## Abstract

We introduce a novel optical propagation delay measurement scheme for distance estimation. It is based on a ring oscillator in which the oscillation signal is replaced by the clock information contained in optical data. A clock-and-data recovery can recover the oscillation signal at the receive end. Correlation of the received pattern with the transmitted pattern and a measurement of the bit duration by a frequency counter allow to determine the distance. The scheme has been realized at 1550 nm wavelength, using an externally modulated laser, a commercial 155.52 Mb/s clock-and-data recovery and a field-programmable gate array. Short-term repeatability is <10 µm at an equivalent free-space distance of 72 m. Measurement interval is 0.1 s. At 3 km distance the relative repeatability is 8·10^{−8}. The readout can be corrected with measured temperature data.

©2009 Optical Society of America

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### Equations (9)

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(1)
$$\begin{array}{c}\frac{2{d}_{meas}}{c}={p}_{meas}{T}_{meas}=\frac{{p}_{meas}{T}_{m}}{{n}_{meas}}\\ \frac{2{d}_{ref}}{c}={p}_{ref}{T}_{ref}=\frac{{p}_{ref}{T}_{m}}{{n}_{ref}}.\end{array}$$
(2)
$$\begin{array}{c}{d}_{meas}-{d}_{ref}=\frac{c}{2}\left({p}_{meas}{T}_{meas}-{p}_{ref}{T}_{ref}\right)\\ =\frac{c{T}_{m}}{2}\left(\frac{{p}_{meas}}{{n}_{meas}}-\frac{{p}_{ref}}{{n}_{ref}}\right).\end{array}$$
(3)
$${H}_{PLL}\left(j\omega \right)=\frac{j2\xi \omega {\omega}_{r}+{\omega}_{r}^{2}}{-{\omega}^{2}+j2\xi \omega {\omega}_{r}+{\omega}_{r}^{2}}.$$
(4)
$${H}_{path}\left(j\omega \right)={e}^{-j\omega \tau}.$$
(5)
$${H}_{o}\left(j\omega \right)={H}_{PLL1}\left(j\omega \right){H}_{PLL2}\left(j\omega \right){H}_{path}\left(j\omega \right).$$
(6)
$$Y\left(j\omega \right)=X\left(j\omega \right)+{H}_{o}\left(j\omega \right)Y\left(j\omega \right)\text{or}$$
(7)
$$Y\left(j\omega \right)=H\left(j\omega \right)X\left(j\omega \right)\text{with}H\left(j\omega \right)=\frac{1}{1-{H}_{o}\left(j\omega \right)}.$$
(8)
$$\Delta {d}_{q}=d\frac{T}{{T}_{m}}$$
(9)
$${\sigma}_{d,q}=d\frac{T}{2\sqrt{3}{T}_{m}}.$$