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Fundamental limits on the digital phase measurement method based on cross-correlation analysis
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View: Figures


Image of FIG. 1.
FIG. 1.

The phase errors obtained by using the arctangent arithmetic (dashed-dotted line labeled in red color) and the arcsine arithmetic (solid line labeled in blue color), respectively. The signal-to-noise-ratio is 35.7 dB.

Image of FIG. 2.
FIG. 2.

The relation between the phase error and the number of samples under various conditions with various resolution of ADC; N refers to the resolution of ADC in unit of bit. Increasing the number of sampling is a useful method to decompress the quantization error.

Image of FIG. 3.
FIG. 3.

The schematic diagram of the experimental setup for observing the cyclic error caused by non-integral-cycle sampling.

Image of FIG. 4.
FIG. 4.

The linear amplitude spectrum density of the phase measurement results. Two cyclic error signals at 4.3 Hz and 8.0 Hz, caused by non-integral-cycle sampling with the frequency differences (between the measured signal and the reference signal) of 2.15 Hz and 4.0 Hz, respectively, were observed.

Image of FIG. 5.
FIG. 5.

The schematics of an ultra-stable heterodyne laser interferometer.

Image of FIG. 6.
FIG. 6.

The displacement noise level of the heterodyne interferometer.

Image of FIG. 7.
FIG. 7.

The stepping motion of a mirror driven by PZT. The applied (peak-to-peak) voltage of 4 mV is corresponding to a 63-pm step height. The red dashed-dotted line is the raw data after removing a fitted three-order polynomial drift, and blue solid line is the data after smoothing with 2-point average.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Fundamental limits on the digital phase measurement method based on cross-correlation analysis