# Complex Degree of Coherence (Cittert-Zernike)

## Homework Statement

A light source consists of two long thin parallel wires, separated by a distance, W. A current is passed through the wires so that they emit light thermally. A filter is placed in front of the wires to only allow a narrow spectral range, centred at λ to propagate to a screen, a distance l from the wires.

i) Obtain an expression for the complex degree of coherence using the van Cittert-Zernike theorem.

ii) Describe what would be observed on this screen.

## Homework Equations

Cittert-Zernike theorem:
Complex degree of coherence γ is given by the normalised fourier transform of the source intensity function.

## The Attempt at a Solution

Ok so the first part is straight forward enough, treating the source intensity as a double delta function, the normalised fourier transform of which is just a cosine function, specifically:

γ=cos $\frac{πWΔx}{λl}$ , where Δx is the separation between two points in the horizontal axis of the observation screen. Note that I'm ignoring the vertical axis at this stage.

It's the intensity seen on the screen that's confusing me. With just the double delta source directly onto a screen, I would be tempted to say the intensity distribution on the screen simply varies in a cosine fashion, as the two wire thermal sources (which are cylindrical wave sources?) interfere according to the coherence function. I feel like I might be missing something however.

Any help to clarify this would be greatly appreciated.

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