Gravitational Interferometer and Kalman

[Enthalpy]

Hello dear friends!

Extreme interferometers like Ligo, Virgo, Leo600, Tama300 try to detect gravitational waves
http://en.wikipedia.org/wiki/Gravitational-wave_detector
and ground movements are one difficulty for them. The mirrors are suspended in several stages to insulate them, sometimes actively.

In addition to suspension, I suggest to measure the ground's movements by other means, and identify by how much these movements transmit into the measure at all frequencies, then subtract this contribution as estimated from the measured ground movements and the transfer function. This so-called adaptive filter is commonly used in acoustics, one method being the Kálmán filter
http://en.wikipedia.org/wiki/Kalman_filter
which routinely attenuates noise sources by 40dB.

In a first method, triaxial accelerometers can measure the ground movements. At least three pieces on a triangle plus one at depth (earthquakes are deep) would pick the distant noise sources' direction, which influences the effect on the interferometer. A too wide basis might be less good against near sources - perhaps. Dedicated sets of sensors can pick noise made by known sources like a machine, maybe a road.

Accelerometers are straightforward hence may be used already; I didn't see them mentioned after short reading. The following one is not shown on the interferometer drawings I saw and could be new. My sketch omits the second arm, the interference components, and all refinements.



I propose to add auxiliary beams between mirrors hold at an earlier stage of the suspension. These would pick ground movements almost as the main beams do, easing the cancellation, but upstream the mechanical filter hence more strongly. The auxiliary beams pick gravitational waves as well, but this contribution is strongly attenuated by the transfer function that mimics the mechanical filter.

Being more shaken, the auxiliary beam is built less sensitive than the main one, by using fewer bounces, a longer wavelength... Different wavelengths would help sort out both beams; consider my filter for strong stopband attenuation
http://www.scienceforums.net/topic/74445-evanescent-wave-optical-filter/
a new interferometer design like Tama300 has it easier.

Marc Schaefer, aka Enthalpy

[Mordred]

the Kalman filter could be used as a filtration method, I can certainly see no reason why you couldn't use it, the only problem I can think of is it may filter out the noise you want to read but that can be managed with the right algorithms. The problem with filtration methods however is they typically slow down reading to recording rates. This may cause some problems in time for signal processing. Unfortunately detecting gravity waves is a tricky subject to develop specifications to practicum. In terms in what frequencies would constitute a gravity wave for example. On that subject I would have no idea, I would assume that once a signal is identified it is then filtered, which seems the most reasonable approach.

 

on that end you may find this article handy

http://www.gravity.uwa.edu.au/docs/review.pdf

Edited July 19, 2014 by Mordred

[John Cuthber]

I'm confused (often the way)

Are you talking about some clever mathematical trick I don't really understand or are you thinking of something analogous to this

http://en.wikipedia.org/wiki/Humbucker

where the interfering signal is measured and automatically subtracted from the signal?

 

Things like cosmic events would affect the two test masses equally but local effects would affect the test mass more because it's less well decoupled from the ground.

[Mordred]

the Kalman filter is a type of noise filtering algorithm so yes its a mathematical technique

 

http://www.cs.cmu.edu/~motionplanning/papers/sbp_papers/integrated3/kleeman_kalman_basics.pdf

 

this article shows the falling body Kalman filter algorithm

 

he wishes to filter out any noises that lie outside the gravitational wave predicted frequency values whatever those may be lol personally don't know what values that would equate to.

Edited July 20, 2014 by Mordred

[Enthalpy]

Hi, thanks for your interest!

 

Yes, the Kálmán filter (and some others) is a mathematical method designed to remove noise, but it doesn't rely at all on frequency segregation. (Don't get put off by Wiki's article: signal people make everything horribly more complicated than necessary).

 

It typically receives data from several sources, one containing mostly the desired signal and some noise, others that contain mostly the undesired noise. In a sound studio, that would be the musician's microphone, and a microphone near the climatizer.

 

(A Kálmán filter can also remove echo, and is commonly used for that as well - not the case here).

 

A mathematical method, fed by both data streams, identifies how the noise mixes with the signal (linearly, that's the only assumption): if expressed as a time function, how strongly for each possible delay; or as a frequency function, with what attenuation (complex or phased) the noise invades the signal for each frequency. The simplest method is a correlation.

 

Then the filter computes how to subtract from the signal the part considered to originate from the noise source, and applies it to the signal. This is of course all digital, and is very efficient to the ear, like 40dB or even more, provided that the mixing function evolves slowly over time. This must be identified permanently, hence the filter is called "auto-adaptive".

 

My sketch shows a tunable low-pass filter in the noise path because the noise itself is low-pass filtered by the suspension stages, so the transfer function identified by the autoadaptive filter is a low-pass. This wouldn't generally be the case; in a sound studio, the transfer function would rather be a wide-band multiple echo.

 

With accelerometers in the ground, the measured noise mixes in a complicated way with the useful signal hence may be less good. For instance cars moving on a nearby road inject noise from varying locations, and the transfer function changes quickly, less good. Waves at a shore can be better filtred out. The advantage of accelerometers is that they fit an existing interferometer. Maybe the suspension points of the mirrors are a better location for the accelerometers. And by the way, four sensors to identify the noise direction isn't a completely standard Kálmán filter - but nearly, so the signal people shall think a bit at it.

 

The very nice setup is with the auxiliary beam and mirrors upstream in the suspension, because this beam measures the noise precisely the same way as the main beam suffers it: same origin, orientation... and even better, the transfer function from an auxiliary mirror to a main one is extremely constant, hence can be identified with huge accuracy, which permit a very strong attenuation of noise. Here very much better than 40dB is possible. Ground noise would essentially vanish.

 

Whether the secondary beam can be added to an existing interferometer is unclear; this may demand to rearrange the suspension, which is one extreme design in a gravitational waves detector. Maybe different detectors, not using a kilometer-long beam, can work. But for a new interferometer design, it's worth considering the scheme - even in the case that it demands small additional vacuum lines.

[Enthalpy]

The Kálmán filter doesn't need a second tube - good, since the tubes make much of the observatory's cost. Movements assessed at each end of the tubes can feed the filter.

 

I propose here to keep the observation of noise by light and deep at the suspension chain, as this is cleaner than an accelerometer at low frequencies, better oriented, and already well filtered.

The observation of noise needs that both ends of the auxiliary path respond differently to ground movements; the filter can live with a deformed, indirect observation. The sketch shows one and approximately two stages of low-pass, so even at frequencies of equal amplitude attenuation, the phase differs (here nearly 90° versus 180°). In real life, the noise would be observed deeper in the suspension chain: not as deep as the main beam, and with chains of different reactions to ground movements, for instance different numbers of stages.

-----

Common to all versions: feed the identification part of the Kálmán filter only when the ground moves enough to perturbate the useful signal, so that the filter sees a true transfer. The rest of the time, use the freezed identified transfer function; the suspension chain won't change its behaviour quickly anyway.

Marc Schaefer, aka Enthalpy

[Enthalpy]

The D=1.25m vacuum tube of Ligo is made of 3mm 304L stainless steel with stiffeners
http://core.kmi.open.ac.uk/download/pdf/4870869.pdf
and perhaps maybe 4mm of aluminium extrusion are cheaper.

Whether the longer weld seams are affordable is unclear. Also, the steel was baked at 444°C to desorb hydrogen, but aluminium should become permeable earlier.

At least, the following tailor-made section shall resist the outer pressure - with margins, so the diameter can increase.


Marc Schaefer, aka Enthalpy

[Enthalpy]

The Kagra or Lcgt project, a cryogenic gravitational wave interferometer being built at the Kamioka mine in Japan
http://en.wikipedia.org/wiki/KAGRA
shows a secondary mirror and beam in but-last position of the suspension chain, resembling much what I describe. See figure 4 of:
"Present status of large-scale cryogenic gravitational wave telescope"
Class. Quantum Grav. 21 (2004) S1161–S1172
and also figure 4 of:
"Status of LCGT" by K Kuroda
Class. Quantum Grav. 27 (2010) 084004 (8pp)

These texts detail little the function; the secondary beam shall sense and actuators shall lock the position of the upper mirror too, so that the metal wires that evacuate the heat from the mirrors don't introduce ground movements into the main mirror. Apparently it's not a part of a Kálmán filter, and the secondary beam is as long as the primary.

Virgo, the gravitational wave interferometer in Italy
http://wwwcascina.virgo.infn.it/
doesn't show secondary mirrors nor beams. No details about Advanced Virgo
https://wwwcascina.virgo.infn.it/advirgo/
Nice theses about the suspension, plus general information:
https://wwwcascina.virgo.infn.it/theses/Tesi_Ruggi.doc
https://wwwcascina.virgo.infn.it/theses/DottCasciano.pdf

[Enthalpy]

Kagra's main Fabry-Perot mirrors absorb 400mW of the light, to be evacuated from 20K where radiation would be difficult. Kagra foresees several wires of pure aluminium, thin and long so their thermal noise shakes the mirrors very little.

Far less simple, but it should be quieter: I suggest to cool the mirrors with light, about like ions are cooled in a trap. This straightforward idea may well exist already.

Light-emitting diodes can in principle do it: when their forward voltage is less than the bandgap, heat provides the missing energy to the electrons, and the emitted photons carry away both contributions. Under normal conditions and a special design, a net effect must be achieveable, when the quantum efficiency exceeds the bias-to-bandgap ratio. Maybe useful elsewhere; here it would better use a small bandgap material like InSb (already 240meV while 20K=1.7meV) or Sn, possibly heterojunctions - and worse, it needs electricity, not good here.

Absorbing and emitting light looks more promising. The source brings photons of energy just smaller than the transition, heat does the rest, the sum leaves the mirror. But because kT is only 1.7meV, this demands a small transition energy and a good quantum efficiency. Here are some configurations, maybe one will work.

• The mirror's sapphire might receive colour centers, say at the back side. If fluorescing at 1060nm, they could absorb photons with 3kT less or 1065nm, so a net cooling demands 0.996 quantum efficiency, err... Smaller transitions would be better. But at least the mirror stays monolithic, which minimizes the thermal noise below the mirror's resonances.
• Introduce light in a thin layer from which only antistokes wavelengths escape easily. How inefficient?
• Have a layer of InSb. At cold, its direct 240meV gap radiates 5.2µm photons and can absorb around 233meV. Net cooling would demand 0.97 quantum efficiency, but InSb isn't a great light emitter.
  http://www.ioffe.rssi.ru/SVA/NSM/Semicond/InSb/index.html
• Use Sn instead. Figures vary; the gap could be 60meV. Is it direct?
• InAs has 415meV direct gap at cold, but it makes superlattices with GaSb, offering transitions small and adjustable at will.
• Absorb light at a not-so-shallow dopant level. Some 15meV to the band avoid ionization at 20K. InSb has usual dopants at 10, 28, 56, 70meV from the valence, InAs at 10, 14, 15, 20meV, Si at 45meV. 4*kT is 24% of 28meV, better. Could F, N, Si, Mg be shallow dopants of sapphire?

To remove the wires, light must achieve all the cooling, starting at 300K. This may need a set of transitions energies or source wavelengths. If using a 28meV shallow level, the 5THz source is uncomfortable presently, but for 4K and 5meV instead, the source at 1000GHz is accessible to semiconductor components: 100GHz with transistors, multiply with varactors.

Waves so much longer than the 1060nm signal should be filtered out. If not, alternate cooling and observation?

The mirrors absorb 1ppm of the measure light, so even if only 0.1% of the cooling light evacuates heat, the added noise from the radiation pressure is small.

The cooling light can be spread at will on the mirror, statically or by scanning, perhaps even on the front side thanks to the different wavelengths, in order to minimize thermal gradients in the mirror.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

Cooling by light needs the de-excitation to be almost always radiative, and meanwhile I doubt that shallow acceptors in a semiconductor de-excite radiatively: angular momenta may well forbid it. A three-level scheme should be better, where heat populates partly a shallow acceptor level, light brings electrons from there to a level deeper in the forbidden band with the proper angular momentum, and fluorescence takes the electrons back to the valence band most often because an additional acceptor depletes it. A quantum well is an alternative to the shallow acceptor.

----------

The sketch represents auxiliary light cooling the main mirror, as compared with Kagra's design on the left part. Light with slightly too weak photon energy impinges on the cold parts which radiate by fluorescence. Kagra holds the main mirror by sapphire cables, but here they isolate from heat, so they're thin and rather of a different material. I've drawn one additional stage at intermediate temperature.



As no metal wires that extract heat from the main mirror inject thermal noise, the auxiliary mirror can be warm and farther upwards in the suspension chain, then with a less sensitive measure there.

Kagra needs <14K to evacuate heat at the auxiliary mirror, and then putting the whole cryo chamber at that temperature that reduces the thermal noise is a logical choice - or do you see an other reason? 77K would radiate very little heat into the main mirror, the parasitic radiation at 1060nm is faint and cool baffles can attenuate it, so 77K or even warmer would be a nice simplification.

A supercritical cooling cycle for the chamber would be quieter, or maybe my "electrocaloric bucket brigade device" if it works meanwhile
http://www.scienceforums.net/topic/78682-electrocaloric-bucket-brigade-device/

Cooling the mirror by light needs that the transition's energy exceeds the chamber's temperature. Though, the transition's energy should not exceed the mirror's temperature too much, because it determines how much fluorescence power the chamber must evacuate: if the mirror's heat provides for instance 5% of the radiative transition energy, the chamber must evacuate 20x more, or 10W - easier at 77K than 0.5W at 14K, but some transition energies are better than others.

Marc Schaefer, aka Enthalpy

[Enthalpy]

Light can cool at depth selectively. Still by photons that pick surrounding heat to achieve a transition of slightly bigger energy.

The target transition could be introduced in the material's depth mainly. This can't be changed after manufacture.

An improved version would introduce different transitions at varied depths, for instance colour centres that respond to different wavelengths. Varied light sources would cool different depths.

Focussing the light at depth in a uniform material wouldn't cool more the focal plane, as the removed heat stays uniform after scanning. But a scheme where several photon absorptions produce the heat loss lets target a chosen depth of a uniform material. While two-photon absorption seems impractical, a multi-level absorption scheme, where for instance a first photon puts an electron on a higher energy level, from where a second photon puts the electron at an even higher energy with the help of heat, operates only where both beams illuminate the material.

How to measure the heat profile? Maybe the comparison of Stokes and Antistokes does it - unclear to me: it's done for silicon at a high temperature. Rather, I suppose that the extinction coefficient of the cooling light tells the temperature. In itself a good thing, as light should cool the warmest locations faster, if the energy mismatch is well chosen.

==========

Is cooling at selective depth interesting for the mirrors of a gravitational interferometer? I ignore that very accurately.

But it looks interesting for thick optics, especially giant telescope mirrors and lenses that take a year to cool from the casting temperature. Are colour centres acceptable for them? Is their ceramic transparent enough?

==========

The Kagra interferometer plans to cool mirrors down to 20K, but big optics must cool from the casting temperature, orange to dark red or near infrared. Thermal radiation is strong at these temperatures. Maybe well chosen dopants could be introduced at varied depths to emit more light at wavelengths that pass through the shallow material. Surrounding the material by mirrors that reflect or absorb specific wavelengths would then suffice to cool varied depths selectively.

Marc Schaefer, aka Enthalpy