Laser Interferomter Gravitational-Wave Observatory

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LIGO 1997 Summer Undergraduate Research Projects

  Optimization of the LIGO End to End Modeling Program
Jacob Lacouture
Mentor: Hiro Yamamoto

The LIGO (Laser Interferometer Gravitational-wave Observatory) project uses a Michelson/Fabry-Perot Interferometer to detect gravitational waves. We generate computer models of how the electromagnetic fields within the interferometer evolve in response to gravitational waves and various noise sources.  By doing this, we are able to estimate what kind of signal is generated by the gravitational wave and how seismic noise and other  interfering factors disturb the evolution of these signals. The computational power required for the modeling is enormous. We use a computer program to do this modeling. Our goal is to reduce the amount of time required for the program execute to 0.1% of its present value. Optimization of specific mathematical procedures has reduced the required processing time by half. Further investigation into parallelization of independent steps and into systems that dynamically reorder the instruction sequences at execution time are still under investigation, but preliminary investigation suggests promising results. As a result of this work,  the required execution time has been reduced to 2.27% of its value 5 months ago.

 
  Non-gaussian Noise in the Suspension Wire
Joseph Lucas
Mentor: Seiji Kawamura

The steel piano wire utilized by the Laser Interferometer Gravitational-wave Observatory (LIGO) to suspend the mirrors is subject to vibration caused by tensile stress within the wire. Material processes such as creep release energy into the wire which set up low-frequency vibrations. Such non-gaussian energy releases are presumed to occur as burst-type signals, which spike and fade at a rate related to the Q-factor of the wire. The frequency and amplitude of these bursts, which were unknown for the material and wire length utilized by LIGO, were investigated to prevent false detection of gravity waves. To accurately measure both the frequency and amplitude of these burst-type vibrations, a Michelson interferometer was constructed. The interferometer utilized a piezo-electric transducer (PZT) driven mirror for one arm and the reflective wire for the other arm. By observing the voltage signal sent to the PZT-driven mirror to keep the Michelson fringe "locked," the vibration in vacuum of the wire can be monitored. In continuing work, the voltage signal will then be digitized, displayed, and stored in the LabView environment running on a Windows-based computer system. Statistical analysis of the data in LabView will then be possible. Finally, conclusions will be drawn about the magnitude of the non-gaussian noise problem, and possible solutions proposed.

 
  Finding a LIGO Core Optics Cleaning Procedure
Diana A. Lavely
Mentor: Dennis Coyne

The Laser Interferometer Gravitational-Wave Observatory (LIGO) is currently under construction. We can learn about gravitational waves by analyzing the interference of laser beams at displacements around 10-19 m.. The optics involved cannot have loss from contaminants totaling over 1 part per million. A procedure to clean to this degree must be found.

There are three commonly used optical cleaning processes -- drag wiping, spin cleaning, and chemical cleaning. The effects of these tests are checked by ringdown analysis and microscopic inspection. The ringdown apparatus introduces light into an optical cavity and measures the time it takes to leak out, which yields the mirror's loss. The dark field microscope shows the difference between contaminants and damage or defect areas

Microscopic inspection showed that drag wiping leaves behind a significant number of contaminants and must not be used on its own. Spin cleaning and chemical cleaning need to be experimented with further. The ringdown apparatus as implemented was found to be inadequate; further  work is required to make it suitable for loss measurement.

 
  Scaling of Thermal Noise in the LIGO Interferometers
Daniel H. Chou
Mentor: Kenneth G. Libbrecht

We have examined the use of scaling relations for the efficient estimation of the thermal noise spectrum arising from the internal normal modes of optical mirrors. Such thermal noise, essentially large-scale Brownian motion, is a fundamental source of noise in the LIGO interferometers and other precision optical experiments. While in general the measured thermal noise depends on the mirror dimensions, shape, and laser spot size, we are able to use scaling relations to reduce the functional dependence and thus greatly simplify calculations. For example it is often possible to analytically reduce the thermal noise function to dependence on a single variable. We have used existing software developed by the LIGO Project to examine the applicability of these scaling relations, and to numerically define the reduced thermal noise functions. These scaling relations facilitate the quick and accurate estimation of the thermal noise spectrum over a wide range of experimental circumstances, including the analysis of pondermotive nonlinearity in Fabry-Perot cavities and the calculations of thermal noise for the larger delay-line mirrors in proposed LIGO interferometer designs.

 
  Photodiode Amplifier for Wavefront Sensing on the LIGO Project
David Whedon
Mentor: Jay Heefner

The Laser Interferometer Gravitational-Wave Observatory expects to detect differential motion on the order of 10^-18 m rms between its arms resulting from the passage of gravitational waves. Predicted by Einstein's general theory of relativity, gravitational waves promise to provide a new window through which to view the universe. The interferometer uses an alignment sensing and control system employing a technique known as wavefront sensing to determine and correct for misalignment in the mirrors. Wavefront sensors pick off light from within the interferometer and examine the mode shapes of both the carrier signal and side bands. The sensor head electronics for one wavefront sensor consisting of a band pass filter tuned to a 25 MHz side band and a notch to attenuate the 2nd harmonic by 50 dB were designed. The design includes an optional 20 dB attenuator for the RF out-put as well as a diode transimpedance amplifier. After simulating the circuit with a SPICE-based software package a prototype was constructed. The prototype was debugged and tested. Modifications were made to the initial prototype which promise to bring the circuit well within specifications.

 
  End-to-End Modeling of the LIGO Interferometers
Sidney Ngone
Mentor: Hiro Yamamoto

The LIGO (Laser Interferometer Gravitational-Wave Observatory) End-To-End Modeling task is to simulate every significant aspect of the LIGO devices. This task encompasses a model of the optics, the electronics and actuators, the control systems and the interferometer cavities. This dynamic model will be essential for the accurate tracking of the noise sources affecting LIGO, answering design questions for the advanced form of LIGO, the production of pseudo data (as a Data Analysis aid) and, more importantly, as a general diagnostics tool.

Primary modeling to date has taken the form of designing a software simulation engine. The engine includes classes and library routines that can be used to assemble an interferometer system or part of such a system using user input from a set of files that describe the intended system. However, the formation of these files, with the use of only a text editor, is highly time consuming. For this reason it has also proven to be difficult to maintain consistency across different versions of these files, when they may or may not describe the same system. As the simulation engine is developed and parts of the engine are completed, the need for an efficient means of forming systems for input to the engine becomes increasingly important. The task of this SURF project is to develop a framework for a graphical user interface tool to aid in the development and maintenance of these system description files. /p>

In this SURF period, the graphical front-end to this application has essentially been completed, allowing the formation of systems by graphical means. The file management task, which includes a certain amount of version control, is yet to be completed. This report includes a list of required features for the completion of the initial release version of ModelBuilder, as well as extra useful features which should be included in the initial release (if time permits).

 
  Simulation of the LIGO Signal
Tim Gollisch
Mentor: J. Kent Blackburn

The goal of the Laser Interferometer Gravitational Wave Observatory (LIGO), built jointly by Caltech and MIT, is to directly measure gravitational waves as predicted by Einstein's General Theory of Relativity.  As a gravitational wave passes through the interferometer, it causes a change in the length of the arms that is of the order of 10^-18 meters and is measured through the change in phase of the laser light. This small signal is quite a challenge for both data acquisition and analysis.

The frequency dependency of the detector, the various sources of noise in the interferometer, the filters that are applied as well as the analog-to-digital-converter all effect the signal quality. In our project we use C++ computer modeling to simulate the acquisition of the data before they enter the analysis.  The resulting model will enhance the understanding of the effects these processes have on the signal. Since the data analysis relies on trying to match templates of expected signals with the data, the model will also be applied to produce realistic streams of data for testing and sizing the templates to be used.

 
  A Phase Modulated Table Top Michelson Interferometer with Feedback Control
Juancarlos Chan
Mentor: Nergis Mevalvala

As part of a larger experiment to measure the coupling of laser amplitude fluctuations to path length differences in a Michelson interferometer, we set up a table-top Michelson interferometer with an RF phase modulation sensing scheme. We used the sensor signal and a simple filter to close a feedback loop to hold the interferometer mirrors within a tiny fraction of a wavelength.

 
  Simulation of the LIGO Signal
David Farnham
Mentor: J. Kent Blackburn

LIGO (the Laser Interferometer Gravitational-wave Observatory) is an instrument for detecting gravitational radiation predicted by general relativity. Due to the weak interaction of gravitational waves with matter, strong astrophysical sources produce the only waves detectable by the instrument. These waves are detected by measuring the differential length of the two arms of an interferometer; for a typical wave, the differential length will be approximately 10~18m. As a result of the small lengths being measured, the gravity wave signature will be concealed by noise. For this project, we created a computer simulation of the output signal using C++. This simulation models the response of the interferometer to a gravitational wave and adds the appropriate noise to produce a signal. The program also simulates the electronic processing performed on this signal. The resulting data stream closely resembles the actual LIGO output. This data stream will be used in data analysis to determining the efficiency at which the gravity-wave signature can be detected in the output signal. This will also enable us to understand how modifying the characteristics of the equipment affects the efficiency of detection.

 
  Coating Strain Induced Distortion in LIGO Optics
Kartik Srinivasan
Mentor: Dennis Coyne

LIGO (Laser Interferometer Gravitational Wave Observatory) core optics are coated with multilayer dielectric (SiO2/Ta2O5) coatings through ion beam sputter (IBS) deposition.   An IBS deposited coating is under compressive strain due to its high density, and this strain causes a deformation in the substrate. Very stringent surface figure requirements are necessary for LIGO to detect gravitational waves, and thus, it is important to study such aberrations in the optics. This was done through analytical and finite element models. The analytical model used Kirchoff thin plate theory to predict the strain induced deformation and provide an approximate analysis of the situation. The finite element models accounted for the three-dimensional elasto-static response of the mirror and included factors that were neglected in the analytical approach (such as edge effects and a thick plate response), thus providing a more accurate picture of the problem. Both models were used to predict deformation for fused silica (initial LIGO) and sapphire (possible future LIGO) optics. The results obtained from these analyses provide estimates for the radius of curvature changes in LIGO optics due to coating strain induced distortion.