RICERCA ITALIANA     

ABSOLUTE TIME OF FLIGHT TELEMETRY WITH MODE-LOCKED PICOSECOND LASERS

Politecnico di Torino

Abstract

We propose to develop a precision measurement system of the two-way time-of-flight of optical pulses from a picosecond laser, based on the evaluation of the phase delay that it induces om the returning pulse train with respect to the outgoing one. In order to obtain micrometer spatial resolution, the time delay must be measured with an uncertainty smaller than 100 fs, a very ambitious task.
However, the target appears within reach if one considers that in the field of Time and Frequency Metrology a measurement system of ultrastable oscillators’ phase instability was developed in the 70ies and is commonly used, which can resolve a few fs. Such system is based on the expansion of the phase difference time delay to be measured with the adoption of a heterodyne method applied symmetrically to the two channels. It is expected that micrometer absolute accuracies and even better repeatability can be obtained in this way.
In order to extend the usefulness of this method to the absolute evaluation of the delay, which is a requirement in absolute telemetry, it is necessary to study all systematic errors produced in the physics and in the electronics. In particular in the research unit of the Politecnico di Torino, possible errors of the electronics will be studied, and a prototype system will be realized with consequently optimized symmetry in order to common mode as much as possible such errors.
In the reasearch unit of the Politecnico di Milano the analysis of critera for the selection of the laser source most suitable for the task will be carried on in collaboration with the INRIM unit. Possible limits to the method which might stem from systematic errors embedded in the physics of the optical pulse and beam optics will be studied, including those which may be generated by instability of the pulse repetition rate. The selected source will most likely be a picosecond laser with 100 MHz rep rate and 10 ps pulses. This frequency will have to be locked to that of a good quality quartz oscillator to make the phase stability adequate.
With the help of fast photodetectors (bandwidth > 10 GHz) it will be possible to detect both optical outgoing and incoming pulse trains with the necessary time resolution and stability, by keeping in check pulse profile distortions produced by detector bandwidth and as a result also their time jitter. In particular, the amplitude and profile instabilities of the pulses will be carefully studied in order to keep them below the limits imposed by the target accuracy of the system.
The experimental validation of the prototype will be carried on at INRIM, and it will done by comparing results given by the prototype telemeter with those produced by a calibrated reference interferometer in measuring the same distance. Such optical path will also be changed to different lengths by moving the carriage on which the retroreflector is mounted. A correction must be applied to both results to take into account the refraction index of air. The complete characterization of the telemeter will consist in the evaluation of corrections, and associated uncertainties, that must be made on the raw data to take into account all known effects, such as the non complete superposition of the two laser beams or the different color of the lasers. <<<

Principal Investigator

Andrea De Marchi Politecnico di TORINO

Research Objectives

The primary aim of this research project is to develop and realize a time-of-flight optical telemetry system based on the use of a mode-locked picosecond laser and on the measurement of time delay with a dual mixer system, also with the aim of inquiring on possible limits to the accuracy and resolution of the system.

To this aim a research programme is organized which foresees the achievement of a number of intermediate benchmarks, both on the physics of the optical pulse, for which adequate analysis of source, its stabilization, and propagation medium is necessary, and on the uncertainties embedded in the behavior of devices, in particular in the medium and long term.

More specifically, the final objective is to obtain micrometer resolution on great distances (more than 10 m), with similar accuracy and a measurement speed allowing to consider as still any object moving at velocities up to a few m/s. What this means is a target resolution of 10 micron in 10 microseconds. However, the system should be capable of varying in a simple way both resolution and measurement speed, with easily made changes on the synthesizer.

Intermediate objectives can be identified for each research unit, according to its specific task within the programme.

For the Per il Politecnico di Milano the aim is to realize a pulsed laser source with the necessary characteristics of stability and pulse shape, as seen at the output od fast photodetectors. For the Politecnico di Torino it is to realiza a dual mixer system capable of working with the desired phase accuracy at a number of input frequencies, harmonics of 100 MHz. For INRIM it is to completely evaluate the performances of the assembled prototype telemeter. <<<

First Results

The proposed laser telemeter has the advantage of being robust and compact: the optical system is essential and internal in the picosecond laser, electronics is modular and composed of few devices, fast: readings have a tuneable rate with time smaller than a millisecond.

Concerning the absolute distance measurement, the system is based on the distance measurement through the optical pulse delay measurement, translated to a phase measurement. Using a commercial device with 1 ns temporal resolution, with a repetition rate of 100 MHz, corresponding to 1.5 m fringe, we would obtain a spatial resolution of 1.5 um, with a reading rate of 1 kHz. The instrument has two independent degrees of freedom, by choosing a higher harmonic the reading rate increases, whereas by increasing the ratio between the input and output frequency of the double balanced mixer increases the spatial resolution, that could reach the micrometer range, competing with a relative interferometer.
Practically, the real limitations of the proposed telemeter comes from the optical part (pulse envelope instability, repetition rate instability) and the electronics part (channel asymmetry, unwanted phase rotations, electronics noise).

The project aims at evaluating the real capability to reach the theoretical resolution reported above and the principal uncertainty causes. Preliminary calculations based on the state of the art allows us to estimate a final uncertainty in a range between 100 nm and 1 um for a range up to 10 m.

One of the possible applications of the proposed telemeter is to be used together with a relative interferometer, since the telemeter would measure the integer number of fringes of the relative interferometer, whereas the relative interferometer would reach resolutions of a thousandth of optical fringe, corresponding to uncertainties in the nanometre range. This potentiality is extremely important for spatial applications and in particular for formation flying satellites , where it is requested the absolute distance measurement between two or more satellites. Concerning absolute measurements in air, the proposed telemeter could be used taking into account that the limiting factor is the refractive index of air that would limit the relative uncertainty to 10^-7.


Different applications which can become very interesting as a function of how well the system will respect expectations are to be looked for in industry. Here it is considered a big shortcoming of laser telemetry that of not being absolute when it is high resolution, and a real dream to be able to obtain absolute and high resolution measures with a high rep rate. As a matter of fact, the availability of a laser telemeter capable of delivering an uncertainty of 10 micron in 10 microseconds could in perspective allow for example the controller of an operating machine in a condition to correct on-line for the distortions of the machine as it is operating, reducing in this way potentially by a full order of magnitude machining uncertainties.
In this function traditional systems cannot be applied as they have not only the problem of being slow, but also the one of needing rezeroing in case the laser beam is interrupted, for example by flying chips, during the measurement.
Even without thinking to on-line operation, though, measurement speed is interesting anyway as it can shorten the duration of machine inactivity for periodic calibration from a couple of days to half an hour. <<<

Timescale

24 months

National and international background

Industrial needs for absolute length measurements on great distances are continually growing, and increasingly stringent are getting proposed accuracy, resolution and speed specifications. Applications are the most various, from aerospace industy, requesting satellite control or tridimensional measurements on wing structures, to geodetics for monitoring slow small ground displacements, for example for quake prediction or for decision making e.g. in the choice of sites for waste disposal.
The ultimate accuracy limits for distance measurements in air are in any case given by the knowledge of the average refraction index along the optical path, because it implies a correction of the raw measure. Details on this can be found in the B form of the INRIM research unit.
For absolute measurements the following methods are used.
Time-of-flight method. The total optical path is derived from the time that it takes to the light to cover it, usually back and forth. With optical pulses, the ultimate limit is set by the time resolution of light detectors. For example, a time resolution of 10 ps corresponds to an uncertainty of 1.5 mm (1.5 10-5 su 100 m).
Interferometry. The total optical path difference between two different paths is given by *********, where *** is the wavelength, N is the integer number of wavelengths and **** is the extra fraction of wavelength. It offers great resolution but it doesn’t provide an absolute measurement if a single wavelength is used. In fact, in the phase measurement only the extra fraction is obtained but not N. A method used to remove the ambiguity on N is to use several wavelengths and a least square approach to find the set of N values which minimizes the error.
Other techniques are based on the synthetic wavelength method [1], more details of which are illustrated in the B form of INRIM. Certain schemes which use a femtosecond laser like in [3] are referrable to a synthetic wavelength method.
A mixed technique was recently proposed by a researcher at JILA in Jan Hall’s lab [4] which also uses a femtosecond laser. A rough measurement of the time-of-flight is obtained by delaying the leading train till the pulses overlap, which yields an estimate of N, and an interference is then produced between the two pulses, which gives the fractional part.
Of all these techniques the only one which can offer fast absolute measurements is the time-of-flight technique, which however doesn’t offer interesting resolution.
The absolute telemetry technique proposed here fits in this scenario with the promise to offer fast absolute measurements with great resolution.
In order to implement it a laser is needed capable of delivering very short pulses with great stability of the repetition rate and of shape and power of the pulses. Adequate seem to be the mode locked picoseconds lasers, which are therefore assumed to start with as the most likely candidates for the task. The best solutions are obtained with Neodimium (Nd) lasers in the near IR (1 micron wavelength), with active or passive mode locking [5] (obtained with saturable absorbers), and rep rates between 50 and 100 MHz. The most used matrices for these applications are YAG (Yttrium Aluminum Garnet) , YVO (Yttrium Orthovanadate) , and YLF (Yttrium Lithium Fluoride), and it will be necessary to find the most suitable solution for the lowest time jitter of the pulse train. These solid state lasers yield very good spatial modes of the output (M^2 of the order of 1.2) and allow therefore efficient power collection.
Photodetectors with 100 GHz bandwidth have been realized [6], and might be conveniently used to detect with minimal distortion light pulses in our system, but may not be necessary. Commercially available [7] 40-45 GHz bandwith detectors may be sufficient in most configurations and even slower ones may be useable in some.
In dual-mixer systems used in Metrology it is possible to resolve about the tenth of a microradian at 10 MHz, that is to say a little more than 1 fs. This is possible with a simple time interval counter with an equivalent clock at 1 GHz (that is to say with 1 ns resolution) because in the system the time interval to be measured is expanded by one million. With a 100 MHz rep rate we should be able with our method to resolve 10 micron in 1 ms, or 1 micron in 10 ms.
The idea to extend the application of the dual-mixer method to the absolute measurement of phase differences was recently visited by a French-Czech group [2], who has promptly zeroed on the most relevant crux of the operation, which is the problem of guaranteeing symmetry between the two channels at the desired level, in particular independently of operational frequency and ageing. A peculiarity of the approach of that group, different in this from our own, was the necessity of operating anywhere in a range of frequencies in order to explore spectral characteristics of some object under test. When working with these requirements the group found that the impedance matching was very difficult and critical, particularly at the mixer input, and observe phase rotations as great as many ps when changing the mismatch. Such an uncertainty would obviously make the system useless in order of the target phase accuracy here assumed.
In the system to be realized for the telemeter here proposed the operating frequency is fixed, therefore the impedance match can be better optimized. On the other hand only the difference in its instability in time between the two channels is relevant, as the rest of the effect is common mode and is therefore irrelevant in the differential method.
In order to validate the technique, results will have to be compared to those obtained on the same distance with a calibrated interferometer. The state of the art on this is well available at INRIM, together with all the necessary know how.

[1] G. Bönsch, E Potulski,"Measurement of the refractive index of air and comparison with modified Edlén's formulae",Metrologia, vol 35,pagg 133-139.
[2] C. Yin, Z. Chao, D. Lin, Y. Xu, J. Xu, " Absolute length measurement using changeable synthetic wavelength chain", Optical Engineering , Volu 41, Issue 4, pp.
746-750.
[3] K. Minoshima and H. Matsumoto, "High-Accuracy Measurement of 240-m Distance in an Optical Tunnel by use of a Compact Femtosecond Laser," Applied
Optics, vol. 39, pp. 5512-5517, 2000.
[4] J. Ye, "Absolute measurement of a long, arbitrary distance to less than an optical fringe," Optics Letters, vol. 29, pp. 1153-1155, 2004.
[5] U. Keller, "Recent Development in Compact Ultrafast Lasers", Nature, Vol. 424, pp. 831-838, 2003.
[6] Heinz-Gunter Bach, "Ultra High-speed Photodetectors and Photoreceivers for Telecom and Datacom also Aiming at THz Applications", European Conference on
Integrated Optics, Copenhagen (DK), April 25-27, 2007.
[7] New Focus INC Mod. 1004 VIS (40 GHz) e Mod. 1014 IR (45 GHz). http://www.newfocus.com
[8] D. W. Allan and H. Daams: “Picosecond time difference measurement system”, Proc. 29th Annual Symp. Freq. Contr., Atlantic City, NJ, USA (1975), pp 404-411
[9] R.Barillet, J.Y.Richard, J.Cermak, L.Sojdr: "Application of dual-mixer time-difference multiplication in accurate time-delay measurements", Proc, 2004 IEEE International Ultrasonics, Ferroelectrics, and Frequency Control joint 50th Anniversary Conference, pp.729-733 <<<