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.

Differential phase decoder in a polarized optical heterodyne interferometer.

A differential-phase decoder (DPD) together with a polarization common-path optical heterodyne interferometer is set up. Based on this interferometric configuration and a novel balanced-detector scheme, the performance of the quantum-noise-limited differential-phase decoder is demonstrated and analyzed. The minimum-detectable differential phase is on the order of 10(-7) rad/sqrt Hz when a 2.5 mW He-Ne laser is used. Verified experimentally, the DPD is immune to the common-phase noise induced by an electro-optic phase modulator or by thermal disturbance within the interferometer. This signifies that the minimum-detectable differential phase can become 10(-8) rad/sqrt Hz if a 300 mW continuous wave laser is employed instead.

Balanced detector interferometric ellipsometer.

A novel balanced detector interferometric ellipsometer (BDIE), composed of a polarized common-path optical heterodyne interferometer incorporating a novel balanced detector, provides an amplitude-sensitive method for measurement of the elliptical parameters of a thin film. The requirement for equal amplitude of the polarized heterodyne signals for balanced detection results in the simultaneous measurement of the elliptical parameters in terms of the azimuth angle of a half-wave plate and the output intensity from the differential amplifier, respectively. The common-path feature of BDIE shows a common phase noise rejection mode and this enhances the sensitivity of the phase measurement. At the same time, the balanced detector configuration of BDIE reduces excess noise of laser intensity fluctuation to give better sensitivity during measurement. The error of measurement of BDIE is derived and analyzed. Finally, the elliptical polarization effect of the laser beam is found to be independent of the measurement of the elliptical parameters.

Application of phase-to-amplitude conversion technique to linear birefringence measurements.

A novel technique that measures the linear birefringence of crystal quartz within the configuration of a Soliel-Babinet compensator (SBC) is proposed. A characteristic of this technique is that phase retardation introduced by quartz is amplitude modulation (AM) instead of phase modulation (PM). The linear birefringence is measured regardless of the azimuth angle of the SBC and the orientation of the linear polarization laser beam. Compared with the single-wedge method, the SBC is similar to a parallel plate that allows for a wider range of refracttive index of the test material to be measured. This proposed method uses a conventional amplitude demodulation method in conjunction with an optical heterodyne technique and a bandpass filter to produce a better signal-to-noise ratio. Although the SBC configuration is more complex than a single element, the independence of azimuth angle and the orientation of the linear polarized laser beam can enhance the sensitivity of the linear birefringence measurement.