Surface Interactions in Photon Monte Carlo Simulations

TL;DR

This work presents a physics-based, photon Monte Carlo framework that resolves surface interactions in telescope optics from first principles by computing electromagnetic boundary conditions at interfaces, including bare, monolayer, and multilayer coatings. It incorporates surface microroughness via Harvey-Shack ABC scattering and models contamination with Mie-Tyndall theory, enabling accurate predictions of wavelength- and angle-dependent throughput and PSF wings. The approach supports non-uniform coatings, provides a tractable Monte Carlo implementation, and demonstrates agreement with WIYN ODI PSF wings while separating microroughness effects from atmospheric turbulence. The results enhance photometric accuracy and PSF modeling, with broad applicability to astronomical instrumentation and non-astronomical optical systems, and are available in PhoSim v6.1 for community use.

Abstract

We implement a comprehensive simulation of photon surface interactions using a Monte Carlo approach. This is effective in simulating the interaction of light with telescope mirrors and lenses. We use a full electromagnetic solution to simulate the wavelength and angular dependence at surfaces. This includes bare interfaces, monolayer interfaces, protected layer coatings, and multilayer coatings. We handle special cases when multilayer data is incomplete or when there is photo-conversion in the interface as with sensors. We implement interactions with surface micro-roughness and predict the corresponding angular distribution using a Monte Carlo implementation of the Harvey-Shack scatter theory for a microroughness power spectrum. Finally, we simulate surface interaction with contamination from dust or condensation using Mie scattering applied efficiently to individual contaminants. The combination of these implementations can efficiently simulate rough to polished surfaces of arbitrary materials that are fully cleaned or dusty. The observational consequences includes complex wavelength and spatial-dependent photometric errors, the dominant effect of the wings of point-spread-functions, dust rings, and wavelength and angle-dependent throughput losses. We find agreement with the point-spread-function wings of WIYN ODI observations of bright stars and properties of dust rings, and demonstrate the ability to disentangle mirror microroughness from the turbulence PSF patterns. The comprehensive numerical implementation of surface interactions has wide applicability in non-astronomical applications as well.

Figures (10)

• Figure 1: Reflectivity or transmission as a function of wavelength. A silver-coated mirror and a fused Silica lens are simulated. We then add a Silicon Nitride and Magnesium Fluoride coating, respectively. For each case, simulations are performed at 0, 10, 20, and 30 degrees the corresponding curves are plotted.
• Figure 2: Simulation of the background across a chip of a generic 1 m telescope with a $r$-band filter that has a non-uniform coating. The amplitude of the non-uniformity is set to 10% and the corresponding variation across the chip is also about 10%.
• Figure 3: Comparison of the Monte Carlo implementation (left) and the analytic solution of the Harvey-Shack scattering for an ABC surface (right), shown on a logarithmic intensity scale. We choose $B=10^{-2}~\hbox{mm}$ and $C=3.5$ to emphasize a larger scattering angle than a typical polished surface to optimally compare the approaches.
• Figure 4: The angular scattering profile based on several roughness parameter choices. The black line shows $B=1~\hbox{cm}$, $\sigma=10~\hbox{nm}$, and $C=3$. The blue lines increase (solid) or decrease (dashed) the normalization to $\sigma=30~\hbox{nm}$ and $\sigma=3~\hbox{nm}$, respectively. The green lines increase (solid) or decrease (dashed) the value of $B=3~\hbox{cm}$ and $B=3~\hbox{mm}$. The red lines increase (solid) or decrease (dashed) the value of $C=3.5$ and $C=2.5$. Therefore, $\sigma$ controls the total amount of scatter, $B$ sets the angular scale, and $C$ determines the roll off at large angle.
• Figure 5: Radial co-added PSF profiles (fractional flux vs. pixel) of WIYN ODI observations of bright stars. The pixel size is 0.11 arcseconds. In each panel, 700 to 1000 star PSF profiles are added together, and then fit using the model described in the text. The light blue is the background, the green is the turbulence profile, and the red convolves the turbulence profile with the microroughness scattering profile. The total of all three is the dark blue model that should match the data.