Optical Simulations

The ultra-high precision of the LISA interferometry relies on many different factors and the suppression of a multitude of noise sources. Some of these noise sources can be studied with optical simulations.

The best-known example and our current work-focus is tilt-to-length coupling noise, i.e., the coupling of angular or lateral jitter into the interferometric phase readout. Another example studied in our simulations is stray light mitigation.

In our simulations, we fundamentally study tilt-to-length coupling noise to understand the underlying concepts (e.g. [1,2,3]). This allows us to define new noise mitigation strategies or refine existing ones. These strategies can be used in any precision interferometer, i.e. in our laboratory test setups, in LISA itself, in future geodesy missions like GRACE-FO, or others.

Directly applied for LISA, we study the magnitude of the coupling in each interferometer and its dependency on alignment and imperfections in the interferometers. For this, we have an implementation of key elements of the interferometry (i.e. the laser beams, optical bench, telescope and test mass) implemented in our in-house software library IfoCAD.

The software library IfoCAD is a key element in our work, which enables us to test how interferometer properties such as the alignment, beam characteristics, or motion in the system affect the interferometric signals. We continuously develop IfoCAD further and extend its applicability for more and more applications.

With the ever-increasing precision needed in simulations, we are often facing a lack of available simulation methods. We are, therefore, investigating the properties of optical simulation methods and how they can be extended for simulating with high precision non-Gaussian beams such as top-hat beams or generally clipped or aberrated beams and their propagation through optical setups.

Naturally, we compare our simulation results and findings with laboratory and space mission data. A key success in our work was the matching of our analytic equations and optical simulations with the LISA Pathfinder tilt-to-length coupling data.

In our current and future work, we focus on the LISA tilt-to-length coupling to prepare the fundamental understanding needed to suppress the noise ideally by design, alignment, and subtraction.

Literature: Simulations Methods

Wanner, G.; Heinzel, G.; Kochkina, E.; Mahrdt, C.; Sheard, B.; Schuster, S.; Danzmann, K.: Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams. Optics Communications 285 (24), pp. 4831 - 4839 (2012)
Kochkina, E.; Wanner, G.; Schmelzer, D.; Tröbs, M.; Heinzel, G.: Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems. Applied Optics 52 (24), pp. 6030 - 6040 (2013)
Wanner, G.; Schuster, S.; Tröbs, M.; Heinzel, G.: A brief comparison of optical pathlength difference and various definitions for the interferometric phase. 10th International LISA Symposium (LISAX), Florida, USA, May 18, 2014 - May 23, 2014. Journal of Physics: Conference Series 610, 012043 , (2015)

Literature: TTL Fundamentals

Hartig, M.-S.; Schuster, S.; Wanner, G.: Geometric tilt-to-length coupling in precision interferometry: mechanisms and analytical descriptions. Journal of Optics 24 (6), 065601 (2022)
Hartig, M.-S.; Schuster, S.; Heinzel, G.; Wanner, G.: Non-geometric tilt-to-length coupling in precision interferometry: mechanisms and analytical descriptions. Journal of Optics 25, 055601 (2023)
Schuster, S.; Wanner, G.; Tröbs, M.; Heinzel, G.: Vanishing tilt-to-length coupling for a singular case in two-beam laser interferometers with Gaussian beams. Applied Optics 54 (5), pp. 1010 - 1014 (2015)

Literature: TTL in LPF

Wanner, G.; Karnesis, N.; LISA Pathfinder collaboration: Preliminary results on the suppression of sensing cross-talk in LISA Pathfinder. 11th International LISA Symposium, Zurich, Switzerland, September 05, 2016 - September 09, 2016. Journal of Physics: Conference Series 840, 012043, (2017)
Armano, M. et al.
Sensor noise in LISA Pathfinder: An extensive in-flight review of the angular and longitudinal interferometric measurement system
Phys. Rev. D 106, 082001

Literature: TTL in LISA

Tröbs, M.; Schuster, S.; Lieser, M.; Zwetz, M.; Chwalla, M.; Danzmann, K.; Fernandez Barranco, G.; Fitzsimons, E. D.; Gerberding, O.; Heinzel, G. et al.; Killow, C. J.; Perreur-Lloyd, M.; Robertson, D. I.; Schwarze, T.; Wanner, G.; Ward, H.: Reducing tilt-to-length coupling for the LISA test mass interferometer. Classical and quantum gravity 35 (10), 105001 (2018)
Chwalla, M.; Danzmann, K.; Dovale Alvarez, M.; Esteban Delgado, J.J.; Fernandez Barranco, G.; Fitzsimons, E.; Gerberding, O.; Heinzel, G.; Killow, C. J.; Lieser , M. et al.; Perreur-Lloyd, M.; Robertson, D. I.; Rohr, J. M.; Schuster, S.; Schwarze, T.; Tröbs, M.; Wanner, G.; Ward , H.: Optical suppression of tilt-to-length coupling in the LISA long-arm interferometer. Physical Review Applied 14 (1), 014030 (2020)

Literature: DLR Reports

Danzmann, K.; Heinzel, G.; Hewitson, M.; Reiche, J.; Tröbs, M.; Wanner, G.; Born, M.; Audley, H.; Karnesis, N.; Wittchen, A. et al.; Paczkowski, S.; Kaune, B.; Wissel, L.: LPF final report for the German contribution to the nominal mission. (2018)
Audley, H.; Born, M.; Danzmann, K.; Hartig, M.-S.; Heinzel, G.; Hewitson, M.; Karnesis , N.; Kaune, B.; Paczkowski, S.; Reiche, J. et al.; Wanner, G.; Wissel, L.; Wittchen, A.: LISA Pathfinder mission extension report for the German contribution, Laser Interferometer Space Antenna. (2020)

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