Working principle and simulation of optical fiber displacement sensor

Roctest, a Canadian company, has produced a commercial fiber-optic displacement sensor (FO-LPDS), which uses the patented Fizeau interferometer demodulation technology (US patent #5202939/#5392117) and has the advantages of simple structure, high precision and fast response. It has been successfully applied in the field of civil engineering. This article will introduce the principle and use of this sensor in detail.

2. Composition structure and working principle

1. Sensor structure

The simplified structure of the sensor is shown in Figure 1. Its connecting rod can move horizontally, and a thin film Fizeau interferometer (TFFI) is fixed on the connecting rod. Its detailed structure is shown in Figure 2.

2. Working Principle

(1) Optical signal modulation

In actual use, the sensor is connected to the reader (Demodulator). The light emitted by the white light diode light source in the reader is incident from one end of the optical fiber connected to the reader, transmitted to the Fabry-Perot sensor, and then emitted by the multimode optical fiber to illuminate the surface of the TFFI interferometer (optical wedge). When the TFFI moves horizontally, the position of the illumination point will also be different. The upper and lower surfaces of the optical wedge are coated with a semi-reflective film, thus forming a Fabry-Perot cavity. When part of the white light emitted by the reader is reflected by the first semi-reflective mirror, the rest of the white light passes through the Fabry-Perot cavity and is reflected back by the second semi-reflective mirror again. The two beams of reflected light interfere with each other, causing the spectrum of the original incident white light to be modulated.

Assume that the material of the optical wedge is glass, and take its refractive index n=1.6. The wavelength range of the incident white light diode is 600nm~1750nm according to the literature [1]. According to Figure 2, the optical path difference of the reflected light on the upper and lower surfaces of the optical wedge is 2nh. Assume that the amplitude of all frequency waves in the spectrum of the light source is a, the phase difference when the two beams interfere at the meeting point is d, the reflectivity of the optical wedge surface is R, and the transmittance is 1-R, then the composite amplitude y is: y=a+aRe-iδ (1)

According to Euler's formula e-iδ＝cosδ－isinδ, we can get: y(t)=a(1+ Rcosδ－iRsinδ) （2）

The light intensity is proportional to the square of the light wave amplitude. If the light intensity at the point where the light waves meet is I, then:

I＝y(t)×y(t)*＝a2(1+R2+2Rcosδ) (3)

For a certain position of TFFI, the height of the wedge surface is h, and the interference phase difference δ corresponding to light of different wavelengths l is:

δ＝(2nh/l)×2p＝4pnh/l (4)

The extreme values ​​of light intensity I are:

I＝a2（1+R2+2R） (5)

In the TFFI interferometer, in order to form a light reflection surface, a layer of film needs to be coated on the upper and lower surfaces of the optical wedge. The coating has a certain thickness, so the reflected light on the upper and lower surfaces of the coating will form interference, which will affect the measurement results. Therefore, the thickness of the coating should be controlled at 1/4 of the central wavelength of the light source. For example, if the wavelength of the light source is 600nm~1000nm, the coating thickness is 800nm ​​(assuming that the refractive index of the coating material is 1), so that most of the reflected light on the upper and lower surfaces of the coating has a phase difference of 180° and the intensity is attenuated.

In the coordinate system shown in Figure 2, let the distance between the incident point and the origin of the coordinate system be x, and the inclination angle of the optical wedge be a. At this time, the corresponding height of the optical wedge surface is h:

h＝7＋xtga (mm) (6)

tga＝18/25000＝7.2′10-4

[page]

Here, x=12.5mm=12500mm is used to calculate the intensity distribution of the modulated light of the sensor. Substituting the value of x into equation (6) yields h=16mm, which is then substituted into equation (4) to obtain d, and then substituted into equation (3) to obtain the light intensity I. Taking the wavelength range of the light source as 0.6mm to 1.75mm and the reflectivity of the wedge coating as R=0.5, the light intensity distribution diagram shown in Figure 3 can be obtained.

It can be seen that a limited number of interference maxima are generated at some wavelengths within the spectrum of the light source. Obviously, at different locations where the sensor is located, the modulation of the light source by TFFI is different, that is, the wavelength corresponding to the interference maximum will change. At smaller wavelengths, the peaks of the interference maximum are denser.

(2) Optical signal demodulation

The function of the reader (signal conditioner) is to demodulate the optical signal sent back by the sensor and calculate the displacement signal from it. The above process can be represented by Figure 4.

[page]

The reader is equipped with a white light source. The light returned from the multimode fiber is converted into parallel light through a cylindrical lens and projected onto the inclined surface of the TFFI interferometer. The lower surface of the TFFI is attached to a CCD sensor that is sensitive to light intensity. As shown in Figure 5, assuming that monochromatic light is evenly irradiated on the upper surface of the wedge, at each point in the x-direction, the reflected light from the upper and lower surfaces of the wedge will interfere, and the light transmitted from the lower surface will be detected by the CCD.

It is assumed here that the demodulated TFFI interferometer structure is exactly the same as that in the sensor, that is, it is taken from the same batch of products, which can eliminate the influence of the optical wedge position tolerance on the measurement results.

[page]

The modulated light signal shown in Figure 3 is input to the demodulation interferometer. For simplicity, only the wavelength corresponding to the maximum light intensity is considered here. The interference results formed by these wavelengths are vector superimposed in the length direction of the CCD. Since it is white light interference, the more times the superposition is performed, the finer and sharper the interference fringes obtained on the CCD are. The simulation results under Matlab are shown in Figure 6.

According to the simulation results, the light intensity value of the CCD at the position of 12.5 mm in length is exactly the maximum, which corresponds exactly to the situation when the optical fiber in the sensor is at the center of the optical wedge (x=12.5 mm).

When the sensor displacement is S, the light wave with the largest interference intensity also has the largest interference on the Fizeau interferometer of the reader. Therefore, by analyzing the coordinate position x=Smax of the point with the maximum light intensity on the CCD, the absolute position S=Smax of the sensor can be obtained.

3. Performance characteristics

According to the previous analysis and relevant information, the white light displacement sensor can measure absolute position, and it has the following characteristics:

(1) Using a white light diode light source instead of a laser light source, there is no need for the preheating time and constant temperature control required by a laser diode, which reduces the requirements for light source stability. In addition, the life of a white light LED is much longer than that of a laser diode LD.

(2) The sensor and the reader use a wedge-shaped thin film interferometer TFFI with the same structure, which can compensate for the measurement error caused by the manufacturing error of TFFI. Usually, the maximum linear error obtained without any compensation is 0.15% of the full scale.

(3) The manufacturing process of TFFI is complex. Currently, it can only provide displacement sensors with a range of 20 mm. It is difficult to manufacture TFFI of larger size, which limits the improvement of the range of this sensor.

(4) This sensor essentially works by using the optical path difference between the upper and lower surfaces of the optical wedge, so it is insensitive to environmental vibrations and changes in optical fiber parameters. The optical wedge (TFFI) is generally made of materials that are insensitive to temperature. There is no lens in the sensor, and the installation of the optical fiber does not require strict alignment, so it can work in harsh environments;

(5) A CCD or PSD light detector can be used in the reader. The light intensity distribution received by the CCD can have multiple extreme points, but through reasonable structural design, it can be guaranteed that there is only one maximum point. The signal processing uses an algorithm for finding the maximum value.

The main performance indicators of this sensor are shown in Table 1:

IV. Conclusion and Outlook

The fiber optic position sensor based on the principle of white light interference can measure absolute linear position and angular displacement, and has the characteristics of simple structure, high precision, wide operating temperature range and insensitivity to vibration, so it is expected to be used in optical transmission systems. At present, the Thiokol Propulsion Jet Propulsion Division of ATK Aerospace has verified this white light interference linear displacement sensor on rocket engines and obtained satisfactory results. The American Davidson Company is also testing this new type of sensor on NAVY's advanced warship SC-21.