Effective cross sections for stray light calculations in laser interferometry: application to LISA science interferometer

Interferometry is often used as a means for providing high sensitivity measurements. But interferometric measurements can also be easily affected by coherent stray light. In many fields, a correct estimation of the amount of stray light is necessary to assess the system performances and to guide the choice of the correct design. The LISA (Laser Interferometer Space Antenna) mission will consist of three spacecraft orbiting the Sun in a triangle constellation with arms of 2.5 Mkm to detect gravitational waves. Detection is carried on thanks to two laser beams emitted by each spacecraft towards the two remote ones. A tiny fraction of the emitted beams is collected by the telescopes in the distant spacecrafts and interfered with the local laser beam, giving six heterodyne phase readouts which carry the imprint of the gravitational wave. Given the goal of reaching a noise floor of a few picometers on the distance measurement, this configuration will be very sensitive to stray light noise and for this reason stray light estimates are an important part of the design process. For a complex optical system stray light simulations can be made with specific optical analysis software (FRED, Zemax,...) which require expensive licences and computational time. To have a quick estimate one can try some manual calculation, but it is not always easy to find which scattering or reflection directions will lead to stray light able to couple into the interferometric measurement, not only with good superposition, but also with matching wavefront. We'll use the divergence of the laser beam to estimate the angular aperture under which a scattering element in the optical system can direct stray light into a detector, and show how these simple considerations can lead to stray light estimates which are in good agreement with the most advanced software simulations. These considerations are applicable to various optical systems.