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Interferometric measurement of angular motion
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View: Figures


Image of FIG. 1.
FIG. 1.

Partial misalignment cancellation of the retroreflected beam.

Image of FIG. 2.
FIG. 2.

Unfolded propagation diagram of a cat's eye retroreflector with a flat mirror.

Image of FIG. 3.
FIG. 3.

Optical layout of the interferometer. A, C, D, E, E′, K, polarizing beam splitters; B, beam splitter; C′, compensation glass cube; F, F′, J, quarter-wave plates; H, H′, aspheric lenses; I, I′, convex mirrors; G, target mirror; PD 1, PD 2, PD 3, photodiodes.

Image of FIG. 4.
FIG. 4.

This is the arm of the interferometer.

Image of FIG. 5.
FIG. 5.

RMS wavefront error in waves with respect to the principal ray for both configurations.

Image of FIG. 6.
FIG. 6.

Plot of the A and C coefficients versus the distance of the mirror from the sweet plane s. The results of a least squares analysis are also shown and described in the text.

Image of FIG. 7.
FIG. 7.

Upper view of the interferometer. Only few of the components are shown.

Image of FIG. 8.
FIG. 8.

The percentage error σ(Δθ) calculated with the simulation coincides with the error predicted by Eq. (19) .

Image of FIG. 9.
FIG. 9.

Normalized amplitude of the signal as the mirror rotates, for the displacement of the mirror s ∈ [−10 mm, 10 mm].

Image of FIG. 10.
FIG. 10.

A photograph of the interferometer on its holder. All components are labeled.

Image of FIG. 11.
FIG. 11.

(a) Lissajous patterns produced by the interferometer in units of volts as given by the amplifiers. The amplitude of the circular pattern shown in blue has been normalized. (b) Calibration of the interferometer using the AC as reference.

Image of FIG. 12.
FIG. 12.

Measurements of the amplitude of the Lissajous patterns at different orientations of the mirror, when this was located at the sweet plane (blue continuous line) or displaced from this plane (dashed lines). Data are normalized by the largest measured amplitude.

Image of FIG. 13.
FIG. 13.

Values of the linear coefficient c 1 from the quadratic fit (28) for three types of linearity measurements. In (a) the parameter c 1 was measured several times at the sweet plane, in (b) as function of the position s of the mirror, and in (c) as function of the angle θ0. The dashed lines show ±1σ confidence level. Error bars on the measured fit coefficients are derived from uncertainties in the measurement mainly limited by noise in the AC and by mechanical vibration in the setup.

Image of FIG. 14.
FIG. 14.

The sensitivity of the interferometer is shown in blue and its mean value is depicted in black. The plot also shows an estimate of the joint laser and readout noise in green. The readout includes the photodiodes, the amplifiers, and the ADC. Finally, the noise produced by the amplifiers and the ADC is shown in orange.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interferometric measurement of angular motion