Elsevier

Optics Communications

Volume 277, Issue 2, 15 September 2007, Pages 251-255
Optics Communications

Angular interferometer using calcite prism and rotating analyzer

https://doi.org/10.1016/j.optcom.2007.05.032Get rights and content

Abstract

An interferometer using a calcite prism and rotating analyzer is proposed for angular displacement determinations. The calcite prism senses the angular displacements and the rotating analyzer transfers the interference signals from dc-type into ac-type. Compact optical setup and using low-cost devices are thus the advantages of the interferometer. The theory of the interferometer is first demonstrated. A setup constructed to realize the interferometer and the results of using this setup are then presented.

Introduction

Angular displacements can be determined by methods using autocollimator [1], [2], total-internal-reflection effect [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], attenuated total reflection effect [13], [14], interferometry [15], [16], [17], [18], [19], [20], [21], and some other special techniques [22], [23], [24], [25]. Among which, the interferometry [16], [17], [18], [19], [20] is more suitable for examining angular errors (pitch and yaw) of long distance translation stages with the performance of high sensitivity. However, in order to increase measurement accuracy, a folded Michelson structure, in which the two reflecting mirrors are replaced by two retro-reflectors whose ridge separation is known and rigidly fixed [16], [17], [18], [19], [20], is required. And for eliminating phase ambiguity and decreasing noise from low-frequency band, a heterodyne light source [20] is in general incorporated into the measurement system. An interferometer with a folded Michelson structure and heterodyne light source is large in size and rather expansive.

In this paper, an interferometer using a calcite prism and rotating analyzer is first introduced for angular displacement determinations. It keeps the inherent performance of an interferometer, i.e., high sensitivity, and possesses the advantages of using compact optical setup and low-cost devices. The principle of the interferometer is first introduced. A setup, which had a sensitivity of 19,540, developed to accomplish the interferometer is then described. And the experimental results, which agree the validity and applicability of the interferometer, of using this setup are finally presented. The results also indicate that the interferometer was with a stability of 1.15 × 10−4 deg. Besides, numerical calculations indicate that the interferometer can achieve a linearity of 0.25% if the angular rotation is within 0.5°.

Section snippets

The interferometer

Fig. 1 depicts the interferometer proposed in this paper. It is composed of a laser source, a non-polarized beam-splitter (NPBS), a calcite prism (CP), a reflecting mirror (M), a right-angle prism (RAP), a quarter-wave plate (QP), an analyzer (A), and two photo-detectors (Dr and Dm). A 45° linear polarized beam from the laser source is first separated into two components by the beam-splitter. The reflected one propagates through the right-angle prism, quarter-wave plate, and analyzer to

Experimental setup

A setup as that shown in Fig. 1 was installed. In which, the laser source was a He–Ne laser (λ = 632.8 nm). The calcite prism was with principal refractive indices of no = 1.6557 and ne = 1.4862, an optic axis at β = 35.5°, and a thickness of t = 9.28 mm. And this prism was clamped on a stage.

The calcite prism was aligned so its surface normal was consistent with the incident beam (i.e., θ → 0. This was done by aligning the prism until the beam reflected from the air–prism interface went along the path of

Experimental results

Both the spectrums of Im and Ir were first examined. As the spectrum of Im shown in Fig. 3, the signals of Im and Ir had a SNR up to 35 dB (The spectrum of Ir was very close to that of Im and is not shown here.).

The validity of the interferometer was then examined. Where the stage was a rotation stage driven by a stepping motor, its rotation angle, Δθ, was examined by the use of a HP 5529A laser measurement system. As the stage was rotated step by step, the interference signals, Ir and Im, of

Discussion

In addition to the performance of high sensitivity and stability, the interferometer has the advantages of compact optical setup and using low-price components, since it is without a dual-frequency light source and the most expensive component of the setup shown in Fig. 1 is just the He–Ne laser. These make the interferometer be a good choice if the angular displacements or angular errors of a stage are to be examined.

In the above experiments, Eq. (11) was utilized for calculating angular

Conclusion

In conclusion, an angular interferometer using compact setup and low-price components has been proposed and described. The setup developed to realize the interferometer was with a sensitivity of 19,540. Experimental results from applying the setup confirm the validity and applicability of this interferometer and indicate that the stability of the interferometer was 1.15 × 10−4 deg.

Acknowledgement

The support of the National Science Council, Republic of China, under Grant NSC 95-2221-E-027-094 is gratefully acknowledged.

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