Application of slant lens fiber in reflective optical fiber displacement sensor

YANG Rui-feng, LANG Guo-wei, GUO Chen-xia, ZHANG Peng, HU Chen-hao, GAI Ting

(1. School of Instrument and Electronics, North University of China, Taiyuan 030051, China；2. Automatic Test Equipment and System Engineering Research Center of Shanxi Province，North University of China, Taiyuan 030051, China)

Abstract： This paper introduces the application of a slant lens fiber in a reflective fiber optical displacement sensor, namely the receiving fiber use the slant lens fiber. Based on the characteristic formula expression of the intensity modulation of planar single fiber pair, a mathematic model of single fiber fair intensity modulation is established. After simulation experiment, the influence of fiber spacing, fiber core diameter and fiber numerical aperture on the modulation characteristics of the sensor is summarized.

Key words： slant lens fiber； single fiber pair； modulation function; fiber displacement sensor

0　Introduction

With the advent of optical fiber and the development of optical fiber communication, optical fiber sensing technology using optical fiber as the sensing medium has been greatly developed. The optical fiber sensor utilizes the advantages of its optical fiber, such as light weight, corrosion resistance, small size, anti-electromagnetic interference, sexuality as well as the unique advantages of combining information sensing and transmission, providing an outstanding performance from a wide range of sensors. The optical fiber sensor has a wider range of detection than traditional sensors and solves the measurement problems that many conventional monitoring techniques are difficult to achieve[1-3]. Because of high reliability, low cost, design flexibility, the reflective optical fiber displacement sensor, has been widely used in displacement, angle, vibration and surface roughness detection[4].

However, the choice of optical fiber is very important. The slant lens fiber is made by grinding the optical fiber end face into a bevel shape. At present, the optical fiber is mostly used for optical coupling, and coupling with laser is used to improve coupling efficiency, offset tolerance and insertion loss[5]. Li S Y[6]built a built-in optical fiber pin grinding about 8° tilt angle, which can greatly reduce the reflected light into the optical fiber transmission, thereby reducing the impact on light source and system, At the same time, in the application of fiber optic sensing, the use of slant lens optical fiber can increase the optical area of optical fiber, so that more light can be entered into the optical fiber. In this paper, the slant lens optical fiber is applied to the reflective optical fiber displacement sensor, which replaces the receiving fiber of traditional single optical fiber to improve the measurement range and measurement sensitivity and to achieve high-precision non-contact measurement.

1　Principle

The traditional coupling of optical fiber to optical path is shown in Fig.1.

It can be observed that the light emitted by laser diode (LD) is sent to the measured reflection surface through the sending optical fiber, and then the reflected light enters the receiving optical fiber after being reflected. Finally, the output is received by the photodetector[7].

Fig.1　Schematic diagram of optical coupling for plane receiving fiber

As shown in Fig.2, the plane receiving optical fiber is replaced by a slant lens receiving optical fiber. The measuring principle is the same as that of the conventional planar optical fiber. With other parameters unchanged, when the distancedbetween the reflection surface and the optical fiber end face changes, the light intensity of the receiving optical fiber will change.The size of the optical power received by the photodetector depends on the distanced.

Fig.2　Schematic diagram of optical coupling for slant lens fiber receiving fiber

2　Light intensity modulation function model

For easy calculation, assuming that the emitted light intensity of the sending fiber is uniform and the reflection surface is mirror-like, with spectral non-selectivity[8], The light flux received by the receiving optical fiber is equivalent to that emitted by the image of the sending optical fiber multiplied by the reflection coefficient of the reflection surface. Therefore, to get the optical fiber modulation functionF, only the ratio of the receiving area of the receiving fiber to the projected area of the sending fiber needs to be obtained and then multiplied by the reflectivity of the reflecting surface[9], namely

(1)

whereS1is the size of the effective receiving area of the receiving optical fiber,S2is the size of the spot where the image of the receiving optical fiber is located at a distancedfrom the reflection surface of the light beam emitted by the sending fiber, andφis the reflectivity of the reflection surface.

The Fig.2 shows

R=h+t+r1,

(2)

(3)

h=asinα,

(4)

(5)

β=arcsinNA,

(6)

whereRis the radius of the spot where the image of the receiving optical fiber is located at a distancedfrom the reflection surface of the light beam emitted by the sending fiber,αis the slant fiber angle,βis the numerical aperture angle of the fiber,NAis the numerical aperture of the fiber,tis the distance between the sending fiber and the receiving fiber, andr1is the sending fiber core diameter. There are four cases when the distancedbetween the end face of the optical fiber and the reflection surface changes, as shown in Figs.3-6.

Fig.3　R≤r-r2

Fig.6　r+r2≤R

The corresponding mathematical model is

(6)

Among them

(7)

whereris the distance between the sending fiber and the receiving fiber axis, andr2is the receiving fiber core diameter.

3　Simulation analysis

According to Eq.(7), the displacement characteristics of this kind of fiber pairs can be simulated. The parameters selected are as follows: core radiusr1=r2=0.3 mm, pitch between optical fiberst=0.2 mm, apertureNA=0.3.

Taking slant receiving fiber optical fiber pairs and planar fiber pairs for comparison, with the receiving fiber slope of 45 °, the specific simulation results are shown in Fig.7.

As seen from Fig.7,βis π/2 that represents the traditional planar receiving fiber,βbetween 0 to π/2 represents the slant lens receiving optical fiber. Under the above conditions, the effective measurement range of both fiber pairs is about 3 mm, and the dead zone is 0.3 mm. For the traditional planar fiber pairs, the slope measurement sensitivity is high and linearity is large in the range of 0.3-1.3 mm; But for slant lens optical fiber, there is a higher linearity in 1.271-1.272 mm measurement range, the resolution is 0.1 μm, and the back slope sensitivity is higher. It can be used in a large range of high-precision measurement, which can effectively improves the measurement range and measurement sensitivity. It also can be seen that as the slope of the end face decreases, the range of high precision measurement of the front slope increases, and the measurable range, measurement sensitivity of the back slope increases, too.

Fig.7　Modulation characteristic contrast curve

Since the parameters that affect the modulation characteristics of light intensity are mainly the optical fiber spacing, the sending fiber core diameter, the receiving fiber core diameter, the optical fiber numerical aperture and the receiving fiber slope. These parameters in the tilt-receiving fiber pairs on the light modulation characteristics of the influence law are discussed, as shown in Fig.8.

Fig.8　Influence of key factors on modulation characteristics

1) In Fig.8(a), the numerical aperture has a great influence on the front slope measurement range, sensitivity, linear range, back slope measurement range and measurement sensitivity of the light intensity modulation curve of the sensor, and with the growth of numerical aperture, the sensitivity of the front slope of the sensor, the measurement range, the measurement sensitivity in the linear range, and the measurement sensitivity and measurement range of the back slope increase. Therefore, in the displacement detection occasions that have high sensitivity requirements but relatively small measurement interval, we should try to use the small numerical aperture of the emitting fiber.However, in case of low-sensitivity requirements, large measurement range and the detection of the reflection surface roughness, a sending optical fiber with a small numerical aperture should be selected as far as possible.In practical applications, larger numerical aperture represents stronger condenser ability of the optical fiber and lower bandwidth of the optical fiber[10]. Therefore in the application, the numerical aperture of the transmitting fiber can not be infinitely increased in order to increase the sensitivity of the sensor.

2) In Fig.8(b), the radius of the sending fiber core mainly affects the linear range of the front slope of the light intensity modulation curve. With the increase of the sending fiber core diameter, the front slope sensitivity of the sensor, the range of the front slope, the sensitivity of high-precision linear measurement, the sensitivity and the measurement range of the back slope reduce. Therefore, in the actual measurement process, under the premise of ensuring the noise ratio, a larger output signal value can be obtained by reducing the diameter of the sending fiber, which can improve the sensor displacement measurement sensitivity.

3) In Fig.8(c), with the increase of the receiving fiber core diameter, the front slope sensitivity of the sensor, the range of the front slope, the linear measurement sensitivity, the measurement sensitivity and the measurement range of the back slope increase. Therefore, a larger output signal can be obtained by increasing the receiving fiber core, which can improve the displacement measurement sensitivity.

4) In Fig.8(d), as the distance between optical fibers increases, the sensitivity of the front slope of the sensor, the range of the front slope, the sensitivity of the high-precision linear measurement, the measurement sensitivity and measurement range of the back slope decrease.

4　Conclusion

In this paper, the receiving optical fiber of fiber pair adopts a slant lens fiber.Based on the expression of the modulation function of light intensity for a planar fiber pair,the mathematic model of optical modulation characteristics of slant lens receiving optical fiber is established.The above-mentioned modulation characteristic function is simulated by computer.Finally, the influences of fiber pitch, fiber core diameter and optical fiber numerical aperture on the modulation characteristics of the sensor are summarized. It is concluded that the application of the slant lens fiber is suitable for high-precision detection. In the design of optical fiber sensors, the numerical aperture and core diameter of the receiving fiber should be increased as much as possible, while the core diameter of the transmitting fiber, the distance between the fibers and the receiving optical fiber slant angle should be minimized. At the same time, it can be applied to double-circular coaxial probes as concave double-coaxial optical fiber probes. It can not only compensate for the fluctuation of light source, the nature of reflective surfaces, and the loss of optical fiber, but also effectively improve front slope measurement sensitivity, back slope measurement range and measurement sensitivity. As a result. The optical fiber sensor measurement performance is improved.