ABSTRACT
We use doubly phase modulated light to measure both the length and the linewidth of an optical resonator with high precision. The first modulation is at RF frequencies and is set near a multiple of the free spectral range, whereas the second modulation is at audio frequencies to eliminate offset errors at DC. The light in transmission or in reflection of the optical resonator is demodulated while sweeping the RF frequency over the optical resonance. We derive expressions for the demodulated power in transmission, and show that the zero crossings of the demodulated signal in transmission serve as a precise measure of the cavity linewidth at half maximum intensity. We demonstrate the technique on two resonant cavities, with lengths 16 m and a 4 km, and achieve an absolute length accuracy as low as 70 ppb. The cavity width for the 16 m cavity was determined with an accuracy of approximately 6000 ppm. Through an analysis of the systematic errors we show that this result could be substantially improved with the reduction of technical sources of uncertainty.
Subject(s)
Anastomosis, Surgical/adverse effects , Arteries/surgery , Gastrectomy , Gastrointestinal Hemorrhage , Intraoperative Complications , Ligation/adverse effects , Peptic Ulcer Perforation/surgery , Stomach/surgery , Anastomosis, Surgical/methods , Arteries/injuries , Arteries/pathology , Duodenum/blood supply , Gastrectomy/adverse effects , Gastrectomy/methods , Gastrointestinal Hemorrhage/diagnosis , Gastrointestinal Hemorrhage/etiology , Gastrointestinal Hemorrhage/physiopathology , Gastrointestinal Hemorrhage/surgery , Humans , Intraoperative Complications/diagnosis , Intraoperative Complications/etiology , Intraoperative Complications/physiopathology , Intraoperative Complications/surgery , Ligation/methods , Male , Middle Aged , Pancreas/blood supply , Reoperation/methods , Treatment OutcomeABSTRACT
An adaptive optical system for precise control of a laser beam's mode structure has been developed. The system uses a dynamic lens based on controlled optical path deformation in a dichroic optical element that is heated with an auxiliary laser. Our method is essentially aberration free, has high dynamic range, and can be implemented with high average power laser beams where other adaptive optics methods fail. A quantitative model agrees well with our experimental data and demonstrates the potential of our method as a mode-matching and beam-shaping element for future large-scale gravitational wave detectors.
ABSTRACT
The Doppler effect in Fabry-Perot cavities with suspended mirrors is analyzed. The Doppler shift, which is intrinsically small, accumulates in the cavity and becomes comparable with or greater than the linewidth of the cavity if the cavity's finesse is high or its length is large. As a result, damped oscillations of the cavity field occur when one of the mirrors passes a resonance position. A formula for this transient is derived. It is shown that the frequency of the oscillations is equal to the accumulated Doppler shift and that the relaxation time of the oscillations is equal to the storage time of the cavity. Comparison of the predicted and the measured Doppler shifts is discussed, and application of the analytical solution for measurement of the mirror velocity is described.
ABSTRACT
Demodulation of intensity noise in the optical heterodyne detector is analyzed for application in interferometric gravitational-wave detectors. The correlation function and the power spectral density of the demodulated intensity noise are derived, taking into account the effect of bandpass filtering at the photodiode and an arbitrary demodulation waveform. The analysis includes demodulation of the rf-modulated shot noise as a special case of the intensity noise. For shot-noise-limited detection, the signal-to-noise ratio is found as a function of the modulation parameters, and the optimization of the signal-to-noise ratio with respect to the demodulation phase is described.
