Improved transition detection algorithm for a self-mixing displacement sensor

Heterodyne polariscope for measuring the principal angle and phase retardation of stressed plastic substrates

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.

Interferometric measurement of temporal behavior of linear birefringence with extended range

Liquid crystal variable retarders (LCVRs) have been extensively used as light polarization modulators for ground-based polarimetric applications. Shortly, LCVRs will be used as polarization state analyzers in two instruments onboard the Solar Orbiter mission of the European Space Agency. Both ground- and space-based polarimeters require LCVR response time values that fulfill the required image acquisition rate of the polarimetric measurements. Therefore, it is necessary to have a reliable method to measure the LCVR optical retardance response times. Response times are usually estimated via optical methods using crossed or parallel polarizers. Nevertheless, these methods measure light intensity transitions to infer the response time instead of directly measuring the changes in the optical retardance. In this work, an experimental setup that uses a Soleil-Babinet variable compensator is proposed. On one hand, this allows one to study the effect of the nonlinear dependence of the light intensity on the optical retardance in the response time determination, which is neglected in most works. On the other hand, the use of the variable compensator allows one to measure the LCVR response times in the highest sensitivity areas of the system that minimizes the uncertainty of the measurement. The six transitions for the Polarimetric and Helioseismic Imager instrument modulation scheme of a representative LCVR have been measured. Based on the results, the optimized conditions to measure response times are found, which can be achieved by using the variable compensator and an IR wavelength (λ = 987.7 nm) as proposed in the experimental setup.

https://avs.scitation.org/doi/pdf/10.1116/1.5122786

Optimization of the response time measuring method for liquid crystal variable retarders

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.

Optical balanced detection in heterodyne interferometric ellipsometry.

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/104 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.

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

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/√Hz (10−13 m/√Hz) level over 100 kHz bandwidth and at 10−8 rad/√Hz (10−15 m/√Hz) level over 125 MHz bandwidth, respectively, under 2.5 mW incident power.

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

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.

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

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