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Temporal coherence compares the field at different times at one location: a narrow spectrum maintains a predictable phase relation over a longer delay. Spatial coherence compares the field at different locations at the same time: different angular source components illuminate a baseline with different phase differences, which wash out interference when averaged. These are properties of correlations, not claims that all thermal source points have a common phase.

Assume a distant spatially incoherent, quasimonochromatic source, small angles, identical slit transmission, matched polarizations and equal mean intensity at the two slits. For an angular component $\theta$, the relative input phase is $-kd\theta$. Let $\phi$ be the additional observation-plane phase. Incoherent angular components add intensities, givingIts extrema are $2F(0)\pm 2|F(d)|$, henceFor symmetric $I(\theta )$, $F(d)$ is a real cosine transform. Physical visibility is its normalized absolute value; the printed proportionality omits that qualification. A negative signed coherence reverses fringe phase rather than giving negative contrast. This is the small-angle Van Cittert-Zernike theorem. Temporal coherence analogously depends on the Fourier transform of the spectrum.

A Michelson stellar interferometer uses separated collecting mirrors to obtain a large adjustable projected baseline without requiring a monolithic objective of that diameter. Each collector supplies light to a common combiner. Optical path compensation keeps the delay within the temporal coherence range; varying mirror separation samples spatial coherence and resolves stellar angular structure finer than a small collector alone.

Let $g_{\star }(Y)$ be the normalized signed coherence of one star, and take the baseline along the projected binary separation. The equal-brightness binary-star visibility for identical profiles centred at $\pm \beta /2$ giveFor uniform circular discs of angular diameter $\alpha$,For binary separation from visibility-zero spacing, the rapid binary visibility zeros satisfy $Y_j=(j+\frac{1}{2})\lambda /\beta$, so their repeated spacing is $\lambda /\beta$. The slower single-star envelope first vanishes at $Y=1.21967\lambda /\alpha$. The stellar angular diameter from a visibility envelope and the binary separation follow by fitting both scales; multiple baselines distinguish envelope zeros from binary zeros.

Angular width alone does not specify a unique brightness profile. If the intended one-dimensional model is a uniform angular strip of full width $\alpha$, replace the disc factor by $\mathrm{sinc}(\pi \alpha Y/\lambda )$ with $\mathrm{sinc}u=\sin u/u$; its first envelope zero is $\lambda /\alpha$. Limb darkening changes the disc envelope too. Rotating the baseline is necessary to recover an unknown separation direction; a single orientation measures only its projection.