Scattered light noise due to dust particles contamination in the vacuum pipes of the Einstein Telescope

TL;DR

This work tackles scattered light noise in next-generation gravitational-wave detectors by focusing on dust contamination of vacuum-beam-pipe baffles in the Einstein Telescope. It employs Mie theory to derive a dust-induced BRDF for particles on reflective surfaces, integrating over particle sizes and refractive indices to predict angular and polarization dependencies, and then couples this with ET geometry to set cleanliness thresholds. Through ISO-cleanroom deposition models and Monte Carlo analyses across wavelength bands ($\lambda=1064$, 1550, 2000 nm), it identifies that mid to large particles with high $\rm{Re}(m)$ and low $\rm{Im}(m)$ are the most problematic, and provides percentile-based density limits and installation guidelines. The results yield practical cleanliness requirements that are similar for ET-HF and ET-LF and highlight the need for careful management of exposure during assembly, offering a foundational framework for controlling stray-light noise in ET and similar high-sensitivity optical systems.

Abstract

High-sensitivity optical measurements such as those performed in interferometric gravitational wave detectors are prone to scattered light noise. To minimize it, optical components must meet tight requirements on surface roughness and bulk defects. Nonetheless, the effectiveness of these measures can be undermined by other sources of scattered light. In this article, we examine scattered light noise caused by particles deposited on surfaces, especially on the baffles inside the vacuum pipes of the Einstein Telescope's interferometer arms. First, we study light scattering by particles deposited on a surface and having diameters from about one tenth to hundred times the light wavelength: we discuss its angular distribution and dependence on particle size and refractive index, and on polarization. Then, we specialize to the case of the Einstein Telescope arms and quantify the maximum allowed density of particles on each arm baffle. We conclude with cleanliness guidelines for the assembly of the vacuum pipes, including the required cleanliness class of the installation environment.

Figures (14)

• Figure 1: An arm of the ET interferometers consists of a Fabry-Perot cavity of length $L = 10$km. The input and output mirrors of such a cavity (the Test Masses, TM, pictured as light-blue rectangles) are suspended at the arm extremes in dedicated chambers connected by a vacuum pipe (1m diameter): concentric conical baffles (black thick lines) are distributed along the pipe. The baffle's inclination angle is $\theta_B = 55^\circ$. Dimensions from Ref.PhysRevD.108.102001. In the right-most part of the scheme it is pictorially shown a light ray arriving at the TM (straight red arrow), being scattered towards a baffle (wiggled red arrow), scattered back from the baffle to the TM itself and finally re-entering the beam (wiggled purple arrows)
• Figure 2: Schematic representation of the four processes by which light reaching a particle deposited on a surface with an angle $\theta_i$ can be scattered at an angle $\theta_s$: (a) direct scattering; (b) scattering towards the surface and hence reflection; (c) reflection by the surface and then scattering; (d) reflection by the surface, scattering by the particle and reflection by the surface. Incident light is shown as thick red arrow, at an incident angle $\theta_i$ defined counterclockwise with respect to the surface normal. Scattered light is shown as purple arrows, eventually emerging at an angle $\theta_s$ defined clockwise with respect to the surface's normal. The scattering angle relevant for the particle interaction assumes two separate values $\theta_E$ and $\theta_O$ in the case of even (cases (a) and (d)) or odd (cases (b) and (c)) number of surface reflections, respectively.
• Figure 3: Polar plot of $Log_{10} \left[cBRDF_{dust}^{(k, z)} \right]$ for $z=1$ (left plots) and $z = 2$ (right plots) for particles of reduced diameter $x=0.3$ (upper plots) and $x=300$ (lower plots). The dashed horizontal line is the direction of incident light; specular reflection direction is also shown as dashed. The black and blue traces together represent the scattering field from a suspended particle. However, if the particle is deposited on a reflecting surface, drawn as a diagonal thick gray line, the blue part of the scattered field is reflected and becomes the green trace. Black and green traces thus represent the $k=E$ and $k=O$ scattering contributions, respectively, and the blue trace is the scattered light as if it were fully transmitted by a transparent surface ($k=T$). All panels have $m=m^*\equiv1.5 + i \, 10^{-3}$ (see Sec.\ref{['sec:ref_index']}) and $R=1$, assumed to be constant across all angles and equal for both polarizations. The reflecting surface is tilted to represent an ET arm-pipe baffle, whose normal forms an angle $\theta_B = 55^\circ$ with respect to the incident light (horizontal). Angular axis spans the scattering angle $\theta_s$ whose origin is at the direction perpendicular to the surface. Due to the large difference in amplitudes, the plots for $x=3$ (a, b) and $x=300$ (c, d) use different radial ranges, but each pair (a, b) and (c, d) shares the same range.
• Figure 4: BRDF contributions corresponding to odd ($k=O$) and even ($k=E$) number of reflections from the surface, for the two polarizations $z=1,2$, as a function of the scattering angle $\theta_s$. The angle of incidence is $\theta_i=\theta_B$ and the surface reflectivity is $R_{S,P}(\theta)=1$ over all angles and for both polarizations. The BRDF is computed for $\lambda=1064nm$. The vertical gray dashed line marks $\theta_s=-\theta_i$. The curves corresponding to all the refractive index values in the $26 \times 19$ grid are shown in gray for particles of reduced diameters $x$ ranging from 0.3 (top left) to 300 (bottom right), as indicated in each panel. The curves corresponding to the refractive indexes $m^*$ (black solid line), of the human skin (red dotted line), and of aluminum (green dashed line) are also shown. In all cases the particles density is $f(x)=10^{6}$ particles/$m^2$.
• Figure 5: Heatmaps of $BRDF_{dust}^{(k,z)}$ at $\theta_s=-\theta_i=-\theta_B$ against $\mathrm{Re}(m)$ in the horizontal axis and $\mathrm{Im}(m)$ in the vertical axis, for $(k, z)$ indicated in the plot titles. All plots assume $R=1$ and a distribution of particles with $x=3$ and density $f(x) = 10^{6}$ particles/m$^2$. Plots in the same row share the same color scale, displayed on the right.