<p>The blind spots are caused by the way the current detectors (&quot;L-shaped&quot; interferometers) work. They are sensitive to a gravitational wave (GW) changing the <em>difference</em> in path length along the interferometer arms at right angles to each other.</p>
<p>Gravitational waves come in two polarisations (plus and cross). These polarisations cause alternate perpendicular expansions and contractions in space, but are rotated by 45 degrees with respect to each other (plot from <a href="http://inspirehep.net/record/818927/plots" rel="nofollow noreferrer">Kalmus 2009</a>).</p>
<p><a href="https://i.sstatic.net/hUYfQ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/hUYfQ.png" alt="Plus and cross polarisation" /></a></p>
<p>A GW source would normally be a mixture of both. The sensitivity to each polarisation depends on the orientation of the interferometer arms with respect to the source direction. For example, a source that is directly overhead with respect to the plane defined by the &quot;L-shaped&quot; interferometer arms will only be detected in the polarisation state that lines up with the arms and not in the other, because it wouldn't make the arm lengths change at all. e.g. Imagine your detector is lined up with the x and y axis indicators in the picture above, then only the plus (<span class="math-container">$+$</span>) polarised waves would be detected because it changes the lengths of the arms in anti-phase (i.e. whilst the x-arm gets longer, the y-arm gets shorter and vice-versa). The cross polarisation would leave the x- and y-arms unchanged.</p>
<p>However, if the waves come from a source <em>in the plane</em> of the interferometer, then neither polarisation causes a relative difference in the arm lengths if the source lies along a line defined by the bisector of the two arms or along an equivalent line at right angles to this. The reason is either that the polarisation of the GW changes the length of both arms by the same amount, or not at all.</p>
<p>Thus there are 4 blind spots on the sky. Note that if a source is perfectly polarised (e.g. an edge-on merging binary system), then there will be addditional blind spots.</p>
<p>There are several solutions: make your interferometer 3 dimensional (i.e. add a third arm at right angles to the other two); build another interferometer with a different plane/orientation to the first (which is essentially what has been done by adding VIRGO, and now KAGRA, to the two LIGO interferometers). Hybrid &quot;3D&quot; interferometers have also been proposed, using a pyramidal shape for the arms (e.g. <a href="https://www.nature.com/articles/s41598-020-72850-6.pdf?proof=t" rel="nofollow noreferrer">Liu &amp; Gong 2020</a>).</p>
<p>As an example, the plots <em>on the left</em> in the picture below show the sensitivity of LIGO (Washington and Louisiana) to unpolarized GWs at the top. These two interferometers are nearly lined up and nearly in the same plane, so you see the 4 blind spots clearly (and the most sensitive &quot;hot spot&quot; directions, which are directly above and below the detectors). The middle plot on the left shows how things improve when you add VIRGO (in Italy), which has a different interferometer plane - there are essentially no blind spots in the combined instrument; and then in a planned 6-detector network at the bottom. (Plot from <a href="https://arxiv.org/abs/1305.0816" rel="nofollow noreferrer">Andersson et al. 2013</a>).</p>
<p><a href="https://i.sstatic.net/l4ajT.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/l4ajT.jpg" alt="Sensitivity plots" /></a></p>
<p>A further way to tackle the blind spots is to construct multiple interferometers within the same triangular design. This is what is planned for the proposed ground-based <a href="http://www.et-gw.eu/index.php/relevant-et-documents" rel="nofollow noreferrer">Einstein Telescope</a>).</p>
<p>The Figure below is taken from the <a href="https://gwic.ligo.org/3Gsubcomm/docs/ET-0007B-20_ETDesignReportUpdate2020.pdf" rel="nofollow noreferrer">Einstein Telescope Design Report (2020)</a> and shows the response of the propsed Einstein Telescope configuration (right) compared with that of the VIRGO interferometer (an &quot;L-shaped&quot; interferometer). In this design, there are multiple interferometers using each adjacent pair of the arms, which eliminates the blind spots in the summed response. Instead the detector response is equal in all azimuthal directions that are at a similar angle to the detector plane and only reduced by a factor of two in the detector plane.</p>
<p><a href="https://i.sstatic.net/6hV64.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6hV64.png" alt="Einstein Telescope response" /></a></p>
<p>Another possibility is offered by space interferometers like <a href="https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna" rel="nofollow noreferrer">LISA</a>. This also has a triangular shape, and consists of multiple interferometers, which eliminate the blind spots in the interferometer plane. However,
a further key advantage of any <em>single|</em> space interferometer observing low-frequency sources (inaccessible to ground-based detectors) is that most sources are expected to be persistent or long-lived signals (as opposed to chirps; e.g. short period white dwarf binaries, thousands of years pre-merger, should dominate LISA detections, <a href="https://arxiv.org/abs/1907.00014" rel="nofollow noreferrer">Lamberts et al. 2019</a>). This means they can be observed continuously whilst the detector orientation changes with time (during its orbit) and means that any anisotropies in the time-averaged detector response will become smoothed out.</p>

CC BY-SA 4.0
2020-02-09T05:22:24.063Z
This is an excellent answer and links to some really interesting papers!
uhoh
CC BY-SA 4.0
2022-05-05T07:31:05.087Z
1) Triangular designs will still not be sensitive to sources in the plane of the detector.
TimRias
CC BY-SA 4.0
2022-05-05T07:32:23.430Z
2) The Einstein Telescope (Europe's next gen ground based GW observatory) is also planned to have a triangular configuration.
TimRias
CC BY-SA 4.0
2022-05-05T09:00:40.967Z
@mmeent (1) This surprised me. I need to look at this more carefully, since an L-shaped interferometer still has sensitivity in (most) of the detector plane.
ProfRob
CC BY-SA 4.0
2022-05-05T22:14:27.700Z
“ many low frequency sources of gravitational waves are expected to be persistent or long-lived signals (as opposed to chirps)” Not sure what you are alluding to here. MBHB mergers are just as chirpy as their stellar mass counterparts, but just on a much slower timescale, allowing then to stay “ in band” for months before merging (enough to allow for a significant change in antenna pattern).
TimRias
CC BY-SA 4.0
2022-05-05T22:30:02.330Z
"Short-period (P<1 hour) white dwarf binaries will be the most numerous sources for the space-based gravitational wave detector LISA. " Lamberts et al. (2019). @mmeent
ProfRob
CC BY-SA 4.0
2022-05-06T05:29:35.397Z
Indeed galactic binaries will be the most numerous LISA source (to the point of being a nuisance). My point was that most of the other main target sources in LISA (eg massive BH mergers, EMRIs) are both chirps and long lived enough that the any weak spots in the antenna pattern will have moved in their lifetime.
TimRias
CC BY-SA 4.0
2020-02-08T15:55:01.147Z
2022-05-07T10:14:34.110Z
2022-05-07T10:14:34.110Z
ProfRob
<p>If gravitational waves (GWs) pass through specific points (which are known as <em>blind spots</em>), current GW detectors aren't able to detect the passing waves. In the future, will we be able to completely overcome this problem or will it always be there to a certain extent?</p>

<space-time><gravitational-waves><interferometry><space-geometry>
Is it possible to overcome the problem of blind spot(s) of current gravitational wave detectors?
learner
# Is it possible to overcome the problem of blind spot(s) of current gravitational wave detectors?

(Asked by: username_0 on 2020-02-08)

If gravitational waves (GWs) pass through specific points (which are known as *blind spots*), current GW detectors aren't able to detect the passing waves. In the future, will we be able to completely overcome this problem or will it always be there to a certain extent?

**Tags:** space-time, gravitational-waves, interferometry, space-geometry

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## 1 answers

### Answer by username_1 on 2020-02-08. Score: 7

The blind spots are caused by the way the current detectors ("L-shaped" interferometers) work. They are sensitive to a gravitational wave (GW) changing the *difference* in path length along the interferometer arms at right angles to each other.

Gravitational waves come in two polarisations (plus and cross). These polarisations cause alternate perpendicular expansions and contractions in space, but are rotated by 45 degrees with respect to each other (plot from [Kalmus 2009](http://inspirehep.net/record/818927/plots)).

[![Plus and cross polarisation](https://i.sstatic.net/hUYfQ.png)](https://i.sstatic.net/hUYfQ.png)

A GW source would normally be a mixture of both. The sensitivity to each polarisation depends on the orientation of the interferometer arms with respect to the source direction. For example, a source that is directly overhead with respect to the plane defined by the "L-shaped" interferometer arms will only be detected in the polarisation state that lines up with the arms and not in the other, because it wouldn't make the arm lengths change at all. e.g. Imagine your detector is lined up with the x and y axis indicators in the picture above, then only the plus ($+$) polarised waves would be detected because it changes the lengths of the arms in anti-phase (i.e. whilst the x-arm gets longer, the y-arm gets shorter and vice-versa). The cross polarisation would leave the x- and y-arms unchanged.

However, if the waves come from a source *in the plane* of the interferometer, then neither polarisation causes a relative difference in the arm lengths if the source lies along a line defined by the bisector of the two arms or along an equivalent line at right angles to this. The reason is either that the polarisation of the GW changes the length of both arms by the same amount, or not at all.

Thus there are 4 blind spots on the sky. Note that if a source is perfectly polarised (e.g. an edge-on merging binary system), then there will be addditional blind spots.

There are several solutions: make your interferometer 3 dimensional (i.e. add a third arm at right angles to the other two); build another interferometer with a different plane/orientation to the first (which is essentially what has been done by adding VIRGO, and now KAGRA, to the two LIGO interferometers). Hybrid "3D" interferometers have also been proposed, using a pyramidal shape for the arms (e.g. [Liu & Gong 2020](https://www.nature.com/articles/s41598-020-72850-6.pdf?proof=t)).

As an example, the plots *on the left* in the picture below show the sensitivity of LIGO (Washington and Louisiana) to unpolarized GWs at the top. These two interferometers are nearly lined up and nearly in the same plane, so you see the 4 blind spots clearly (and the most sensitive "hot spot" directions, which are directly above and below the detectors). The middle plot on the left shows how things improve when you add VIRGO (in Italy), which has a different interferometer plane - there are essentially no blind spots in the combined instrument; and then in a planned 6-detector network at the bottom. (Plot from [Andersson et al. 2013](https://arxiv.org/abs/1305.0816)).

[![Sensitivity plots](https://i.sstatic.net/l4ajT.jpg)](https://i.sstatic.net/l4ajT.jpg)

A further way to tackle the blind spots is to construct multiple interferometers within the same triangular design. This is what is planned for the proposed ground-based [Einstein Telescope](http://www.et-gw.eu/index.php/relevant-et-documents)).

The Figure below is taken from the [Einstein Telescope Design Report (2020)](https://gwic.ligo.org/3Gsubcomm/docs/ET-0007B-20_ETDesignReportUpdate2020.pdf) and shows the response of the propsed Einstein Telescope configuration (right) compared with that of the VIRGO interferometer (an "L-shaped" interferometer). In this design, there are multiple interferometers using each adjacent pair of the arms, which eliminates the blind spots in the summed response. Instead the detector response is equal in all azimuthal directions that are at a similar angle to the detector plane and only reduced by a factor of two in the detector plane.

[![Einstein Telescope response](https://i.sstatic.net/6hV64.png)](https://i.sstatic.net/6hV64.png)

Another possibility is offered by space interferometers like [LISA](https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna). This also has a triangular shape, and consists of multiple interferometers, which eliminate the blind spots in the interferometer plane. However,
a further key advantage of any *single|* space interferometer observing low-frequency sources (inaccessible to ground-based detectors) is that most sources are expected to be persistent or long-lived signals (as opposed to chirps; e.g. short period white dwarf binaries, thousands of years pre-merger, should dominate LISA detections, [Lamberts et al. 2019](https://arxiv.org/abs/1907.00014)). This means they can be observed continuously whilst the detector orientation changes with time (during its orbit) and means that any anisotropies in the time-averaged detector response will become smoothed out.

> **Comments:**
> **username_2**: This is an excellent answer and links to some really interesting papers!  
> **username_3**: 1) Triangular designs will still not be sensitive to sources in the plane of the detector.  
> **username_3**: 2) The Einstein Telescope (Europe's next gen ground based GW observatory) is also planned to have a triangular configuration.  
> **username_1**: @mmeent (1) This surprised me. I need to look at this more carefully, since an L-shaped interferometer still has sensitivity in (most) of the detector plane.  
> **username_3**: “ many low frequency sources of gravitational waves are expected to be persistent or long-lived signals (as opposed to chirps)” Not sure what you are alluding to here. MBHB mergers are just as chirpy as their stellar mass counterparts, but just on a much slower timescale, allowing then to stay “ in band” for months before merging (enough to allow for a significant change in antenna pattern).  
> **username_1**: "Short-period (P<1 hour) white dwarf binaries will be the most numerous sources for the space-based gravitational wave detector LISA. " Lamberts et al. (2019). @mmeent  
> **username_3**: Indeed galactic binaries will be the most numerous LISA source (to the point of being a nuisance). My point was that most of the other main target sources in LISA (eg massive BH mergers, EMRIs) are both chirps and long lived enough that the any weak spots in the antenna pattern will have moved in their lifetime.  

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