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Gravitational Interferometer and Kalman

  1. Jul 21, 2014 #1
    Hello everybody!

    Extreme interferometers like Ligo, Virgo, Leo600, Tama300 try to detect gravitational waves
    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
    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 interferometers 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 "evanescent wave optical filter" for strong stopband attenuation. A new interferometer design like Tama300 has it easier.

    This looks useful. Have you seen it used at a gravitational wave detector?

    Marc Schaefer, aka Enthalpy

    Attached Files:

  2. jcsd
  3. Jul 30, 2014 #2

    Greg Bernhardt

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  4. Jul 31, 2014 #3


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    Ground based interferometers must be absolutely enormous to be useful. A minor earthquake, or a passing car can otherwise interfere with any putative signal. Beam splitters have been proposed, but, the sensitivity has not yet been demonstrated sufficient to filter out background 'noise', save for unusually strong signals. Even in space, you have the issue of solar wind, energetic cosmic rays, and a variety of other factors [some unknown] to contend with.
  5. Oct 3, 2014 #4
    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

    Attached Files:

  6. Oct 3, 2014 #5
    The D=1.25m vacuum tube of Ligo is made of 3mm 304L stainless steel with stiffeners
    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

    Attached Files:

  7. Dec 25, 2014 #6
    The Kagra or Lcgt project, a cryogenic gravitational wave interferometer being built at the Kamioka mine in Japan
    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
    doesn't show secondary mirrors nor beams. No details about Advanced Virgo
    Nice theses about the suspension, plus general information:
  8. Dec 25, 2014 #7
    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.
    • 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
  9. Dec 25, 2014 #8


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    Was there something specific about this you wanted to discuss?
  10. Dec 28, 2014 #9
    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.

    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
  11. Dec 28, 2014 #10
    Hi Drakkith and the other, thanks for your interest!

    Well, if someone has already seen a Kalman filter at a gravitational wave interferometer, or knows the function of the auxiliary mirror of Kagra, or knows a better reason why Kagra's chamber will be so cold, or has seen light cooling something else than ions in a trap... Any thread in a forum is an implicit invitation to discussion!
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