Broadband device for measuring the cross-correlation of signals

Description

Technical field :

[0001] The invention relates to the field of analog processing of optical and radio frequency signals, and more particularly to the analog processing of wideband optical and radio frequency signals using frequency-shifting optical cavities. Previous technique:

[0002] Knowledge of signal cross-correlation is essential in many applications.

[0003] For example, in the field of optics, cross-correlation of signals is used in astronomy (interferometry) and in OCT (Optical Coherent Tomography). In the latter case, a broadband optical signal is sent into a sample. An interferometric setup (Michelson interferometer) combining the incident and backscattered fields on a detector allows the measurement of the delay corresponding to the maximum coherence between the transmitted and reflected waves, thus enabling the determination of the reflector's position. However, this type of setup requires scanning a delay line and therefore involves significant acquisition times.

[0004] In the field of radio frequency (RF) signals, signal correlation is used for many applications.

[0005] For example, in radio astronomy, the correlation of RF signals received by different antennas allows imaging of the source. The problem of correlation in radio astronomy is particularly complex, as the number of signals to be mutually correlated exceeds several dozen. This problem also arises in heterodyne optical interferometry, where the optical signal collected by the telescope is mixed with an optical local oscillator (CW laser) to produce an RF signal. The correlation of the optical fields is then applied to the correlation of the RF signals. Signal correlation can be performed in two ways. The analog method consists of multiplying the two signals (in an RF mixer) to calculate the value of C ( t ) = 〈 s 1 ( t ) s 2 ( t + τ )〉 for a certain value of the delay tand repeat the measurement by varying this delay. This technique is slow, requires a variable RF delay line, is limited by the bandwidth of the RF multipliers ("mixers") - in practice, 20 GHz - and is only suitable for stationary or sufficiently long signals.

[0006] Another way to calculate the correlation of RF signals is to record them and then perform a digital correlation. However, this technique requires significant computing power, especially when the spectral bandwidth of the signal to be analyzed exceeds 1 GHz. Indeed, acquiring the signal at such frequencies requires very complex, expensive, and energy-intensive acquisition (digital-to-analog converters) and processing techniques. It is possible to disperse the signal into smaller spectral bands and perform the correlation operations band by band, but at the cost of added complexity. For example, the ALMA correlator uses 134 million processors simultaneously. Furthermore, the convolution operation must be performed in real time, which requires significant resources.

[0007] Another application of signal correlation is transmitter (or passive radar) localization. By measuring the time delay between two signals emitted by the same source (i.e., by calculating their correlation product), the transmitter's position can be determined through triangulation. In the absence of an analog electronic correlator, the correlation is performed digitally, with the drawbacks described previously (constraints on signal acquisition and processing).

[0008] Another application of analog correlation of RF signals is radar pulse compression using matched filtering. This concept allows, in radar for example, sending a long (and therefore energetic) signal towards a distant target, measuring the return signal, and correlating it with the sent signal. The result of this correlation, as a function of the delay, produces a peak that can be much shorter ("compressed") than the sent signal, thus eliminating background noise. This pulse compression technique can be performed digitally, but again, it is necessary to digitize the signals, which is problematic when their spectral bandwidth exceeds several GHz.

[0009] Alternatively, compression can be achieved by using the property of a Fourier transform of a cross correlation of functions g And f worth: F [ f ★ g ]( u ) = F ( f ( -t )). F ( g ( t )) . Compression is achieved using a suitable filter, namely a spectral filter whose Fourier transform is the time-reversed inverse of one of the signals to be correlated. This technique is possible when the reference signal is known and constant, as implementing a real-time tunable spectral filter is not feasible with current technologies.

[0010] BOURDAROT G. ET AL, Toward a large bandwidth photonic correlator for infrared heterodyne interferometry: A first laboratory proof of concept, Astronomy&Astrophysics, July 2020, Volume 639, Article A53, pages 1 to 7, discloses a device configured to perform a cross correlation of the 2 signals.

[0011] The invention aims to overcome some of the aforementioned problems of the prior art by using two frequency-shifting optical cavities to achieve cross-correlation of two RF or optical signals without requiring scanning and with high bandwidth. Summary of the invention :

[0012] The invention is defined by independent claims 1 and 14. The dependent claims define certain embodiments of the invention. More specifically, an object of the invention is a broadband device for measuring the cross-correlation of a first signal and a second signal, comprising: a first suitable source to generate said first signal s 1 ( t ) ; a second source adapted to generate said second signal s 2 ( t) ; a first frequency-shifting optical cavity comprising a first frequency shifter adapted to shift the optical frequency of the first signal by a first frequency f 1 per round trip in said first cavity, said first cavity having a first travel time t 1; a second frequency-shifting optical cavity comprising a second frequency shifter adapted to shift the optical frequency of the second signal by a second frequency f 2 per round trip in said second cavity, said second cavity having a second travel time t 2; the first and second optical cavities being adapted so that a maximum number of round trips of the first and second signals in the first and second cavities is equal to Na predetermined detector adapted to consistently detect the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generate a photocurrent proportional to a light intensity detected by said detector, a low-pass filter adapted to filter photocurrent frequencies below min f 1 2 f 2 2 , a processor configured to calculate a squared modulus of a Fourier transform of said photocurrent, so as to generate an output signal that is representative of a real-time cross-correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2 ), n ∈ [1, N ] .

[0013] According to particular modes of the invention: The device includes a monochromatic laser, the first and second sources comprising respectively: a first and a second RF source adapted to generate a first and a second RF signal s1(t), s2(t) and a first and a second modulator adapted to modulate in amplitude, by said first and said second RF signal s1(t), a laser beam generated by said continuous laser, so as to form said first and said second signal the first source is configured to generate a plurality of i ∈ [1, p ] first sub-signals s 1 ,i ( t ) superimposed spatially and temporally to form the first signal, each first i sub-signal having a first center frequency f 1, i distinct from the others, and in which the second source is configured to generate a plurality of j ∈ [1 , q ] second sub-signals s 2, i (t ) superimposed spatially and temporally to form the second signal, each j second sub-signal presenting a second center frequency f 2, i distinct from the others, the said output signal then being a cross-correlation of each first sub-signal with each second sub-signal, C i , j τ = s 1 , i t s 2 , j ∗ t − τ , with t = n ( t 1 - t 2 ) , n ∈ [1, N The first and second cavities are adapted to check the condition. f 1 × t 1 = f 2 × t 2, modulo 1, said processor being then configured to calculate a Fourier transform of said photocurrent, so as to generate an output signal which is the real part of a real-time cross-correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2), n ∈ [1, N] ; the first and second cavities are adapted so that f 1 × t 1 ≠ f 2 × t 2 modulo 1, said processor being further configured to calculate a square modulus of a Fourier transform of said photocurrent, the output signal (SS) then corresponding to a square modulus of a real-time cross correlation between the first signal and the second signal, C τ 2 = s 1 t s 2 ∗ t − τ 2 , with t = n ( t 1 - t 2), n ∈ [1, NThe first and second cavities comprise, respectively, a first and a second amplifier adapted to compensate for the losses induced by the first and second cavities; the first frequency shifter is a first acousto-optical modulator excited by a first local oscillator adapted to vary said first shift frequency, and wherein the second frequency shifter is a second acousto-optical modulator excited by a second local oscillator adapted to vary said second shift frequency; the first cavity comprises a first controllable delay line adapted to vary the first travel time. t 1 and wherein the second cavity comprises a second controllable delay line adapted to vary the second travel time t2; the first and second cavities are ring-fiber cavities comprising respectively a first and second doped fiber amplifier and a first and second bandpass optical filters configured to fix said maximum number N of round trips in the first and second cavities;The device includes stabilization means for the first and second cavities adapted to maintain over time the coherence of said first signal transmitted by the first cavity with said second signal transmitted by the second cavity. The device includes a single ring cavity, said device further comprising: a first coupler (adapted to inject said first signal into said single cavity in a first direction), a second coupler (adapted to inject said second signal into said single cavity in a second direction), said first cavity corresponding to the single cavity into which the first signal is injected in the first direction of injection, said second cavity corresponding to the single cavity into which the second signal is injected in the second direction of injection. said single ring-shaped cavity comprising: a first circulator adapted to direct the first signal to a first controllable delay line adapted to vary the first travel time t 1 and comprising said first frequency shifter a second circulator adapted to direct the second signal to a second controllable delay line adapted to vary the second travel time t 1 comprising said second frequency shifter, a doped fiber amplifier, and a bandpass optical filter configured to fix said maximum number N of round trips the first and second cavities are configured so that 1 τ 1 − τ 2 ≥ 40 GHz ; the first and second cavities are configured so that N is greater than 200

[0014] Another object of the invention is a method for measuring the cross-correlation of a first and a second signal using a first frequency-shifting optical cavity having a first travel time t 1 and a second frequency-shifting optical cavity comprising a second frequency shifter having a second travel time t 2, a maximum number of round trips of the first signal and the second in the first and second cavity being equal to N predetermined, said method comprising the following steps: A. generate said first signal s 1 ( t ) and said second signal s 2 ( t B. inject said first signal into the first frequency-shifting optical cavity and shift the optical frequency of the first signal by a first frequency f 1. By passing the signal back and forth through said first cavity, inject said second signal into the second frequency-shifting optical cavity and shift the optical frequency of the second signal by a second frequency. f2 by round trip in said second cavity; C. coherently detect the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generate the photocurrent proportional to the detected light intensity, a maximum number of round trips of the first and second signals in the first and second cavities respectively before they are transmitted, being equal to a predetermined N, and D. filter out photocurrent frequencies below min f 1 2 f 2 2 E. Calculate the squared magnitude of a Fourier transform of said filtered photocurrent, so as to generate an output signal that is representative of a real-time cross-correlation between the first signal and the second signal. C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2), n ∈ [1, N ]. Brève description des figures :

[0015] Other features, details and advantages of the invention will become apparent from the description provided with reference to the accompanying drawings given by way of example, which represent, respectively: There figure 1 , a schematic view of a broadband cross-correlation measurement device according to the invention, The figure 2 , a schematic view of a broadband cross-correlation measurement device according to a first embodiment of the invention, The figure 3 , a schematic view of a broadband cross-correlation measurement device according to a second embodiment of the invention The figure 4 , a schematic view of a broadband cross-correlation measurement device according to a third embodiment of the invention The figure 5 , a method for measuring cross-correlation according to the invention The figure 6, a schematic view of a broadband cross-correlation measurement device according to a fourth embodiment of the invention

[0016] References to figures, when they are identical, correspond to the same elements.

[0017] References to figures, when they are identical, correspond to the same elements.

[0018] In the figures, unless otherwise indicated, the elements are not to scale. Detailed description:

[0019] There figure 1Figure D is a schematic representation of a device for measuring the cross-correlation of signals according to the invention. As will be explained later, thanks to a first frequency-shifting optical cavity BDF1 and a second frequency-shifting optical cavity BDF2, the device D of the invention makes it possible to determine a frequency-space representation of the squared magnitude of the cross-correlation of two or more signals. Furthermore, by means of a particular condition linking these cavities, the device of the invention makes it possible to determine a frequency-space representation of the cross-correlation of two or more signals.

[0020] By "broadband," we mean that the device's bandwidth is greater than or equal to 20 GHz, preferably greater than or equal to 40 GHz. The parameters controlling the device's bandwidth will be specified later in the description.

[0021] The device D of the invention comprises a first radiation source S1 adapted to generate a first signal of interest s 1 ( t ) Si1 and a second radiation source S2 adapted to generate a second signal of interest s 2 ( t ) Si2.

[0022] The first signal Si1 is injected into the first frequency-shifting optical cavity BDF1. This cavity BDF1 has a first travel time t 1 (round-trip time in the cavity) and includes a first frequency shifter AOM1 adapted to shift the optical frequency of the first signal by a first frequency f 1 round trip in the first cavity.

[0023] Similarly, the second signal Si2 is injected into the second frequency-shifting optical cavity BDF2, which has a second travel time. t2 and which includes a second AOM2 frequency shifter adapted to shift the optical frequency of the second signal by a second frequency f 2 per round trip in the second cavity.

[0024] The first optical cavity BDF1 and the second optical cavity BDF2 can be indifferently and without departing from the scope of the invention a linear cavity or a ring cavity, and a free space cavity or a fiber cavity.

[0025] Essentially, the first and second optical cavities are adapted so that the maximum number of round trips of the signal in the first and second cavities is equal to a number N predetermined. Thus, by calling f 0, the center frequency of the signal of interest, the first and second cavities each generate a frequency comb comprising respectively the frequencies f 0 + n × f 1 and f 0 + n × f2, with n ∈ [1; N ] . In concrete terms, the first and second cavities produce replicas of the signal of interest, shifted both temporally (by multiples of t 1 and τ 2 respectively), and in frequency (multiples of f 1 and f 2 respectively).

[0026] According to one embodiment, in order to control this maximum number of round trips N, the first and second loops include respectively a first and second bandpass filter BP1, BP2 (not shown in figure 1 but visible in figure 3 And 4 ), with a bandwidth adapted to transmit the frequencies respectively f 0 + n × f 1 and f 0 + n × f 2 , with n E [1; N].

[0027] The first frequency shifter AOM1 and the second frequency shifter AOM2 are preferably acousto-optic modulators controlled by a first local oscillator (OL1) and a second local oscillator (OL2) (not shown in the figures). The excitation frequency generated by the first and second local oscillators allows the first frequency to be varied. f 1 and the second frequency f 2. Alternatively, the first and second frequency shifters are single sideband electro-optical modulators (or SSB MZM, for single sideband Mach Zehnder modulator).

[0028] Device D further includes a PD detector adapted to coherently detect the first signal Si1 transmitted by the first cavity and the second signal Si2 transmitted by the second cavity. The PD detector is typically a photodiode or any other photodetector known to those skilled in the art. Preferably, the PD detector is formed by balanced photodiodes in order to detect very small variations in the light signal.

[0029] This PD detector detects in real time a light intensity that corresponds to the coherent summation of all the replicas of the signal of interest, shifted both temporally and in frequency (the frequency shifts), by the first and second cavities, and then generates a photocurrent Tr proportional to this detected light intensity. For the device to function, it is essential that the first signal Si1 transmitted by BDF1 be coherent with the signal Si2 transmitted by BDF2.

[0030] The photocurrent Tr is then filtered by an analog low-pass filter LP adapted to allow photocurrent frequencies lower than the Nyquist frequencies associated with the first signal Si1 and the second signal Si2 to pass through, i.e. min( f 1 / 2; f 2 / 2)

[0031] Finally, device D includes a UT processor configured to calculate a Fourier transform (FT) of the photocurrent filtered by the LP filter, thus generating an output signal SS. Through this output signal, device D allows the determination of a frequency representation of the cross correlation of s 1 ( t ) with s 2 ( t ) sampled by N points. More precisely, SS is representative of a real-time cross-correlation between the first signal and the second signal, i.e. C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2 ) = n. Δ n, n ∈ [1,N ] .

[0032] Indeed, the inventors have demonstrated that the photocurrent Tr is expressed in the following form: I t = ∑ n C t nΔτ e − i 2 πnΔft e − iπ f 1 τ 1 − f 2 τ 2 n 2

[0033] According to a first embodiment of the invention, the first and second cavities are adapted to verify the condition f 1 × t 1 = f 2 × t 2 modulo 1. In this first variant, the output signal SS then corresponds to the real part of a real-time cross-correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with t = n (τ 1 - t 2), n ∈ [1 , N ] . The Fourier transform of the photocurrent Tr thus allows direct access to the real part of the cross-correlation function, at time t, between Si1 and Si2 sampled by N points by a step Δ t = ( t 1 - t 2), or I̅ ( n Δ f, t ) ∝C ( t, n Δ t ) .

[0034] According to a second embodiment of the invention, the first and second cavities are adapted so that f 1 × t 1 ≠ f 2 × t 2 modulo 1. The processor is then configured to calculate a square modulus of a Fourier transform of the photocurrent Tr, the output signal SS then corresponding to a square modulus of a real-time cross-correlation between the first signal and the second signal, C τ 2 = s 1 t s 2 ∗ t − τ 2 , with t = n ( t 1 - t 2 ), n E [1,N]. The squared magnitude of the photocurrent Fourier transform Tr thus allows access to the squared magnitude of the cross-correlation function at time t, between Si1 and Si2 sampled by N points by a step Δ t = ( t 1 - t 2).

[0035] For the sake of clarity, the development of the equations explaining these results is presented at the end of this description.

[0036] An important advantage of the device of the invention is that it allows the real part of the cross correlation (or the squared magnitude of the cross correlation) of two signals to be measured instantaneously, sampled by N points without needing to scan a delay line. Acquisition is therefore faster and avoids potential problems related to signal fluctuations during acquisition. In the invention, the signals do not need to be stationary. Furthermore, the invention allows the cross-correlation function to be obtained by a simple Fourier transform of a relatively slow signal (sampled at less than a few tens of MS / s), an operation that is not computationally expensive.

[0037] For the sake of brevity, in the remainder of this document, we will simply say that the device measures the cross-correlation of two signals. It is understood that this sentence covers the first variant of the invention and the specific case where f 1 × t 1 = f 2 × t 2, modulo 1, and the processor generates an output signal that corresponds to the real part of the cross correlation, and the second variant of the invention, namely the more general case where f 1 × t 1 ≠ f 2 × t 2, modulo 1 and the processor generates an output signal that corresponds to the square modulus of the cross correlation.

[0038] Preferably, the LP low-pass filter is suitable for filtering photocurrent frequencies below a min value[ N × | f 1 - f 2 | ; f 1 / 2; f2 / 2)], before the calculation of the photocurrent TF by the UT processor. Filtering of frequencies below N × | f 1 - f 2 | allows, if this value is lower than the Nyquist frequencies f 1 / 2; f 2 / 2, to process the photocurrent Tr with a processor including slower processing electronics (typically 50 Mech / s).

[0039] The temporal resolution of the device (that is, the time it takes the system to calculate and produce the correlation function) is equal to t 1 - - t 2. Note that the data is obtained in real time, meaning that the determined cross-correlation function is updated every period t 1- t 2. In device D of the invention, the bandwidth is equal to LS in = 1 / ( t 1 - t 2). This characteristic is very interesting because by minimizing the difference t1 - t 2, it is possible to maximize the bandwidth of device D. Thus, according to one embodiment, the temporal resolution is less than ten picoseconds, which allows the correlation of signals with spectral widths of several tens of GHz. Alternatively, according to another embodiment, t 1 - t 2 is worth a few hundred microseconds, to allow the correlation of spectrally fine signals (typically a few MHz).

[0040] Furthermore, the temporal resolution t 1 - t 2 also corresponds to the sampling period of the cross correlation function C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2), n ∈ [1 , N ] .Preferably, in order to sample the cross-correlation function with enough points, the first and second cavities are configured so that a maximum number of round trips N is greater than 200, preferably greater than 500.

[0041] According to one embodiment, the first cavity includes a first delay line DL1 (not shown) controllable and adapted to vary the first travel time t 1 and / or the second cavity includes a first DL2 delay line (not shown) controllable and adapted to vary the second travel time t 2. Thus, it is possible to control the difference ( t 1 - t 2) in order to control the temporal resolution and bandwidth LS in of device D. Preferably, the difference ( t 1 - t 2) is such that the bandwidth LS inis greater than or equal to 20 GHz, preferably greater than or equal to 40 GHz.

[0042] An advantage of embodiments of the invention includes delay lines DL1, DL2 and / or frequency shifters AOM1, AOM2 which allow for varying f 1 and f 2 is therefore to allow control of the scale of the correlation function (fixed by Δ f / Δ t, with Δ f = f 1 - f 2) and easily verify the condition f 1 × t 1 = f 2 × t 2 while maximizing bandwidth.

[0043] It is noted that in embodiments of the invention in which the first and second cavities BDF1, BDF2 respectively comprise a first and second bandpass filter BP1, BP2, the bandwidth LS in is equal to a spectral width LS BP of the first and second bandpass filters when this spectral width LS BPis less than 1 / ( t 1 - t 2). In other words, the bandwidth is equal to LS in = min(1 / ( t 1 - t 2); LS BP ).

[0044] According to one embodiment, the first and second cavities comprise respectively a first and second amplifier EDFA1, EDFA2 (not shown in figure 1 but visible in figure 4 ) adapted to compensate for the losses induced by the first and second cavities.

[0045] According to a first embodiment of the invention, illustrated in figure2 The first source S1 comprises a first monochromatic continuous wave laser CW1, a first source AM1 adapted to generate a first RF signal s 1 ( t ) , and a first Mod1 modulator adapted to modulate in amplitude, by the first RF signal s 1 ( t ) ,The laser radiation generated by the first continuous laser is used to form the first signal of interest. Similarly, the second source S2 comprises a second monochromatic continuous laser CW2 and a second source AM2 adapted to generate a second RF signal. s 2 ( t ) , and a second Mod2 modulator adapted to modulate in amplitude, by the second RF signal s 2 ( t ), the laser radiation generated by the second continuous laser so as to form the second signal of interest. Alternatively, the device comprises a single monochromatic laser amplitude modulated by the first and second RF sources so as to form the first and second signals of interest respectively.

[0046] In the first embodiment of the invention, the device D allows the cross-correlation of the first signal of interest to be determined with the second signal of interest. When the first and second lasers CW1, CW2 have a coherence time sufficiently long for the laser radiation to remain coherent within the cavities BDF1, BDF2 respectively (typically on the order of a hundred µs), then the output signal SS is the cross-correlation of the first RF signal s 1 ( t ) with the second RF signal s 2 ( t ) sampled by N points with a step t 1 - t 2. This first embodiment is particularly interesting given the bandwidth LS inof the device which can be greater than 40 GHz while obtaining a cross correlation function with a very short acquisition time, these values ​​not being unattainable by prior art devices performing cross correlation of RF signals.

[0047] In a second embodiment, the first and second sources S1, S2 are optical sources generating a first and a second signal of interest Si1, Si2 in the form of light radiation. s 1 ( t ) , s 2 ( t ) for example a laser source. In the second embodiment of the invention, the device D makes it possible to determine a cross-correlation of the first signal with the second signal sampled by N points with a step t 1 - t 2.

[0048] There figure 3This schematically illustrates a third embodiment, compatible with the first and second embodiments, in which the entire optical path of the first and second signals of interest Si2, Si2 from the source S1, S2 to the photodiode detection point is fiber-connected. This simplifies the alignment of the device and reduces its sensitivity to shocks and vibrations. In this third embodiment, the first and second cavities BDF1, BDF2 are ring-fiber-connected cavities comprising, respectively, a first and second doped fiber amplifier EDFA1, EDFA2 and a first and second bandpass optical filter BP1, BP2. The first signal Si1 is injected into the first cavity BDF1 via a fiber coupler C1, and the second signal Si2 is injected into the second cavity BDF2 via a fiber coupler C2.

[0049] As explained previously, the first and second doped fiber amplifiers EDFA1, EDFA2, for example Erbium Doped Fiber Amplifiers (EDFAs), are adapted to compensate for the losses induced in the cavities BDF1, BDF2. The bandpass optical filters BP1, BP2 are configured to fix the maximum number N of round trips in the first and second cavities and to limit the noise arising from the amplified spontaneous emission of the doped fiber amplifiers.

[0050] Advantageously, in the third embodiment, the device D includes stabilization means ST (not shown) for the first and second cavities BDF1, BDF2, adapted to maintain coherence over time between the first signal transmitted by the first cavity and the second signal transmitted by the second cavity. The stabilization device ensures that the radiation transmitted by the two cavities BDF1, BDF2 is mutually coherent. Such a device is well known to those skilled in the art and is described, for example, in "Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs," Opt. Express 26, 13800-13809 (2018).

[0051] There figure 4This schematically illustrates a fourth embodiment, compatible with the first and second embodiments, which constitutes an alternative to the third embodiment. This fourth embodiment aims to overcome the problem of maintaining coherence over time between the first signal Si1 and the second signal Si2 transmitted by the first and second cavities. To this end, the device comprises a single fiber ring cavity BDF configured to form the first and second cavities BDF1 and BDF2, depending on the injection direction. This single counter-propagating ring cavity configuration limits the effects of fiber length fluctuations (vibrations, thermal drift, etc.) which can differ between the first and second cavities of the third embodiment, and which lead to a loss of coherence with each round trip. It also reduces the number of optical components required.

[0052] Similar to the third embodiment, in device D of the fourth embodiment, the entire optical path of the signal of interest from the first and second sources S1, S2 to the photodiode detection point is fiber-connected. Device D includes a first fiber-connected coupler C1 adapted to inject the first signal Si1 into the single cavity BDF in a first direction. S 1. In addition, device D includes a second fiber coupler C2 adapted to inject the second signal Si2 into the single cavity BDF in a second direction S 2. The BDF cavity comprises: a first circulator CO1 adapted to direct the first signal Si1 to a first delay line DL1 comprising the first frequency shifter AOM1; a second circulator CO2 adapted to direct the second signal Si2 to the second delay line DL2 comprising the second frequency shifter AOM2; a bidirectional (operating in both directions) EDFA-doped fiber amplifier; a bandpass optical filter BP configured to fix the maximum number N of round trips. Thus, the first cavity BDF1 corresponds to the single cavity BDF into which the first signal Si1 is injected in the first injection direction. S 1 and the second cavity BDF2 corresponds to the single cavity BDF into which the second signal Si2 is injected according to the second injection direction S 2.

[0053] Alternatively, according to a variant of the fourth embodiment, instead of a single EDFA amplifier and a single BP bandpass optical filter common to the first signal Si1 and the second signal Si2, the first delay line DL1 comprises a first EDFA amplifier1 and a BP bandpass optical filter1 and the second delay line DL1 comprises a second EDFA amplifier2 and a BP bandpass optical filter2.

[0054] Another object of the invention is a method for measuring the real part or the squared modulus of the cross correlation of a first and a second signal of interest, implemented by the device D of the invention. figure 5 illustrates this method schematically.

[0055] The method of figure 5 includes the following steps: A. Generate the first and second signals of interest Si1, Si2; B. Inject the first signal Si1 into the first frequency-shifting optical cavity BDF1 and shift the optical frequency of the first signal by a first frequency f 1. By round trip in the first cavity, and inject the second signal into the second optical cavity with frequency shift BDF2 and shift the optical frequency of the second signal Si2 by a second frequency f 2. by round trip in the second cavity; C. coherently detect the sum of the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generate the photocurrent Tr proportional to the detected light intensity; D. filter out photocurrent frequencies lower than min f 1 2 f 2 2 E. Calculate the Fourier transform of the filtered photocurrent, so as to generate the output signal SS which is representative in the frequency space of the real-time cross-correlation between the first signal and the second signal. C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2 ), n ∈ [1, N ].

[0056] The method of figure 5 has the notable advantage of being broadband and not requiring scanning to sample the cross correlation function.

[0057] According to a first variant of the method of the figure 5 The first and second cavities are adapted to check the condition f 1 × t 1 = f 2 × t2, modulo 1 and step E then consists of calculating a Fourier transform of said photocurrent, so as to generate an output signal SS which is the real part of a real-time cross correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with t = n ( t 1 - t 2), n ∈ [1, N ].

[0058] According to a second variant of the method of the figure 5 The first and second cavities are adapted so that f 1 × t 1 ≠ f 2 × t 2 modulo 1, step E further comprising the calculation of the square modulus of a Fourier transform of said photocurrent, the output signal SS then corresponding to a square modulus of a real-time cross correlation between the first signal and the second signal, C τ 2 = s 1 t s 2 ∗ t − τ 2 , with t = n ( t 1 - t 2), n ∈ [1 , N ] .

[0059] There figure 6 presents a fifth embodiment in which the first source S1 is configured to generate a plurality of i ∈ [1, p ] first sub-signals s 1 ,i ( t ) superimposed spatially and temporally to form the first signal Si1, each i first sub-signal presenting a first center frequency f 1, i distinct from the others. Similarly, the second source is configured to generate a plurality of j ∈ [1, q ] second sub-signals s 2, i ( t ) superimposed spatially and temporally to form the second signal, each j second sub-signal presenting a second center frequency f 2, i distinct from the others. Thus, the SS output signal is a cross-correlation of each first sub-signal with each second sub-signal, C i , j τ = s 1 , i t s 2 , j ∗ t − τ , with t = n ( t 1 - t 2 ), n ∈ [1 , N ] . Preferably, the integration time, the first central frequencies f 1, i and the second central frequencies f 2, i and the parameters t 1, t 2 are adapted so that there is no overlap between the different cross-correlation functions C i , j τ = s 1 , i t s 2 , j ∗ t − τ , with t = n ( t 1 - t 2 ), n ∈ [1 , N ] .

[0060] It is understood that these first and second sub-signals can be either optical signals as in the second embodiment of the invention or RF signals amplitude modulating a continuous CW laser radiation as in the first embodiment of the invention.

[0061] The use of a large number of signals of interest is particularly interesting in applications in optical interferometry and radio astronomy in which it is crucial to correlate several signals in order to locate the position of a transmitter.

[0062] The equations demonstrating that the output signal SS is the cross-correlation function of Si1 and Si2 are developed below.

[0063] We note t 0 is the frequency of the injection laser, t 1, t 2. The travel times in the loops, f 1 , f 2. The shift frequencies per revolution, s 1 ( t ) the first signal of interest and s 2 ( t ) the second signal of interest.

[0064] The electric fields at the output of the first and second cavities are respectively: E 1 t = ∑ n = 0 N s 1 t − nτ 1 E 0 e i 2 πf 0 t e i 2 πnf 1 t e − iπf 1 τ 1 n 2 E 2 t = ∑ n = 0 N s 2 t − nτ 2 E 0 e i 2 πf 0 t e i 2 πnf 2 t e − iπf 2 τ 2 n 2

[0065] The intensity detected by PD is: I t = w t ∗ E 1 t E 2 ∗ t Orw ( t ) is a time window centered in t (related to the detection response) and * is the convolution product. Omitting the term E 0 E 0 ∗ we have I t = w t ∗ ∑ n , m s 1 t − nτ 1 s 2 t − mτ 2 e i 2 π nf 1 − mf 2 e − iπ f 1 τ 1 n 2 − f 2 τ 2 m 2 I t = ∫ w t − t ′ ∑ n , m s 1 t ′ − nτ 1 s 2 t ′ − mτ 2 e i 2 π nf 1 − mf 2 t ′ e − iπ f 1 τ 1 n 2 − f 2 τ 2 m 2 dt ′

[0066] We choose the frequencies f 1 and f 2 such that Δ f = f 2 - f 1 ≤ f 1 / 2 N, f 2 / 2 N. The duration of the window w(t) is chosen to be on the order of 1 / N Δ f. It is therefore greater than 2 / f 1 and 2 / f 1. Thus, only pairs of integers ( n, m = n ) have a non-zero contribution in the integral.

[0067] It is assumed here that f 1 -t 1 = f 2 t 2. We then have: I t = ∫ w t − τ ′ ∑ n s 1 t ′ − nτ 1 s 2 t ′ − nτ 2 e − i 2 πn Δ ft ′ dt ′

[0068] Over the duration of the window, e -i2πnΔft'< can be likened to e -i2πn Δ feetbecause the window duration is shorter than the function period e -i2πn Δ< ft'< .

[0069] Thus we have: I t = ∑ n e − i 2 πn Δ ft ∫ w t − t ′ s 1 t ′ − nτ 1 s 2 t ′ − nτ 2 dt ′ I t = ∑ n s 1 t − nτ 1 s 2 t − nτ 2 e − i 2 πn Δ ft where <> represents the average measured over the duration of the window.

[0070] By shifting the origin of time, we have I t = ∑ n s 1 t s 2 t − n Δ τ e − i 2 πn Δ ft where Δ t = t 2 - t 1 . We define the cross-correlation function at time t for the delay T : C ( t, T ) = < s 1 ( t ) s 2 ( t - T ) >.

[0071] In other words: I t = ∑ n C t , n Δ τ e − i 2 πn Δ ft e − iπ f 1 τ 1 − f 2 τ 2 n 2

[0072] The values ​​of the Fourier transform of I ( t ) at frequencies n Δ f, are : I ˜ n Δ f , t ∝ C t , n Δ τ e − iπ f 1 τ 1 − f 2 τ 2 n 2

[0073] If the system is set up so that f 1 t 1 = f 2 t 2, then I ˜ n Δ f , t ∝ C t , n Δ τ which allows access to the real part of the cross-correlation function at that instant t .

[0074] Note that this result is valid when for all f 1 t 1 = f 2 t 2 modulo 1 (see equation 5). By modulo 1, we mean here f 1 t 1 = f 2 t 2 + k, with k ∈ ℕ .

[0075] Otherwise, in the general case, that is to say f 1 t 1 ≠ f 2 t 2, modulo 1 the square moduli of the Fourier transform of I ( t ) at frequencies n Δ f, are : I ˜ n Δ f , t 2 ∝ C t , n Δ τ 2 which allows access to the squared modulus of the cross-correlation function at that instant t .

[0076] The system thus allows the calculation, within the photodetection signal spectrum, of the cross-correlation function of the input signals as a function of their temporal delay. This yields a time-to-frequency mapping. The coefficient of this mapping is simply Δ f / Δ t.

[0077] The time step of the correlation function is Δ t The range of accessible delays is N Δ t.

Claims

1. A wideband device (D) for measuring the cross-correlation of a first signal and a second signal, comprising: - a first source (S1) designed to generate said first signal s1(t) (Si1); - a second source (S2) designed to generate said second signal s2(t) (Si2); - a first frequency-shifting optical cavity (DBDF, BDF1) comprising a first frequency shifter (AOM1) designed to shift the optical frequency of the first signal by a first frequency f1 per round trip in said first cavity, said first cavity having a first trip time τ1 ; - a second frequency-shifting optical cavity (DBDF, BDF2) comprising a second frequency shifter (AOM1) designed to shift the optical frequency of the second signal by a second frequency f2 per round trip in said second cavity, said second cavity having a second trip time τ2 ; the first and the second optical cavity being designed such that a maximum number of round trips of the first and the second signal in the first and the second cavity is equal to predetermined N - a detector (PD) designed to coherently detect the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generate a photocurrent (Tr) proportional to a luminous intensity detected by said detector, - a low-pass filter (LP) designed to filter frequencies of the photocurrent that are lower than min f 1 2 f 2 2 , - a processor (UT) configured to compute a Fourier transform of said photocurrent filtered by said low-pass filter, so as to generate an output signal (SS) representative, in the frequency space, of a real-time cross-correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with τ = n(τ1 - τ2), n ∈ [1, N].

2. The device as claimed in claim 1, wherein the device comprises a monochromatic laser (CW), the first and the second sources respectively comprising: a first and a second RF source (AM1, AM2) designed to generate a first and a second RF signal s1(t), s2(t) and a first and a second modulator (Mod1, Mod2) designed to amplitude-modulate, using said first and said second RF signal s1(t), laser radiation generated by said continuous-wave laser, so as to form said first and said second signal.

3. The device as claimed in claim 1 or 2, wherein the first source is configured to generate a plurality of i ∈ [1, p] first sub-signals s1,i(t) that are spatially and temporally superposed so as to form the first signal, each i first sub-signal having a first center frequency f1,i different from the others, and wherein the second source is configured to generate a plurality of j ∈ [1, q] second sub-signals s2,j(t) that are spatially and temporally superposed so as to form the second signal, each j second sub-signal having a second center frequency f2,i different from the others, said output signal then being representative of a cross-correlation of each first sub-signal with each second sub-signal, C i , j τ = s 1 , i t s 2 , j ∗ t − τ , with τ = n(τ1 - τ2), n ∈ [1, N].

4. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are designed to verify the condition f1 × τ1 = f2 × τ2 modulo 1, said output signal (SS) then corresponding to the real part of a real-time cross-correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with τ = n(τ1 - τ2), n ∈ [1, N].

5. The device as claimed in any one of claims 1 to 3, wherein the first and the second cavity are designed such that f1 x τ1 ≠ f2 × τ2 modulo 1, said processor furthermore being configured to compute a square modulus of a Fourier transform of said photocurrent, the output signal (SS) then corresponding to a square modulus of a real-time cross-correlation between the first signal and the second signal, C τ 2 = s 1 t s 2 ∗ t − τ 2 , with τ = n(τ1 - τ2), n ∈ [1, N].

6. The device as claimed in any one of the preceding claims, wherein the first and the second cavity respectively comprise a first and a second amplifier (EDFA, EDFA1, EDFA2) designed to compensate for the losses induced respectively by the first and the second cavity.

7. The device as claimed in any one of the preceding claims, wherein the first frequency shifter is a first acousto-optic modulator excited by a first local oscillator (OL1) designed to vary said first shift frequency and wherein the second frequency shifter is a second acousto-optic modulator excited by a second local oscillator (OL2) designed to vary said second shift frequency.

8. The device as claimed in any one of the preceding claims, wherein the first cavity comprises a first controllable delay line (DL1) designed to vary the first trip time τ1 and wherein the second cavity comprises a second controllable delay line (DL2) designed to vary the second trip time τ2.

9. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are fiber ring cavities (BDF1, BDF2) comprising respectively a first and a second doped fiber amplifier (DFA1, DFA2) and a first and a second optical bandpass filter (BP1, BP2) configured to set said maximum number N of round trips in the first and the second cavity.

10. The device as claimed in the preceding claim, comprising stabilizing means (ST) for stabilizing the first and the second cavity that are designed to maintain, over time, the coherence of said first signal transmitted by the first cavity with said second signal transmitted by the second cavity.

11. The device as claimed in claim 7, comprising a single ring cavity (BDF), said device furthermore comprising: - a first coupler (C1) designed to inject said first signal (V1) into said single cavity in a first direction, - a second coupler (C2) designed to inject said second signal (V2) into said single cavity in a second direction, said first cavity corresponding to the single cavity into which the first signal is injected in the first injection direction, said second cavity corresponding to the single cavity into which the second signal is injected in the second injection direction, said single ring cavity comprising: ∘ a first circulator (CO1) designed to direct the first signal to a first controllable delay line (DL1) designed to vary the first trip time τ1 and comprising said first frequency shifter (AOM1), ∘ a second circulator (CO2) designed to direct the second signal to a second controllable delay line (DL2) designed to vary the second trip timeτ1 and comprising said second frequency shifter (AOM2), ∘ a doped fiber amplifier (DFA), ∘ an optical bandpass filter (BP) configured to set said maximum number N of round trips.

12. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are configured such that 1 τ 1 − τ 2 ≥ 40 GHz.

13. The device as claimed in any one of the preceding claims, wherein the first and the second cavity are configured such that N is greater than 200.

14. A method for measuring the cross-correlation of a first and a second signal (Si1, Si2) using a first frequency-shifting optical cavity (BDF1) having a first trip time τ1 and a second frequency-shifting optical cavity (BDF2) comprising a second frequency shifter (AOM1) having a second trip time τ2, a maximum number of round trips of the first signal and of the second in the first and the second cavity being equal to predetermined N, said method comprising the following steps: F. generating said first signal s1(t) and said second signal s2(t); G. injecting said first signal into the first frequency-shifting optical cavity (BDF1) and shifting the optical frequency of the first signal by a first frequency f1 per round trip in said first cavity, injecting said second signal into the second frequency-shifting optical cavity (BDF2) and shifting the optical frequency of the second signal by a second frequency f2 per round trip in said second cavity; H. coherently detecting the first signal transmitted by the first cavity and the second signal transmitted by the second cavity and generating the photocurrent (Tr) proportional to the detected luminous intensity, a maximum number of round trips of the first and the second signal respectively in the first and the second cavity before they are transmitted being equal to predetermined N, and I. filtering frequencies of the photocurrent that are lower than min f 1 2 f 2 2 , J. computing a Fourier transform of said filtered photocurrent, so as to generate an output signal (SS) that is representative of a real-time cross-correlation between the first signal and the second signal, C τ = s 1 t s 2 ∗ t − τ , with τ = n(τ1 - τ2), n ∈ [1, N].