I. INTRODUCTION Strain measurement is very important in the fields of mechanics, materials science and engineering. In many optical measurement techniques, the diffraction method provides direct strain information. Ball [1] first used diffraction grating strain gauges, and this strain measurement technology has been developed and is now widely used. Based on the grating diffraction method, a new practical optical strain sensor that can replace the resistance strain gauge is proposed by using the position sensitive detector and the diffraction grating. The instrument design principle and data processing technology are different from the traditional methods. This new sensor provides dynamic strain measurement with a wide measurement range. The sensitivity of the sensor is 1me and the spatial resolution is 0.1mm, which is superior to all previous strain sensors. The outstanding features of the new optical strain sensor are: 1 non-contact measurement (readout), the strain information is optically transmitted from the grating to the signal processing unit; 2 the gauge length is variable, determined by the diameter of the laser beam, and the laser beam size It is adjustable; 3 strain measurement range is large, from small strain to large strain can be continuously measured; 4 can measure strain at different points of the test sample, can monitor the whole object to be tested with extremely high spatial resolution .

Second, the working principle Figure 1 shows the strain measurement principle of the optical strain sensor using the diffraction grating and the position sensitive detector. The diffraction grating adheres to the surface of the sample, illuminating a point on the plane of the grating when the monochromatic collimated beam is incident perpendicularly onto the plane of the linear grating (>40 line/mm), and on a screen parallel to the plane of the grating A set of diffracted spots can be observed. In Fig. 1, a laser beam is incident on a reflective diffraction grating perpendicular to the surface of the sample. For the high-frequency diffraction grating, only the diffracted beam of ±1 diffraction order actually used for strain measurement can be observed. This diffracted beam is received by a high resolution level detector from the grating L. When the grating follows the deformation of the sample, the deformation in the plane and the displacement of the plane outside the incident direction of the beam will cause the movement of the diffracted beam. For an incident laser beam perpendicular to the surface of the specimen, the displacement of the ±1 order diffracted beam along the length of the sensor is given by: (1) where p is the spatial frequency of the grating. B—the diffraction angle of the ±1st order diffracted beam; l—the laser wavelength; if the sample undergoes a small deformation, the grating line spacing (spatial frequency) will change Dp. According to equation (1), the diffraction angle changes Db, so that: (2) This means: (3) where ex is the positive strain along the x direction. Assuming that the diffracted beam is perpendicular to the position sensor plane, the displacement along sensor 1 is: (4) For sensor 2, simply change b to -b to get: (5) Therefore, by equation (4) and equation (5) The basic strain measurement equation is:

Third, the sensor system and measurement method

1. Sensor System Hardware Figure 2 shows the sensor system configuration, which can be applied to the laboratory and industrial field. It consists of a laser source, two position sensitive sensors, two 633 nm bandpass filters, a converging lens and a grating. The grating has a spatial frequency of 1200 lines/mm and adheres to the surface of the sample. A He-Ne laser beam (632.8 mm) having a diameter of about 1 mm was incident at any point on the grating plane. The position sensitive detector is an optoelectronic device based on a single photodiode. The main features of the system are: 1 spatial resolution is higher than other devices (such as CCD); 2 use two voltage signals to determine the position of the beam on the sensing area, to facilitate rapid processing of the signal; 3 small volume; 4 relative position resolution High (1/5000); 5 is not affected by changes in light intensity, so that the position can be accurately measured even when the light intensity changes; 6 spectral sensitivity is wide (300 to 1100 nm), so laser beams of different wavelengths can be utilized; 7 response time Fast (<20ms) for dynamic strain measurement. The output voltage signals of the two position sensitive sensors are sent to the computer through the A/D converter, and the maximum data sampling rate is up to 105 times/s. Two 633nm filters eliminate background light and reduce noise effects.

2. Adjustment method If the laser beam cannot be perpendicularly incident on the surface of the sample, it will cause serious measurement error. The misalignment of such a laser beam is difficult to remove unless the grating-to-laser reflected zero-order beam coincides with the incident beam. The coincidence of such beams must be in the vertical direction to ensure a symmetric distribution of the ±1 order diffracted beams. The key to system tuning is to have the incident laser beam perpendicular to the surface of the specimen. Care must be taken to check that the grating is firmly adhered to the specimen surface and that the specimen is fully positioned. In addition, the position sensitive sensor can be adjusted so that the diffracted ±1 order beam is located exactly at the center of the two position sensitive sensor planes.

3. Measurement methods The main measurement steps are as follows: 1 The preparation of the sample and the diffraction grating is similar to that of the Moire interferometer; 2 The distance L from the position sensor to the grating is determined between 100 and 500 mm and input to the computer software. L=250mm cannot be selected; 3 The initial test before loading is to measure the average of x10 and x20; 4 pressurize the sample and measure the average of x1 and x2; 5 Calculate the strain using equation (6). All calculations are done automatically by computer software.

4, interface software flow is completed with LabVIEW, including data sampling, filtering, calculation, reading and writing memory, display and so on. The data processing speed is very high, and the entire processing cycle is about 0.1s. All signal processing and data acquisition are automatic. The strain measurement results are continuously displayed on the PC screen in the form of numbers and graphs.

IV. System characteristics The important influence on the sensor system is the error caused by the noise of the position sensitive detector and the noise error of the A/D converter and the systematic error caused by the deviation of the incident laser beam from the normal direction of the sample.

1. Random noise The random noise of the sensor system limits the measurement sensitivity and spatial resolution of the system. The four main noise sources of the position sensitive detector are: 1 intensity noise associated with the light source; 2 amplifier voltage noise; 3 thermal noise generated by the feedback resistor; 4 shot noise caused by the direct current current, the size of which is in position with the spot position The position of the sensitive detector changes on the receiving surface, the noise at the center is the smallest, and the noise at the edge is the largest. The A/D converter noise variance is D2/12, where D is the digitized value and 12 is the 12-bit converter used.

2. Position resolution If a recorder is used, the relative resolution of the position detector is 1/5000. The double-ended output voltage signal of the position sensitive detector is -5V~+5V, corresponding to the center coordinate of the spot being -5mm~+5mm. The 12-bit A/D converter can only resolve 2.4mm. Considering the influence of the position sensor noise, the position resolution of the entire sensor system is about 0.3mm.

3. Strain Sensitivity The average residual noise is independent of the position of the spot on the plane of the position sensitive detector. Let x denote noise, x is the recording position signal, and x* is the position signal with noise, then x*=x+x, then equation (6) becomes: (7) where, and is the initial center position of the diffracted beam , as a constant treatment, and is the center position of the spot after the sensor is pressurized, is the final result of averaging 1000 readings. The strain error due to random noise is: (8) Therefore, the standard deviation of the strain error is: (9) where sx—standard noise deviation (approximately 0.3 mm); r—from position sensitive sensors 1 and 2, respectively Correlation coefficient of noise x1 and x2, the correlation coefficient of two channels is measured as r=0.4, which is obtained by sampling 1000 channels of two channels without averaging. Using the actual parameters: the grating frequency is 1200 line/mm, the laser wavelength is l=632.8mm, b=49.4°, tanb=0.9492, L=150mm, and the maximum noise error is ss=0.9me. This value is taken as strain sensitivity, which varies with distance. The change of L is shown in Table 1. Table 1 Strain sensitivity ss as a function of L L (mm) 150200250300350400450500 ss (me) 0.90.70.60.50.40.40.30.3.

4. System error A systematic error occurs when the incident laser beam deviates from the normal direction of the sample. If the angle of deviation of the incident laser beam from the normal of the sample is q, it is obtained by equation (3) (refer to Fig. 3): (10) where Db1 and Db2 are variations in the diffraction angle due to the deformation of the sample and the deviation from q. Therefore, equation (6) can be written as: (11) If there is no other error source, only the error caused by q is considered, then Db1 can be determined by the following equation: (12) Reserved to the second order q, we can get: (13) By the same method: (14) From this: (15) Substituting equation (13) and equation (15) into equation (11), the strain error is: (16) 5. Spatial resolution measurement strain The spatial resolution is determined by the diameter of the incident laser beam. The actual applied laser beam has an original diameter of 1 to 2 mm without any treatment. The method of improving the spatial resolution is to converge the incident beam with a lens and then incident on the sample to be tested. A low-loss plastic lens with a focal length of 10 cm can be used in the sensor system to reduce the incident beam with an original diameter of 1.5 mm to 0.1 mm.

V. Sensor system technical parameters and characteristics The technical parameters and characteristics of the sensor system are as follows: 1 sensitivity is 1me; 2 spatial resolution is variable, the range is 0.1~2mm; 3 strain size is up to 15%; 4 measurement position is flexible, Any point on the grating plane can be measured; 5 can be used for dynamic and continuous strain measurement; 6 data acquisition and processing are automated; 7 users can easily observe the system interface; 8 compact structure, small size.

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Label: Application of Photoelectrons in Sensor Technology

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