Laser surface velocimeter

A laser surface velocimeter (LSV, English ) is a non-contact optical measuring device for determining speed (a velocimeter ) and, derived from this, the length on moving surfaces ( surface ). LSV operate according to the Laser - Doppler principle and thereby the cost of a moving object back-scattered laser light. They are widely used for production control in industrial processes.

Working principle

The difference Doppler method

Difference Doppler method

The Doppler effect describes how the state of motion of an observer or receiver influences the result of a frequency measurement on a light wave that propagates in the stationary reference system with the speed c, a wavelength λ and a frequency f , when the observer or receiver moves at the speed v compared to the moving frame of reference. The non-relativistic view that is permissible for low speeds shows that the observer measures a frequency f ' which is related to his speed v as follows:

${\displaystyle f'=f\left(1-{\frac {v}{c}}\right)}$

The preceding analysis is an approximation for small velocities compared to the speed of light, which is very well fulfilled for practically all technically relevant velocities.

The measurement task on the moving objects, which in principle can be of any length, requires a measurement setup with an observation axis of the sensor perpendicular to the direction of movement of the measurement object.

LSVs work according to the so-called difference Doppler method. Here, two laser beams , each incident at an angle φ to the optical axis, are superimposed on the surface of the measurement object. For a point P that moves at the speed v through the intersection of the two laser beams, the frequencies of the two laser beams are Doppler-shifted according to the above formula. The following frequencies occur at point P of the measurement object, which is moving with velocity v :

${\displaystyle f_{\text{P1,2}}=f_{\text{1,2}}\left(1-{\vec {v}}\cdot {\frac {{\vec {e}}_{\text{1,2}}}{c}}\right)}$

${\displaystyle {\vec {e}}_{\text{1,2,e}}}$ = Unit vectors of laser beams 1 and 2 and in the direction of the detector

f _1,2 = frequencies of laser beams 1 and 2

f _{P1, P2} = Doppler-shifted frequencies of laser beams 1 and 2 at point P.

The point P now emits scattered waves in the direction of the detector. Since P moves with the measurement object, the scattered radiation emitted in the direction of the detector is also Doppler-shifted. The following applies to the frequency of the scattered waves in the direction of the detector: ${\displaystyle {\vec {e}}_{\text{e}}}$

${\displaystyle {\begin{aligned}f_{\text{e1,e2}}&=f_{\text{P1,P2}}\left(1-{\frac {{\vec {v}}\cdot {\vec {e}}_{\text{e}}}{c}}\right)\\&=f_{\text{1,2}}\left(1-{\frac {{\vec {v}}\cdot {\vec {e}}_{\text{1,2}}}{c}}\right)\left(1-{\frac {{\vec {v}}\cdot {\vec {e}}_{\text{e}}}{c}}\right)\end{aligned}}}$

The scattered waves are superimposed on the detector. The interference of the scattered waves from the two laser beams results in different frequency components in the superposition. The low-frequency beat frequency of the superimposed scattered rays, which corresponds to the Doppler frequency f _D , is evaluated using measurement technology . At the same frequency (same wavelength) of the two incident laser beams, this results as the difference between f _e2 and f _e1 :

${\displaystyle {\begin{aligned}f_{\text{D}}&=f_{\text{e2}}-f_{\text{e1}}\\&=f\left({\vec {v}}\cdot {\frac {{\vec {e}}_{\text{1}}-{\vec {e}}_{\text{2}}}{c}}\right)\left(1-{\frac {{\vec {v}}\cdot {\vec {e}}_{\text{e}}}{c}}\right)\end{aligned}}}$

With vertical movement of the point P in relation to the optical axis and with the same angle of incidence φ, the following applies:

${\displaystyle {\vec {v}}\cdot ({\vec {e}}_{\text{1}}-{\vec {e}}_{\text{2}})=2v\sin \varphi }$

and

${\displaystyle {\vec {v}}\cdot {\vec {e}}_{\text{e}}=0}$

This finally gives:

${\displaystyle f_{\text{D}}={\frac {v}{\Delta s}}}$

The Doppler shift is therefore directly proportional to the speed . An illustrative explanation that leads to the same result is the following:

Illustrative representation

Principle of laser surface velocimetry

The two laser beams overlap in the measurement volume and create an interference pattern of light and dark stripes in this area of ​​the room.

The strip spacing Δ s is a device constant that depends on the laser wavelength λ and the angle between the measuring beams 2φ:

${\displaystyle \Delta s={\frac {\lambda }{2\sin \varphi }}}$

If a particle moves through the stripe pattern, the light scattered back by it is modulated in its intensity.

A photoreceiver in the measuring head therefore generates an alternating current signal whose frequency f _{D is} directly proportional to the speed component of the surface in the measuring direction v _p , and the following applies:

${\displaystyle f_{\text{D}}={\frac {v_{\text{p}}}{\Delta s}}={\frac {2v}{\lambda }}\sin \varphi }$

f _D = Doppler frequency

v _p = speed component in the measuring direction

Δ s = strip spacing in the measurement volume

The heterodyne method

LS velocimeters work in the so-called heterodyne mode, that is, the frequency of one of the measuring beams is offset by e.g. B. 40 MHz shifted. The strips in the measuring volume travel at a speed corresponding to the offset frequency f _B . This makes it possible to recognize the direction of movement of the measuring object and to measure at zero speed. The resulting modulation frequency f _mod on the photoreceiver is in heterodyne mode:

${\displaystyle f_{\text{mod}}=f_{\text{b}}+{\frac {v_{\text{p}}}{\Delta s}}=f_{\text{b}}+{\frac {2v}{\lambda }}\sin \varphi }$

The modulation frequency is determined in the controller by Fourier transformation and converted into the measured value for the speed v _p . The length measurement is done by integrating the speed signal.

Areas of application

LSVs are used for cutting control in the hot and cold area, for controlling flying saws, for measuring the length of piece goods on plasterboard, cardboard, wood or shaped sheets, as well as for measuring the roll length of cables, wire, textile, paper, cardboard or Foil. Speed ​​measurements with LSVs are used for process control in cold and hot rolling mills , for example for measuring the degree of stretching with the help of differential speed determinations, for measuring elongation and skin-pass degree or for mass flow control. Furthermore, a synchronization of speeds is possible z. B. for slip measurement and compensation or for lamination processes .

See also

• Doppler effect
• Laser Doppler anemometry
• Speed ​​measurement

literature

• Precision work under extreme conditions. In: QZ. No. 6, 2007, pp. 37-39 ( online ).
• S. Musielak: Speed ​​measurement in the corrugated board industry - non-contact speed measurement compared to conventional measuring methods. In: Sensor Magazin No. 2, 2011, pp. 8–11.
• W. Stork, A. Wagner, J. Drescher, KD Mueller-Glaser: Miniaturized laser-Doppler velocimeter for speed and length measurement on moving solid surfaces. In: Laser Magazin. No. 4, 1995 ( online ).

Web links

• Peter M. Nawfel: Laser based, noncontact speed sensor helps reduce breaks on high speed unwind . TAPPI, 2004.
• Functional principle of laser surface velocimetry