It is easy to measure length accurately by means of optical interferometry. However, the measurement range of a single-frequency interferometer is limited to less than half the wavelength without a moving carriage to count interference fringes. To resolve this problem, a frequency scanning method had been developed. However, its phase resolution is not so high that the integer part of the order of the interference fringe can be accurately determined. We proposed a method to measure any length absolutely and accurately, by combining a high-resolution phase measurement technique with a frequency scanning technique. In this paper, this method was investigated by using a frequency scanning heterodyne interferometer. With heterodyne phase measurement, we achieved high resolution, higher than quarter wavelength, using the wide-range frequency scanning method. This means that we can measure the absolute length with nanometre accuracy, since the integer part of the order of the interference fringe for a wavelength is determined with the frequency scanning. We measured distances up to about 4 mm with an accuracy of about 3 nm.
Based on the idea of measuring small rotation angles with a parallel interference pattern (PIP), a method is developed to measure large rotation angles accurately. Two parallel PIP's that have different periods are used to measure a rotation angle of an object. The measurement made with a small-period PIP provides a high accuracy, and the measurement made with a large-period PIP provides a wide range. An accurate measurement for wide-range angles is made by combining the two measured values. The accuracy of the phase detection is determined by the periods of two PIP's. Rotation angles from approximately -30 to 30 arc min can be measured with an accuracy of 0.2 arc sec. Analytical results are supported by experimental results.
Based on measuring one-dimensional small rotation angles by using a parallel interference pattern (PIP), a method for measuring two-dimensional (2D) small rotation angles by using two different PIP's that are orthogonal to each other is proposed. We simultaneously measure the 2D small rotation angles Δθ and Δφ by detecting the phases of the orthogonal PIP's reflected by an object at two detection points. A sensitivity of 4.9 mrad/arcsec and a spatial resolution of 1.5 × 1.5 mm(2) are achieved in the measurement. Theoretical analysis and experimental results show that error ε(1) in the measurement of Δφ is almost equal to -0.01Δθ and error ε(2) in the measurement of Δθ is almost equal to -0.01Δφ. For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant.
We propose a method for measuring rotation angles by using a parallel interference pattern. At two points on a parallel interference pattern reflected by an object, we detect phase changes in the reflected parallel interference pattern caused by rotations of the object. A high sensitivity, or a high ratio of the phase change to the rotation angle, 17 mrad/arcsec, can be achieved by determining the positions of two detection points. A high spatial resolution of ~0.5 mm is also obtained. We analyze the measurement error caused by the alignment of the parallel interference pattern and a random measurement error caused by the phase detection. The theoretical analyses and the experimental results make the characteristics of the method clear and show that the method has an accuracy of 0.2 arcsec for small rotation angles.
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