This paper presents an improved method of high precision tilt measurement using a phase shifting cyclic interferometer. Tilt measurement with a cyclic interferometer is a highly stable and reliable experimental technique and tilts as low as 5 μrad has been reported using the same. Here we employ Polarizing Phase Shifting Interferometry (PPSI) as well as multiple reflections for improving the sensitivity. Using a combination of these two techniques tilts as low as 500 nrad has been measured.

Nano scale tilt measurement using a polarizing phase shifting cyclic interferometer

Accurate measurement of angles is extremely important in various metrological applications. Interferometry has always
been an excellent technique for accurate measurements. Several methods have been proposed for accurate tilt measurement
using interferometric techniques. Almost all of them use the Michelson configuration which is extremely sensitive to
environmental vibrations and turbulences. We know that a cyclic interferometer is extremely stable. Even though it is not
sensitive to displacement changes, it is twice sensitive to tilt compared to that of a Michelson interferometer. We have
enhanced the sensitivity to measure tilt using multiple reflections in a cyclic interferometer. Since the input beam is
collimated, we have studied the effect of aberration of the input beam on the accuracy of tilt measurement. Experimental
results on this study are presented in this paper.

Effect of beam quality on tilt measurement using cyclic interferometer

Scanning mirrors appear to be key components in optoelectronic systems for line-of-sight (LOS) stabilization. For improving the angular accuracy of a scanning mirror based on the eddy current displacement sensor measurement, an angular error-correction method is proposed and demonstrated. A mathematic angular error model with physical parameters was developed, and the cross-validation method was employed to determine the reasonable order of the Maclaurin series used in the error model, which increased the exactitude and robustness of the correction method. The error parameters were identified by accurately fitting the calibrated angular errors with the error model, which showed excellent error prediction performance. Based on the angular calculation model corrected by the error model, the closed-loop control system was established to obtain accurate deflection angles. Experimental results show that within the deflection angle of ±1.5 deg, the angular accuracy was improved from 0.28 deg to less than 1.1 arcsec, and the standard deviation for six measurements was less than 1.2 arcsec, which indicates that the angle correction method was effective in improving the linearity of the eddy current sensors and reducing the influence of manufacturing and installation errors.

https://www.mdpi.com/1424-8220/19/2/367/pdf

Improving Angular Accuracy of a Scanning Mirror Based on Error Modeling and Correction.

Precise measurement of extremely small tilt angles is of immense importance in various scientific and technological applications. Interferometry has always been a tool of great importance in such applications. Most of the conventional interferometric techniques use a Michelson configuration and the problem with this interferometer is that it is extremely sensitive to environmental turbulances and vibrations. In our privious works, we had introduced a cyclic interferometer for the measurement of tilt angles which showed excellent stability against environmental turbulances and vibrations as well as twice the sensitivity. Also, with the introduction of multiple reflections, sensitivity as low as 5 micro radian had been achieved by us. To improve the sensitivity further, we had employed phase shifting techniques. The cyclic configuration being a same path interferometer, we used a polarizing phase shifting technique. For acieving this, we developed a new scheme of polarizing phase shifting techique which is rather simpler compared to those reported in the literature. With this we could precisely measure angles as low as 2 nano radians. However, in these measurements we found that the precise alignment of the quarter wave plate plays an important role in the visibility of the fringes which affects the accuracy of measurement. In this work, we numerically investigate the effect of the misalignment of the quarter wave plate on the visibility of the fringes and consequently on the accurcy of the measurement.

Effect of Visibility of the Fringes on the Tilt Measurement Using a Cyclic Interferometer and Polarization Phase Shifting

Naderishahab, Tahereh M.S.O.E July 2017 High accuracy tilt or roll angle measurement is required for a variety of engineering and scientific applications. Optical interferometry is normally used because it is non-contact and can measure tilt with a very high degree of accuracy. In this thesis, a cyclic interferometer has been developed with four mirrors to measure tilt angles as small as a few nanoradians. To measure the phase, a novel and simple method of phase shift by polarization was developed to enhance measurement sensitivity and accuracy. Since the cyclic interferometer is insensitive to external vibrations and turbulences, polarization phase step was accomplished with relative ease. To introduce the phase shift, a quarter wave plate and a half wave plate were used with a polarized laser beam. Multiple reflections were also introduced in the cyclic interferometer to enhance tilt measurement capability. A new method was developed to evaluate phase and eventually measure the tilt even in the case of changing fringe visibility. The results of these studies show that the multiple reflection cyclic interferometer can be used to measure object tilts in the order of 0.2 nanoradians or 10 arc second.

/pdf/nanoscale-tilt-measurement-using-a-cyclic-interferometer-17avr1ru6v.pdf

Nanoscale tilt measurement using a cyclic interferometer with phase stepping and multiple reflections

Measurement of tilt plays an important role in metrological applications and consequently, several methods have been proposed in the recent past. Classical interferometric methods can measure angles with high accuracy but are easily susceptible to external turbulences. We propose to use a cyclic interferometer to measure tilt in which the sensitivity to tilt measurement is double when compared with that of the classical Michelson interferometer. Since the counter propagating beams travel identical paths, the interferometer is insensitive to external vibrations and turbulence and thus can be used under harsh environmental conditions. The novelty in the technique lies in creating multiple reflections in the tilt mirror to enhance the measurement accuracy by the way of increasing the sensitivity. This paper presents the basics of the interferometer and experimental results to quantify the increase in sensitivity. By increasing the number of reflections, it is shown that sensitivity can be further improved to measure tilt angles below 5   μ rad .

Umapathy Somasundram

Papers

Increasing the sensitivity for tilt measurement using a cyclic interferometer with multiple reflections