# Paraxial Propagation of Scattered Light Based on the Chirp Z-Transform

## TL;DR

This paper introduces a new method for simulating light propagation in optical systems using the chirp z-transform, improving efficiency and flexibility.

## Contribution

The paper introduces a novel integration of the chirp z-transform with the Wigner function to enhance simulation flexibility and efficiency.

## Key findings

- The proposed method allows targeted simulation of regions of interest in the frequency domain.
- Simulations using the RC telescope system show consistency with traditional methods but with increased efficiency.
- The approach reduces memory requirements for complex optical system simulations.

## Abstract

In the simulation of partially coherent light propagation within optical systems utilizing the Wigner function, the constraints imposed by the Fourier transform necessitate that the dimensions of the input and output matrices remain congruent. Consequently, the extent of the image plane is dictated by the dimensions of the light source matrix and the propagation distance. For optical systems of greater complexity, such simulations are highly memory-intensive. This paper innovatively incorporates the displacement theorem of the chirp z-transform and integrates it with the Wigner function. This approach affords enhanced flexibility in the simulation of partially coherent light transmission, enabling the targeted simulation of regions of interest within the frequency domain of the optical system, thereby significantly improving simulation efficiency. The efficacy of this novel method is demonstrated through the simulation of a Wigner transmission algorithm based on the chirp z-transform, applied to an RC (Ritchey–Chrétien) telescope system. The RC telescope, known for its optical design that minimizes aberrations and provides high-quality imaging, serves as a critical foundation for the simulation. The resultant simulations exhibit a high degree of consistency with traditional methods while offering increased flexibility, thus corroborating the validity and effectiveness of the proposed approach.