I. Introduction
Compared with traditional sensors, fiber optic sensors have a series of unique advantages, such as high sensitivity, resistance to electromagnetic interference, corrosion resistance, good electrical insulation, explosion-proof properties, flexible optical path, simple structure, small size, and light weight. Therefore, fiber optic sensors have become an inevitable development trend in airborne optical sensors.
Roctest, a Canadian company, manufactures a commercially available fiber-optic linear position and displacement sensor (FO-LPDS). This sensor utilizes Fizeau's patented interferometer demodulation technology (US patent #5202939/#5392117) and boasts advantages such as simple structure, high accuracy, and fast response. It has already been successfully applied in the field of civil engineering. This article will detail the principles and applications of this sensor.
II. Composition 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 practical use, the sensor is connected to the demodulator. Light emitted from the white LED light source in the demodulator is incident from one end of the optical fiber connected to the demodulator, transmitted to the Fabry-Perot sensor, and then emitted from the multimode optical fiber, illuminating the surface of the TFFI interferometer (optical wedge). The position of the illumination point changes as the TFFI moves horizontally. Both the upper and lower surfaces of the optical wedge are coated with semi-reflective films, thus forming a Fabry-Perot cavity. When a portion of the white light emitted by the demodulator is reflected by the first semi-reflective mirror, the remaining white light passes through the Fabry-Perot cavity and is reflected back again by the second semi-reflective mirror. The two reflected beams interfere with each other, modulating the spectrum of the originally incident white light.
Assuming the material of the optical wedge is glass, with a refractive index of n=1.6, and the wavelength range of the incident white light diode is taken as 600nm～1750nm according to reference [1]. According to Figure 2, the optical path difference of the reflected light from the upper and lower surfaces of the optical wedge is 2nh. Assuming the amplitude of all frequencies of light waves in the light source spectrum 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 combined 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）
Light intensity is proportional to the square of the light wave amplitude. Let the light intensity at the point where the light waves meet be I, then:
I＝y(t)×y(t)*＝a2(1+R2+2Rcosδ) (3)
For a certain position in TFFI, with the height of the optical wedge surface being h, 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 a TFFI interferometer, a film needs to be deposited on both the upper and lower surfaces of the optical wedge to form a light-reflecting surface. Since the film has a certain thickness, the reflected light from the upper and lower surfaces will interfere, affecting the measurement results. Therefore, the thickness of the film should be controlled to 1/4 of the center wavelength of the light source. For example, if the light source wavelength is 600nm~1000nm, the film thickness should be 800nm (assuming the refractive index of the film material is 1). In this way, most of the reflected light from the upper and lower surfaces of the film will have a 180° phase difference, resulting in attenuation of intensity.
In the coordinate system shown in Figure 2, let the distance from the incident point to the origin be x, the tilt angle of the light wedge be a, and the corresponding height of the light wedge surface be h:
h＝7＋xtga (mm) (6)
tga = 18/25000 = 7.2 × 10⁻⁴
Here, we take x = 12.5 mm = 12500 mm to calculate the intensity distribution of the sensor-modulated light. Substituting the value of x into equation (6) gives h = 16 mm. Substituting this into equation (4) gives d. Substituting d into equation (3) gives the light intensity I. Taking the wavelength range of the light source as 0.6 mm to 1.75 mm and the reflectivity of the light wedge coating as R = 0.5, we can obtain the light intensity distribution diagram shown in Figure 3.
It is evident that a finite number of interference maxima are generated at certain wavelengths within the spectral range of the light source. Clearly, the modulation of the light source by the TFFI differs depending on the sensor's location; that is, the wavelength values corresponding to the interference maxima change. At shorter wavelengths (l), the peaks of the interference maxima are also denser.
