Working principle of grating digital sensor

Grating digital sensor usually consists of light source 5 (condenser 4), metering grating, photoelectric device 3 and measuring circuit, as shown in Figure 12.1.2. The metering grating consists of scale grating 1 (main grating) and indicator grating 2, so the metering grating is also called grating pair, which determines the measurement accuracy of the whole system. Generally, the main grating and indicator grating have the same line density, but the main grating is much longer than the indicator grating. During measurement, the main grating is connected to the object to be measured and moves with it, while the indicator grating is fixed, so the effective length of the main grating determines the measurement range of the sensor.

1. Moiré fringes
Place the main grating and the scale grating on top of each other, keeping a small gap between them and making a small angle θ between the lines of the two gratings, as shown in Figure 12.1.3. When there is light, due to the light blocking effect (for gratings with a line density of ≤50 lines/mm) or the diffraction of light (for gratings with a line density of ≥100 lines/mm), alternating light and dark fringes are formed in a direction roughly perpendicular to the grating lines. At the overlap of the lines of the two gratings, light passes through the gap to form a bright band; at the offset of the two grating lines, a dark band is formed; these alternating light and dark fringes are called moiré fringes. The relationship between the spacing of the moiré fringes and the grating pitch W and the angle θ (in rad) between the two grating lines is (12.1.1) (12.1.2)

K is called the magnification factor.
Moiré fringes have the following important characteristics:
(1) The movement of the moiré fringes corresponds to the movement of the grating.
When the indicator grating is stationary, the angle θ between the main grating and the indicator grating is always maintained, and the main grating is relatively moved in the direction perpendicular to the grating, the moiré fringes will move in the direction of the grating grating; when the grating moves in the opposite direction, the moiré fringes also move in the opposite direction. For every grating pitch W that the main grating moves, the moiré fringes also move a spacing S accordingly. Therefore, by measuring the movement of the moiré fringes, the size and direction of the grating movement can be measured, which is much easier than measuring the grating directly.
(2) Moiré fringes have a displacement magnification effect. When the main grating moves a grating pitch W
in the direction perpendicular to the grating , the moiré fringes move a fringe pitch . When the angle θ between the two grating gratings is small, it can be seen from formula (12.1.1) that when W is constant, the smaller θ is, the larger B is, which is equivalent to magnifying the grating pitch W by 1/θ times. For example, for a grating with 50 lines/mm, W = 0.02mm. If , then the spacing of the moiré fringes , K = 573, is equivalent to magnifying the grating pitch by 573 times. Therefore, the magnification of the moiré fringes is quite large, and high-sensitivity displacement measurement can be achieved. (3) Moiré fringes have an error averaging effect. Moiré fringes are formed by many lines of the grating, and have an averaging effect on the line errors. They can largely eliminate the influence of local and short-period errors caused by the line errors, and can achieve a higher measurement accuracy than the line accuracy of the grating itself. Therefore, the metrological grating is particularly suitable for small displacement and high-precision displacement measurement. (4) The spacing S of the moiré fringes changes with the angle θ of the grating lines . Since the angle θ of the grating lines can be adjusted, the spacing of the moiré fringes can be adjusted according to the size of θ as needed, which brings convenience to practical applications. When the relative movement direction of the two gratings remains unchanged, changing the direction of θ will change the movement direction of the moiré fringes. 2. Photoelectric conversion The relative displacement of the main grating and the indicator grating produces moiré fringes. In order to measure the displacement of the moiré fringes, the optical signal must be converted into an electrical signal through a photoelectric device (such as a silicon photocell). Place a photoelectric device at an appropriate position of the grating. When the two gratings move relative to each other, the light intensity on the photoelectric device moves with the moiré fringes, and the light intensity changes to a sine curve, as shown in Figure 12.1.4. At position a, the two grating lines overlap, the transmitted light intensity is the largest, and the electrical signal output by the photoelectric device is also the largest; at position c, the light intensity decreases because half of the light is blocked; at position d, the light is completely blocked and becomes completely black, with the lowest light intensity; if the grating continues to move, the light intensity transmitted to the photoelectric device gradually increases. The light intensity change on the photoelectric device is approximately a sine curve. When the grating moves one grating distance W, the light intensity changes by one cycle. The output voltage of the photoelectric device can be expressed by the formula (12.1.3) where ——the DC component in the output signal; ——the amplitude of the AC component in the output signal; x——the relative displacement of the two gratings.

The sine signal is converted into a square wave pulse signal through a shaping circuit, and a square wave pulse is output after each cycle. In this way, the total number of pulses N corresponds to the number of grating pitches moved by the grating, so the displacement of the grating is
(12.1.4)