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INTRODUCTION

So you've found the Sensitivity Curve Generator, and now you are wondering how to use it, and what all the choices are. This short document should help get you started.

The online sensitivity curve generator is a basic tool designed to provide the end user with a numerical representation of the sensitivity curve for a space based gravitational wave interferometer, such as LISA.

The tool takes a series of inputs from the user which describe the observatory configuration, and computes the expected sensitivity curve averaged over all polarization states and all sky locations. The choices the user makes for the observatory parameters affect the performance in a variety of ways; how the tool uses each of these numbers is described in detail below.

The curves generated are for an equal arm, Michelson configuration, and conform to the standard LISA curves which may be found in the literature (a list of starting points is given at the bottom of this page). The LISA Project has produced a white paper which describes the baseline sensitivity curve for the LISA mission: Sensitivity Curve White Paper

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CHOICES USER CAN MAKE

In addition to making choices about the raw numbers describing the observatory, the tool is currently configured to let the user make two choices regarding how the curves are computed.

(1) Type of Output Curve
The user can specify the type of curve for the tool to output, either a curve of dimensionless strain amplitude vs. frequency, or a curve of root spectral density ("spectral amplitude") vs. frequency. The transformation between these two types of curves is made assuming an integration time of T = 1 yr, such that the strain h is related to the spectral amplitude hf by: h = hf/sqrt(T)

(2) Setting for Noise Floor
The user can specify the limiting noise source on the observatory "floor", namely in the mid-frequency region where the instrument is most sensitive. The default choice is to limit the sensitivity in the mid-frequency floor by the position noise budget, which is specified by a single number. The expectation for an instrument like LISA is that there will be other sources of noise which contribute in this frequency regime as well (pointing noise, clock jitter, etc.). These noise sources are difficult to quantify, and so current convention is to specify an overall noise budget which groups all these noise sources (including shot noise) into a single numerical specification. For an example breakdown, see the LISA Pre-Phase A report, Table 4.1.

If the user chooses position noise budget, the limting noise on the floor will be set using the value the user inputs for one way position noise (default value of 20 pm per root Hz).

If the user chooses shot noise, the limting noise on the floor will be computed using observatory parameters (telescope diameter, laser power, etc) from the rest of the page.

In a future upgrade to this page, we will break all the contributing noise sources out so they may be individually specified.

CURVE GENERATOR INPUT FIELDS

Most of the choices for observatory parameters are fed into algorithms which compute a variety of instrumental noise spectra which ultimately limit the performance of the observatory. By altering the parameters, you can explore how different design choices in the construction of an observatory affects the sensitivity performance, which feeds directly into what kind of science can be done with the instrument.

  • SNR (Signal to Noise Ratio)
    Default Value: 1.0
    Impacts: Overall level of curve

    This specifies the SNR value for a threshold detection at the level of the plotted sensitivity curve. The default value is 1.0, but some LISA literature (e.g. the LISA Pre-Phase A Report) uses SNR = 5.

  • Armlength
    Default Value: 5.0e9 meters
    Impacts: Location of "corners" on curve

    This specifies the armlength in the observatory (assumed to be equal for all arms). The choice of armlength affects the sensitivity in a variety of ways: (1) The transfer frequency, f* = c/(2 pi L), is defined by the right-hand corner of a stanard sensitivty curve, where the sensitivity begins to drop off. It scales inversely with the armlength, shifting to higher frequencies as the arms get shorter. (2) The acceleration wall (limiting noise at low frequencies) shifts to higher frequencies.

  • Telescope Diameter
    Default Value: 0.3 meters
    Impacts: Shot noise level (mid-frequency sensitivity)

    This specifies the diameter of the telescope which transmits and receives laser light. The telescope diameter does not affect the performance of the instrument except as it directly relates to the computation of shot noise. If the user specifies that the floor should be set by the position noise budget, then this value is not used in the current version of the tool.

  • Laser Wavelength
    Default Value: 1064 nanometers
    Impacts: Shot noise level (mid-frequency sensitivity)

    This specifies the wavelength of the interferometer laser light (currently, this is for Nd:YAG lasers). The laser wavelength does not affect the performance of the instrument except as it directly relates to the computation of shot noise. If the user specifies that the floor should be set by the position noise budget, then this value is not used in the current version of the tool.

  • Laser Power
    Default Value: 1.0 Watt
    Impacts: Shot noise level (mid-frequency sensitivity)

    This specifies the transmitted power of the interferometer lasers. The laser power does not affect the performance of the instrument except as it directly relates to the computation of shot noise. If the user specifies that the floor should be set by the position noise budget, then this value is not used in the current version of the tool.

  • Acceleration noise spectrum
    Default Value: 3.0e-15 m/[s^2 rt Hz]
    Impacts: Low frequency loss in sensitivity

    This specifies the acceptable level of acceleration noise in the instrument, which is the limiting factor on performance at low frequencies. Acceleration noise has a 1/f^2 dependence, so the sensitivity decreases at lower frequencies.

  • Position noise budget (one way)
    Default Value: 2.0e-11 m/[rt Hz]
    Impacts: Mid-frequency sensitivity level

    This specifies the total contribution of position type noises (including laser shot noise) in the instrument. This value is used for the noise spectrum (instead of a computation of laser shot noise from the above quantities) if the user chooses Floor Set by Position Noise Budget.

    If you have Problems with the Generator

    This page is currently a beta test! Please email suggestions and bug reports about this page to shane@srl.caltech.edu. Be sure it include a complete list of parameters for the observatory you were designing -- it will greatly aid me in debugging your problem on this end.

    Clear skies!
    -- Shane

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    Sensitivity and LISA Literature (A Small Sample)

    Mission Documents

    1. LISA Pre-Phase A Report, 2nd Edition (1998)
    2. LISA Final Technical Report (2000)
    3. LISA Sensitivity White Paper (2002)

    Basis for Online Tool

    1. Larson, Hiscock and Hellings (PRD, 62, 062001 [2000])
    2. Larson, Hellings and Hiscock (PRD, 66, 062001 [2002])

    Time Delay Interferometry

    1. Tinto and Armstrong (PRD 59, 102003 [1999])
    2. Armstrong, Estabrook and Tinto (ApJ, 527, 814 [1999])
    3. Estabrook, Tinto and Armstrong (PRD 62, 042002 [2000])
    4. Tinto,Estabrook and Armstrong (PRD 65, 082003 [2002])

    Other Sensitivity Calculations

    1. Schilling (CQG, 14, 1513 [1997])
    2. Cornish and Larson (CQG, 18, 3473 [2001])
    3. Cornish (PRD, 65, 022004 [2002])
    4. Cornish and Rubbo (PRD, 67, 022001 [2003])

    White Dwarf Background

    1. Hils and Bender (CQG, 14, 1439 [1997])
    2. Hiscock, Larson, Routzahn and Kulick (ApJ, 540, L5 [2000])

    Footer Map Page Maintained by: Shane L. Larson
    Email: shane@srl.caltech.edu
    Last Updated: 17 Sept 2002