Analysis of measurement accuracy in sinusoidal phase modulating interferometry

Recently, laser interferometry is widely used as a measuring system in many fields because of its high resolution and its ability to measure a broad area in real-time all at once. In conventional laser interferometry, for example Out-of-plane ESPI (Electronic Speckle Pattern Interferometry), In plane ESPI, Shearography and Holography, it uses PZT or other components as a phase shift instrumentation to extract 3-D deformation data, vibration mode and others. However, in most cases PZT has some disadvantages, which include nonlinear errors and limited time of use. In the present study, a new type of laser interferometry using a laser diode is proposed. Using Laser Diode Sinusoidal Phase Modulating (LD-SPM) interferometry, the phase modulation can be directly modulated by controlling the laser diode injection current thereby eliminating the need for PZT and its components. This makes the interferometry more compact.

We propose a simple setup for measurement of a small 2-D rotation angle using a Twyman-Green laser diode interferometer. Sinusoidal phase-modulating interferometry is adopted to detect the phase of the interference signal with a high accuracy and to perform the phase lock to eliminate the phase fluctuation at the standard detection point. By detecting the phases at three points along an axis, the 1-D rotation angle is measured with an accuracy of 0.5 arcsec in the range of 282 arcsec and with a spatial resolution of 3 mm. The 2-D rotation angle measurement is easily made by adding two more detection points.

The issues are considered, associated with the estimation of the measurement accuracy of the information parameters of the useful signal in the conditions of simultaneous action of multiplicative and additive noise, which in general have non-Gaussian character of the distribution. Two approaches to representation of the multiplicative noise are analyzed. It is shown that when considering of multiplicative noise in the form of deterministic or quasideterministic process the measurement accuracy is affected as non-Gaussian nature of the additive noise and average power of the multiplicative noise. It is shown that with the increase of the average power of the multiplicative noise effect of non-Gaussian nature of the additive noise on the measurement accuracy is reduced. It is shown that if the multiplicative noise is a random process, then the potential measurement accuracy under its influence can be reduced by more than an order of magnitude. Accounting non-Gaussian character of equivalent noise formed by additive noise and a multiplicative part, leads to a significant reduction in the potential loss of measurement accuracy.

A sinusoidal phase-modulating laser diode interferometer using a self-pumped phase-conjugate mirror is proposed. Since the laser diode has some attractive features in size, power waste, and wavelength tunability compared with the ordinary gas lasers, it is suitable for the light source of the interferometers. But to our knowledge, the interferometer which is constructed with a self-pumped phase-conjugate mirror and a laser diode is not well examined, although various applications of self-pumped phase-conjugate mirror has been proposed. Especially, the phase-conjugate wave goes back into the light source, it is important to examine the influences of the feedback effect for laser diode. We have examined the characteristics of the phase- conjugate interferometer and carried out the wave-front measurements using a sinusoidal phase-modulating interferometry.

A method is proposed for accurately measuring a sectional profile of a metal cylinder. In this method a sinusoidally vibrating sinusoidal interference pattern is used to generate an exact spatial scale along one direction. Light from top points of a metal cylinder surface is extracted by spatial filtering in an afocal imaging system to form an image of the top points. A time-varying signal is detected in the image, and a sectional profile of the metal cylinder is measured from the phase of the detected signal on a position where the amplitude of the signal has a maximum value. Detection of the amplitude and the phase is carried out easily and exactly with sinusoidal phase-modulating interferometry.

Simultaneous measurement of the Henry factor of 14 longitudinal modes is implemented using a novel method based on sinusoidal phase modulation, without using any filter. Excellent agreement with fiber transfer function technique is achieved.

Intelligent instrumentation plays a crucial role in industrial applications, with its measurement accuracy and reliability directly influencing operational efficiency. This article presents the integration of the HART communication protocol to enhance data transmission within smart instruments, focusing on internal structure and process control optimization. A HART smart instrument multiplexer system is established, utilizing an analog PID control algorithm for data regulation and optimal control techniques for automatic parameter adjustment. Additionally, the three-parameter Weibull distribution is employed to assess the reliability of smart meters, deriving distribution characteristics and estimating parameters through failure rate analysis. The performance of the designed HART smart meter multiplexer system is thoroughly evaluated, including control performance, reliability, channel function, and measurement accuracy. Notably, the system demonstrates a minimal overshoot in analog PID control at 0.911%, with a steady-state error range of -5°C to 4°C. Furthermore, the implementation of this system significantly reduces the risk of hazardous failures by 41.91%. In conditions of 350°C temperature and 1.2MPa pressure, the system accurately measures superheated steam flow with a relative error of only 0.05%. By optimizing the settings of smart instruments, this system not only enhances measurement accuracy in industrial production but also improves reliability, supporting diverse applications in the chemical industry.

Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source

The subject matter of the study is the thread inspection method using the WAVELINE W800R profilometer and its verification. This includes determining the accuracy parameters of the calibration method and confirming its suitability for practical application. The aim of the work is to investigate and evaluate the suitability of a thread gauge calibration method using the WAVELINE W800R profilometer based on an analysis of measurement precision, reproducibility, and accuracy. The tasks include: the development and application of an evaluation algorithm for the calibration method; determination of key metrological characteristics affecting measurement accuracy; assessment of the method’s repeatability and within-laboratory reproducibility; analysis of the method’s stability under the influence of various factors; and determination of measurement accuracy using a comparison coefficient. The methods used involve experimental studies of the calibration method’s accuracy with the application of statistical tests (Cochran, Grubbs, Fisher, and Student's t-test) to verify variance homogeneity and exclude outliers. Multiple repeated measurements of thread parameters were carried out, along with an analysis of the influence of external factors and a comparison of results using the k-criterion. The results confirmed the feasibility of using the WAVELINE W800R profilometer for high-precision measurement of thread gauges. The method demonstrated sufficient repeatability and within-laboratory reproducibility. The conducted analysis of the method’s stability under varying environmental conditions confirmed its robustness. The method passed the accuracy verification using the comparison coefficient and complies with metrological control requirements. Conclusions: the thread inspection method using the WAVELINE W800R profilometer has proven suitable for laboratory use; it can be implemented in metrological practice for the control of thread gauges. At the same time, it was established that the verification process is time-consuming, which should be considered when organizing calibration activities. It is recommended to perform re-verification of the method after the calibration of reference equipment.

The analysis of the influence of multiplicative noise acting simultaneously with additive noise in the form of white noise on the accuracy of the joint measurement of two information parameters of the useful signal at a low level of this noise is carried out. The conditions are determined when two signal parameters are measured together and one of them is the frequency, there are error variances equal to the variances when each of the parameters is measured separately. The accuracy of the joint measurement of frequency and time of arrival of the useful signal is determined. It is shown that for signals without angular modulation, errors in measuring the frequency and time of arrival of the signal do not depend on whether these parameters are measured separately or jointly. The variances of errors of the joint measurement of parameters under the influence of slow multiplicative noise are determined. The accuracy of the joint measurement of frequency and time of arrival of the frequency-modulated signal is determined. It is shown that when frequency and arrival time of a broadband frequency-modulated signal are measured together, the effect of multiplicative noise is much stronger than when these parameters are measured separately. For the latter case, the measurement error coefficient is determined.

The reference wave phase was modulated with a sinusoidal vibrating mirror attached to a Piezoelectric Transducer (PZT), the integration was performed by a CCD, and the charge storage period of the CCD image sensor was one-quarter period of the sinusoidal phase modulation. With the frequency- synchronous detection technique, four images (four frames of interference pattern) were recorded during one period of the phase modulation. In order to obtain the optimum modulation parameter, the values of amplitude and phase of the sinusoidal phase modulation were determined by considering the measurement error caused by the additive noise contained in the detected values. The PZT oscillation was controlled by a closed loop control system based on PID controller. An ideal discrete digital sine function at 50Hz with adjustable amplitude was used to adjust the vibrating of PZT, and a digital phase shift techniques was used to adjust vibrating phase of PZT so that the phase of the modulation could reach their optimum values. The CCD detector was triggered with software at 200Hz. Based on work above a small coherent signal masked by the preponderant incoherent background with a CCD detector was obtained.

We present a system that measures the full-field amplitude and phase distributions of objects that vibrate with small amplitudes. The system is based on TV–holography combined with sinusoidal phase modulation, discrete vibration-phase shifts, and digital image processing. Different new algorithms, based on a linear approximation of the fringe function, are discussed. Averaging techniques, used to reduce the effects of noise sources and to increase the resolution of the system, are also introduced. For one of the algorithms, tested in combination with the averaging techniques, the amplitude threshold was approximately 1/3000 of the wavelength of the applied laser light. The amplitude resolution was of the same magnitude. The phase accuracy is amplitude dependent and was about 3° for amplitudes greater than 5 nm.

The principle through the turbine flowmeter,establish a relationship between the flow rate measurement of Coaxial phase water detector,calculate the actual measurement accuracy,and for several factors affect the accuracy of experiments were carried out,obtained the pattern of flow measurement.

We derive an optimum filter function to detect a target degraded by multiplicative noise and additive overlapping noise and placed in background noise. The filter is designed to maximize the metric peak-to-output energy, which is the ratio of the expected value squared of the output peak at the target position to the expected value of the average output energy. The optimum filter provides improved discrimination as well as robustness to input noise. One advantage of the filter described here over the homomorphic filters is that the additional preprocess on the input image, that is, the input logarithmic operation, is not required for reducing the effects of multiplicative noise. The performance of the filter is examined in terms of discrimination against background noise and robustness to multiplicative and additive input noise. Both multiplicative amplitude noise and multiplicative complex noise are considered.

In sinusoidal phase-modulating interferometry an optical path length (OPD) larger than a wavelength is measured by detection of sinusoidal phase-modulation amplitude Z(b) of the interference signal that is produced by sinusoidal scanning of the wavelength of a light source. A light source with a large scanning width of wavelength is created by use of a superluminescent laser diode for the error in the measured value obtained by Z(b) to be smaller than half of the central wavelength. In this situation the measured value can be combined with a fractional value of the OPD obtained from the conventional phase of the interference signal. A sinusoidal wavelength-scanning interferometer with the light source measures an OPD over a few tens of micrometers with a high accuracy of a few nanometers.