constant; the precise value depends on spectral response and the coherence-width convention.

The Sun subtends angular diameter $\delta \simeq 1919^{\prime \prime }\simeq 9.3\times 10^{-3}\mathrm{rad}$ at one astronomical unit.^[ref] Consequently the sunlight coherence comparison gives a transverse scaleusing $\lambda =550\mathrm{nm}$ only as an illustrative visible wavelength. The uniform-disk spatial coherence model has first coherence zero at $1.22\lambda /\delta$, about $72\mu \mathrm{m}$ at that wavelength. The small angular size permits coherence across tens of micrometres, while the broad spectrum destroys coherence over much shorter path differences. Spectral filtering increases ${\ell }_c$; spatial filtering changes the transverse scale.^[ref]