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Finesse: Frequency domain INterfErometer Simulation SoftwarE
Daniel Brown and Andreas Freise 26.06.2017
Finesse [1] is a numeric simulation for laser interferometers
using the frequency domain and Hermite-Gauss modes. It is open
source software distributed for OSX, Linux, and Windows. You
can download the binaries at:
The source code is available at:
This document gives a short overview of the main features of
Finesse. Please see the file INSTALL for information on
installing and running Finesse.
For results using Finesse please cite the following DOI:
author = {Brown, Daniel David and
Freise, Andreas},
title = {Finesse},
month = may,
year = 2014,
note = {{You can download the binaries and source code at
doi = {10.5281/zenodo.821364},
url = {}
Table of Contents:
1. Interferometer signals
2. Beam geometry and imaging
3. Documentation, support and examples
4. Examples of the impact of Finesse on commissioning tasks
5. Finesse with Python and MATLAB
6. References
1. Interferometer signals
Finesse can be used to compute a great variety of interferometer
signals for control systems, including longitudinal control,
alignment control and thermal compensation, for example:
- transfer functions and error signals using up to five
demodulations per photodiode.
- detectors for amplitude, phase, intensity (all three can be
given integrated over the beam or as CCD-like images), user-
defined split detectors
- noise propagations, such as laser frequency noise or oscillator
phase noise
- quantum noise and radiation pressure effects such as optical
2. Beam geometry and imaging
One of the main features of Finesse is the extensive integration
of physics related to the beam shape. This makes it possible to
study interferometer signals in the presence of defects such as
misalignments and mode mismatch, mirror surface defects, thermal
deformations and mis-centred, split photo detectors.
Finesse can also model imaging properties of optical systems,
for example, it automatically determines eigenmodes of cavities
and interferometers. Gouy phases and beam waist positions can be
plotted as functions of positions of optical elements.
3. Documentation, support and examples
The program is easy to use for students: For the basic use, including
graphical output, no commercial software is required. The implemented
physics is well documented in a 200 pages manual. Simple examples are
provided as well as detailed input files for all main interferometric
gravitational-wave detectors. The manual and examples can be found on
the main Finesse page at
In addition we provide resources and self-study material on laser
interferometry in the form of Jupyter notebooks using Finesse
For questions and discussions related to Finesse we are hosting
a mailing in Birmingham and LIGO chat channel. Instructions on how
to join these are provided at:
The simulation code has been developed and improved continuously
over the last ten years. It has been frequently and successfully
tested against experimental data from GEO 600, LIGO and Virgo.
The code is under version control and is executed within a nightly
test-suite to maintain stability during the ongoing development.
4. Examples of Finesse usage for commissioning tasks
The following examples highlight Finesse analyses of pressing problems
in detector commissioning. Finesse predictions have been used to
improve the detector performance and the Finesse results have been
shown to match experimental results:
- lock acquisition of the power-recycled GEO 600 interferometer:
a suspension tilt instability was discovered as the source of
severely distorted interferometer error signals [2]
- thermal compensation of GEO 600: a wrong radius of curvature was
discovered to cause unexpected beam patterns in the dark fringe.
Finesse results for the beam pattern as a function of heater power
were used to find the current operating point of the thermal
compensation. [3]
- detector characterisation of the Virgo arm cavities: Finesse has
been used to characterise all details of the Virgo north arm
cavity from the cavity Finesse to the astigmatism of the mode
matching telescope. [4]
- thermal lensing induced bi-stable operating point in Virgo: Finesse
results were crucial in understanding the origins of a double zero
crossing in a longitudinal error signal of Virgo. [5]
- RF modulation induced change in interferometer noise couplings:
Detailed measurements and Finesse simulations were used to
understand the laser power noise coupling due to RF sidebands in
higher order modes and how it limits the detector sensitivity. [6]
- simulations of the alignment control signal of the Advanced LIGO
input mode cleaner [7]
- Advanced LIGO commissioning investigation into power loss at the
central beam-splitter [8]
5. Finesse with Python and MATLAB
Finesse is a stand-alone executable written in C. It is, however,
well interfaced with Python and MATLAB. A number of MATLAB tools
(m files and mex files) are provided to run Finesse simulations
from MATLAB or to communicate with a running Finesse process from
within MATLAB. In addition a new suite of Python tools called
PyKat ( is available to interact
with Finesse from Python.
6. References
[1] A. Freise, G. Heinzel, H. Lueck, R. Schilling, B. Willke and
K. Danzmann, "Frequency-domain interferometer simulation with
higher-order spatial modes", Classical and Quantum Gravity, Vol.21,
(2004), available at
[2] A. Freise: "The Next Generation of Interferometry: Multi-Frequency
Optical Modeling, Control Concepts and Implementation", Ph.D.
Thesis, University of Hannover (2003),
[3] H. Lueck, A. Freise, S. Gossler, S. Hild, K. Kawabe and K. Danzmann,
"Thermal correction of the radii of curvature of mirrors for
GEO 600", Classical and Quantum Gravity, Vol.21, (2004)
[4] A. Freise, M. Loupias : "The VIRGO north arm cavity: Examples for
the use of the interferometer simulation Finesse", VIRGO note
VIR-NOT-EGO-1390-269 (2004)
[5] J. Marque: 'Input mirrors thermal lensing effect Frequency
modulation PRCL length in Virgo' talk at LSC meeting, LIGO
document number LIGO-G070338-00-Z (2007)
[6] J. R. Smith, J. Degallaix, A. Freise, H. Grote, M. Hewitson,
S. Hild, H. Lueck, K. A. Strain and B. Willke, "Measurement
and simulation of laser power noise in GEO 600", Classical
and Quantum Gravity, Vol.25, (2008)
[7] K. Kokeyama, K. Arai, P. Fulda, S. Doravari, L. Carbone,
D. Brown, C. Bond and A. Freise, ‘Finesse simulation for the
alignment control signal of the aLIGO in- put mode cleaner’,
LIGO note T1300074,, (2013)
[8] C. Bond, P. Fulda, D. Brown and A. Freise: ‘Investigation of beam
clipping in the Power Recycling Cavity of Advanced LIGO using Finesse’,
LIGO note T1300954,, (2013)
[9] D. Brown, R. J. E. Smith, and A. Freise:
Fast simulation of Gaussian-mode scattering for precision interferometry
Journal of Optics, 2016,
[10] Daniel David Brown
Interactions of light and mirrors: advanced techniques for modelling
future gravitational wave detectors
Ph.D. thesis, University of Birmingham, 2016
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