ZHANG Xiong-xing，LV Wen-tao，ZHANG Tian-yang，KOU Wan-ying，CHEN Qing-qing，WANG Wei

（School of Optoelectronics Engineering, Xi’an Technological University, Xi’an, Shannxi 710021, China）

* Corresponding author，E-mail: wangwei@xatu.edu.cn

Abstract: In order to realize the demodulation of the cavity length of the fiber-optic FP sensor, a new optical wedge-type non-scanning correlation demodulation system is proposed, and the characteristics and structure of the devices used in the system are analyzed and studied. First, by simulating the light sources with different spectral distributions and the optical wedges with different surface reflectivities, the correlation interference signals are analyzed and the optimal structure parameters of the system components are given. Then by comparing the light intensity distribution characteristics of the Powell prism and cylindrical lens on the linear array CCD, more uniform spectral distribution is achieved. Finally, the specific implementation scheme and data processing method of the demodulation system are given. The experimental results show that when the light source spectrum has a Gaussian distribution and large spectral width and the reflectivity of the wedge surface is R=0.5, the characteristics of the correlation interference signal are obvious and convenient for demodulation. Finally, the demodulation system achieves the demodulation effect with an error of less than 0.025% within the cavity length range of 60 μm-100 μm. This optical wedge-type non-scanning correlation demodulation method can realize the sensing demodulation of the fiber-optic FP cavity and improve the power adaptability of different types of fiber-optic FP sensors.

Key words: fiber-optic FP sensor; non-scanning correlation demodulation; optical wedge; Powell prism; linear array CCD

1 Introduction

As an important branch of optical fiber sensing,the technology of optical Fiber-optic FP sensor is developing rapidly. It is characterized by high precision, small size and anti-interference, and is widely used in aerospace, civil engineering, medical treatment and other fields[1-3]. The changes in external physical quantities will affect the cavity length of a FP sensor. By demodulating the cavity length information, different physical quantities such as pressure, temperature and strain can be measured[4-5].

Fiber-optic FP sensors are divided into intrinsic type and non-intrinsic type. The intrinsic fiber FP sensor is an internal cavity structure composed of optical fibers. It can sense the changes of external information by using the sensing of optical fiber.The non-intrinsic type, however, is an external cavity structure generally filled with air or vacuum and formed by hollow-core fiber, capillary, elastic membrane or other sensitive elements. These sensitive elements are used to sense the changes of physical quantities, while the optical fiber is only used for signal transmission[6-7]. Fiber-optic FP sensors can be fabricated by MEMS, chemical etching, direct welding, laser processing and other methods. With a simple structure and wide range of applications,they are of great significance for structural status detection under harsh working environment[8-10].

Due to the application advantages of FP sensors, the demodulation techniques for these sensors have also developed rapidly, mainly including intensity demodulation and phase demodulation[11]. Intensity demodulation is relatively traditional, and is easily interfered by external factors and optical device performance, which may result in low demodulation accuracy[12]. Phase demodulation is to calculate the cavity length according to the phase information of the obtained interference spectrum signal. It is less affected by the light intensity,so the demodulation accuracy is higher[13]. Correlation demodulation is to introduce a dynamic reference cavity into the demodulation system in accordance with the principle of cavity length matching,and then obtain the cavity length information through the correlation operation between the output signal of FP sensor and the reference cavity signal. According to the control mode of reference cavity, the demodulation techniques can be divided into scanning demodulation and non-scanning demodulation. In the scanning demodulation system,piezoelectric ceramics or a mechanical moving part is generally used to control the length of the reference cavity. In this scheme, the introduction of dynamic tuning signal and mechanical part often leads to low demodulation rate and low accuracy. The non-scanning demodulation system, however, is based on Fizeau interferometer with optical wedge and FP sensor as correlation components, so it has high structural stability and has been widely used[14-16].

The key of the non-scanning correlation demodulation system of fiber-optic FP sensor is to obtain the correlation interference signal with evident characteristics, and then search for the signal peak to obtain the sensor cavity length. The demodulation system is generally the combination of a broadband light source, a large-aperture fiber collimator, a cylindrical lens, an optical wedge and a CCD. The spectral distribution of light source and the surface reflectivity of optical wedge will also affect the contrast of correlation interference signals[17-19]. The effects of triangular, rectangular and Gaussian broadband light sources with different spectral distributions and of the optical wedges with different surface reflectivities on the correlation interference signals were simulated and analyzed. In the structural design of the demodulation system, the correlation module is generally the combination of a large-aperture fiber collimator and a cylindrical lens. The optimization of this design is also ongoing. Because the cylindrical lens can cause non-uniform light intensity distribution, the demodulation difficulty will be increased. In order to solve this problem, the demodulation system is optimized in this paper by proposing a new optical wedge demodulation system based on Powell prism, which can eradicate the problem of non-uniform light intensity distribution and eliminate the phenomenon of central hot spot and fading edge of Gaussian beam during demodulation.

2 Demodulation principle

The non-scanning correlation demodulation method is shown in Figure 1. The length of the reference FP cavity introduced by this method varies with space, which is realized by changing the optical wedge thickness. The optical wedge has different thicknesses at different positions. These different wedge thicknesses can be regarded as multiple FP fiber sensors with different cavity lengths. The structure diagram of optical wedge is shown in Figure 2.

As can be seen from Figure 1, the demodulation system is composed of a broadband light source, an optic fiber coupler, a fiber-optic FP sensor and a correlation module. The outgoing light of the broadband light source is transmitted via the optical fiber coupler to the fiber-optic FP sensor,where the two-beam interference occurs. Then the return light carrying the cavity length information is transmitted to the correlation module, also via the optical fiber coupler. The correlation module includes a fiber collimator, a Powell prism, an optical wedge, and a linear array CCD. The fiber collimator shapes the light returning from the fiber into parallel beams, which, in turn, travel to the Powell prism and are converted into linear beams. Then the linear beams enter the optical wedge, where the multiple beam interference occurs on two surfaces.After being modulated by the wedge, the light travels to the CCD. Finally, the signal is processed to get the cavity length information.

The intensity of the interference light generated by the fiber-optic FP sensor, denoted asIr, can be expressed as:

whereRis the reflectivity of the end face of the fiber-optic FP cavity,nis the refractive index of the cavity of the fiber sensor,lis the length of the FP cavity, λ is the wavelength of the light wave, andIiis the intensity of the light entering the demodulation system.

The light source used in the non-scanning correlation demodulation method is a broadband light source. When calculating the total light intensity of the correlation interference signals, the light intensity values of the correlation interference signals generated by all wavelengths should be added to obtain the total light intensity of the signals output through the fiber-optic FP sensor and optical wedge, as shown:whereR1represents the reflectivity of the wedge surface, θ represents the wedge angle, andxrepresents any position on the long side of the right triangle.

The analysis of the correlation interference signals in Equation (2) shows that, in the non-scanning correlation demodulation method, when the maximum correlation signal is observed, the wedge thickness corresponds to the cavity length of the fiber-optic FP sensor, namelyxtanθ=l. This phenomenon is called cavity length matching. Thus, the cavity length of the fiber-optic FP sensor can be demodulated.

3 Characterization of demodulation devices

3.1 Light source

In practical applications, the spectral distribution of a light source is not completely uniform. In order to analyze the influence of different spectral distributions on the demodulation signal, three spectral distribution curves with different shapes,namely Gaussian shape, triangle and rectangle, were chosen in this paper, as shown in Figure 3 (Color online). Among them, the Gaussian and triangular spectra were used to simulate the spectrum of SLED light source, while the rectangular spectrum was used to simulate the spectrum of erbium-doped fiber laser source. The 3 dB bandwidths and central wavelengths of the three light sources were all the same. Since the spectral response range of linear array CCD was 400 nm?1100 nm, the central wavelengths of the three spectral curves were assumed to be 850 nm. As can be seen from the figure, when the spectral curves of the three broadband light sources have the same 3 dB bandwidth, the effective spectral width of the Gaussian light source is the largest, while that of the rectangular light source is the smallest.

Considering the spectral distribution characteristics of the light source and the spectral distribution characteristics of the light traveling in space,the mathematical model of correlation interference signals can be obtained according to equation (2):

wherexpis the position of the central wavelength,xis the length of the distance fromxp,Bxis the FWHM of the Gaussian distribution function of the light traveling in space, andf(λ) is the mathematical model of the spectral distribution of different light sources.

To obtain the spectral distribution curves of the three light sources, the central wavelength of the simulated light source was assumed to be 850 nm,the 3 dB bandwidth was 60 nm, the length of the fiber-optic FP cavity was 80 μm, the thickness of the optical wedge was between 50 μm and 100 μm,and the length of the optical wedge was 0.03 m.Through simulation, the intensity distribution curves of the optical wedge were obtained under the spectral distributions of different light sources (Fig. 4).

Fig. 1 Schematic diagram of optical wedge demodulation system for fiber-optic FP sensor圖 1 光纖法珀傳感器光楔式解調(diào)系統(tǒng)示意圖

Fig. 2 Schematic diagram of optical wedge structure圖 2 光楔結(jié)構(gòu)示意圖

Fig. 3 Three kinds of spectral distribution curves圖 3 3種光譜分布曲線

Fig. 4 The output light intensity distribution of correlation interference signal under different spectral distributions圖 4 不同光譜分布下相關(guān)干涉信號輸出分布

Fig. 5 Output spectrum of SLED圖 5 SLED輸出光譜

Fig. 6 Light intensity distributions of (a) cylindrical lens and (b) Powell prism圖 6 (a)柱透鏡和(b)鮑威爾棱鏡光強(qiáng)分布效果圖

Fig. 7 Light intensity distributions of the background signals from cylindrical lens and Powell prism detected by CCD圖 7 柱透鏡和鮑威爾棱鏡光強(qiáng)分布經(jīng)CCD探測基底信號圖

Fig. 8 Comparison of correlation interference signals obtained by the optical wedges with different surface reflectivities圖 8 不同表面反射率的光楔的相關(guān)干涉信號對比圖

Fig. 9 Optical wedge structure of fiber-optic FP sensor demodulation system. (a) Schematic diagram of optical wedge fabrication; (b) combination of CCD and optical wedge圖 9 光纖法珀傳感器解調(diào)系統(tǒng)的光楔結(jié)構(gòu)。(a)光楔制作示意圖；(b)CCD結(jié)合光楔實(shí)物圖

Fig. 10 Schematic diagram of fiber-optic FP sensor圖 10 光纖法珀傳感器示意圖

Fig. 11 Experimental optical wedge demodulation system for the fiber-optic FP sensor. (a) Overall structure; (b) detailed picture of the sensor; (c) internal structure of dark box圖 11 光纖法珀傳感器光楔式解調(diào)實(shí)驗(yàn)系統(tǒng)。(a) 整體結(jié)構(gòu) (b) 傳感器細(xì)節(jié)圖 (c) 暗盒內(nèi)部結(jié)構(gòu)

It can be seen from the comparison that, when the 3 dB bandwidths and spectral ranges of all the spectra are the same, the curve of the light intensity distribution under the action of Gaussian spectrum has less background signal noise and higher output signal contrast than those of triangular and rectangular spectra to facilitate accurate peak-finding and high-precision demodulation. Influenced by the characteristics of Gaussian spectrum itself, the integral spectral range of Gaussian spectrum is larger than that of triangular or rectangular spectrum.However, when the spectral range is larger, different groups of correlation interference fringes are superimposed on each other, leading to more sparse correlation interference signal fringes, higher fringe contrast and greater light intensity. In addition, the wide-spectrum light source has a suppression effect on the noise, mainly because it has a small coherence, which reduces the coherence error introduced by the noise. According to the analysis, a SLED with a 3 dB bandwidth of 60 nm was selected as the broadband light source, whose spectrum was shown in Figure 5.

3.2 Powell lens

In the optical wedge non-scanning correlation demodulation method, the correlation module is generally the combination of a large-aperture fiber collimator, a cylindrical lens, an optical wedge and a CCD. The light passes through the fiber collimator to the cylindrical lens. The cylindrical lens converts the light into linear beams, which, in turn, shine on the optical wedge. Then the wedge outputs the correlation interference signals. The CCD collects the optical signals and converts them into electrical signals. For the correlation module of this structure, it was found in the experiment that for the lens reason,the DC bias distribution of the obtained correlation interference signals was not uniform, which affected the demodulation of the cavity length. Therefore, the fiber collimator and the cylindrical lens were optimized. The size of the fiber collimator was reduced and the cylindrical lens was changed into a Powell prism, so as to greatly reduce the system size and eliminate the influence of non-uniform bias distribution.

Different from cylindrical lens, Powell prism can convert the light very well, so that the light is distributed evenly within the fan angle of Powell prism, rather than more in the middle and less at the edge in a cylindrical lens. The light intensity distributions of the cylindrical lens and Powell prism are shown in Figure 6. The beam distribution formed after the light passes through the cylindrical lens is shown in Figure 6(a). It can be found that, the light intensity is mainly concentrated in the middle and decreases with the distance from the center, as seen in the Gaussian distribution. The beam distribution formed after the light passes through the Powell prism is shown in Figure 6(b). After passing through the Powell prism, the light energy is evenly distributed within the fan angle. This distribution effectively eliminates the defect that the light intensity is stronger in the middle and weaker at the edge.

In an experiment, the combination of a largeaperture collimator and a cylindrical lens was compared with the combination of a small-aperture collimator and a Powell prism, and a linear array CCD was used to detect the two groups of signals. The results are shown in Figure 7, where the abscissa represents the CCD pixel serial number and the ordinate represents the relative intensity. The results show that the background signal distribution obtained by Powell prism is more uniform than that obtained by cylindrical lens, so the use of Powell prism as the beam-shaping structure is more beneficial to signal demodulation.

3.3 Optical wedge

Optical wedge is the key device to realize the demodulation in the system. It directly determines whether the correlation operation can be implemented. Therefore, optical wedge is very important for the whole demodulation system. The design and selection of optical wedge need to consider the cavity length range of the sensor. The initial cavity length of the fiber-optic FP sensor used in the experiment was about 80 μm. In order to expand the measurement range as much as possible, the wedge thickness range was roughly set as 50 μm?100 μm. According to Equation (2), the reflection coefficient of the wedge can affect the light intensity of the correlation interference signal. In order to better determine this relationship, the light intensity distribution of the correlation interference signal was simulated when the reflection coefficientRwas 0.1, 0.3, 0.5,0.7 and 0.9.

The simulation results are shown in Figure 8(Color online). As can be seen from the figure, the light intensity of the correlation interference signal decreases gradually with the increase of the reflectivityR, and the contrast of the correlation interference signal reaches its maximum atR=0.5.Therefore, it was determined that the outer surface of the wedge should be coated with an antireflection film covering the entire spectral range, while the inner surface should be coated with a semi-reflection semi-transmission film covering the entire spectral range.

The wedge width should be consistent with the CCD width. Two glass sheets were used to fabricate the optical wedge. At first, two clean glass sheets of suitable length were chosen, with one side coated with an anti-reflection film and the other side coated with a semi-reflection semi-transmission film. Two film shims, 50 μm and 100 μm thick respectively, were prepared. Then the semi-reflection semi-transmission surfaces of the two glass sheets leaned against each other. The 50-μm thick shim was sandwiched at one end between the glass sheets and the 100-μm thick shim at the other end. Finally,an optical wedge was formed by bonding the ends of the two glass sheets with ultraviolet glue. Then,the finished optical wedge was pasted on the CCD with ultraviolet glue, as shown in Figure 9.

4 Experimental verification

Non-intrinsic fiber-optic FP sensor is typically fabricated by inserting single-mode fibers into a hollow glass tube (Figure 10). At first, two segments of single-mode fibers with flat ends and one segment of hollow glass tube are prepared. Then the two fibers are inserted into the glass tube from both ends to form a FP cavity in tube with air as the medium.Usually, the joints between the glass tube and the fibers are fixed with UV glue in order to obtain a stable cavity structure. Alternatively, the fiber sections can be coated with film to improve the reflectivity and form a non-intrinsic fiber-optic FP sensor with high fineness.

The non-scanning correlation demodulation system for fiber-optic FP sensor was built, as shown in Figure 11. The system was composed of a SLED

light source with the central wavelength of 850 nm and the 3 dB bandwidth of 60 nm, a 2×1 fiber coupler, a fiber-optic FP sensor, a fiber collimator, a 30-mm long Powell prism, an optical wedge (50 μm?100 μm thick), a linear array CCD and a data processing unit. Among them, the fiber collimator, the Powell prism, the optical wedge and the CCD were fixed in a dark box.

An fiber-optic FP sensor with an initial cavity length of 80.067 μm was connected to the established experimental platform. The correlation interference signals were converted by CCD into electrical signals for data processing. The curve of the collected correlation interference signal is shown in Fig. 12 (Color online). The abscissa represents the pixel point position, and the ordinate represents the relative intensity of the correlation interference signal converted into a digital signal.

As can be seen from the blue curve in Fig. 12,the acquired signal contains not only the useful signal, but also low-frequency bias and high-frequency noise. At first, the signal was converted to the frequency domain through Fourier transform. The frequency band where the signal was located was determined. Then, inverse Fourier transform was applied to the signal in this frequency band to achieve bandpass filtering. The red curve in the figure represents the signal obtained by the bandpass filter. It can be seen that compared with the original signal,the high-frequency noise and low-frequency bias in the filtered signal have been removed, and the curve has become smooth with an obvious envelope.Then, direct peak-searching calculation can be made. Alternatively, the envelope curve of the filtered signal can be fitted and finally, the maximum peak position on the fitted envelope curve can be found. The calculation result shows that, the maximum value of the correlation interference signal generated by the fiber-optic FP sensor with an initial cavity length of 80.067 μm is at the pixel point position 1729.739.

Fig. 12 Signals collected by CCD in the optical wedge demodulation system for fiber-optic FP sensor圖 12 光纖法珀傳感器光楔式解調(diào)系統(tǒng)CCD采集信號圖

Fig. 13 Test results of optical wedge demodulation system for fiber-optic FP sensor圖 13 光纖法珀傳感器光楔式解調(diào)系統(tǒng)測試結(jié)果圖

By calibrating the demodulation system and the standard fiber-optic FP sensor, the correspondence relation between the pixel point position at the peak value of the correlation interference signal and the cavity length is obtained asL=11.889·n+59 511.072 nm, whereLis the cavity length of the FP sensor,nis the pixel serial number corresponding to the peak position of the correlation interference signal, and the fitting coefficient isR2=0.999 9. 8 fiber-optic FP sensors with the cavity lengths of 65.002 μm, 69.141 μm, 73.125 μm,75.109 μm, 80.067 μm, 83.692 μm, 89.388 μm and 93.474 μm respectively were connected to the demodulation system one by one. The measured and fitting results are shown in Figure 13. It can be seen that the maximum error is 9 nm and the fullscale measurement error is less than 0.025%.

Under different light source power, the demodulation ranges of the optical wedge demodulation systems using Powell prism and cylindrical lens were compared, as shown in Fig. 14, and the corresponding data is also given in Table 1. It can be seen that the demodulation system using Powell prism has strong light source stability, small demodulation range fluctuation and relatively stable performance. When the power of the light source is less than 6 mW, the demodulation system using cylindrical lens cannot realize demodulation because of the disappearance of the correlation interference signal.This further demonstrates the advantage of Powell prism in the adaptability to light source power.

Fig. 14 Comparison of demodulation ranges of the demodulation systems using Powell prism and cylindrical lens under different light source powers圖 14 不同光源功率下采用鮑威爾棱鏡及柱透鏡的解調(diào)系統(tǒng)的解調(diào)范圍對比圖

Tab. 1 Test data表 1 測試數(shù)據(jù)

5 Conclusion

In this paper, a non-scanning correlation demodulation method based on optical wedge was proposed for the demodulation of fiber-optic FP sensor, and the demodulation system was optimized.The simulation analysis of light source and optical wedge found that, when the light source spectrum was Gaussian distribution, the bandwidth was large and the surface reflectivity of optical wedge was R=0.5, the correlation interference signal of the demodulation system could achieve a higher contrast,which was convenient for accurate peak searching and demodulation. In addition, by applying the Powell prism, the influence of light intensity was greatly improved in a certain range of light power,and the adaptability of this modulation system to the light source power was enhanced. Through the calibration of this system, the final measurement range error was reduced to less than 0.025%.

中文對照版

1 引 言

光纖法布里-珀羅(法珀)傳感器作為光纖傳感的重要成果，得到了快速發(fā)展，其具有精度高、體積小、抗干擾等特點(diǎn)，廣泛應(yīng)用在航空航天、土木工程、醫(yī)療等領(lǐng)域[1-3]。由于外界物理量的變化會影響法珀傳感器的腔長，故可以通過解調(diào)腔長信息，實(shí)現(xiàn)對于壓力、溫度、應(yīng)變等不同物理量的測量[4-5]。

光纖法珀傳感器可分為本征型和非本征型，本征型結(jié)構(gòu)的光纖法珀傳感器屬于內(nèi)腔式結(jié)構(gòu)，其腔體由光纖構(gòu)成，利用光纖可以傳感的特征感知外界信息的變化。而非本征型是一種外腔式結(jié)構(gòu)，腔體一般是空氣或真空，腔體的形成多采用空芯光纖、毛細(xì)管或彈性膜片等敏感元件，用于感知物理量的變化，光纖僅僅起到傳輸信號的作用[6-7]。光纖法珀傳感器可以通過MEMS、化學(xué)刻蝕、直接熔接、激光加工等方法制備，其結(jié)構(gòu)簡單適用性強(qiáng)，對于嚴(yán)苛工作環(huán)境下的結(jié)構(gòu)狀態(tài)檢測有著重要意義[8-10]。

由于法珀傳感器自身的應(yīng)用優(yōu)勢，針對這種傳感器的解調(diào)技術(shù)也得到了迅速發(fā)展，主要包括強(qiáng)度解調(diào)法、相位解調(diào)法和相關(guān)解調(diào)法[11]。強(qiáng)度解調(diào)法較為傳統(tǒng)，受外界和光學(xué)器件性能的干擾容易導(dǎo)致解調(diào)精度低[12]。相位解調(diào)法根據(jù)獲得的干涉光譜信號的相位信息來求解腔長，該解調(diào)方法受光強(qiáng)的影響較小，解調(diào)精度更高[13]。相關(guān)解調(diào)法是基于腔長匹配原理，在解調(diào)系統(tǒng)中引入動(dòng)態(tài)參考腔，對法珀傳感器輸出信號與參考腔信號進(jìn)行相關(guān)運(yùn)算得到腔長信息。根據(jù)參考腔的控制方式又分為掃描式與非掃描式，掃描式解調(diào)系統(tǒng)一般采用壓電陶瓷或機(jī)械運(yùn)動(dòng)部件控制參考腔長，這種方案引入的動(dòng)態(tài)調(diào)諧信號與機(jī)械部件導(dǎo)致解調(diào)速率與精度較低。非掃描式解調(diào)系統(tǒng)基于斐索干涉儀，采用光楔與法珀傳感器作為相關(guān)元件，結(jié)構(gòu)穩(wěn)定性高，得到廣泛應(yīng)用[14-16]。

光纖法珀傳感器非掃描相關(guān)解調(diào)系統(tǒng)關(guān)鍵在于獲得特征明顯的相關(guān)干涉信號，進(jìn)而對信號進(jìn)行尋峰處理得到傳感器腔長信息。解調(diào)系統(tǒng)一般采用寬帶光源、大口徑光纖準(zhǔn)直器、柱透鏡、光楔與CCD的組合，不同光譜分布的光源以及光楔表面的反射率大小也會影響相關(guān)干涉信號的對比度[17-19]。

本文模擬分析了三角、矩形和高斯3種不同寬帶光源以及不同表面反射率的光楔對傳感相關(guān)干涉信號的影響。解調(diào)系統(tǒng)結(jié)構(gòu)設(shè)計(jì)中相關(guān)模塊一般采用大口徑光纖準(zhǔn)直器、柱透鏡的組合，這種設(shè)計(jì)的優(yōu)化也在不斷進(jìn)行，由于柱透鏡會帶來光強(qiáng)分布不均勻的情況，導(dǎo)致解調(diào)難度加大。為了解決這個(gè)問題，本文對解調(diào)系統(tǒng)進(jìn)行了優(yōu)化，提出一種基于鮑威爾棱鏡的新型光楔式解調(diào)系統(tǒng)，從根本上去除了光強(qiáng)分布不均勻的問題，消除了解調(diào)中高斯光束光場分布不均勻的問題。

2 解調(diào)原理

非掃描式相關(guān)解調(diào)方案如圖1所示，該方法引入的參考法珀腔長是隨空間變化的，其腔長的改變通過光楔厚度來實(shí)現(xiàn)。不同位置處的楔厚不同，這些不同的楔厚可以視為多個(gè)腔長不同的法珀光纖傳感器，光楔結(jié)構(gòu)示意圖見圖2。

從圖1可以看出，該解調(diào)系統(tǒng)由寬帶光源、光纖耦合器、光纖法珀傳感器和相關(guān)模塊組成。寬帶光源的出射光經(jīng)光纖耦合器傳輸?shù)焦饫w法珀傳感器，發(fā)生雙光束干涉，攜帶腔長信息的返回光再經(jīng)光纖耦合器傳輸?shù)较嚓P(guān)模塊。相關(guān)模塊包括光纖準(zhǔn)直器、鮑威爾棱鏡、光楔以及線陣CCD。光纖準(zhǔn)直器將光纖返回光整形為平行光束照射至鮑威爾棱鏡，鮑威爾棱鏡將其轉(zhuǎn)換成線狀光束，線狀光束照射進(jìn)入光楔內(nèi)部并在兩個(gè)表面發(fā)生多光束干涉，經(jīng)過光楔調(diào)制后的光照射在線陣CCD上，最后進(jìn)行信號處理得到腔長信息。

經(jīng)過光纖法珀傳感器后生成的干涉光光強(qiáng)Ir可以表示為：

其中R表示光纖法珀腔端面的反射率，n表示光纖傳感器腔體的折射率，l表示光纖法珀腔的腔長，λ表示光波的波長，Ii表示進(jìn)入解調(diào)系統(tǒng)的光強(qiáng)大小。

非掃描相關(guān)解調(diào)法使用的光源為寬帶光源，在計(jì)算相關(guān)干涉信號光強(qiáng)時(shí)，應(yīng)該將所有波長產(chǎn)生的相關(guān)干涉信號的光強(qiáng)值進(jìn)行累加，經(jīng)過光纖法珀傳感器和光楔后輸出信號的光強(qiáng)為：式中R1表 示光楔表面的反射率，θ表示光楔的楔角，x表示直角長邊任意位置。

對式(2)相關(guān)干涉信號進(jìn)行分析可以得到，在非掃描相關(guān)解調(diào)法中，相關(guān)信號最大處的楔厚大小對應(yīng)著光纖法珀傳感器腔長的大小，表示為xtanθ=l，即腔長匹配，據(jù)此可以實(shí)現(xiàn)光纖法珀傳感器的腔長解調(diào)。

3 解調(diào)系統(tǒng)器件特性分析

3.1 光源

實(shí)際應(yīng)用中，光源光譜絕非完全均勻分布，為了分析不同光譜分布對解調(diào)信號的影響，文中選擇了3種不同形狀的光譜分布曲線，分別為高斯形、三角形以及矩形，如圖3（彩圖見期刊電子版）所示，其中，高斯形與三角形光譜模擬SLED光源光譜，矩形光譜模擬摻餌光纖光源光譜。3種光源光譜的3 dB帶寬、中心波長均相同。由于線陣CCD光譜響應(yīng)范圍為400~1100 nm，假定3種形狀光譜曲線的中心波長為850 nm，從圖3可以看出，當(dāng)3種寬帶光源光譜曲線具有相同的3 dB帶寬時(shí)，高斯形光譜曲線的有效譜寬最大，矩形光源最小。

考慮光源光譜分布和光在空間傳播時(shí)的分布特性，根據(jù)式(2)得到相關(guān)干涉信號的數(shù)學(xué)模型為：

其中，xp表示中心波長的位置，x表示距離xp的量，Bx表示光源在空間傳播時(shí)的高斯分布函數(shù)的半峰全寬，f(λ)表示不同光源的光譜分布數(shù)學(xué)模型。

針對3種光源光譜分布曲線，模擬光源中心波長為850 nm，3 dB帶寬為60 nm，光纖法珀腔長80 μm，光楔厚度變化范圍為50~100 μm，光楔長度為0.03 m，仿真得到不同光源光譜分布情況下，光楔上的光強(qiáng)分布曲線。

通過對比可以看出，在保證各光譜3 dB帶寬且光譜范圍一致的條件下，相對于三角形光譜、矩形光譜，高斯形光譜作用下輸出光強(qiáng)分布曲線的基底信號噪聲小，輸出信號對比度高，便于準(zhǔn)確尋峰，實(shí)現(xiàn)高精度解調(diào)。由于高斯光譜自身的特性，其積分光譜范圍大于三角光譜以及矩形光譜，而當(dāng)光譜范圍越大時(shí)，各組相關(guān)干涉條紋相互疊加，使得疊加后的相關(guān)干涉信號條紋稀疏，條紋對比度更高，光強(qiáng)更大。此外，寬譜光源對噪聲有抑制作用，主要原因是其具有較小的相干性，減小了噪聲引入的相干誤差。結(jié)合分析選用3 dB帶寬為60 nm SLED作為寬帶輸入光源，光源光譜圖如圖5所示。

3.2 鮑威爾棱鏡

光楔式非掃描相關(guān)解調(diào)法相關(guān)模塊一般采用的都是大口徑光纖準(zhǔn)直器、柱透鏡、光楔和CCD的組合結(jié)構(gòu)，光經(jīng)過大口徑光纖準(zhǔn)直器后到達(dá)柱透鏡，柱透鏡將光轉(zhuǎn)換為線狀光束，線狀光束照射在光楔上，從光楔輸出相關(guān)干涉信號，CCD采集光信號并轉(zhuǎn)換為電信號。對于這種結(jié)構(gòu)的相關(guān)模塊組合，從實(shí)驗(yàn)中發(fā)現(xiàn)，由于柱透鏡本身的原因，導(dǎo)致得到的相關(guān)干涉信號的直流偏置分布不均勻，影響腔長的解調(diào)。因此，對光纖準(zhǔn)直器和柱透鏡做了優(yōu)化，光纖準(zhǔn)直器尺寸變小，柱透鏡調(diào)整為鮑威爾棱鏡，很大程度上減小了系統(tǒng)的體積并消除了偏置分布不均勻帶來的影響。

與柱透鏡不同的是，鮑威爾棱鏡能很好地將光進(jìn)行轉(zhuǎn)換，使光均勻分布在鮑威爾棱鏡的扇角范圍內(nèi)，不存在像柱透鏡那樣中間部分光強(qiáng)集中，邊緣部分光強(qiáng)較弱的情況。柱透鏡和鮑威爾棱鏡的光強(qiáng)分布，如圖6所示，其中圖6(a)是光經(jīng)過柱透鏡后形成的光束分布，其光強(qiáng)主要集中在中間區(qū)域，距離中心越遠(yuǎn)光強(qiáng)越弱，類似于高斯分布；圖6(b)是光經(jīng)過鮑威爾棱鏡后形成的光束分布，光在經(jīng)過鮑威爾棱鏡后，其能量均勻分布在扇角范圍內(nèi)，這種分布有效避免了中間部分光強(qiáng)集中而邊緣光強(qiáng)較弱的情況。

將大口徑準(zhǔn)直器加柱透鏡組合與小口徑準(zhǔn)直器加鮑威爾棱鏡結(jié)構(gòu)進(jìn)行實(shí)驗(yàn)對比，使用線陣CCD探測兩組信號，結(jié)果如圖7所示，橫坐標(biāo)為線陣CCD的像素序列號，縱坐標(biāo)表示相對強(qiáng)度值，結(jié)果表明通過鮑威爾棱鏡獲得的基底信號分布較柱透鏡更為均勻，因此選擇鮑威爾棱鏡作為光束整型結(jié)構(gòu)更有利于信號解調(diào)。

3.3 光楔

光楔是實(shí)現(xiàn)系統(tǒng)解調(diào)的關(guān)鍵器件，直接決定著相關(guān)運(yùn)算的實(shí)現(xiàn)。光楔的設(shè)計(jì)與選取需要結(jié)合傳感器的腔長范圍，實(shí)驗(yàn)所使用的光纖法珀傳感器的初始腔長為80 μm左右，為了盡可能地提升測量范圍，粗略設(shè)置光楔的楔厚范圍為50 μm~100 μm。根據(jù)式(2)知，光楔的反射系數(shù)會影響相關(guān)干涉信號的光強(qiáng)。為了更好地確定光楔的反射系數(shù)對相關(guān)干涉信號的影響，在反射系數(shù)R分別為0.1、0.3、0.5、0.7、0.9五種情況下，對相關(guān)干涉信號的光強(qiáng)分布進(jìn)行仿真實(shí)驗(yàn)。

仿真結(jié)果如圖8（彩圖見期刊電子版）所示。從圖中可以看出，相關(guān)干涉信號的光強(qiáng)隨著反射率R的逐漸增大而逐漸減小，相關(guān)干涉信號的對比度在R=0.5的時(shí)候達(dá)到最大。因次，光楔外表面鍍涵蓋整個(gè)光譜范圍的增透膜，而內(nèi)表面鍍涵蓋整個(gè)光譜范圍的半反半透膜。

光楔寬度應(yīng)與CCD的寬度保持一致，采用兩塊玻璃板制作光楔。取兩塊適合長度的干凈玻璃片，其中一面鍍增透膜，一面鍍半反半透膜，準(zhǔn)備50 μm和100 μm厚度的薄膜墊片，將兩塊玻璃片的半反半透面靠在一起，在玻璃片的一端墊入50 μm薄膜另一端墊入100 μm薄膜，最終使用紫外膠將兩塊玻璃片端點(diǎn)固定在一起即可形成光楔。最后，將制作好的光楔使用紫外膠粘貼在CCD上，結(jié)果如圖9所示。

4 實(shí)驗(yàn)驗(yàn)證

使用單模光纖插入空芯玻璃管制作非本征型光纖法珀傳感器是一種典型做法（見圖10）。準(zhǔn)備兩段端面平整的單模光纖和一段空芯玻璃管，將兩段單模光纖分別從空芯玻璃管兩端插入，兩根光纖在管內(nèi)形成以空氣作為介質(zhì)的法珀腔。一般為了獲得穩(wěn)定的腔結(jié)構(gòu)，可使用紫外膠在玻璃管與光纖接合處做固定處理，亦可通過在光纖截面鍍膜提升反射率，形成高精細(xì)度的非本征光纖法珀傳感器。

搭建如圖11所示的光纖法珀傳感器非掃描相關(guān)解調(diào)系統(tǒng)。選擇中心波長為850 nm，3 dB帶寬為60 nm的SLED光源、2×1光纖耦合器、光纖法珀傳感器、光纖準(zhǔn)直器、鮑威爾棱鏡、長度為30 mm，厚度為50~100 μm的光楔、線陣CCD以及數(shù)據(jù)處理單元，其中，光纖準(zhǔn)直器、Powell棱鏡、光楔以及線陣CCD固定在暗盒中。

將初始腔長為80.067 μm的光纖法珀傳感器接入搭建好的實(shí)驗(yàn)平臺，通過CCD將相關(guān)干涉信號轉(zhuǎn)換為電信號，再經(jīng)數(shù)據(jù)處理。圖12（彩圖見期刊電子版）是采集到的相關(guān)干涉信號曲線分布圖，橫坐標(biāo)表示的是像素點(diǎn)所在位置，縱坐標(biāo)表示的是相關(guān)干涉信號轉(zhuǎn)換為數(shù)字信號后的相對強(qiáng)度值。

從圖12中藍(lán)色曲線可以看出，獲取的信號中，除了有效信號外，還存在著低頻偏置和高頻噪聲，首先使用傅立葉變換將信號轉(zhuǎn)換到頻域，確定信號所在的頻段，再對該頻段范圍的信號做傅立葉反變換，實(shí)現(xiàn)帶通濾波。圖中的紅色曲線表示經(jīng)帶通濾波器后得到的信號，與原始信號相比，信號中的高頻噪聲和低頻偏置已經(jīng)被去除掉，曲線變得光滑，包絡(luò)明顯，可以直接進(jìn)行尋峰計(jì)算，也可以對濾波后的信號進(jìn)行包絡(luò)曲線擬合，最后對擬合好的包絡(luò)曲線尋找最大峰值位置。計(jì)算得到初始腔長為80.067 μm的光纖法珀傳感器形成的相關(guān)干涉信號的最大值在像素點(diǎn)為1729.739位置處。

通過對解調(diào)系統(tǒng)與標(biāo)準(zhǔn)光纖法珀傳感器進(jìn)行標(biāo)定，得到相關(guān)干涉信號峰值像素點(diǎn)與腔長的對應(yīng)關(guān)系式為： L=11.889·n+59 511.072 nm，式中，L為法珀傳感器的腔長值，n為相關(guān)干涉信號峰值位置對應(yīng)的像素序列號，擬合系數(shù) R2=0.999 9，將8組腔長分別為65.002、69.141、73.125、75.109、80.067、83.692、89.388、93.474 μm的光纖法珀傳感器接入解調(diào)系統(tǒng)，結(jié)果擬合圖如圖13所示，其最大誤差為9 nm，滿量程測量誤差小于0.025%。

不同光源功率下，采用鮑威爾棱鏡與柱透鏡的光纖法珀傳感器光楔式解調(diào)系統(tǒng)解調(diào)量程對比如圖14 所示，數(shù)據(jù)見表1。可以看出采用鮑威爾棱鏡的解調(diào)系統(tǒng)的光源穩(wěn)定性較強(qiáng)，解調(diào)范圍波動(dòng)較小，較為穩(wěn)定。當(dāng)光源功率小于6 mW時(shí)，采用柱透鏡的解調(diào)系統(tǒng)由于相關(guān)干涉信號消失，無法實(shí)現(xiàn)解調(diào)，進(jìn)一步說明了鮑威爾棱鏡在光源功率適應(yīng)性上的優(yōu)勢。

5 結(jié) 論

本文針對光纖法珀傳感器解調(diào)，提出一種基于光楔式的非掃描相關(guān)解調(diào)方案，并且對于解調(diào)系統(tǒng)進(jìn)行了優(yōu)化。針對光源與光楔的選擇進(jìn)行模擬分析，得到光源光譜為高斯分布且?guī)捿^大時(shí)以及光楔表面反射率 R=0.5時(shí)，解調(diào)系統(tǒng)的相關(guān)干涉信號對比度更高，便于準(zhǔn)確尋峰解調(diào)。并且通過使用鮑威爾棱鏡，在一定光功率范圍內(nèi)大幅改善了光強(qiáng)的影響，提高了解調(diào)系統(tǒng)對于光源的功率的適應(yīng)性。通過對系統(tǒng)進(jìn)行標(biāo)定得到最終測量程誤差小于0.025%。