Moiré stripes

Take a transmission grating as an example. When a small angle θ is formed between the line pattern on the indicator grating and the line pattern on the scale grating, and the two grating scale facets are placed relatively parallel, under the illumination of the light source, the On the almost vertical grid pattern, light and dark stripes are formed. This kind of fringe is called "moiré fringe". Strictly speaking, the direction of the moiré fringe arrangement is perpendicular to the bisector of the angle between the two grating lines. The distance between two bright lines or two dark lines in the moiré fringe is called the width of the moiré fringe, which is represented by W.

W=ω /2* sin(θ /2)=ω /θ.

Moiré fringe has the following characteristics:

(1) Variation law of Moiré fringe

The two gratings move relative to one grating pitch, and the Moiré fringe moves one fringe distance. Due to the effects of light diffraction and interference, the changing law of the Moiré fringe is similar to a sine (co)sine function, and the number of changing cycles is synchronized with the number of grating pitches of the relative displacement of the grating.

(2) Amplification effect< /p>

In the case where the angle between the two grating lines is small, the following relationship exists between the width W of the moiré fringe, the grating pitch ω and the angle θ of the grating line. In the formula, the unit of θ is rad, and the unit of W is mm. Since the inclination angle is very small and sinθ is small, then W=ω/θ, if ω=0.01mm and θ=0.01rad, then the above formula can get W=1, that is, the grating is enlarged by 100 times.

(3) The effect of averaging error

Moiré fringe is formed by a number of grating fringes. For example, for a grating with 100 lines per millimeter, a moiré fringe with a width of 10mm has 1000 lines, so that the adjacent errors between the grating pitches are averaged. Eliminates errors caused by uneven grating pitch, breakage, etc.

Detection and data processing

Electronic subdivision and direction method

The essence of grating measurement displacement is to measure the positional weighing with the grating pitch as a standard ruler. High-resolution grating rulers are generally more expensive and difficult to manufacture. In order to improve the system resolution, it is necessary to subdivide the moiré fringe, and the grating sensor system mostly adopts the electronic subdivision method. When two gratings overlap with a slight inclination angle, moiré fringes will be generated in a direction roughly perpendicular to the grating scribed line. As the grating moves, the moiré fringes will also move up and down. In this way, the measurement of the grating pitch is converted to the measurement of the number of moiré fringes.
Within the width of a moiré fringe, placing 4 optoelectronic devices at a certain interval can realize the function of electronic subdivision and direction identification. For example, a grating ruler with a grating line of 50 pairs/mm has a grating pitch of 0.02mm. If four subdivisions are used, a count pulse with a resolution of 5μm can be obtained, which has reached a very high level in general industrial measurement and control. Accuracy. Since the displacement is a vector, it is necessary to detect its magnitude and its direction, so at least two photoelectric signals with different phases are required. In order to eliminate common-mode interference, DC components and even harmonics, a differential amplifier composed of a low-drift operational amplifier is usually used. The 4 photoelectric signals obtained by the 4 photosensitive devices are respectively sent to the input terminals of 2 differential amplifiers. The phase difference of the two signals output from the differential amplifier is π/2. In order to obtain the direction and count pulses, the two channels need to be The signal is reshaped, and they are first reshaped into a square wave with a duty ratio of 1:1. Then, by comparing the phase of the square wave, the moving direction of the grating ruler can be obtained. By counting the square wave pulses, the displacement and speed of the grating ruler can be obtained.