Chung-Ping Chang

Influence of intensity loss in the cavity of a folded Fabry-Perot interferometer on interferometric signals

Fabry-Perot interferometer is often used for the micro-displacement, because of its common optical path structure being insensitive to the environmental disturbances. Recently, the folded Fabry-Perot interferometer has been investigated for displacement measurements in large ranges. The advantages of a folded Fabry-Perot interferometer are insensitive to the tilt angle and higher optical resolution. But the design of the optical cavity has become more and more complicated. For this reason, the intensity loss in the cavity will be an important parameter for the distribution of the interferometric intensity. To obtain a more accurate result of such interferometer utilized for displacement measurements, the intensity loss of the cavity in the fabricated folded Fabry-Perot interferometer and the modified equation of the folded Fabry-Perot interferometer will be described. According to the theoretical and experimental results, the presented model is available for the analysis of displacement measurements by a folded Fabry-Perot interferometer.

Fabry–Pérot interferometer utilized for displacement measurement in a large measuring range

The optical configuration of a Fabry-Pérot interferometer is uncomplicated. This has already been applied in different measurement systems. For the displacement measurement with the Fabry-Pérot interferometer, the result is significantly influenced by the tilt angles of the measurement mirror in the interferometer. Hence, only for the rather small measuring range, the Fabry-Pérot interferometer is available. The goal of this investigation is to enhance the measuring range of Fabry-Pérot interferometer by compensating the tilt angles. To verify the measuring characteristic of the self-developed Fabry-Pérot interferometer, some comparison measurements with a reference standard have been performed. The maximum deviation of comparison experiments is less than 0.3 μm in the traveling range of 30 mm. The experimental results show that the Fabry-Pérot interferometer is highly stable, insensitive to environment effects, and can meet the measuring requirement of the submicrometer order.

Application of neutral network interval regression method for minimum zone circle roundness

The goal of this work is to develop an accurate, efficient and robust algorithm for minimum zone circle roundness. In this paper, we use an interval bias adaptive linear neural network (NN) structure together with a least mean squares (LMS) learning algorithm, and an appropriate cost function to carry out the interval regression analysis. Through the system transformation, the minimum zone roundness can be related to a linear programming (LP) problem, which can be solved by the interval regression method. The interval regression method by NNs developed in this paper is applicable in linear regression analysis which has a complicated constraint, and where the least squares (LSQ) method cannot be used.

Multi-interferometric displacement measurement system with variable measurement mirrors

Laser interferometers have been widely implemented for the displacement sensing and positioning calibration of the precision mechanical industry, due to their excellent measuring features and direct traceability to the dimensional definition. Currently some kinds of modified Fabry-Perot interferometers with a planar mirror or a corner cube prism as the measurement mirror have been proposed. Each optical structure of both models has the individual particularity and performance for measuring applications. In this investigation, a multi-interferometric displacement system has been proposed whose measurement mirror can be quickly and conveniently altered with a planar mirror or a corner cube reflector depending on the measuring demand. Some experimental results and analyses about the interpolation error and displacement measurements with both reflectors have been demonstrated. According to the results, suggestions about the choice of a measuring reflector and interpolation model have been presented. With the measuring verifications, the developed system with a maximum standard deviation less than 0.2081 μm in measuring range of 300 mm would be a compact and robust tool for sensing or calibrating the linear displacement of mechanical equipment.

Interval polynomial regression by use of a neural network for minimum zone problems

Determining the parametrization of the curve is a fundamental problem in approximation and interpolation. The goal of this paper is to develop an accurate and robust algorithm for the minimum zone problems. In this paper, we use an interval bias adaptive linear neural network structure together with an appropriate cost function and the least mean squares learning algorithm to carry out the interval regression analysis. Through appropriate choice of the output function of the input neuron, the interval polynomial regression use of a neural network (IPRNN) method developed in this paper is applicable to many problems (interval algebraic polynomial approximation, evaluation of straightness, roundness and ellipticity and so on). Generally, these problems have complicated constraints and the LSQ method cannot be used.

Modified Fabry-Perot interferometer for displacement measurement in ultra large measuring range

Laser interferometers have demonstrated outstanding measuring performances for high precision positioning or dimensional measurements in the precision industry, especially in the length measurement. Due to the non-common-optical-path structure, appreciable measurement errors can be easily induced under ordinary measurement conditions. That will lead to the limitation and inconvenience for in situ industrial applications. To minimize the environmental and mechanical effects, a new interferometric displacement measuring system with the common-optical-path structure and the resistance to tilt-angle is proposed. With the integration of optomechatronic modules in the novel interferometric system, the resolution up to picometer order, high precision, and ultra large measuring range have been realized. For the signal stabilization of displacement measurement, an automatic gain control module has been proposed. A self-developed interpolation model has been employed for enhancing the resolution. The novel interferometer can hold the advantage of high resolution and large measuring range simultaneously. By the experimental verifications, it has been proven that the actual resolution of 2.5 nm can be achieved in the measuring range of 500 mm. According to the comparison experiments, the maximal standard deviation of the difference between the self-developed Fabry-Perot interferometer and the reference commercial Michelson interferometer is 0.146 μm in the traveling range of 500 mm. With the prominent measuring characteristics, this should be the largest dynamic measurement range of a Fabry-Perot interferometer up till now.