Measuring Optical Length and Analyzing Accuracy Error Based on All-Fiber Optic Interferometer

Jun Su, Qi Qiu, and Shuang-Jin Shi

1.Introduction

In recent years, along with the popularity of optical fiber technology, the all-fiber optical system has been widely applied to the engineering.In such type of optical systems, the accurate measurement of optical length is a very important research direction.Especially in such application domains such as the fiber optical sensor and fiber delay line[1]-[3], the accuracy in measurement determines the level of system performance.

The existing measurement programs of the optical length are mainly divided into the relative measurement and the absolute measurement.The relative measurement is used to measure the optic path of the optical system mainly by reading the appearing and disappearing mode of coherent fringes, which requires the consecutive changes of the optic path during the measurement, thus the application such as measuring the length of a fiber cannot be achieved.To achieve the absolute measurement, there are a lot of programs, such as in principle, the optic group delay measurement, grating null measurement, and optical time domain reflectometer (OTDR) measurement[4],[5].However,such programs have a lot of limiting factors and meanwhile some shortcomings in the accuracy, the consistency of repeated measurements and of measuring blind zones, etc.Therefore, this paper will propose an all-fiber length measuring system based on the M-Z (Mach-Zehnder)interferometer coherent null detection.

2.Null Detection Length Measuring System

The null detection all-fiber length measuring system mainly comprises null adjustable M-Z fiber optic interferometer, coherent intensity detecting circuit, and measured data processing module.Fig.1 shows the structure diagram.

In the system, the null adjustable M-Z fiber optic interferometer acquires optical path null mainly by scanning, of which the structure is shown in Fig.2.The road-spectrum amplified spontaneous emission (ASE) light source is led out as the coherent source of the system after passing through the optical fiber filter and is divided into upper and lower branches by a 3 dB coupler, of which the upper branch optical waves are fed into the optical path to be measured such as the fiber delay line, and the lower branch optical waves are led into the length compensated optical fiber.The length compensation optical fiber is used to ensure that the equivalency of the upper and lower optical paths can be realized by the optical path length compensation provided by the electric-controlled translation stage, i.e., the optical path null is acquired.The polarization maintaining (P-M) coupler in the system(beam-splitting: 10:90) realizes the supervision on the optical power of upper and lower branches in coordination with the detecting circuit and feeds back the power to the electric-controlled P-M attenuator, so as to realize the equivalency of the optical power in upper and lower branches and to acquire maximum coherent fringes intensity.Optical waves of upper and lower branches are subject to coherent combination in the P-M coupler(beam-splitting: 50:50) and the output optical waves are led into the coherent intensity detecting circuit.

Fig.1.Block diagram of null detection all-fiber length measuring system.

Fig.2.Structural diagram of null adjustable M-Z fiber optic interferometer.

During system measurement, a fiber collimator is driven by the electric-controlled translation stage for the radial shift.When the optical path difference of upper and lower branches is fallen within the coherent length of the light source, the vertex of the amplitude envelope of output optical power is the null of the optical path and the radial coordinate is LAdue to the variation in coherent fringes intensity.After the optical path changes, the fiber collimator keeps on scanning to get the radial coordinate of the next coherent null, i.e.LB, and then, the length change of the optical path to be measured is:

where n refers to the refractive index of fiber.

The coherent intensity detecting circuit is mainly used for the photoelectric conversion of the output optical power intensity of optical fiber interferometer and for the amplification and filtering of signals, and then, the analog signal is converted to digital data via high-speed sampling and sent to the measured data processing module by the universal serial bus (USB) data interface for processing.Fitting of sampled data is carried out by the measured data processing module through software, so as to get the envelope function of the coherent signal for determining the coordinate of envelope vertex.

3.Analysis on the Principle of Null Detection

The length measurement is based on null detection,which mainly applies the optical characteristic of relatively short coherent length of the broad-spectrum light source to get the envelope vertex of coherent optical power, so as to make sure whether the two optical paths are subject to an equal length, i.e.“null”[6].Accordingly, the light source output light spectrum in system directly determines the shape of the coherent power envelope and the accuracy of system positioning[7].In order to get a high-quality broad-spectrum light source, the scheme of the ASE light source with an optical fiber filter is adopted for this system.

3.1 Theory of Coherent Positioning

Board-spectrum optical waves are led out by the ASE light source basing on spontaneous emission and the spectral power flatness is superior to 0.5 dB commonly[8].At the same time, for the optical fiber band-pass filter used for filtering is characterized in the flat pass band, spectral intensity of coherent light source can be regarded as a“rectangular” spectrum, which is shown in Fig.3.

In Fig.3, λ0indicates the central wavelength of the spectrum, λ1and λ2indicates the upper and lower cut-off wavelength of 3 dB spectrum width, and α indicates the internal power density of the spectrum.

It can be seen from the theory of interference that the superimposition of various spectral components in optical spectral is incoherent.Provided that the power intensities of two branches are equivalent[9], the coherent intensity is given by

where x=k-k0=2π/λ-2π/λ0, k0denotes the wave vector of central wavelength, and Δβ refers to the optical path difference between two branches.After being subject to integration in items, (2) can be written as

Fig.3.Spectral composition diagram of coherent light source.

The spectrum of the coherent light source is symmetrical basing on the central wavelength λ0, and the spectrum(λ2-λ1) is much smaller than central wavelength λ0, so it is obviously that B(Δβ)≈0, and then, the following formula can be gotten by (3) according to the formula of the coherent light intensity of dual beam:

It can be seen from (5) that envelope of coherent intensity is subject to the modulation of function Ψ=A/P, the function of coherent visibility curve.The formula below can be gotten by bringing λ1and λ2to (4) to fulfill integration and to solve the expression of Ψ:

For λ2-λ1, the spectral width of coherent spectrum is much smaller than λ0, the central wavelength.cos(·) in (6) is approximated to 1 within coherent length.Accordingly, the above formula can be simplified as follow:

For the parameters of the ASE light source and optical fiber filter in this length measuring system, the envelope curve is drawn via MATLAB, as shown in Fig.4.

Fig.4.Emulated envelop curve of coherent intensity.

Fig.5.Screenshot of coherent wave oscilloscope.

The optical fiber filter with the spectral width of 18.4 nm and central wavelength 1550.2 nm is used in this measuring system.The width of primary null is determined as 261 μm by emulation.By checking the screenshot of the oscilloscope in experiment as shown in Fig.5, it can be seen that the measured width of the primary null is 256 μm.Accordingly, the fitting degree of emulation and actual measurement is high.In addition, the coherent visibility curve function is able to correctly reflect the outline of coherent envelope, which can be used as the formula for the fitting of sampled data.

4.Simulations and Analyzing on Null Error

After acquiring the sampled data of coherent null envelope, the coherent visibility curve function can be used for fitting the data, so as to get the horizontal coordinate of vertex.This process may bring certain measurement error of necessity.It is found out that the measurement error is mainly affected by the signal-to-noise ratio of the sampled data and the fluctuation of the coupling efficiency of the fiber collimator.

4.1 Impact of Signal-to-Noise ratio of Sampled Data on Null Error

During the process of converting the coherent power intensity to electrical signal and sending the sampled data to measured data processing module for data fitting, the measuring system will superpose noises onto envelope signal.Such noises mainly include photoelectric transformation noise, amplifier noise, and sampling quantization noise, etc[10].In order to simplify the process of analysis, aforesaid different kinds of noises are uniformly regarded as white noises to carry out numerical simulation.Standard data of the coherent envelope is obtained via (7) and is superposed with noise as per different signal-to-noise ratio, and then, it is subject to data fitting under the least square method by making use of (8),so as to analog the measuring process.ξ in (8) refers to the horizontal coordinate of the vertex after fitting.Refer to Fig.6 for the standard deviation of the ξ and the outcomes obtained under different signal-to-noise ratios and spectral width of light source.

Fig.6.Curve of vertex deviation under different signal-to-noise ratio and line width.

where σ refers to the noise factor.

It can be seen from the result of emulation that the positioning error of vertex can be effectively decreased by increasing the spectral width of light source and enhancing the signal-to-noise of the system.In this system, the signal-to-noise ratio of fitting data is greater than 20 dB, the spectral width of optical fiber filter is 18.4 nm and, the positioning error of vertex can be smaller than 1 μm.

4.2 Impact of the Fluctuation of Coupling Efficiency of Fiber Collimator on Null Error

During the process of acquiring coherent envelope, a fiber collimator is driven by the electric-controlled translation stage for radial shift.During this process, under the effect of the accuracy and stability of the translation stage, coupling efficiency of the fiber collimator may subject to fluctuation, resulting in the variation in the power intensity of lower branch.Accordingly, the power intensities are no longer equivalent, further affecting the shape of coherent envelope and leading positioning error of the vertex.At this point, the coherent intensity can be expressed as follows:

Provided power intensities of the upper and lower optical paths are equivalent at null, Ⅰ1and Ⅰ2can be expressed as follow:

where η indicates the variance of light intensity for unit distance.Substituting Ⅰ1and Ⅰ2into (9), the following expression can be obtained:

Fig.7.Curve of vertex deviation under different fluctuation of light intensity and line width

The following formula can be obtained through substituting the coherent visibility curve function by contrasting with (5) under the fluctuation of power intensity:

For η is unknown during the process of length measurement, (8) is still used for data fitting.Refer to Fig.7 for the result of emulation by analyzing the error of vertex under this circumstance.

It can be seen from the result of emulation that under certain fluctuation of power intensity, it is helpful to decrease the positioning error of vertex by properly increasing the spectral width of light source.In this measuring system, |η| is no greater than 0.4 dB/mm and measuring error is smaller than 1 μm.

5.Conclusions

This paper proposes an all-fiber length measuring system based on the M-Z interferometer coherent null detection.In this system, the position of the vertex is obtained through data fitting which is capable of improving the tolerance of the system against noise and fluctuation of the light power intensity and getting micron level accuracy in measurement.In experiment, the length of an optical fiber is measured, of which the measuring error is smaller than 2 μm, reaching up to the limit for the positioning error of the translation stage.This measuring system, by which the absolute length of the optical path can be measured with high precision, is good for engineering applications.

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