# Wave Tracing

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**.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.kostacloud.com/kostacloud/advanced-optics-ray-trace/wave-tracing.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.