Patent Grant
10317288
This application is a National Stage of International patent application PCT/EP2016/055639, filed on Mar. 16, 2016, which claims priority to foreign French patent application No. FR 1500603, filed on Mar. 26, 2015, the disclosures of which are incorporated by reference in their entirety.
The field of the invention is that of the measurement and possibly of the control of the frequency modulation of a laser source.
Up to now, the measurement of the frequency modulation of a laser source was most often achieved using a Michelson or Mach-Zehnder interferometer one of the two arms of which included an acousto-optical modulator. An example of a system of this type is shown in
The frequency is determined by analyzing the signal output from the interferometer; it is a question of a beat signal between the two signals respectively emerging from the two arms.
The signal measured by the photodiode (excluding any DC component) is then:
x(t)∝ cos(φ(t)−φ(t−τ)+2πfmaot)
where φ(t) is the phase of the laser source, where fmao is the frequency of the acousto-optical modulator and τ is the delay induced by the optical fiber and corresponding to the path difference between the two arms of the Mach-Zehnder interferometer 2. The phase difference φ(t)−φ(t−τ) is characteristic of the frequency f(t) of the laser according to the following relationship:
φ(t)−φ(t−τ)=2π∫t τtf(t)dt≅2πτf(t) (1).
To evaluate the frequency of the laser, it is therefore advisable to calculate:
x(t)·exp(−2iπfmaot)
then to apply a low-pass filter of cut-off frequency lower than fmao. z(t) is then found such that:
z(t)∝ exp(iφ(t)−iφ(t−τ)).
The evaluation of the complex argument of z(t) then finally allows the frequency of the laser to be deduced according to equation (1).
This method relies on the frequency translation induced by the acousto-optical modulator.
Acousto-optical modulators are components that are liable to directly penalize the size, weight, electrical power consumption, reliability and cost of the systems in which they are used. These penalties may also be indirect. For example, it may be necessary to electromagnetically shield the detection chain because of interference caused by the acousto-optical modulator. In addition, it may also be noted that working at high intermediate frequencies requires a more complex detection chain to be used.
Other solutions allow the frequency modulation of the laser source to be measured. The simplest solution is based on the use of an interferometer that is “unambiguous” in the vicinity of the phase quadrature, such as for example a Mach-Zehnder interferometer with a very short delay or an optical resonator of large free spectral range. An example of a system of this type, equipped with a Fabry-Perot resonator is shown in
In this case, the signal output from the interferometer or the resonator and measured by the photodiode may be written:
x(t)=A·F(f(t))
where A is a proportionality factor depending on the injected power and F a function that is monotonic (and therefore invertible) over the possible range of excursion of the frequency f(t)=fmoy+Δf(t) of the laser. For example, in the case of the short-delay interferometer, if the powers are perfectly balanced, we have:
x(t)∝ cos(φ(t)−φ(t−τ))+1≅cos(2πτf(t))+1.
A necessary condition for the function to be invertible is for τ to be sufficiently small that |2πΔf(t)τ|<π.
Thus, this technique is unfortunately not suitable for applications in which a large modulation dynamic range and a high measurement precision are required simultaneously. In addition, the dependency of the proportionality factor A on power may decrease the precision with which the frequency may be measured. Lastly, drift in the system may lead to drift in the measurement (for example loss of the power balance between the two channels of the interferometer or any spectral shift in the response of the resonator).
A last solution consists in simultaneously measuring the phase component and quadrature component of the interferometric signal generated by a two-arm double interferometer. An example of this type of system with a Mach-Zehnder interferometer is shown in
In this case, x(t)=A·cos(φ(t)−φ(t−τ))+B and y(t)=C·sin(φ(t)−φ(t−τ))+D are measured, where A, B, C, D are factors dependent on the injected power and the balance of the powers between the channels of the interferometers. Perfect knowledge of these factors allows the following to be measured:
This technique is advantageous because it allows a good compromise between precision and dynamic range to be obtained using interferometers of high finesse (i.e. including a long delay). This technique makes it possible to avoid using any acousto-optical modulators. Nevertheless, it requires a time-invariant quarter wave plate. In addition, it requires the phase to be very precisely controlled, two signals to be acquired simultaneously and good knowledge of the factors A, B, C, D, which depend on incident power and on the balance of the powers of the channels, and which are thus liable to drift over time.
The aim of the invention is to mitigate these drawbacks. Specifically, there remains to this day a need for a method for measuring the frequency modulation of a laser source that simultaneously satisfies all of the aforementioned requirements in terms of providing a good compromise between precision and dynamic range, and in terms of the cost, bulk and reliability of the system used to implement the method.
According to the invention, the measurement of the frequency modulation of a laser source is also achieved using a two-arm interferometer (for example of Mach-Zehnder or Michelson type) one of the two arms of which is offset with a delay, but under the following operating conditions:
More precisely, one subject of the invention is a method for measuring the frequency modulation f(t) of a laser source that comprises the following steps:
It is mainly characterized in that
This method allows the modulation frequency of a laser source to be measured with a good compromise between precision and dynamic range using a simple two-arm interferometer that does not include any acousto-optical modulators. This allows drawbacks associated with the use of this component (cost, bulk, reliability, etc.) to be avoided. Furthermore, the proposed solution is based on an analysis of a signal that may be low-frequency, thereby allowing certain constraints on the detection chain and processing of the signal, such as constraints on the sampler, to be relaxed.
The calculation preferably includes:
The period T is typically about a few μs (from 5 μs to 1 ms), and the delay τ typically varies over a duration varying from one-hundred milliseconds to one minute (from 100 ms to 1 mn).
According to one variant of the invention, the variation as a function of time of the delay τ is stimulated by means of a piezoelectric device.
The invention may be used to calibrate the control signal in order to get as close as possible to a frequency modulation defined beforehand by the user. To this end, the invention also relates to a method for calibrating the frequency of the laser source of a lidar to a setpoint f0(t), which comprises the following steps:
The number of iterations is generally lower than 10.
Another subject of the invention is a computer program, said computer program comprising code instructions allowing the steps of the method such as described to be carried out when said program is executed on a computer.
The invention also relates to a system for measuring the frequency modulation f(t) of a laser source that comprises:
The interferometer is for example of Mach-Zehnder or Michelson type.
Advantageously, the interferometer does not include any acousto-optical modulators.
Other features and advantages of the invention will become apparent on reading the following detailed description, which is given by way of nonlimiting example with reference to the appended drawings, in which:
In all the figures, elements that are the same have been referenced with the same references.
A first example of a measuring system able to implement the method according to the invention will now be described with reference to
Another example of a measuring system able to implement the method according to the invention, in which the Mach-Zehnder interferometer of the preceding example is replaced by a Michelson interferometer, will now be described with reference to
All these configurations may be optical-fiber based.
In the case of the system of
In these two examples, some of the field of the laser 1 is injected into the interferometer 2, one of the arms of which is offset by a delay T by the delay line 21; the rest of the field is for example intended for a telemetry or anemometry application and, as may be seen in
The method according to the invention works if the various modulation periods have been acquired under distinct interference conditions. This may be achieved “naturally”, for example because of thermal drift in the interferometer or drift in the wavelength of the laser. It may also be stimulated, for example if one of the two interferometer arms includes a system for modulating phase (by about π/2). This phase modulation being low-frequency (typically lower than 10 Hz), it may be achieved simply via a piezoelectric effect or a thermal effect.
The frequency measurement according to the invention allows the AOM found in the examples of the prior art to be omitted. It is based on processing of the beat signal output from the interferometer 2. In this architecture, this beat signal may be written:
x(t)=cos(φ(t)−φ(t−τ)+ψ(t,τ))
where the phase of the laser at the time t is written
φ(t)+ψ(t)
in which expression φ(t) expresses the phase variation associated with the frequency modulation and ψ(t) contains all the terms associated with the average frequency and with the parasitic phase fluctuations (for example stemming from phase noise). ψ(t,τ) is a phase that depends on the variation in optical path between the arms of the interferometer 2 but that fluctuates little on the scale of the period of the frequency modulation. In practice τ varies significantly with respect to λ/c (typically Δτ>10% λ/c, where c is the speed of light and λ the wavelength of the source) but varies little relatively (typically less than 1% i.e. (Δτ/τ)<0.01, Δτ being the variation in T over a plurality of periods T).
Since the frequency f(t) of the laser is proportional to the derivative of the phase:
x(t)=cos(φ(t)−φ(t−τ)+ψ(t,τ))
x(t)=cos(2π∫t-τtf(u)du+ψ(t,τ)
≈ cos(2πτf(t)+ψ(t,τ))
The developed processing aims to isolate the contribution of the frequency f(t) with respect to the phase fluctuations ψ(t, τ), i.e. to remove ψ(t, τ) to within a constant. This processing assumes that the modulation signal is periodic (of period T) and uses two timescales to measure the frequency f(t):
In practice, it is necessary to measure the signal xi(t) over m distinct periods with a long timescale covering a plurality of modulation periods, to obtain:
xi(t)=x(t−kiT) where 1≤i≤m, ki∈,0≤t<T.
The measurements of xi(t) at these times kiT are said to be homologous. The frequency emitted by the laser can be reconstructed only at the end of a plurality of measuring periods spaced apart by a longer timescale.
It is assumed that thermal and ageing effects are sufficiently small, or more generally that the interference conditions are sufficiently stable, for the phase shift ψ(t,τ) between the interferometer arms to remain constant over a modulation period T, i.e.:
ψ(t−kiT,τ)≈cste=ψi for 0<t<T
It is then possible to index the measured time vectors in the form:
xi(t)=cos(2πτf(t−kiT)+ψi)=cos(2πτf(t)+ψi)
and to consider the time-dependent vector: x(t)=(x1(t), . . . , xm(t))T,
the symbol T in the exponent meaning the transpose.
In the two-dimensional case, the vector
x(t)=(x1(t),x2(t))T=(cos(2πτf(t)+ψ1), cos(2πτf(t)+ψ2))T describes an ellipse if ψ1≠ψ2 as illustrated in
The coordinates of the point P are (cos(α(t)+ψ1), cos(α(t)+ψ2)). α can only be determined to within a constant. If a plurality of points P(α) are acquired an ellipse characterized by
ψ2−ψ1
is described, but there is no immediate geometric construction allowing the ellipse of ψ1 and ψ2 to be deduced. In two dimensions, to determine α from all the points of the ellipse, one technique consists in transforming the ellipse into a circle so as to return to a natural definition (i.e. an angle) for α. To do this, the following operations may be carried out:
With these operations, which transform the axes x1 and x2 to A1 and A2,
In the same way, for a dimension m, x(t) must describe an ellipse in a correctly chosen plane of m. On this ellipse, the phase of the point x delivers directly:
α(t)=2πτf(t).
To determine the axis of the ellipse, the covariance matrix: Γ=<x(t)x(t)T> is calculated then diagonalized in order to define the eigenvectors vi and the eigenvalues λi:
Γvi=λivi
In practice, only the 3 largest eigenvalues are non-negligible. Therefore, the projection of x in the sub-space formed by (v1, v2, v3) is calculated, thereby allowing the dimensionality of the problem to be decreased. An example of an experimental result for the path {x(t), 0≤t≤T} of the vector x(t) in this sub-space is presented in
where pw(x) designates the projection of x along the axis w.
By projecting the points x along w0, a slightly elliptical shape is obtained that, after re-normalization, as may be seen from
α(t)≅2πτf(t),
and therefore the frequency over time as illustrated in
It has been possible to simultaneously evaluate various frequencies f(t) in this way, using this technique, for example by implementing a complex frequency f(t) comprising over a given period T a portion that is
Constant
Sinusoidal
Parabolic
Triangular.
A method for treating the signals xi(t) based on organization thereof in a vector form has been described. Other processing methods may be envisaged, such as, for example: an iterative linear regression; a simulated anneal; or recursive, genetic or Monte Carlo algorithms taking into account all of the measurements.
This method may in particular be used to calibrate the frequency of the laser source of a lidar to a setpoint f0(t), without using any AOMs. Such a procedure allows possible drifts in the transfer function of the laser (related to temperature, to the ageing of the diode, etc.) to be avoided. The main calibrating steps described with reference to
A first step consists in defining a linear transformation between the control voltage and the frequency of the laser. This linear transformation may advantageously be obtained by measuring the transfer function of the frequency modulation. This is then done by using a known white noise (for example in a frequency band comprised between 0 and 150 kHz) as the control voltage of the modulation of the form
where the φk are independent random phases, and by measuring the emitted frequency, using the method described above. The modulation transfer function is obtained with the relationship:
The calibrating process is then iterative in order to take into account the (experimentally observed) nonlinearity in this transfer function:
from the frequency setpoint, a first voltage to be applied to the laser diode is calculated using a linear transformation of this setpoint, for example using the modulation transfer function, such that:
U1(t)=TF−1{TF{f0(t)}v×FTM−1(v)};
the emitted frequency f1(t) is measured using the method described above;
the error in frequency with respect to the setpoint Δfi(t)=fi(t)−f0(t) is deduced from the preceding measurement;
this error allows a correction of the control voltage defined from Δfi(t) and the function defined above (for example the FTM) to be defined:
Ui+1(t)=Ui(t)−TF−1{TF{Δfi(t)}v×FTM−1(v)};
the system repeats the preceding 3 points in order to refine the required control voltage and therefore the emitted frequency.
Two iterations generally allow a satisfactory result be obtained and, typically, 3 to 4 iterations are sufficient to achieve the minimal accessible error (i.e. about 1 minute) as illustrated in
These calibrating and measuring methods allow the AOM found in the examples of the prior art to be omitted. However, use thereof is not excluded; specifically an AOM may optionally be added to one of the arms of the interferometer in order to avoid low-frequency noise.
The beat signal may be processed using hardware and/or software elements. This processing may be achieved using a computer-program product stored on a computer-readable medium, this computer program comprising code instructions allowing the steps of the reconstruction method to be carried out. The medium may be electronic, magnetic, optical, electromagnetic or be a storage medium employing infrared. Such media are for example semiconductor memories (random access memories (RAMs), read-only memories (ROMs)), tapes, floppy disks, hard disks or optical disks (compact disc-read-only memory (CD-ROM), compact disc-read/write (CD-R/W) and DVD).
Although the invention has been described with reference to particular embodiments, obviously it is in no way limited thereto and comprises any technical equivalent of the means described and combinations thereof if the latter fall within the scope of the invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 15 00603 | Mar 2015 | FR | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/EP2016/055639 | 3/16/2016 | WO | 00 |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2016/150783 | 9/29/2016 | WO | A |
| Number | Name | Date | Kind |
|---|---|---|---|
| 5808743 | Stephens | Sep 1998 | A |
| 20080317075 | Vanier | Dec 2008 | A1 |
| 20110051763 | Vanier | Mar 2011 | A1 |
| Entry |
|---|
| B. Nowakowski et al., “Development of a Miniature, Multichannel, Extended-Range Fabry-Perot Fiber-Optic Laser Interferometer System for Low Frequency SI-Traceable Displacement Measurement,” Nov. 1, 2014, XP055246904. |
| T. Schwarze et al., “Advanced phasemeter for deep phase modulation interferometry,” Optics Express, vol. 22, No. 15, Jul. 21, 2014, pp. 18214, XP055246228. |
| Number | Date | Country | |
|---|---|---|---|
| 20180073932 A1 | Mar 2018 | US |
