WO2020071914A1

WO2020071914A1 - Interrogation of an optical sensor array

Info

Publication number: WO2020071914A1
Application number: PCT/NL2019/050662
Authority: WO
Inventors: Aurèle Joseph Louis ADAM; Fellipe GRILLO PETERNELLA; Hendrik Paul URBACH
Original assignee: Technische Universiteit Delft
Current assignee: Technische Universiteit Delft
Priority date: 2018-10-05
Filing date: 2019-10-03
Publication date: 2020-04-09
Anticipated expiration: 2021-04-05
Also published as: NL2021771B1

Abstract

Anew interrogation method based on integrated Fourier transform spectroscopy is disclosed. The integrated Fourier Transform spectrometer comprises a planar spatial heterodyne spectrometer based on Fourier transform (SHS-FT). Further, the spectrometer is implemented using an array of Mach-Zehnder interferometers(MZI). The integrated FT spectrometer is implemented as a3x3 multi-mode interferometer allowing phase detection of each MZI of the array of MZIs and having an increased signal to noise ratio (SNR). The interrogator comprises a photodetector array integrated on the device, which further enhances the SNR, since no losses are present in decoupling light from the chip.

Description

Interrogation of an optical sensor array

Field of the invention

The invention relates to interrogation of an optical sensor array, and, in particular, though not exclusively, to interrogation systems for interrogation of an optical sensor array based and to methods for interrogating such optical sensor array.

Background of the invention

Nowadays, photonic sensors are used in a wide range of applications.

Acoustic and ultrasound sensors, pressure sensors, biochemical and gas sensors are examples of sensors developed based on optical technology. The sensors are cheap, immune to electromagnetic radiation and operate under a wide range of temperatures.

Moreover, it is easy to build large arrays of optical sensor. Typically, optical sensors such as fiber Bragg gratings (FBGs) can be arranged in an array wherein each optical sensor is configured to respond at a certain wavelength to external excitations, e.g. a change in temperature or the like. Alternatively, arrays of integrated sensors, such as an array of ring resonators may be fabricated in the same chip, each of them responding to a different external excitation. The optical responses of the sensors are multiplexed into one optical sensor signal and send via e.g. an optical fiber to an optical interrogation system for demultiplexing the optical sensor signal into individual sensor responses.

Different methods for interrogating such optical sensor arrays are known. One well-known approach is demultiplexing an optical sensor signal of the sensor array using a dispersive spectrometer such as an arrayed waveguide grating (AWG) or an etchelle.

Another approach is the so-called edge filtering technique, wherein the reflection of the FBGs is conveyed to an optical filter with a known transmission which is linear in the operation range of the sensor. The main drawback of this approach is the trade-off between the sensitivity and the operation range. Yet another known interrogation method is to use a passive interferometer such as a Mach Zehnder interferometer (MZI). An MZI can be used in combination with a demultiplexing element, such as an AWG, to interrogate an array of optical sensors such as an array of FBGs. Typically, the optical elements for interrogating the sensor arrays, i.e. the MZIs and interferometers, are integrated into a photonic chip. Despite the high resolution that can be achieved using this method, special care should be taken in order to proper align the AWG outputs to the reflection spectrum of FBGs. In case a dispersive component, such as AWG or an echelle, is used as an interrogator, the sensitivity of the sensor array depends on its spectral resolution of AWG or an echelle. Increasing the sensitivity of the interrogation system requires the fabrication of larger component, thus affecting the costs of fabrication (which scales with the area of an optical IC). In case an AWG and an MZI array are used as an interrogator, the spectral response of each individual sensor should be accurately aligned with the peaks of the AWG. Such scheme is highly sensitive to variations due to the manufacturing process. In case of integrated sensors, given the current manufacturing standards for integrated optics accurate optical alignment of the sensor response and AWG is very difficult to meet. This is even more complicated in case the individual sensors will be densely packed in the optical spectrum, so that accurate demultiplexing of the signals is required.

US2014/0375999 describes an integrated Fourier transform spectrometer including an array of interleaved planar waveguide Mach-Zehnder interferometers (MZIs), wherein the output of each MZI is coupled to a 4x4 multimode interference (MM I) coupler. This spectrometer, which employs more than 30 interferometers, is optimized for

reconstructing a spectrum and not for interrogating an array of optical sensors.

Hence, from the above it follows that there is a need in the art for improved methods and systems for interrogation of optical sensor arrays. In particular, there is a need in the art for integrated optical interrogation devices that enable accurate and reliable readout of sensor arrays comprising a large number of sensors.

Summary of the invention

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system." Functions described in this disclosure may be implemented as an algorithm executed by a microprocessor of a computer. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied, e.g., stored, thereon.

In an aspect, the invention relates to an interrogation system for an optical sensor array. In an embodiment, the system may include an input configured to receive an optical sensor signal from the optical sensor array, the optical sensor signal including optical responses (optical sensor peaks) of a plurality of sensors in the optical sensor array, each sensor being responsive to a different wavelength; a plurality of Mach-Zehnder

interferometers (MZIs) configured to receive the optical sensor signal, wherein each of the MZIs is configured to monitor an optical response of a sensor of the optical sensor array at a wavelength at which the sensor is responsive; a plurality of optical couplers (OCs), preferably L x P multimode interferometers (MMIs) or L x P directional couplers (DCs) wherein the number of input ports L > 2 and wherein then number of output ports P > 3, each of the OCs being configured to perform interference of signals originating from arms of an MZI, and to generate at its output a plurality of optical output signals, each output signal of the OC being a phase-shifted version of the input signal; and to generate at its output a plurality of optical output signals, each output signal of the OC being a phase-shifted version of the input signal; and, a post-processor configured to transform the optical output signals of the n-th OC into a first value V_x,n and a second value V_y,n wherein the first and second values represent a real and imaginary part of an n-th complex Fourier coefficient V_n of the Fourier series of the optical spectrum of the optical sensor signal.

The invention defines an on-chip photonic Fourier transform (FT) spectrometer based on MZI interferometers configured to interrogate and demultiplex an array of photonic- based sensors such as FBG strain sensors. The interrogation scheme is highly flexible, provides a high sensitivity, and offers a high tolerance to the fabrication process that used to fabricate the spectrometer and/or the sensor array. When compared with prior art

interrogation methods, the invention allows the use of a reduced number of Mach-Zehnder interferometers while maintaining a high sensitivity. The light beams in the MZI interfere within a 3x3 multimode interferometer, which allow determination of 90 degrees phase shifted signals, increasing the signal to noise ratio (SNR). As will be described hereunder in more detail, the ability to determine the orthogonal voltage values also allows reduction of the device footprint. The interrogation scheme determines the peak position of the sensors using the information of their line shape. As long as the orthogonality is kept, the number of interferometers that is needed to obtain the information is strongly reduced thereby improving its footprint. Moreover the interrogation method provides a high etendue compared to prior art interrogation techniques based on grating spectroscopy.

In an embodiment, the post-processor may be configured to determine a modulation _<5) (t) of the j-th sensor peak of the j-th sensor of the optical sensor array based on the complex Fourier coefficients V_n of the optical sensor signal, the modulation being caused by an external excitation applied to the j-th sensor.

In an embodiment, the modulation S_j t ) may be determined by solving the equation:

wherein FSRi is the free spectral range of the first MZI and wherein values of coefficients A_nj are predetermined values stored in a memory of the post-processor.

In an embodiment, the preprocessor may be configured to determine the spectrum of the input signal based on the equation:

In an embodiment, the spectrum may be used as a first estimate for solving equation (10). In an embodiment, the post-processor may be configured to solve equation (10) using a Newton method, a homonopy continuation method or any other numerical or algebraic method.

In an embodiment, the post-processor may be configured to execute a calibration method for determining the coefficients A_nj.

In an embodiment, the calibration method may include one or more of the following steps:

exciting the j-th sensor having an optical sensor peak at during a predetermined time;

measuring the real and imaginary parts ( '_x^. V'y._n) of the complex Fourier coefficients V_n{t) for each MZI;

fitting the measured real and imaginary parts in the complex plane to an ellipse and determining the coefficients A_nj for the j-th sensor based on the fitting data using a relation

wherein xh = 2n/FSRn.

In an embodiment, each OC of the plurality of OCs includes three output ports, the phase difference between the output signals at the three output ports being 120 degrees.

In an embodiment, the post-processor may further include photodetectors configured to transform the optical output signals of each OC into electrical output signals, preferably the photodetectors being integrated on the optical chip.

In an embodiment, the postprocessor may further include an arithmetic module for transforming the electrical output signals of each OC into the first value V_x,n and the second value V_{y n} representing the real and imaginary part of the n-th complex Fourier coefficient V_n. In an embodiment, the plurality of OCs and the plurality of MZIs may define M interferometers each interferometer being formed by an OC connected to the output of an MZI and wherein the optical sensor array comprises M optical sensors, the number of spectrometers M being equal to or larger than the number of interferometers N (M > N).

In an embodiment, the plurality of MZIs and the plurality of OCs may be integrated on an optical chip.

In an embodiment, the optical sensor array may include a plurality of fiber Bragg gratings (FBGs), each FGB being configured to reflect light at a predetermined wavelength, wherein an external excitation, e.g. temperature and/or mechanical stress, of a FGB causes a modulation of the wavelength at which the light is reflected by the FGB

In an aspect, the invention may relate to a sensor system comprising:

a light source for exposing an optical sensor array to light; an optical sensor array comprising a plurality of optical sensors, each of the plurality of optical sensors being configured to be responsive to an external excitation, preferably the external excitation including a physical parameter, e.g. a change in temperature or a change in stress; and, an interrogation system for interrogating the optical sensor array according to any of the embodiments described above.

In an aspect, the invention may relate to a method of interrogating an optical sensor array comprising: a plurality of Mach-Zehnder interferometers (MZIs) receiving an optical sensor signal from the optical sensor array, the optical sensor signal including optical responses (optical sensor peaks) of a plurality of sensors of the optical sensor array, each sensor being responsive to a different wavelength; wherein each of the MZIs is configured to monitor an optical response of a sensor of the optical sensor array at a wavelength at which the sensor is responsive; each OC of a plurality of OCs receiving at its input an output signal from one of the plurality of MZIs, and generating at its output a plurality of optical output signals, each output signal of the OC being a phase-shifted version of the input signal; and, transforming the optical output signals of the n-th OC into a first value V_x,n and a second value V_y,n, the first and second values representing a real and imaginary part of an n-th complex Fourier coefficient V_n of the Fourier series of the optical spectrum of the optical sensor signal.

In an embodiment, the method may further comprise: determining a modulation <5) (t) of the j-th sensor peak of the j-th sensor of the optical sensor array based on the complex Fourier coefficients V_n of the optical sensor signal, the modulation being caused by an external excitation applied to the j-th sensor.

In an embodiment, the modulation may be determined by solving the equation:

wherein FSRi is the free spectral range of the first MZI and wherein coefficients A_nj are predetermined and stored in a memory of the post-processor.

In yet a further aspect, the invention may relate to a method for calibrating an interrogation system according to any of the embodiments described above, wherein the method may including the steps of: exciting the j-th sensor having an optical sensor peak at during a predetermined time; measuring the real and imaginary parts

V_y.n) of the complex Fourier coefficients V_n(t) for each MZI; fitting the measured real and imaginary parts in the complex plane to an ellipse and determining the coefficients A_nj for the j-th sensor based on the fitting data using a relation V_n{t)~

wherein xh = 2 /FSRn.

The invention may also relate to a computer program product comprising software code portions configured for, when run in the memory of a computer, executing any of the method steps as described above.

The invention will be further illustrated with reference to the attached drawings, which schematically will show embodiments according to the invention. It will be understood that the invention is not in any way restricted to these specific embodiments.

Brief description of the drawings

Fig. 1 schematically depicts an optical interrogation system according to an embodiment of the invention;

Fig. 2A and 2B depict the optical spectrum of a sensor signal and a representation of complex Fourier coefficients of the sensor signal;

Fig 3 depicts a schematic of a spectrometer according to an embodiment of the invention;

Fig. 4 depicts a postprocessor for a spectrometer according to an embodiment of the invention.

Fig. 5 depicts a flow diagram of an interrogation method according to an embodiment of the invention.

Fig. 6 depicts examples how to apply an external excitation onto a photonic sensor.

Fig. 7 depicts experimental measurements using an interrogation system according to an embodiment of the invention. Fig. 8 depicts the layout of a photonic chip comprising a spectrometer according to an embodiment of the invention.

Detailed description

Fig. 1 depicts a schematic of an interrogation system according to an embodiment of the invention. In particular, Fig. 1 depicts an interrogation system for interrogation of an optical sensor system including an array of optical sensors. The optical sensor system may include at least one light source 102 configured to generate a broadband light beam, wherein the light source is optically coupled to a plurality (an array) of photonic sensors 108I._N. The light source may be configured to send a source light signal 104 via an optical fiber to a circulator 106. The plurality of photonic sensors, e.g. a photonic sensor array including a plurality of FBGs, may be coupled via an optical fiber to the circulator which may relay the source light signal towards the photonic sensors. Each photonic sensor may be configured to reflect light of a particular wavelength of the source light signal back to the circulator. The thus generated optical responses of the different photonic sensors may form a sensor signal 110 which is transmitted back to the circulator which relays the sensor signal (including the plurality of optical responses) towards an optical interrogation system 111 for demultiplexing the sensor signal into the individual optical responses and monitoring the individual optical responses. The monitoring may include detecting a modulation of the optical response indicating an external excitation (e.g. temperature or mechanical stress) of one the one or more sensors in the sensor array. The optical interrogation system may include a photonic chip 112 and a post-processor 114 controlled by a computer 116.

Different types of photonic sensors may be employed, e.g. strain sensors for detecting changes in the length of the fiber due to strain or tension, temperature sensors for detecting changes in the length of the fiber due to temperature changes or any other photonic sensor. If the sensors do not sense an external excitation, the sensor signal may include peak amplitudes at different predetermined wavelengths A (i=1-N) at which the detectors reflect the source light signal. These peak amplitudes may be referred to as the photonic sensor peaks.

In response to an external excitation (e.g. temperature change DT or change in strain AS) that is sensed by the photonic sensor, the wavelength at which the sensor reflects light is lightly modulated. For example, the second photonic sensor IO8₂ which operates at peak wavelength A_å may be configured as a photonic strain sensor. Thus, if a change in strain AS is detected the sensor, the sensor signal may include optical response of the second photonic sensor that includes a modulation Dl2 of the photonic sensor peak at wavelength A_å. Similarly, the N-th photonic sensor, which operates at a wavelength A_N may be configured as a photonic temperature sensor. Thus, if a change in temperature AT s detected by the sensor, the sensor signal may include a modulation DA_N of the photonic sensor peak at wavelength A_N as shown in the inset 132 of Fig. 1. The photonic sensor array may be configured so that superposition of sensor peaks is avoided.

As will be described hereunder in greater detail, the photonic chip may include different optical elements, including a plurality of Mach-Zehnder interferometers (MZIs), wherein signal interference of signals originating from arms of each MZI is performed in an optical coupler (OC), e.g. a multimode interferometer (MMI) or a directional coupler (DC). For example, 3x3 MMIs or a 3x3 DCs may be used as an OC. More generally, L X P DCs or L X P MMIs may be used as OCs wherein the number of input ports L > 2 and wherein then number of output ports L > 3 may be used.

As will be described hereunder in more detail, each MZI/OC pair is able to determine one of the complex coefficient of the Fourier series of a sensor signal that includes optical response of an optical sensor array.

The MMI or the DC includes an input port and a plurality of output ports, wherein the MMI or the DC is configured to generate at each of its output ports a phase shifted version of the input signal. For example, in case of a 3x3 MMI or a 3x3 DC, three phase shifted output signals are produced wherein the phase difference between each output signal is 120°. Similarly, in case of a 4x4 MMI or a 4x4 DC, four phase shifted output signals are produced wherein the phase difference between each of the output signals is 90°. The output ports of each MMI may be optically connected to photodetectors (e.g. three photodiodes in case of a 3x3 MMI or a 3x3 DC) for transforming the optical output of the MMI or the DC into an electrical signal. In an embodiment, the photodetectors are integrated together with the other optical elements into an integrated optical chip.

A postprocessor 114 may include transimpedance amplifiers for amplifying the electrical signals generated by the photo-detectors. Additionally, the postprocessor may include electronics to process the outputs of the amplifiers into an output signal that provides a direct correlation with the modulated photonic sensor peak. Thus, in response to an external excitation, a photonic sensor m of the sensor array may cause a modulation S_m(t) of the photonic sensor peak at a predetermined wavelength A , which may be detected by the spectrometer and translated into an electrical signal by photodetectors on the optical chip. For example, in case of a 3x3 MMI or the 3x3 DC, the three photodetectors will measure 120 degree phase-shifted sine voltage signals Vi,V2,V3 of a certain amplitude A. These phase shifted voltage signals may be transformed by the postprocessor into sets of orthogonal voltage signals V_x,n, V_y,n (n=1 ,... ,N) wherein N is the number of sensors in the sensor array. The sets of orthogonal voltage signals may form the output signal 134 of the post-processor 114. Each set of measured voltages (½.„, V_y.n) represent the components of a complex value V_n = V_{X l} + iV_{y n}, wherein V_x,n, and V_y,n form the real and imaginary part of a nth complex Fourier coefficient. The complex Fourier coefficient is one of the coefficients of the Fourier series of the optical spectrum of the sensor signal 110. In that sense, each MZI provides one of the coefficients of the Fourier series. A modulation S_m(t) of the m-th photonic sensor peak at wavelength A_m will cause a phase modulation of all the complex coefficients V_n. As will be described hereunder in more detail, this will lead to a set of coupled polynomial equations. The solution gives the individual modulation of each sensor.

When presented in the complex plane, the points V_x,n(t) and V_y,n(t) may form a so-called Lissajous curve describing the phase of the Fourier coefficient in time. Fig. 2A and 2B depict the process of measuring the modulation of a photonic sensor peak belonging to a sensor that is excited by an external excitation. Both figures depict the optical spectrum 200i,_{2 O}f the sensor signal and a representation 202i,_{2 O}f the complex coefficients Anj of the sensor signals in the complex plane for the case of four sensors (N=4). The coefficients are located on a circle of the complex plane.

For this situation, the complex voltage Vn would be given as:

where Y„ where is the environmental phase drift, A_nj- = \A_n2

a set of coefficients to be determined experimentally according to your calibration procedure herein defined; _oj the wavelength of the sensors at the rest where _<S (t) = 0. Fig. 2A and 2B illustrate the phases of coefficients A_u·. As long as the response of the sensors do not overlap and the phases exp (i ysw i^o_j + ¾ (£))) is kept different, the response of the sensors can be demodulated.

Monitoring (modulation of) the modulation of _<5)(t) as a function of time allows individual readout of a sensor of the sensor array. Such interrogation process is very robust against variations caused by the manufacturing process - both for the interrogator chip and the sensor chips. Variations due to fabrications of the interrogator chip may cause an additional phase shift to each MZIs - which is incorporated to the coefficients A_nj ;may cause a small change of the MZI FSR - which may add a small fractional number to the integer exponent n of equation (10); and, may cause a change in the eccentricity of the ellipse - which may be corrected during the calibration (which will be described hereunder in more detail). Variations of the fabrication of the sensor chip may cause that the position of the non-excited photonic sensor peak is not exactly positioned at the wavelength as determined by design. For example, as shown in Fig. 2B, due to variations in the

manufacturing process of the optical chip of the sensors the second and third sensor may exhibit a response at l’_å and l’ 3 instead of l_å and _? so that the position of the associated Fourier coefficients is shifted relative to the position as initially designed (e.g. as shown in Fig. 2A). As long as variation in the wavelength response does not result in a situation wherein the photonic sensor peaks of two or more sensors coincide, the responses of each sensor are still well defined and modulation of the phase can still be measured despite variations in optical chip parameters. In contrast to prior art interrogation systems, the interrogation system according to the invention offers a high tolerance to the fabrication process that is used to fabricate the optical chip.

Fig 3 depicts a schematic of a spectrometer according to an embodiment of the invention. As shown in this figure, the spectrometer may include a photonic integrated circuit 302 (a photonic or optical chip) coupled to a postprocessor 304. The photonic chip may include first stage 308 including one or more interferometers, preferably Mach Zehnder interferometers (MZIs), a second stage 310 including one or more optical couplers, such as multi-mode interferometers (MMIs) or directional couplers (DCs) and a third 312 stage including an opto-electronic interface. Here, signal interference of signals originating from arms 319i_,2 0f an MZI, 320 is performed an optical coupler 324, e.g. 3x3 MMI,. The MZI / optical coupler pair form an interferometer

Further, a postprocessor 304 may be coupled to the opto-electronic interface of the photonic chip wherein the postprocessor may include a transimpedance amplifier module 314 and an arithmetic module 316. As shown in Fig. 3, MZI, and MMI, / DC, may form a interferometer which is configured to monitor one optical response of the plurality of optical responses in the sensor signal generated by a sensor array and configured to produce phase shifted versions of the monitored optical response. These phase-shifted output signals, three in case of a 3x3 MMI or 3x3 DC, are transformed into three phase shifted electrical signals Vi_{, i}, Vj_,2 , Vi.3 326_I-3 wherein the phase difference between the signals is 120°. These signals are subsequently amplified and transformed to an orthogonal (i.e. 90 degrees phase-shifted) values ½_* and V,

Fig. 4 depicts a more detailed view of the postprocessor 400 for a spectrometer according to an embodiment of the invention. As shown in this figure, the electrical signals generated by the photodetectors that are integrated in the optical ship are amplified by an amplifier stage 404 and an arithmetic stage 406 wherein the arithmetic stage electronically transforms the voltages associated with the output signals of the MMI or the DC to a voltage pair that represent the real and imaginary part of a complex voltage V_n = V_n,x + iV_n.y 408, 410 (as will be explained hereunder in more detail). Although in this example, the arithmetic stage represents an electronic module that is configured to transform the three phase shifted voltage signals into the complex voltage, other means for implementing the arithmetic stage may be used, e.g. a software program configured to provide the functionality of the arithmetic stage.

Fig. 5 depicts a flow diagram of an interrogation method according to an embodiment of the invention. As shown in this figure the method of interrogating an optical sensor array may start (step 502) with an input of an interrogation system receiving an optical sensor signal from the optical sensor array. As described with reference to Fig. 1 , the optical sensor signal may include a plurality of optical responses (optical sensor peaks) of the sensors in the sensor array, if the optical sensor is exposed to light of a broadband light source. Further, each of the sensors in the sensor array is configured to be response to a predetermined wavelength wherein different sensors are response to different wavelengths. The interrogation system may include a plurality of Mach-Zehnder interferometers (MZIs) and a plurality of optical couplers (OCs), e.g. multi-mode interferometers (MMIs) or directional couplers (DCs). The output of each MZI is connected to an OC

In a further step 504, the plurality of MZIs may receive the optical sensor signal and each MZI may monitor an optical response of a sensor of the optical sensor array at a wavelength at which the sensor is responsive. Moreover, in step 506 each of the MMIs or the DCs may receive at its input output signals from one of the plurality of MZIs, i.e.

signals originating from the arms of each MZI, which will interfere in the optical coupler (OC), The OC is configured to generate at its output ports a plurality of optical output signals, wherein each output signal of the OC may be a phase-shifted version of the input signal. For example, in case of a 3x3 MMI or a 3x3 DC, the three output ports may provide three optical output signals wherein the phase difference between the optical output signals is 120 degrees. Thereafter, in step 508, a post-processor may transform the optical output signals of the n-th OC into a first value V_yn and a second value V_y.n wherein the first and second values represent a real and imaginary part of an n-th complex Fourier coefficient V_n of the Fourier series of the optical spectrum of the optical sensor signal. Here, the modulation may be caused by an external excitation (e.g. a change in temperature, mechanical stress, etc.) of the sensor.

A micrograph of the spectrometer chip is shown in Fig. 8. The chip was fabricated in a multi-project wafer run in Smart Photonics foundry and its dimensions are 4.0 mm * 4.5 mm. The chip has a total of 7 inputs, but only inputs 1-6 where used, as indicated in the figure. The light signal is split in beams (using 50:50 MMI splitters) and guided to a plurality of Mach-Zehnder interferometers, in this case 9 MZIs. The other inputs provide access to a limited group of MZIs, allowing us to characterize the sensor with a reduced number of interferometers. For instance, by coupling the sensor signal in the inputs 6, only the MZIs 1-7 are used. The chip may be glued to a chip holder, which is a printed circuit board. Pads of the chip holder were wirebonded to pads of chip. Outputs of the chip holder were connected to another PCB, which implements an array transimpedance amplifiers (TIA module) and provide a linear combination of the photodetector outputs as described with reference to Fig. 3 and 4.

The on-chip Fourier transform spectroscope may be based on Mach-Zehnder interferometers. All waveguides have a 1.5 micron width. Each MZI has a different arm’s length AL. The arm’s length difference AL range from 0.710 mm to 6.39 mm in steps of 0.710 mm. At the end of the MZI, the light signal from the two arms interfere with in a 3x3 MMI (360 micron length, 11.4 micron width). The transmission spectrum of each MZI was measured using a tuneable laser (a broadband light sources as described with reference to Fig. 1). The laser power was set to 20 mW and a sweep of the laser wavelength (A_L) was performed ranging from 1550 nm to 1553 nm in steps of 1 pm, while the outputs from the 27

photodetectors (3 per each MZI) were recorded. Fig. 4B shows the measured voltages of outputs of MZI 1 (AL = 0.710 mm), as well as a fit to right side of equation 1 :

where T_{MZI ij} is the transmission spectrum of the j-th output of the i-th MZI. Here A are the amplitudes of the interferometric fringes, FSR is the free spectral range of the i-th interferometer, y_i the phase of the j-th device output (j = 1 ,2,3). The free spectral range of the spectrometer corresponds to the FSR of the fundamental MZI, FSR The right side of equation (1) can be obtained by expanding the term n_ef AL/X in Taylor series around A₀ = 1550.0 nm. The group index of the waveguides was determined using the expression n_g =/(FSRX o) for Ao = 1550.0 nm. The mean value is 3.64 and the free spectral range of the fundamental MZI is 930 pm. The FSR of j-th MZI is given by FSR_j = FSR/j. The MZIs and 3x3 MM Is were designed to produce interferometric oscillations (fringes) representing signals with same amplitude and 120° phase shifted. To calculate two 90° phase-shift fringes the following equations are used, which are electronically calculated based on the arithmetic module as described with reference to Fig. 4:

In case of a balanced 3*3 MMIs, the Lissajous curve (¾(T₀), l^(A₀)) may produce a circle with radius R. V_{i x} and V_iy may have slightly different amplitudes and a phase difference deviating from 90°, which may deform a circle to an ellipse.

Schematics of an optical sensor system which uses an interrogation system according to an embodiment of the invention are depicted in Fig. 1 and 6. As described with reference to Fig. 1 light from a broadband source may be sent, via a circulator to the FBG sensor array. The sensors may reflect three optical response signals back to the circulator. As we said, this embodiment it not only limited to FBG sensors. Depending on the type of the sensor employed, this setup may have to change. For instance, in case the goal is to interrogate an array of integrated ring resonators, the broadband source should be directly connected to the input of the sensor array and the output is conveyed to the interrogator chip.

Fig. 6 depicts examples illustrating the application of an external excitation onto a photonic sensor. As depicted in Fig. 6 two types of sensors may be employed: strain sensors and temperature sensors. To induce well controlled vibrations to the strain sensors, a piezo actuator 606 may be used for controllably stretching the fiber 602 that includes a photonic sensor 604. Similarly, the changes in temperature may be induced based on a Peltier element 608. In both of cases, the peak wavelength will be modulated according to the external excitation.

The interferometer outputs were connected to integrated photodetectors (PD) as described with reference to Fig. 3. In this particular example, the spectrometer may have 9 MZIs and 3 photodetectors per MZI resulting in the 28 electrical outputs (27 + ground). The outputs may be conveyed to another PCB which comprising the transimpedance amplifiers (TIA) for the photo-detectors and an arithmetic module to electronically implement equation 2 as described above. The outputs were sampled by an analogue to digital module.

The expressions for determining the peak reflection of the FBGs as a function of time may be derived as follows. The value of the voltages at the output of the TIAs is:

where V_nm is the output voltage signal related to m-th output of the n-th interferometer;

is the combined spectrum of the sensor signal. The peak wavelength may be given by A_t (t) = l_oί - 5, (t) herein l_0| is the position of the peak without any external excitation and 5_j (t) represents the modulation of the peak wavelength (which needs to be determined), G = aP₀gR_ph where P₀ is the peak of the input spectral density, a the overall attenuation coefficient and g the transimpedance gain and R_ph the photo-detector responsivity. The arithmetic module (of Fig. 4) may combine the signals from the three outputs of the interferometers according to equation (2), resulting in the two orthogonal (90 degree phase shifted) voltages V_{n x} and V_{n x} :

were the parameter Y_h represents the environmental phase drift, caused by local variations of temperature within the photonic chip. The photonic chip was characterized in a controlled temperature laboratory, so the drift is assumed constant during the characterization of the sensors. Here, x_offn and y_otfn are voltage offsets associated with the amplifiers and dark voltages of the photodetectors. These offsets may be removed by averaging. Since the free spectral range of the MZI is progressively reduced FSRn = (1/n)FSRi , V_jx and V_{j y} are, by definition, coefficients of a Fourier series. The spectrum may be obtained by the expression:

wherein in this example FSR^ = 0.93 nm. In most of spectrometer applications only the even terms are considered. In the wavelength domain, the argument of the MZI transfer function may be expanded around l₀ = 1550 nm (see equation 1) wherein both the odd and even terms are taken into account. An initial estimative of the peaks can be obtained by taking the maximum value of the S(A) around the initial peak position. As described hereunder, due to the limited resolution of the spectrometer, this approach leads to a difference between the original and the reconstructed spectrum. Then, _n(t) may be determined by solving a non linear equation system. By defining a complex voltage as V_n = V_{n x} + iV_{n y} and using equations (4)-(5) the following expression may be derived:

wherein x_h = 2 /FSR_n. Since S(A = 0) « 0, the integration limits may be extended from - to + By substituting the definition of ( l ) =

:

wherein the term sj (l - l_0] - db)) represents the modulation of the sensor spectrum performed by the external modulation. The right side of equation (8) represents the Fourier transform of s A) evaluated at xh = 2n/FSRn . Using the shift property of Fourier transformation, equation (8) can be rewritten as follows:

wherein 5^~ (x) is the Fourier transform of Sj(A). Using the expression A_nj

equation (9) can be rewritten as follows:

Let zj

In case of 3 sensors and 3 interferometers equation (10) represents a system of polynomial 9 equations and 3 variables which may be solved numerically. This scheme can be readily expanded to the general case, i.e. a M*N system wherein M is the number of interferometers and N the number of sensors. Equations (11) illustrate the set of equations that need to be solved for the 3x3 case. Since the variables z_; are complex exponentials, the unit modulus needs to be imposed.

As long as M > N and the lines are orthogonal, the system is determined. Eq. 6 represents the standard Fourier Transform procedure and requires the interferometers to have progressive smaller FSR values according to the relation FSR_n = (1 /n)FSR₀. On the other hand, equation (11) imposes no restrictions on the FSR values, except by the fact that the FSR must be different and the number of interferometers must be at least equal to the number of sensors, keeping the system of equations determined. This allows a strong reduction on the number of interferometers and on the overall footprint of the device. As shown by the experimental results, for two sensors only two interferometers are needed. The fact that M > N, i.e. , the system is overdetermined, increases the signal to noise ratio and allows compensation for the noise.

Thus, from the above it follows that each of the interferometers receiving a sensor signal at its input port is capable of determining components of a complex value V_n = V_{x n} + iV_{y n}, wherein V_x.n, and V_y.n form the real and imaginary part of a nth complex Fourier coefficient. The complex Fourier coefficient is one of the coefficients of the Fourier series of the optical spectrum of the sensor signal. A modulation S_m(t) of the m-th photonic sensor peak at wavelength A_m will cause a phase modulation of all the complex coefficients ίz. Thus modulations of photonic sensor peaks of the sensors may be determined solving a set of equations as defined by equation (10). The solution gives the individual modulation of each sensor. The equations may be solved using a known scheme such as a Newton method, a homonopy continuation method or any other numerical or algebraic method. For ideal noiseless photodetectors, the difference between the original and reconstructed spectra may be zero. Thus, the interrogator is not limited by the resolution of the FT spectrometer. Assuming that the FBG sensors have a Lorentzian line shape, Eq. (10) may be rewritten as follows:

where s_0j and w are the peak value and the full width half maxima of the j-th sensor re flection spectrum. The damping factor exp(-f„w/2) can be written as exp(-f„w/2) = exp(-OPD/Lc ), where Lc is the coherent length. As we discussed in, the coherent length limits the maximum value of OPD which allow the interferometric fringes, expressed in Eq. (1 1), that can be resolved experimentally. Comparing equation (14) and (12), the following expression can be obtained:

From equation (13) it is clear that a strong attenuation occurs in case the FSR of the MZI is comparable or smaller than the sensor FWHM.

The coefficients A_nj may be experimentally determined using a calibration procedure. Let z be the time instance at which the calibration of j-th sensor started and f_jend the time instance of the end of calibration of this sensor. During the time interval ^ti ^{< t <} f_jt1= f_jend all sensors are kept at rest, while sensor j is excited. In case sensor j is a temperature sensor, a large temperature is applied during the calibration. If the sensor is a strain sensor, a large strain is applied. For an ideally balanced 3x3 MMI, the n-th complex voltage excited during the interval z < ^ <

is given by F_n(t) = \A_nj\e‘^^j + constant, which represents a circle arc in the complex plane. Deviation from this ideal behaviour are not uncommon and the circle is deformed to an ellipse. At the end of the calibration of sensor j, the angle arg(i^n) remains constant and the next sensor can be calibrated. An ellipse may be fit to the data points (y_{x n}(ty, V_{y n}(ty) where V_{x n}(t)' and V_{y n}(ty are the unbalanced orthogonal voltages measured during the calibration. The larger the excitation, the larger the angular deflection resulting in an accurate extraction of the ellipse parameters. Thus, this way the semi-axis values a and b (where a > b) as well as the angle a that represents the ellipse rotation with respect to the real axis may be obtained. In order to map the ellipse to a circle, the following correction may be performed:

14}

Here

and V are the corrected values of the orthogonal voltages it can be determined that \A_nj\=b and that the argument of A_nj is given by arg( \_nj) =

arctan₂ (Vy _n(t_jend) - yo, V_x,n{t_jen_d) ^xo_>

is the four quadrant arc tangent and (x₀, y₀) the circle centre in the complex plane. When the calibration of all sensors have been finished, the offsets may be determined by averaging:

where Teal is the instant time of the end of calibration procedure.

Experiments have been performed for a case in which two sensors (one for temperature and other for strain) and only two MZIs are employed (MZI 1 and MZI 2, FSR = 0.93 and 0.437 nm, respectively). The peak wavelengths of the sensors at t = 0 are at

1549.84 nm and 1550.87 nm. Since low speed experiments have been performed, frequency components of the voltages V1 and V2 above 40 Hz have been filtered out. The full width half maxima (FWHM) is around 80 pm. Equation (11) for this situation can be rewritten as:

P 6)

Since low speed experiments have been performed, frequency components of the voltages V1 and V2 above 40 Hz have been filtered out. For this particular case, the solutions can also be determined analytically and are given by equations (16) and (17). In this case two pairs of solutions are obtained:

where

Following the interrogation and calibration procedures described above, the sensors were individually excited by applying about 550 me strain in sensor 1 (for 0 < t., < 2 s) and 38° C heat for sensor 2 (5 < T₂ < 10 s). Fig. 7A-7D depict experimental measurements using an interrogation system according to an embodiment of the invention. These excitations induced a modulation on the peak of reflection of the FBGs, leading to the oscillations correspondent to the interferometric fringes in the output signals of MZIs 1 and 2, shown in Fig. 7 A. The complex voltage V_t(t) = I _,n(t) + iV_y,n(t) was calculated and the ellipses were fitted to the measured data. By applying the linear transformation defined in equation 14, circles arcs were obtained as shown in Fig. 7B. This way, the coefficients Ajn as described above with reference to the calibration method, can be determined. During the calibration, the angular deflection of the circle arc for MZI 1 was twice as large as for MZI 2, for both sensors. This can be explained by the fact that FSR2 = 2FSR-] inducing a deflection for sensor 2 according to equation (10) that is twice as large.

For t > 25s, both sensors are simultaneously excited, deforming the circle arcs to an arbitrary Lissajous curve. A small heat was applied to the temperature sensor, while we applied different strain values to the other FBG. Replacing the values of A_jn and the V_n to equations (16) and (17), the solutions of Eq. (15) were obtained as depicted in Fig. 7C. Strain was applied to the FBG by stretching it using a step motor, which applies a well- controlled and linear deformation (as observed in Fig. 7C). On the other hand, the FBG that was excited by a heating and cooling process exhibits exponential behaviour as a function of time (as observed in Fig. 7C).

In Fig. 7C, we indicated a few points where the two solution values

interchanged^., (f) ® z₂{t ) and z₂(t) z^t)), caused by a discontinuity in the square root term s(t). The discontinuities are visible in Fig. 3D, which shows the root locus of the pair

order to correct for this effect, the line element ds = (cfifiiz;) / dt)² + ( 3(zi)/dt)²dt can be determined.

When the solutions interchange, ds presents a peak where the two solutions are manually exchanged (as shown in Fig. 7C).

The smallest amplitude of wavelength shift is about 2.1 ± 0.2 pm, indicating that the interrogator can detect very small phase shifts. This limit is not imposed by the interrogator but corresponds to the minimum deformation that our step motor has could apply. For two MZIs, the correspondent resolution of the spectrometer would be 250 pm, meaning that the interrogation method is at least 100 times better that the spectral resolution of the Fourier transform spectrometer.

For the case where reflection spectrum of the FBGs are identical, the solution pairs

represent the mathematical equivalence of two cases: (a) d₁ as temperature and d₂ as strain sensor or (b)

as strain and d₂ as temperature sensor. This can be derived from equation (15). In the experimental case, however, the amplitudes of the reflected peaks are different (the peak of l₁ is about 20% higher than the peak of l₂). By solving equation (16) analytically, no imposition has been made about the modulus of z_}-.

Thus, in case the modulus the peaks have different amplitudes s ¹ s₂, one of the solution pairs will be spurious with the modulus different than 1. Let z be time average of variable z along the measurement. For the current situation ( z ,z₂ ) = (1.15,0.85), while (z , zf) = (1.009,1.011), indicating that the first pair should be discarded. Nevertheless, since the values of amplitude of the peaks are in the same order of magnitude, the argument of

differ only in 3%, as indicated in Fig. 7C.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.

Claims

1. Interrogation system for an optical sensor array comprising: an input configured to receive an optical sensor signal from the optical sensor array, the optical sensor signal including optical responses (optical sensor peaks dips or any other line-shapes) of a plurality of sensors in the optical sensor array, each sensor being responsive to a different wavelength;

a plurality of Mach-Zehnder interferometers (MZIs) configured to receive the optical sensor signal, wherein each of the MZIs is configured to monitor an optical response of the optical sensor array at a wavelength at which the sensor is responsive;

a plurality of optical couplers (OCs), preferably L x P multimode interferometers (MM Is) or L x P directional couplers (DCs) wherein the number of input ports L > 2 and wherein then number of output ports P > 3, each of the OCs being configured to perform interference of signals originating from arms of an MZI, and to generate at its output a plurality of optical output signals, each output signal of the OC being a phase-shifted version of the input signal; and,

a post-processor configured to transform the optical output signals of the n-th MM I into a first value V_x,n and a second value V_y,n wherein the first and second values represent a real and imaginary part of an n-th complex Fourier coefficient V_n of the Fourier series of the optical spectrum of the optical sensor signal.

2. Interrogation system according to claim 1 wherein the post-processor is further configured to determine a modulation <5 (t) of the j-th sensor peak of the j-th sensor of the optical sensor array based on the complex Fourier coefficients V_n of the optical sensor signal, the modulation being caused by an external excitation applied to the j-th sensor, preferably the modulation <5 (f) being determined by solving the equation:

3. Interrogation system according to claim 2 wherein the post-processor is configured to execute a calibration method for determining the coefficients A_nj, the calibration method including the steps of: for a predetermined time exciting the j-th sensor having an optical sensor peak at a predetermined wavelength ;

measuring the real and imaginary parts ( V_Kn, V_y,n ) of the complex Fourier coefficients V_n(_.t ) for each MZI;

fitting the measured real and imaginary parts in the complex plane to an ellipse and determining the coefficients A_nj for the j-th sensor based on the fitting data using a relation V

wherein xh = 2 /FSRn.

4. Interrogation system according to any of claims 1-3 wherein each OC of the plurality of OCs includes three output ports, the phase difference between the output signals at the three output ports being 120 degrees.

5. Interrogation system according to any of claims 1-4 wherein the post processor further includes photodetectors configured to transform the optical output signals of each MMI / DC into electrical output signals, preferably the photodetectors being integrated on the optical chip.

6. Interrogation system according to claim 4 wherein the postprocessor further includes an arithmetic module for transforming the electrical output signals of each OC into the first value V_x,n and the second value V_y representing the real and imaginary part of the n-th complex Fourier coefficient V_n.

7. Interrogation system according to any of claims 1-6, wherein the plurality of OCs and the plurality of MZIs define N interferometers, each spectrometer being formed by an OC connected to the output of an MZI and wherein the optical sensor array comprises M optical sensors, the number of interferometers M being equal to or larger than the number of interferometers N (M > N).

8. Interrogation system according to any of claims 1-7 wherein the plurality of MZIs and the plurality of OCs are integrated on an optical chip.

9. Interrogation system according to any of claim 1-8 wherein the optical sensor array includes a plurality of fiber Bragg gratings (FBGs), each FGB being configured to reflect light at a predetermined wavelength, wherein an external excitation, e.g.

temperature and/or mechanical stress, of a FGB causes a modulation of the wavelength at which the light is reflected by the FGB.

10. Optical sensor system comprising:

a light source for exposing an optical sensor array to light;

an optical sensor array comprising a plurality of optical sensors, each of the plurality of optical sensors being configured to modulate the transmission or reflection spectrum by an external excitation, preferably the external excitation including a physical parameter, e.g. a change in temperature or a change in stress; and,

an interrogation system for interrogating the optical sensor array according to any of claims 1-9.

1 1. Method of interrogating an optical sensor array comprising: a plurality of Mach-Zehnder interferometers (MZIs) receiving an optical sensor signal from the optical sensor array, the optical sensor signal including optical responses (optical sensor peaks, dips or any other line-shapes) of a plurality of sensors of the optical sensor array, each sensor being responsive to a different wavelength; wherein each of the MZIs is configured to monitor an optical response of a sensor of the optical sensor array at a wavelength at which the sensor is responsive;

each OC of a plurality of OCs receiving at its input an output signal from one of the plurality of MZIs, and generating at its output a plurality of optical output signals, each output signal of the MMI being a phase-shifted version of the input signal; and,

transforming the optical output signals of the n-th OC to a first value V_x,n and a second value V_y.n. the first and second values representing a real and imaginary part of an n- th complex Fourier coefficient V_n of the Fourier series of the optical spectrum of the optical sensor signal.

12. Method according to claim 11 further comprising:

determining a modulation 5_;-(t) of the j-th sensor peak of the j-th sensor of the optical sensor array based on the complex Fourier coefficients V_n of the optical sensor signal, the modulation being caused by an external excitation applied to the j-th sensor, preferably determining the modulation <5 j (t) by solving the equation:

13. Method for calibrating an interrogation system according to any of claim 1- 9 including the steps of:

for a predetermined time exciting the j-th sensor having an optical sensor peak at a predetermined wavelength;

measuring the real and imaginary parts (V_X n, Vy_,n) of the complex Fourier coefficients V_n(t) for each MZI;

fitting the measured real and imaginary parts in the complex plane to an ellipse and determining the coefficients A_nj for the j-th sensor based on the fitting data using a relation V_n(t)~ \A_nj\e'^ⁿ^ wherein xh = 2w/FSRn.