Ray-based method for simulating cascaded diffraction in high-numerical-aperture systems

Abstract

The electric field at the output of an optical system is in general affected by both aberrations and diffraction. Many simulation techniques treat the two phenomena separately, using a geometrical propagator to calculate the effects of aberrations and a wave-optical propagator to simulate the effects of diffraction. We present a ray-based simulation method that accounts for the effects of both aberrations and diffraction within a single framework. The method is based on the Huygens-Fresnel principle, is entirely performed using Monte Carlo ray tracing, and, in contrast to our previously published work, is able to calculate the full electromagnetic field. The method can simulate the effects of multiple diffraction in systems with a high numerical aperture.

A Monte Carlo ray-tracing simulation of coherent X-ray diffractive imaging

“…Another option to circumvent this problem is to translate all rays hitting a pixel to its centre (W ¼ 0). This is followed in the work by Mout et al (2018), and has also been tested by us, yielding the same results. We emphasize that this requirement, and the way it is addressed in both cases, only relates to the way interference is evaluated in a ray-tracing context and should not be confused with the Nyquist sampling requirement of CDI.…”

“…Relevant features of the method reported by Mout et al (2018) can be applied to our implementation for further testing of more complex and unsolved cases. Specifically, the vectorial expression for the accumulation of rays at each step allowing for a cascaded system indicates a viable path for the implementation of thick samples through cascaded objects.…”

“…The model does not in fact assume paraxial propagation, and the spherical factor in the amplitude is accounted for each ray rather than set to the detector distance as in the far-field hypothesis. Mout et al (2018) also used a general expression for the weight of the rays, which could help to optimize the number of traced rays to achieve an adequate signal-to-noise ratio, reducing the computational cost of this method. We show in a basic example in Appendix B that not all portions of a detector are affected equally by Monte Carlo noise, which points to the study of specific, dynamical sampling strategies.…”

“…Outside of the X-ray context, the use of a geometrical approach for simulating diffraction dates back to the work of Young & Keller (see Kumar & Ranganath, 1991) and raytracing simulation of diffraction is widely explored: Mahan et al (2018) established the conditions under which a Fresnel-Huygens principle is well described; Andreas et al (2015) reported a vectorial ray tracer applied to laser interferometry in non-paraxial cases; Mout et al (2016Mout et al ( , 2018 have described the theory that makes Monte Carlo ray-tracing consistent, demonstrating diffraction of a multiple-component microscope in this framework. These works bear strong similarities with the ray-tracing scheme we have used here to simulate CDI, which will be described.…”

A Multiple Huygens Surface Based Ray Tracing Framework with GPU Acceleration

“…With n Huygens surfaces, one can, thus, reduce the number of consecutive UTD evaluations and reduce the maximum ray path distance by a factor of n + 1 on average, which can address both challenges better than the reciprocity based method. With the interpretation of the Huygens principle that each point on a wavefront can be considered as a new elementary source [9], the utilization of multiple cascaded Huygens surfaces in ray tracing simulations is an attractive way to go, but it has been only recently that corresponding activities have been reported [10] [11]. The efficiencies of the demonstrated algorithms are, however, not satisfactory, which is mainly due to two challenges: First, since theoretically each point on the Huygens surface is considered to be a source, this can lead to exponential growth in the number of rays.…”