Measurement of residual wedge angle with a reversal shear interferometer

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Abstract

A technique for determination of residual wedge angle of high optical quality transparent parallel plate using a reversal shear interferometer-based optical system has been discussed. In this technique the parallel plate to be tested is used to introduce angular tilt in the preset two-beam interference fringes of a reversal shear interferometer. The parallelism is calculated from the angular tilt of the fringes. The technique is more sensitive compared to techniques using Fizeau interferometer and is most suitable for highly parallel transparent plate with very low residual wedge angle.

Introduction

There are standard techniques for measurement of residual wedge angle of high optical quality transparent parallel plates as given in Refs. [1], [2], [3], [4], [5]. Fizeau interferometer is the most common instrument for this purpose. By measuring the spacing of the Fizeau fringes formed due to the interference of laser beams reflected from the two plane surfaces of the parallel plate, one can determine the residual wedge angle [3]. Measurement uncertainty arises when the fringe spacing is greater than the diameter of the parallel plate or the beam aperture. For instance, with He–Ne (λ=632.8nm) laser, Fizeau fringes has limitations for residual wedge angle below 1 arc sec for parallel plate with clear apertures <30.0mm diameter. A technique which has no such limitations and which is suitable for the measurement of low residual wedge angle in sub arc sec regime has been presented in Ref. [6]. An interferometric technique to simultaneously test both surface flatness and parallelism of parallel plates has been reported [7]. Hibino et al. [8] reported a wavelength scanning Fizeau interferometer for testing a nearly parallel plate.

In the present paper, we describe a new technique for determination of residual wedge angle of high optical quality transparent parallel plate from the measurement of angular tilt of the two beam interference fringes of a reversal shear interferometer [9], [10], [11] (RSI) caused by the residual wedge angle of the parallel plate, which is placed in the path of the incident beam of the RSI, with its wedge orthogonal to the beam folding axis of the RSI.

Section snippets

Principle

Optical schematic of the set up used in the present experiment is shown in Fig. 1. Light from a He–Ne (λ=632.8nm) laser source is allowed to pass through a spatial filtering arrangement consisting of a microscope objective (MO) and an appropriate pinhole (PH) placed at the front focal plane of the microscope objective. Pinhole is also situated at the back focal plane of a well-corrected telescope objective (TO) and thus an expanded collimated beam is produced. The plane wave-front corresponding

Theoretical analyses

We define sensitivity of measurement (Sr) as the rate of change of angular displacement θ w.r.t. the wedge angle δ. Differentiating Eq. (5) w.r.t. δ we obtainSr=dθ/dδ={4(n-1)d/λ}cos2θ.Accuracy of measurement of δ would depend upon the measurement accuracies of θ and d, i.e., δ(θ,d). The differentiation of δ(θ,d) givesdδ=dδθ+dδd=[δ(θ,d)/θ]dθ+[δ(θ,d)/d]dd,where dδ represent the measurement inaccuracy of δ,dθ and dd represent measurement inaccuracies of angular displacement θ and initial

Results and discussion

Optical schematic of the experimental set up used for the measurement of residual wedge angle of high optical quality transparent nearly parallel plate is shown in Fig. 1. Results obtained for a sample plate of diameter 50.0 mm are presented. Fringes obtained without the parallel plate and that with parallel plate are shown in Fig. 7(a), (b), respectively. Plate beam splitters have been used in our experiment.

The hollow roof prism used in the experiment has been obtained by using plane glass

Conclusion

A reversal shear interferometer-based technique for determination of residual wedge angle of high optical quality transparent parallel plate has been presented.

Though the principle of measurement is apparently similar to that of the Fizeau technique [6], there is significant improvement of sensitivity and measurement accuracy and a maximum of two-fold increase can be obtained for small residual wedge angle with the present technique.

An estimate of the order of magnitude of the lower limit of

Acknowledgements

We thank scientific and technical staffs of our Optical Workshop for their technical support.

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