RU2715479C1 - Method of determining transfer function of a phase modulator in a sagnac interferometer - Google Patents

Abstract

FIELD: optics.

SUBSTANCE: invention relates to fiber optics. Method for determining the transfer function of a phase modulator in a Sagnac interferometer includes feeding a phase modulator electric input of a voltage control signal comprising an auxiliary meander signal, amplitude of which provides shift of the operating point of the interferometer to the linear portion of the interferometric function, and measurement of obtained signal of interferometer, which is used to determine transfer function of phase modulator. At the electric input of the phase modulator, simultaneously with the auxiliary signal, a second control signal of voltage in the form of a meander with an amplitude corresponding to the optical phase shift and with a certain period is supplied and the obtained signal of the interferometer is measured, from which the phase signal is calculated. Pulse characteristic of the phase modulator is calculated from the phase signal and, subjecting the obtained pulse characteristic to the method of identifying the transfer function, determining the desired transfer function of the phase modulator of the Sagnac interferometer.

EFFECT: high accuracy of determining the transfer function of a photomultiplier in a Sagnac interferometer.

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Description

The invention relates to the field of fiber optics, in particular, to the field of creating fiber-optic sensors of physical quantities, constructed according to the Sagnac interferometer scheme, and can be used to determine the transfer function of the phase modulator (FM) in the Sagnac interferometer. By the transfer function of the FM is meant the function of converting the electrical voltage applied to the electrodes of the FM into a phase shift of the optical radiation propagating in the FM. The transfer function of the FM determines its amplitude-frequency and phase-frequency characteristics.

A known method of measuring the transfer function of a phase modulator (FM) in the Sagnac interferometer [US Patent No. 9518825, IPC G01C 19/72), date publ. 09/18/2014]. The method consists in the following: a digital filter is installed in front of the electrical input of the FM, the transfer function of which is calculated by the adaptive method so that it is inverse to the transfer function of the FM. The transfer function of the FM is calculated from the transfer function of a digital filter in accordance with the following expression:

H _FM (z) = 1 / N _FC (z),

where H _FM (z) is the transfer function of the FM, H _FC (z) is the transfer function of the digital filter, z is the complex variable.

Since in the known method, the FM in the Sagnac interferometer is part of the optical scheme of the fiber-optic gyroscope (FOG), the signals of the FOG measuring path are used as an error signal to fine-tune the digital filter.

The disadvantages of this method are: the need for large computing power, the feasibility of the method only in the VOG signal processing scheme, and the influence on the measurement accuracy of the transfer function of the FM parameters of the VOG control system.

A known method of measuring the transfer function of the FM in the Sagnac interferometer, selected as a prototype [US Patent No. 5504580, IPC G01C 19/72), date publ. November 30, 1994]. The method consists in the following: a voltage control signal is applied to the FM electrical input, which is a meander whose amplitude provides a phase shift of the operating point of the Sagnac interferometer by ± π / 2 radians, with a periodic reset of the control voltage, the amplitude of which corresponds to a phase shift of the optical signal by 2π radians , and the frequency of discharges is many times less than the frequency of the meander. Between the FM driver output and the FM electrical input, an analog filter is installed, which is a resistive-capacitive circuit, and the capacitance and resistance values are selected so that the response of the Sagnac interferometer to the control voltage signal is an inertialess process. The transfer function of the analog filter can be calculated based on the selected values of the resistive-capacitive circuit, and the transfer function of the FM is calculated from the transfer function of the analog filter in accordance with the following expression:

H _FM (z) = 1 / N _FA (z),

where N _FA (z) is the transfer function of the analog filter.

The disadvantages of this method are: the adjustment of the analog filter in manual mode by selecting the nominal values of the resistance and capacitance of the analog components, as the transfer function of the FM adopted a function having one zero and one pole, which reduces the accuracy of the measurement of the transfer function of the analog filter and, accordingly, the transfer function Fm.

The method solves the problem of increasing the accuracy of determining the transfer function of the FM in the Sagnac interferometer.

где

где

- среднее значение сигнала

K=Т/τ - количество отсчетов длительностью τ в периоде T сигнала S_инт, k=[1…K/2] - порядковый номер отсчета сигнала

N - количество периодов T в сигнале S_инт,

=[1…N]- порядковый номер периода, причем Ф[1]=2Δϕ₁, а из фазового сигнала Ф рассчитывают импульсную характеристику фазового модулятора S_ФМ, согласно выражению

и, подвергая полученную импульсную характеристику методу идентификации передаточной функции, определяют искомую передаточную функцию фазового модулятора интерферометра Саньяка.The problem is solved as follows. The method for determining the transfer function of the FM in the Sagnac interferometer includes applying to the electrical input of the phase modulator a control voltage signal containing an auxiliary signal in the form of a meander, the amplitude of which provides a shift of the operating point of the interferometer by a linear portion of the interferometric function, and measuring the received signal of the interferometer, which is used to determine the transfer phase modulator functions. New is that the second voltage control signal in the form of a meander with an amplitude corresponding to the optical phase shift Δϕ ₁ = Nπ (where N = 1,2,3 ...) and with a period T >> is fed to the electrical input of the phase modulator simultaneously with an auxiliary signal τ, where τ is the time of the optical signal bypassing the fiber-optic circuit of the Sagnac interferometer, and the received signal of the interferometer S _{int is} measured from which the phase signal is calculated

Where

Where

- average signal value

K = T / τ - the number of samples of duration τ in the period T of the signal S _int , k = [1 ... K / 2] - the serial number of the signal sample

N is the number of periods T in the signal S _int ,

= [1 ... N] is the sequence number of the period, with Ф [1] = 2Δϕ ₁ , and from the phase signal Ф the impulse response of the phase modulator S _{FM is} calculated, according to the expression

and, subjecting the obtained impulse response to the identification function of the transfer function, determine the desired transfer function of the phase modulator of the Sagnac interferometer.

The essence of the invention is illustrated as follows. A special modulation signal is applied to the FM, representing the sum of two signals: the first signal M ₁ is a meander with an amplitude corresponding to the optical phase shift Δϕ ₁ = Nπ (where N = 1,2,3 ...), and with a period T, where T / 2 is the time sufficient to obtain the transfer function, and T >> τ, where τ is the time of the optical signal bypassing the fiber-optic circuit of the Sagnac interferometer; the second auxiliary signal M ₂ is a meander with an amplitude corresponding to the optical phase shift Δϕ ₂ = π / 4 with a period of 2τ.

Half of the period of a signal M _{1 of} duration T / 2 is a stepwise action with an amplitude of 2Δϕ ₁ , whose function in z-space is expressed as follows:

Given that the fiber circuit of the Sagnac interferometer delays the optical signal propagating through it for a time τ, the transfer function of the fiber circuit H _VK can be represented as a delay line, and expressed as follows:

Given (1), (2) and the transfer function of the FM N _FM , the phase shift of the Sagnac interferometer Δϕ _IS1 when applying the M ₁ signal to the FM is expressed as follows:

According to (3), Δϕ _IS1 is the FM response to the delta function with an amplitude of 2Δϕ ₁ . Thus, when a step effect is applied to the FM electrodes of the Sagnac interferometer, the resulting phase difference of the Sagnac interferometer is the impulse response of the FM, which is due to the compensatory nature of the Sagnac interferometer: a stepwise change in the modulation signal causes a non-zero phase difference of the Sagnac interferometer only during the time τ after the jump of the modulation signal .

However, since the Sagnac interferometer is characterized by low sensitivity when the operating point is located in the region of the apex of the cosine interferometric dependence, an auxiliary meander M ₂ with a period of 2τ and amplitude is added to the modulation signal, which ensures the displacement of the operating point of the interferometer by the most sensitive part of the cosine sinusoidal interferometric response - to the quadrature point .

The rectangular bias signal M ₂ is expressed in z-space as follows:

Given (2) and (4), the phase shift of the Sagnac interferometer Δϕ _IS2 when the FM signal M ₂ is applied is expressed as follows:

Due to the fact that expression (5) contains only one harmonic corresponding to the frequency of the meander M ₂ , the transfer function H _FM at a given frequency can be taken equal to unity. Given this assumption, expression (5) is transformed as follows:

According to (6), Δϕ _IS2 is a meander with amplitude π / 2.

According to the claimed method, the phase shift of the Sagnac interferometer Δϕ of the _IC is affected by the modulation signal (M ₁ + M ₂ ), the transfer function of the fiber circuit of the Sagnac interferometer N _VK , as well as the transfer function of the FM N _FM . Thus, taking into account (3) and (6), the phase shift of the Sagnac interferometer when a signal is fed to the FM (M ₁ + M ₂ ) is expressed as follows:

The first term of expression (7) is the impulse response of the FM, and the second term of expression (7) does not contain information about the transfer function of the FM, and serves as an auxiliary signal for shifting the operating point of the Sagnac interferometer to a linear portion of the cosine interferometric response, and is demodulated in accordance with a demodulation algorithm, the essence of which is illustrated by the following:

равный половине полученного усредненного сигнала длительностью Т/2, соответствующий ступенчатому воздействию сигнала М₁. Преобразованный таким образом сигнал интерферометра имеет вид:1) The recorded output signal of the interferometer, S _int , is averaged over time T, where T is the period of the modulation signal M ₁ , to reduce the random measurement error. For further operations use a signal

equal to half the received average signal of duration T / 2, corresponding to the stepwise effect of the signal M ₁ . The interferometer signal thus transformed has the form:

N - количество периодов T в сигнале S_ИНТ,

=[1…N] - порядковый номер периода.where K = T / τ is the number of samples of duration τ in the period T of the signal S _INT , k = [1 ... K / 2] is the serial number of the signal sample

N is the number of periods T in the signal S _INT ,

= [1 ... N] - serial number of the period.

имеет косинусоидальную зависимость и, при подаче на ФМ сигнала (М₁+М₂), выражается как:2) Interferometric response of the Sagnac interferometer,

has a cosine dependence and, when a signal is applied to the FM (M ₁ + M ₂ ), it is expressed as:

where I ₁ , I ₂ are the intensities of the interfering optical signals, Δϕ _E is the phase shift of the Sagnac interferometer caused by external influences on the fiber circuit of the interferometer.

нормируют на среднее значение и вычитают постоянную составляющую. Поскольку вычитание постоянной составляющей производят после указанной нормировки, то это равносильно вычитанию единицы из нормированного значения.Given I ₁ and I ₂ in expression (8), the resulting data sample

normalize to the average value and subtract the constant component. Since the subtraction of the constant component is performed after the specified normalization, this is equivalent to subtracting the unit from the normalized value.

текущий шаг демодуляции может быть также реализован вычислением функции Arcsin от полученных данных. Рассчитанный таким образом фазовый сигнал Ф, содержащий информацию о передаточной функции ФМ, имеет вид:In view of the cosine dependence of the interferometric response (8), the response is linearized. For this, the Arccos function is calculated from the obtained data, and since, in accordance with expression (7), the second term Δϕ of the _IC shifts the operating point of the interferometer by π / 2 radians, π / 2 is additionally subtracted. Given the well-known equality

the current demodulation step can also be implemented by calculating the Arcsin function of the received data. The phase signal Ф calculated in this way, containing information on the transfer function of the FM, has the form:

- среднее значение сигнала

Where

- average signal value

3) Since the interference function is periodic with a period of 2π, it is necessary to restore the phase shift of the first response point of the interferometer, which, in accordance with the modulation signal M _1, is a multiple of 2π and amounts to 2Δϕ ₁ . Accordingly, the first point of the obtained data is assigned the value 2Δϕ ₁ :

Ф [1] = 2Δϕ ₁ .

4) The auxiliary signal of modulation M ₂ is a meander with a period of 2τ, which shifts the operating point of the Sagnac interferometer to the points ± π / 2, in which the cosine function has a different character - in one case it decreases and increases in the other. Therefore, due to the phase shift of the interferometer caused by the transfer function of the FM and external influences on the fiber circuit of the interferometer, the even and odd samples of the data sample are shifted relative to the zero value with a different sign. Thus, the next step in the demodulation algorithm is the absolute values of the data sample - | Ф |.

When various external factors, such as angular rotation or a magnetic field, act on a fiber circuit of a Sagnac interferometer, an induced phase shift occurs, which is proportional to the value of this action Δϕ _E in expression (8). When measuring the transfer function of the FM in a Sagnac interferometer, such effects on the fiber circuit must remain constant throughout the entire measurement. To exclude the influence of Δϕ _E on the measurement results of the FM transfer characteristic, the constant component due to Δϕ _E is subtracted, thereby obtaining the FM response to the pulsed effect.

The resulting FM response to a pulsed action with an amplitude of 2Δϕ _{1 is} normalized to 2Δϕ ₁ , thereby obtaining a pulsed FM response, S _FM , is a response to a single pulsed effect:

5) The obtained impulse response of the FM is subjected to one of the known methods for identifying the transfer function, for example, the autoregressive method, thereby determining the desired transfer function of the FM.

The greater the order of the transfer function, the more accurately it determines the dynamic properties of the object, in this case, the Sagnac interferometer. Therefore, by the accuracy of the method for determining the transfer function is meant the order of the transfer function, to the accuracy of which the method allows to determine it. In comparison with the prototype, where the transfer function of the FM is determined to the first order, due to the limitation imposed by the number of used components of the analog filter, the inventive method allows to determine the desired transfer function of the FM with an accuracy of a higher order, due to the fact that it is determined by the pulse FM characteristics obtained in digital form with high resolution. Thus, in the claimed method, the accuracy of determining the transfer function of the FM in the Sagnac interferometer is determined by the resolution of the measuring system used to obtain the impulse response of the FM, and the selected method of identifying the transfer function.

The essence of the proposed method is illustrated by drawings.

In FIG. 1 shows a block diagram of a Sagnac interferometer supplemented with a modulation / demodulation unit for measuring the transfer function of the FM.

In FIG. 2 shows a) a modulation signal supplied to the FM electrical input; b) the ideal phase shift of the Sagnac interferometer for the described modulation signal; c) phase signal Ф calculated from the measured signal of the interferometer and containing information about the impulse response of the FM; d) the impulse response of the FM Sagnac S _FM interferometer obtained by the described method.

The inventive method can be carried out using the device shown in FIG. 1. The device contains an optical radiation source 1, an optical X-coupler 2, an optical coupler 3 (X or Y type), a phase modulator (FM) 4 and a fiber circuit 5, which together form a Sagnac interferometer or a ring interferometer. The optical signal registration circuit contains a photodetector 6 and an amplification circuit 7. The modulation / demodulation unit 8 implements a demodulation algorithm for the signal received from the amplifier 7 and generates a modulation signal supplied to the amplification circuit 9, from the output of which the signal is supplied to the FM input 4. FM 4 can be combined with an optical splitter 3 into a single multifunctional integrated optical circuit.

The inventive method is as follows. The optical radiation from the source 1 is fed to the input of the X-splitter 2 and then to the input of the splitter 3, which ensures the separation of the incoming radiation into two optical beams of equal intensity, each of which bypasses the fiber circuit 5 in opposite directions, and is also phase modulated when passing through the FM 4. Next, both beams are again combined in the splitter 3, the total optical beam passes through the X-splitter 2, and then enters the photodetector 6, which records the interferometric response of the interferometer a Sagnac, S _int . The current of the photodetector 6 is amplified by the amplification circuit 7, the output signal of which falls into the modulation / demodulation unit 8, where the recorded interferometric response is subjected to the described demodulation algorithm. The modulation / demodulation unit 8 generates a modulation signal representing the sum of two signals: the meander M ₁ (with an amplitude corresponding to the optical phase shift Δϕ ₁ = Nπ (where N = 1,2,3 ...), and with a period T, where T / 2 is the time sufficient to obtain the transfer function, and T >> τ, where τ is the time taken by the optical signal to traverse the fiber circuit 5) and the meander М ₂ with an amplitude corresponding to the optical phase shift Δϕ ₂ = π / 4 and with a period of 2τ. Next, the generated modulation signal passes through the amplification circuit 9 and enters the electrical input FM 4.

As a result of the described demodulation algorithm, the modulation / demodulation unit 8 calculates the desired transfer function FM, N _FM .

As a specific example, we propose a method for measuring the transfer function of an FM Sagnac interferometer, in which a multifunctional integrated-optical circuit (MIOS) made on the basis of a single-crystal niobate plate acts as an FM and an optical X-coupler (items 3 and 4 in FIG. 1) lithium (LiNbO ₃ ) x-cut, the channel waveguides of which are made using titanium diffusion technology. An erbium fiber superluminescent source with a central wavelength of 1550 nm acts as a source of optical radiation. As an optical splitter (pos. 2 in Fig. 1), a fiber X-splitter with a division ratio of 50/50 acts. The interference optical response from the fiber optic X-splitter 2 is fed to a photodetector, which is a PDI-80 photodiode, and an amplification circuit based on the ADA4817 transimpedance amplifier. The algorithm for demodulating the recorded interferometric response is implemented in a modulation / demodulation unit, which is a combination of an analog-to-digital converter with a resolution of 18 bits, which converts an analog electrical signal from a photodetector and amplifier into digital form, a programmable logic integrated circuit, in which demodulation algorithms and generating a modulation signal, as well as a digital-to-analog converter with a resolution of 20 bits, which converts digitally th signal into an analog electric signal, which is fed to the input of the amplification electric circuit, the output of which is fed to the FM electrical input.

In FIG. 2. shows the signals obtained experimentally in accordance with the proposed method. Based on the impulse response (Fig. 2, d) using the autoregressive method, the transfer function of the FM was calculated. The resulting transfer function of the FM used in the measurements shown in FIG. 2, has the form of a sixth order low pass filter:

Thus, the inventive method allows to determine the transfer function of the FM in the Sagnac interferometer with increased accuracy.

Claims (1)

A method for determining the transfer function of a phase modulator in a Sagnac interferometer, comprising applying to the electrical input of the phase modulator a control voltage signal containing an auxiliary signal in the form of a meander whose amplitude provides a shift of the operating point of the interferometer by a linear portion of the interferometric function, and measuring the received signal of the interferometer, which is used for determining the transfer function of the phase modulator, characterized in that the electrical input of the phase module simultaneously with the auxiliary signal, the second voltage control signal is supplied in the form of a meander with an amplitude corresponding to the optical phase shift Δϕ ₁ = Nπ (where N = 1,2,3 ...), and with a period T >> τ, where τ is the optical bypass time the signal of the fiber-optic circuit of the Sagnac interferometer, and measure the received signal of the interferometer S _int , which is used to calculate the phase signal

Where

Where

- average signal value

K = T / τ - the number of samples of duration τ in the period T of the signal S _int , k = (1 ... K / 2] - the serial number of the signal sample

N is the number of periods T in the signal S _int ,

= [1 ... N] is the sequence number of the period, and Ф [1] = 2Δϕ ₁ , and from the phase signal Ф the impulse response of the phase modulator S _{FM is} calculated according to the expression

and, exposing the obtained impulse response to the identification function of the transfer function, determine the desired transfer function of the phase modulator of the Sagnac interferometer.

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