Gravitational Wave Observatory Designer
Gravitational Wave Observatory Designer
this might take some time, there are more than 40 parameters we have mission parameters from LISA, eLISA and OGO (more to come) you can always resume work on a set of parameters processed before

I'm new to all of this and have not the slightest clue what to do next.

Gravitational Wave Observatory Designer
Mission Instrument Metrology Temperature Clock

The trade-off between the fundamental mission parameters is quite tricky. While many very long laser links are advantageous for low frequency gravitational wave astronomy, a large spacecraft separation in a complex constellation will result in less stable orbits. This in turn leads to larger Doppler shifts and a higher maximum frequency of the inter spacecraft heterodyne laser interferometry – and due to technical reasons this frequency should be kept as low as possible.

Shorter arms can in part be compensated by a shorter laser wavelength and a more powerful and highly efficient optical link. Be careful, your parameters might violate technical feasibility or budgetary constraints. If the beam diameter at the receiver is larger than the telescope, GWO Designer will adjust the beam waist position automatically to maximize the intensity at the receiver and find the optimal local oscillator power to improve the signal power to noise ratio.

Constellation & Orbit

The GWO Designer will not check whether the parameters provided are realistic. The evaluation of the heterodyne frequency for example requires orbit simulations and a constellation specific laser frequency locking scheme. As a rule of thumb: the maximum heterodyne frequency should be close to the maximum Doppler shift (≈ 4 MHz per 1 million km arm length for heliocentric orbits) plus the minimum frequency for which the given lasers' relative intensity noise value is true (≈ 5 MHz for 1e-8/√Hz).


A fundamental limit of the observatory's sensitivity is the power to shot noise ratio in the interferometric readout. Here the received beam power becomes important. It depends on a number of parameters.

Interferometers are used to optically read out the position of gravitational reference points (freely floating proof masses). These interferometers are constructed with fused silica optics that are bonded to an optical bench made out of an ultra-low expansion glass-ceramic.

The heterodyne signal from the combination beam splitter of the interferometers is detected by photodiodes. A transimpedance amplifier then converts the photocurrent into a proportional voltage.


Quality and other properties of the optical bench will affect the thermal stability and beat note intensity. A change in temperature of the optical results in a uniform change of the material properties that leads to a phase shift in the heterodyne signals. If there are more than one interferometer is located on a single optical bench, this effects will only cancel out if the pathlength is the same for both interferometers. There may also be losses in the optical transmissoin or an imperfect mode overlap in the interferometry.

Optical pathlength difference (OPD)

Yield (losses & efficiency)

Photo receiver

Photodiode properties and preamplifier noise contribute to what generally is declared as shotnoise.



The metrology system uses interferometer to determine the distance between the free-floating test masses. The phase of the interferometer is read and, after stripping off and processing the auxiliary signals, converted into meters.

The test masses determine the end points of the measured distances. To make the measurement not only precise but also accurate, these end points must be as undsiturbed as possible. The level or permissable noise is specified in equivalent acceleration.

Measurement and post processing

A complex metrology system will measure the interferometric signals up to the maximum heterodyne frequency and also generate correction signals like the reference frequency and pseudo random noise codes for inter spacecraft ranging. This data will later be used to suppress the otherwise overwhelming influences of laser frequency noise and timing jitter.

Proof masses

Proof masses freely floating in the spacecraft act as gravitational reference points. Spurious forces on these proof masses like acceleration by residual Coulomb forces are indistinguishable from gravitational waves and can limit the overall sensitivity of the observatory.

While the side of the spacecraft that faces the Sun will heat up, other parts will be exposed to the -270°C (-455°F) of outer space. Thermal insulation and temperature control is challenging in such an environment. While in heliocentric orbits it is possible to always point the same side of the spacecraft towards the Sun, geocentric orbits will highly increase temperature noise.

Here you can specify realistic temperature noise for two places inside the spacecraft (at the electronics and at the optical bench).


Temperature noise at the metrology system.


Temperature noise at the optical bench.

Temperature noise plot for electronics (blue) and optics (yellow). Please enter corner frequencies (f1, f2) with respective noise levels, a noise floor as well as slopes (f[slope]) below and above the corner frequencies. Update the plot when you change values.

Timing jitter in the metrology system leads to phase noise in the digital representation of the heterodyne signal. Thus a constellation wide reference frequency is required. No oscillators are available that produce a stable enough signal, hence the reference frequency is modulated onto the laser beams and synchronized throughout the constellation.

It is crucial that the modulation, transmission and read-out of the reference frequency is phase stable during the entire process since all excess noise will undermine the synchonization efforts.

Transmission lines

The reference frequency is passed along electrical cables and optical fibers. Its phase is shifted when the properties of the transmission lines are changing due to temperature fluctuations. Also electrical components in the transmission line may add timing jitter to the reference frequency.

Electrical signal

Optical signal


A signal phase stable to the reference is modulated as sidebands onto the lasers by electro-optic modulators and the overall laser power is amplified subsequently. Both components may add additional phase noise to the sidebands. The actual modulation usually happens at a higher frequency to compensate for the fact that in general only a few percent of the laser power is dedicated to the sidebands.


Electro-optic components

Gravitational Wave Observatory Designer


A new creation. What shall we name it?

Gravitational Wave Observatory Designer
Overview Displacement Single link Observatory

Mission accomplished

This plot shows a comparison of strain sensitivities for different observatories. All submitted parameters were considered.

Tab through the individual plots for displacement noise contributions, single link strain sensitivities and characteristic strain amplitude of astrophysical sources detactable by your observatory. You may also download images, raw data and additional documents. A detailed report compiled specifically for your very own gravitational wave observatory explains all calculations step by step and features additional plots and figures.

Disclaimer: All data was generated automatically. No one can be held responsible for any errors or omissions or for the results obtained from the use of this information. If you use any plots and figures or publish findings related to the Gravitational Wave Observatory Designer, please cite: Barke, Simon et al. Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors 2015 Class. Quantum Grav. 32 095004.

Displacement noise contributions

Gravitational waves alter the distance between spacecraft which results in a phase shift in the interferometric read-out. We measure this phase shift and calculate the apparent spacecraft displacement. There are multiple noise sources that are indistinguishable from such a spacecraft displacement and hence limit the observatory's sensitivity. We consider the contributions shown in this plot of displacement noise over gravitational wave frequency. All contributions were calculated based on the specified set of parameters.

Did you know: you can click anywhere in the plot to display coordinate values, or click on labels in the key to hide individual traces.

Single link strain sensitivities

Gravitational waves stretch and compress spacetime perpendicular to the direction of travel. This plot shows the impact of gravitational waves on one single laser link (red trace) limited by the calculated displacement noise. It was avaraged over all sky positions (source directions of the gravitational waves) and both gravitational wave polarizations.

Two possibly limiting noise contributions are plotted individually: the carrier signal read-out noise (blue) and the proof mass acceleration noise (green).

The wiggles on the right hand side proceed from a sloppy avaraging over only 25 sky positions in total. For a perfect avarage the slope would become continuous.

Astrophysical sources

The scientific value of an observatory is related to the number and type of sources it can detect. Here we plot the observatory's detection limit where the signal-to-noise ratio equals 1. It is compared to the characteristic gravitational wave strain amplitudes for selected gravitational wave sources. For quasi-monochromatic sources the accumulated signal after one year of observation time is given. Amplitudes of all other broadband sources are plotted as is, although their actual SNR can be higher due to matched filtering techniques during data analysis.

There are three categories of astrophysical phenomena that are known to emit gravitational waves at frequencies and amplitudes accessible to laser interferometric observatories in space: massive black hole binaries, the coalescence of two supermassive black holes; extreme Mass Ratio Inspirals (EMRIs), a compact star or stellar mass black hole captured in a highly relativistic orbit around a massive black hole; ultra-compact binaries, systems of white dwarfs, neutron stars, or stellar mass black holes in tight orbit.

This is a beta version. Results, associated figures and documents generated by this web application may be incomplete or contain errors. In particular, received power (number of photodiodes, balanced detection, beamspitters) are currently under investication. Only use this to compare relative parametric dependencies.

We are currently developing on a production server. This gives you all the latest bugfixes, but debug code also slows things down and may break everything from time to time.

If you find anything strange, confusing or plain wrong: please contact

Gravitational Wave Observatory Designer


Personalize your documents!



I made these just for you. Enjoy!


Gravitational Wave Observatory Designer

Resume your work!

To restore mission parameters please provide the code found in the associated documents.

Please provide the code found in the associated documents.
Gravitational Wave Observatory Designer Help

Preprint paper Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors S Barke et al 2015 Class. Quantum Grav. 32 095004.

What is this all about?

Some of the most interesting sources of gravitational waves (like supermassive black hole mergers, dense stars captured by supermassive black holes, and pairs of dense stars) emit at frequencies between 10 µHz and 10 Hz. However, due to seismic disturbances, this frequency range is not accessible from Earth. A laser interferometric gravitational wave observatory in space is known to be the most promising option to detect gravitational waves in this frequency range and hence was recently selected by the European Space Agency (ESA) to be launched in the 2030s as 3rd large mission of the Cosmic Vision program. The selection was supported by renowned scientists such as Stephen Hawking including many Nobel Prize and Fields Medal laureates.

You are about to design your very own a spaceborne gravitational wave obervatory. There is a huge parameter space to cover. The goal obviously is to construct the most sensitive observatory within technical and budgetary constraints.
So far, two carefully thought out design studies (LISA and eLISA, see exist that both deliver outstanding performance. Usually reports on new concepts refer to one of the these studies and determine the observatory's sensitivity by just three parameters: the well known interferometer topology, its shot noise limit, and the acceleration noise on its gravitational reference points. But: There are many other technical noise sources, and when you change just one mission parameter, one of those might limit the final observatory's sensitivity.

This tool will help you to understand the influences of design choices, point out the limiting noise sources, and help you to carefully balance out all mission parameters. You can also directly compare the observatory's sensitivity dependent on certain parameters. All calculations are fully documented and you may download a detailed report on your personal gravitational wave observatory.

Why should I care about gravitational waves?

Gravitational waves are the next big thing in astronomy. In contrast to electromagnetic radiation, gravitational radiation travels unimpeded throughout the entire universe, and even electromagnetically dark objects are capable of producing gravitational waves. Their continuous observation will enable us to study these dark objects directly for the very first time.

Alongside indirect yet irrefutable proof of the existence of gravitational waves (see pulsar PSR B1913+16, evidence for gravitational waves produced during cosmic inflation (red-shifted to 10-16 Hz) was recently found as static polarization pattern imprint in the cosmic microwave background radiation. But there are many other sources out there and the potential for new discoveries is enormous.

If you want to know more about gravitational waves and learn how to detect them, just have a look at the Gravity Ink. video series on YouTube. Another source of detailed information is, a web portal about Albert Einstein's theories of relativity and their applications.

Integer, decimals, scientific notation? Arrays!

All parameters can be given as integer value (100), decimals (100.0) or scientific notation (1e2). Negative values are not accepted with only a few exceptions. Most parameters support a comma-separated array of values (2.5e-3, 0.75, 100) and individual sensitivities are computed for all parameter combinations. This feature is extremely powerful since you can directly compare the influence of certain parameters. Please note that due to limited resources a maximum of 8 combinations is supported.

Why is this page so damn slow?

Web Components are the most exciting thing to happen in web development since HTML5 and are referred to as 'the building blocks of the future web'. This web application was designed with Polymer, an open-source Web Components-based library. While only Chrome (and other Blink-based browsers like Opera) ship with native platform support for Web Components, a JavaScript foundation layer provides compatibelity for the latest version of all evergreen web browsers: Firefox, Internet Explorer and Safari. This foundation layer slows things down though. Additionally, the complexity of this application with fixed elements, transparancies and shadows requires a fast CPU or a modern browser with GPU accelerated compositing. If you desire a smooth performance even on slow computers and older mobile devices, we highly recommend Chrome version 36 or higher.

Who is responsible for this web application?

This website is a project by Simon Barke as part of his PhD thesis in physics at the Max Planck Institute for Gravitational Physics. All calculations are based on work done by members of the eLISA Consortium, in particular contributions by Gerhard Heinzel, Yan Wang, Simon Barke, Juan Jose Esteban Delgado, and Michael Tröbs. Gravitational wave sources were predicted by Antoine Petiteau (supermassive black hole binaries) and Alberto Sesana (extreme mass ratio inspiral) for the eLISA White Paper. Data for known galactic gravitational wave sources was collected by Gijs Nelemans.

Gravitational Wave Observatory Designer About

Gravitational Wave Observatory Designer - Version 1.1b1

Wep application by Simon Barke et al. – related publication under preparation.

Plese refer to the help document for more information about the application itself and the people involved in the project.


Version history

Version 1.1b1 (2015/07/22)

Point Ahead Angle options, data and plot downloads

Version 1.0b2 (2014/09/01)

bug fixes, detailed PDF report (incomplete)

Version 1.0b1 (2014/07/30)

redesigned GUI with Polymer

Version 0.8.1 (2014/05/19)

first public availablility (AEI Sensitivity Calculator)

Version 0.8 (2013/04/23)

implementation of 24-link octahedral configuration

Version 0.7 (2012/06/20)

initial internal release

Legal Disclosure

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Simon Barke
Dachenhausenstr. 5
30167 Hannover


Telephone: +49 177 4774666

Images and graphics

  • Albert Einstein Institute / Milde Marketing / Exozet
  • Airbus Defence and Space (EADS Astrium)
  • Simon Barke

Open source software


Accountability for content

The contents of this web application have been created with the utmost care. However, I cannot guarantee the contents' accuracy, completeness or topicality. According to statutory provisions, I am furthermore responsible for my own content of this web application. In this context, please note that I am accordingly not obliged to monitor merely the transmitted or saved information of third parties, or investigate circumstances pointing to illegal activity. My obligations to remove or block the use of information under generally applicable laws remain unaffected by this as per §§ 8 to 10 of the Telemedia Act (TMG).

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My web application and their contents are subject to German copyright law. Unless expressly permitted by law (§ 44a et seq. of the copyright law), every form of utilizing, reproducing or processing works subject to copyright protection on my web application requires the prior consent of the respective owner of the rights. Individual reproductions of a work are allowed only for private use, so must not serve either directly or indirectly for earnings. Unauthorized utilization of copyrighted works is punishable (§ 106 of the copyright law).

Disclaimer translated by twiggs translations Übersetzungsbüro.

Privacy Statement

The submission of personal data (e.g. name and affiliation) is entirely voluntary. All date is processed by my servers in accordance with the provisions of German data privacy law. It is used to generate related documents and stored for later use. Your personal data are not passed on to third parties and are protected by a twelve digit hexadecimal number (recovery code). Everyone in the posession of the recovery code is able to access your personal data. This data privacy policy applies only to our web application. If links route you to other web pages, please inquire there about how your data are handled in such cases.

Gravitational Wave Observatory Designer

Recovery code

To restore all mission parameters at a later date, provide the following code:

You are about to design a space-based gravitational wave observatory. If you don't know what that is, this video is for you.