Interferometric measurement of temporal behavior of linear birefringence with extended range.

A heterodyne interferometer is developed to measure the static and temporal behaviors of birefringence of a liquid crystal variable retarder. The interferometer is designed based on the analysis of the polarization state of a coherent wave. Since the optical components of the interferometer are fixed without any adjustment, the phase retardation and the azimuthal angle of a liquid crystal variable retarder is measured independently in real time, where the environmental perturbations and common mode noises can be reduced. From the analysis and experimental demonstrations, the phase retardation can be determined in the [0, 4π] range. Meanwhile, the orientational variation of the azimuthal angle of the optic axis is found.

Optical balanced detection in heterodyne interferometric ellipsometry.

The control of the state of polarization of a light wave for noise reduction is implemented as optical balanced detection in a common path heterodyne interferometer, which is presented in this work for measuring ellipsometric angles in real time. These angles are determined accurately in terms of quadrature interference amplitudes and phase information by maximum likelihood estimation. Thus, the interference noise is significantly reduced by the common path design associated with the optical balanced detection approach.

Carrier-suppressed modulation and self-mixing demodulation for vibration measurement.

We present a double-sideband suppressed-carrier (DSB-SC) technique achieved by an optical balanced detection approach for measuring small vibrations. The baseband signal is recovered by demodulating the DSB-SC signal with a self-mixing approach without local oscillator, which is usually required in coherent detection. The achievement of carrier suppression and vibration measurement is experimentally demonstrated, and the result closely agrees with the theoretical predictions.

Determination of linear displacement by envelope detection with maximum likelihood estimation.

We demonstrate in this report an envelope detection technique with maximum likelihood estimation in a least square sense for determining displacement. This technique is achieved by sampling the amplitudes of quadrature signals resulted from a heterodyne interferometer so that the resolution of displacement measurement of the order of λ/10(4) is experimentally verified. A phase unwrapping procedure is also described and experimentally demonstrated and indicates that the unambiguity range of displacement can be measured beyond a single wavelength.

Excess noise reduction by optical technique in amplitude-sensitive heterodyne interferometer for small differential phase detection.

An amplitude-sensitive technique associated with a heterodyne interferometer for detecting small differential phase is reported. The excess noise with the amplitude-sensitive technique is reduced by optical subtraction instead of electronic subtraction. The differential phase introduced by the orthogonally polarized laser beams is converted to the amplitudes of two heterodyne interferometric signals, which presents amplitude and phase quadrature simultaneously. Thus the excess noise power and quantum noise power are both differential phase dependent. The advantages of differential and additive operations by optical technique and the real time differential phase determination without phase lock in are demonstrated experimentally. The theoretical signal-to-noise ratio (SNR) and minimum detectable differential phase are derived, which takes quantum noise and excess noise into consideration. The experimental results demonstrated the resolutions of differential phase detection closes to 10(-6) rad/square root(Hz) (10(-13) m/square root(Hz)) level over 100 kHz bandwidth and at 10(-8) rad/square root(Hz) (10(-15) m/square root(Hz)) level over 125 MHz bandwidth, respectively, under 2.5 mW incident power.