Balancing a retroreflector to minimize rotation errors using a pendulum and quadrature interferometer.

A corner-cube retroreflector has the property that the optical path length for a reflected laser beam is insensitive to rotations about a mathematical point called its optical center (OC). This property is exploited in ballistic absolute gravity meters in which a proof mass containing a corner-cube retroreflector is dropped in a vacuum, and its position is accurately determined with a laser interferometer. In order to avoid vertical position errors when the proof mass rotates during free fall, it is important to collocate its center of mass (COM) with the OC of the retroreflector. This is commonly done using a mechanical scale-based balancing procedure, which has limited accuracy due to the difficulty in finding the exact position of the COM and the OC. This paper describes a novel way to achieve the collocation by incorporating the proof mass into a pendulum and using a quadrature interferometer to interrogate its apparent translation in its twist mode. The mismatch between the COM and OC generates a signal in a quiet part of the spectrum where no mechanical resonance exists. This allows us to tune the position of the COM relative to the OC to an accuracy of about 1 µm in all three axes. This provides a way to directly demonstrate that a rotation of the proof mass by several degrees causes an apparent translation in the direction of the laser beam of less than 1 nm. This technique allows an order of magnitude improvement over traditional methods of balancing.

Analytic signal demodulation of phase-modulated frequency-chirped signals.

Both interferometers and frequency-modulated (FM) radios create sinusoidal signals with phase information that must be recovered. Often these two applications use narrow band signals but some applications create signals with a large bandwidth. For example, accelerated mirrors in an interferometer naturally create a chirped frequency that linearly increases with time. Chirped carriers are also used for spread-spectrum, FM transmission to reduce interference or avoid detection. In both applications, it is important to recover the underlying phase modulations that are superimposed on the chirped carrier. A common way to treat a chirped waveform is to fit zero crossings of the signal. For lower signal-to-noise applications, however, it is helpful to have a technique that utilizes data over the entire waveform (not just at zero crossings). We present a technique called analytic signal demodulation (ASD), which employs a complex heterodyne of the analytic signal to fully demodulate the chirped waveform. ASD has a much higher sensitivity for recovering phase information than is possible using a chirp demodulation on the raw data. This paper introduces a phase residual function, R(θ), that forms an analytic signal and provides a complex demodulation from the received signal in one step. The function defines a phase residual at each point on the chirped waveform, not just at the zero crossings. ASD allows sensitive detection of phase-modulated signals with a very small modulation index (much less than 0.01) that would otherwise be swamped by noise if the raw signal were complex demodulated. The mathematics used to analyze a phase-modulated chirped signal is quite general and can easily be extended for frequency profiles more complicated than a simple chirp.

Complex heterodyne for undersampled chirped sinusoidal signals.

We describe a method for analyzing frequency-chirped sinusoidal signals using a complex heterodyne, sometimes also known as complex demodulation on the digitized waveform. This method allows one to use prior knowledge of the signal to reduce the effective bandwidth of the signal. The method can be used to extract a frequency-chirped signal even when it is sampled well below the Nyquist criterion. Accordingly, the method facilitates the use of less-expensive data acquisition and signal processing hardware than has traditionally been used for these applications. This technique is particularly useful for high-precision (parts in 10(9)) interferometer applications in which there exists a differential acceleration between the two arms (commonly found in absolute gravity meters or gradiometers).

Long term follow up after perimesencephalic subarachnoid haemorrhage.

OBJECTIVES: To evaluate the long term sequelae of perimesencephalic subarachnoid haemorrhage (PMSAH). METHODS: Twenty one consecutive patients were studied. All patients were examined by CT, angiography, MRI, multimodal evoked potentials, and transcranial Doppler sonography. All relevant clinical data during hospital stay and outcome at discharge were obtained by reviewing the charts. Long term follow up was evaluated by reviewing the outpatient files and dedicated outpatient review. Patients were specifically questioned about their perceived recovery, residual complaints, and present occupational status. RESULTS: Apart from the initial CT confirming the diagnosis of PMSAH all other examinations disclosed no abnormalities. None of the patients developed any complications during hospital stay, and all patients were discharged in good clinical condition and without neurological deficits. At long term follow up 62% of the patients had residual complaints consisting of headaches, irritability, depression, forgetfulness, weariness, and diminished endurance. Apart from four patients who had already retired before the PMSAH, only seven of the remaining 17 patients (41%) returned to their previous occupation, whereas nine patients (53%) retired from work and one man became unemployed. One patient had a recurrence of PMSAH 31 months after the first event. CONCLUSION: PMSAH can have considerable long term psychosocial sequelae, and may also recur. Prognosis may not be as good as previously reported.

Frequency stability measurements on polarization-stabilized He-Ne lasers.

We present detailed stability measurements on six He-Ne lasers which have been stabilized by matching the intensity of the two orthogonal polarization modes. The frequencies of five different lasers were closely monitored for 1 month. Another laser was studied for 2 yr. All the lasers exhibited a stability of 1 part in 10(10) over the periods of about an hour and better than 1 part in 10(8) over 1 yr. An absolute accuracy of ~1 part in 10(9) can be attained by interpolating the linear drift between calibrations performed 6 months to 1 yr apart. These 1-mW lasers are rugged and simple to operate.