Eikonal Method for Calculation of Coherence Functions

A method is presented for computing the cross-spectral density of a special class of partially coherent fields in which the coherent modes obey an eikonal equation. This method allows for statistical analysis of optical systems based on simple ray tracing.

Figure 1

The normalized spectral densities, $S_n$, for the three LEDs used in the first example.

Figure 2

(a) Log of the spectral density at $\nu =5\times {10}^{14}\mathrm{Hz}$ ($\lambda =600\mathrm{nm}$) shown in arbitrary units. (b) Cross-spectral density at points along the line shown in part (a). (c) Modulus of the spectral degree of coherence at points along the line shown in part (a). (d) Cross-correlation as a function of time taken at $(x,y)=(0.3,0.0)\mathrm{mm}$ and $(x,y)=(-0.1,-0.1)\mathrm{mm}$.

Figure 3

(a) The spectral density normalized by the peak incident spectral density, $S_0(\nu )$. (b) Cross-spectral density similarly normalized, at points along the line shown in part (a). (c) Modulus of the spectral degree of coherence at points along the line shown in part (a). The plane of interest is located at $z=7\mathrm{mm}$. $N=60$ modes are displayed.