# How is photon time of flight/range over sub-millimeter distances measured?

I was reading a paper that described how the force a low-thrust torsion pendulum was measured. In it, the paper states a laser is bounced off a mirror and the displacement is "...based upon the beam reflection time." The paper states that the device can measure sub-micrometer displacements.

Conceptually as I understand it, this measurement device would have 4 major components. A laser emitter, a mirror, a detector, and a controller. The controller would power on the laser, then note how long it takes for the detector to respond to the signal.

However, the time of flight difference for ranges this size are vanishingly small. For instance, it'd take a photon roughly $3.336×10^{-12}$ seconds to travel an additional 1mm along the beam path.

If you flip that over to cycles per second, that would suggest the controller has to operate at around ~300 GHz. Only then could it check the sensor often enough to have the temporal resolution to resolve a 1mm change in the beam path length.

This seems like an absurd clock speed for any sort of computer controller. Is there another component, or concept that I'm missing?

• I'm not an experimentalist, but I guess one would use interference patterns to deduce suddenly occurring changes in the time of flight. – ACuriousMind Aug 11 '14 at 17:43

## 2 Answers

Can you cite the paper, please?

Assuming that it's a modern version of an old experiment, my first guess would be, that the observation uses the fact that the light will induce a constant moment on the torsion pendulum. The response of the pendulum will be an oscillatory motion, for short amounts of time (seconds to minutes), that motion around the original equilibrium point is proportional to the time the light is turned on. The timescales on which such an experiment runs will be between seconds and many minutes, and not at the inverse of the laser frequency.

I've come to the conclusion that the language used in the paper is probably not completely accurate. The paper mentions determining displacement based on "reflection time." I believe that the device actually uses trigonometry and the angle formed by the bounced laser beam to determine the displacement of the torsion pendulum. The angle is measured using a CCD.

(Note: there were going to be significantly more links for sources. However, I am unable to make a post with more than 2 links until I have 10+ reputation...)

I've come to this conclusion based on assumptions and other research. First the paper suggests that this is a relatively common piece of equipment in the aerospace industry. In addition other papers suggest that sub-millimeter time of flight ranging is near state of the art. These papers used a component called a Single-Photon Avalanche Diode (SPAD) to measure the time of flight.

Additional research on this component indicates that they can commonly measure events in the $\approx100$ps range and state of the art devices can measure down to the $1$ps range. This is fast enough for millimeter resolution, but not the sub-micrometer resolution claimed by the paper.

Further the paper refers to the measuring device as a Linear Displacement Sensor. After additional research, you can find off-the-shelf devices (matching my earlier description) that claim sub-micrometer resolutions.

With all of that in mind, the answer to this question is two-fold. First the paper does not measure time of flight of the reflected photons, but instead measures the angle of the beam formed by the reflection. Second, high resolution (sub-millimeter) time of flight for ranging can be achieved with a sensor that utilizes a SPAD.