Generalized Van Cittert-Zernike Schell propagator: an efficient algorithm for simulating partially coherent light

By: Manuel Montoya, Maria J. Lopera, Yunfeng Nie, and David Blinder

The research is focused on developing new mathematical models for describing light propagation physics. Specifically, we study the fundamentals of optical coherence theory, and we design algorithms that take it into account. Our main goal is to help improve the current state of incoherent holographic imaging and display systems, where incoherent implies the use of common light sources, such as LEDs and sunlight, thus avoiding the traditional requirement of using lasers for holography. And as a more general goal, we intend to expand the tools available for performing optical simulations, making an impact in the broader field of optics and photonics.

Figure 1: Optical setup for the experiments.

In this first publication, we introduced a new wave propagation algorithm that is useful for simulating how partially coherent light travels through space. The algorithm can be efficiently computed by a series of Fast Fourier Transforms in only one forward propagation, which gives it a unique advantage when comparing it with standard methods. We validated our method through a series of numerical and optical experiments, where we performed the double pinhole experiment, the double slit experiment, and we analyzed the diffraction of a USAF resolution test target with different levels of coherence in the illumination. We implemented multiple variations of the algorithm and compared it with other existing methods. The results show that our method achieves up to 100x speed improvements and 1000x accuracy improvements with respect to the state-of-the-art methods in computer-generated holography and digital holography.

key findings

• We introduced a new wave propagation algorithm that is useful for simulating how partially coherent light travels through space.

• The algorithm can be efficiently computed by a series of Fast Fourier Transforms in only one forward propagation, which gives it a unique advantage when comparing it with standard methods.

• It achieves up to 100x speed improvements and 1000x accuracy improvements with respect to the state-of-the-art methods in computer-generated holography and digital holography. 

Figure 2: Figure comparing execution times of different methods, in logarithmic scale. These experiments were run in Hydra.

Figure 3: Simulation vs Experimental images of a USAF with different sizes of the light source.

Simulation of light propagating after passing through a USAF resolution target. Click to play.

Simulation of the double pinhole diffraction as the size of the light source increases. Click to play.

How did VSC contribute to the research?

VSC helped us in this research by providing the necessary computing infrastructure that we need to run simulations of optical phenomena, and it will become even more important for our future research as we will introduce optimization algorithms and deep learning.

Read the full publication in Optica Publishing here

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