Wave Tracing

Beam Propagation Method in KostaCLOUD

In KostaCLOUD Physical Optics is handled using the Wave-Tracing module (WT) approach provides a semi-analytic approach based on the fundamental solution propagating waves using a mixed domain approach via Rayleigh-Sommerfield and Angular Spectrum Method to solve beam propagation through an optical system. Effectively we are keeping all of our terms in their respective linear spaces to ensure the most accurate solution and apply convolutions to split domains upon evaluation at the detection plane.

$$u(\vec{r}') = -\frac{i}{\lambda z} \int_S U_0(\vec{r}) \frac{e^{i k r}}{|r|} \cos \chi \text{dA}\\ E(\vec{k_\perp},z) = U_0(\vec{k_\perp}) e^{i \sqrt{\mathbf{k}^2-k_x^2-k_y^2} z}$$

The advantages of WT:

• WT is that it is represented in a semi-analytic representation, which is exact until the final step of evaluation on the Image Surface.

• WT does not require re-sampling like Gaußlets (Gaussian Beam Decomposition)

• WT is valid for all angles.

• WT has no aliasing issues due to convolution kernels.

• WT is natively non-sequential.

• WT is valid in Near Field all the way to Far Field.

• WT is Highly Parallelizable.

• No additional setup required by user to use!

• Scattering, Vector-Beams (Polarization), GRIN, etc. built into WT framework natively.

These methods are used to calculate the MTF, PSF, and various other wave quantities.