Laser Doppler anemometry

2D laser Doppler anemometer on a flow channel . Two pairs of beams with slightly different wavelengths are used to measure the longitudinal or vertical components of the flow velocity at the point of intersection. The objective is connected to the laser system (not shown) by light guides. This facilitates scanning movements of the lens together with the associated detector on the other side of the flow channel. The air, also in the duct, is thick with smoke to make the laser beams visible (see the apparent gap when the beams pass through the side wall of the duct).

The laser-Doppler anemometry ( LDA ) is a contactless optical measuring method for the selective determination of velocity components in the fluid flows (liquids or gases). A laser beam is split into two beams with the aid of a beam splitter . At the measuring point, these rays cross again and an interference fringe pattern is created in the area of the crossing . A particle moving through the fringe pattern together with the fluid generates a scattered light signal in a photodetector , the frequency of which is proportional to the velocity component perpendicular to the interference fringes. This is a beating between the differently Doppler-shifted scattered light of both laser beams. By combining three laser Doppler systems with different laser wavelengths, all three flow velocity components can be recorded selectively.

functionality

The laser Doppler technique is based on the determination of the Doppler shift of the scattered light of a moving object that is illuminated with laser light. Since the frequency of light cannot be measured directly, it is brought into the range of a few megahertz by superimposing a reference beam.

Different model concepts have been established for the explanation of the signal generation. The interference fringe model for a two-beam arrangement is very clear, but strictly speaking only applies to very small particles ( ). The somewhat more complex Doppler model, from which the name laser Doppler technology is derived, describes the signal generation more comprehensively, includes the interference fringe model and also explains the signal generation for so-called single-beam or reference-beam laser Doppler systems. Another approach that is equivalent to the Doppler model is the description of stationary light scattering, e.g. B. Mie scatter . ${\ displaystyle d << \ lambda}$

Interference fringe model

Many laser Doppler systems in the field of flow measurement technology work with two coherent laser beams crossing each other at an angle 2 (see structure of laser Doppler systems). At intersections interfere the two shafts with each other and there is an interference fringe system ideally equidistant plane interference surfaces. The interference surfaces are perpendicular to the plane spanned by the laser beams and parallel to the bisector of the laser beams and are spaced apart ${\ displaystyle \ phi}$

{\ displaystyle \ Delta x = {\ frac {\ lambda} {2 \ sin \ phi}}.}

If a very small particle moves through this periodic interference fringe system, it scatters the local grid-like intensity distribution. The frequency of the detected scattered light signal is thus proportional to the speed component perpendicular to the interference surfaces. ${\ displaystyle v_ {x}}$

{\ displaystyle f_ {S} = v_ {x} \, {\ frac {2 \ sin \ phi} {\ lambda}}}

Doppler model

Vector relationships of the Doppler effect for the single-beam and two-beam laser Doppler technology

The direction-dependent Doppler shift of the scattered light of a particle in a laser beam can be represented by the vectorial description of the Doppler effect . In the case of the laser Doppler system, the particle initially acts as a moving receiver, which records the Doppler shifted frequency of a stationary transmitter of the frequency , the laser. The wave scattered by the moving particle is now detected by a stationary detector. Thus, the Doppler effect has to be applied a second time and this results in the frequency of the scattered light ${\ displaystyle f_ {L}}$

{\ displaystyle f = f_ {L} \, {\ frac {\ left (1 - {\ frac {{\ vec {v}} \ cdot {\ vec {e}} _ {L}} {c}} \ right)} {\ left (1 - {\ frac {{\ vec {v}} \ cdot {\ vec {e}} _ {D}} {c}} \ right)}},}

where the unit vector is in the direction of the laser beam axis and the unit vector is from the particle to the stationary receiver. For particle speeds much lower than the speed of light , the following approximation can be given: ${\ displaystyle {\ vec {e}} _ {L}}$ ${\ displaystyle {\ vec {e}} _ {D}}$ ${\ displaystyle v}$ ${\ displaystyle c}$

{\ displaystyle f \ approx f_ {L} \, \ left (1 - {\ frac {{\ vec {v}} \ cdot {\ vec {e}} _ {L}} {c}} + {\ frac {{\ vec {v}} \ cdot {\ vec {e}} _ {D}} {c}} \ right) = f_ {L} \ left (1 - {\ frac {\ vec {v}} { c}} ({\ vec {e}} _ {L} - {\ vec {e}} _ {D}) \ right)}

The observed Doppler shift is therefore dependent on the velocity vector , the orientation of the laser beam axis and the direction of observation . The actual frequency shift due to the Doppler effect can not be measured directly due to the inertia of optical detectors (for direct measurement of the Doppler shift see Global Doppler Velocimetry ). For this reason, the scattered light of the frequency is superimposed with a reference wave of similar frequency and optically mixed at the detector. The result of this mixture gives a detector signal with the difference frequency of the two waves. ${\ displaystyle {\ vec {v}}}$ ${\ displaystyle {\ vec {e}} _ {L}}$ ${\ displaystyle {\ vec {e}} _ {D}}$ ${\ displaystyle f}$ ${\ displaystyle f_ {R}}$ ${\ displaystyle f_ {R} -f}$

The laser Doppler systems now differ according to the direction of observation and reference frequency for the optical mixture:

Single-beam laser Doppler systems

If the scattered light is detected in backscattering (scattering angle 180 °) ( ) and the originally radiated wave is superimposed ( ), the result is the measurable signal frequency ${\ displaystyle {\ vec {e}} _ {L} = - {\ vec {e}} _ {D}}$ ${\ displaystyle f_ {R} = f_ {L}}$

{\ displaystyle f_ {S} = f_ {R} -f = {\ frac {2v_ {z}} {\ lambda}},}

where v _{z is} the velocity component in the direction of the axis of the laser beam. This arrangement is known as a laser Doppler vibrometer and is used to determine the vibration state of surfaces in backscattering.

To determine flow velocities in biological and medical applications, the receiving optics are often arranged at a defined angle to the perpendicular laser beam ( ). The reference wave for mixing is generated by scattering on the surrounding immobile tissue. If one takes into account that for these applications the speed vector has only one component , e.g. B. blood flows parallel to the skin surface, this can be determined using the laser Doppler technique. Problems arise with additional speed components. ${\ displaystyle {\ vec {e}} _ {L} - {\ vec {e}} _ {D} = const}$ ${\ displaystyle v_ {x}}$
In the same way, the scattered light from a moving particle can be detected at a fixed angle and mixed with the original laser frequency in the receiving optics. In this case, one speaks of a single-beam laser Doppler system. The first laser Doppler systems implemented were constructed in this way.

Two-beam laser Doppler system

In flow measurement technology, however, the two-beam laser Doppler system has established itself. Here, two laser beams are focused at an angle 2 on a point on the moving structure or in a fluid. The scattered waves of both laser beams are Doppler shifted differently, but the position vector from the scattering center to a stationary detector is the same for both scattered light signals ${\ displaystyle \ phi}$

{\ displaystyle {\ vec {e}} _ {D1} = {\ vec {e}} _ {D2} = {\ vec {e}} _ {D}.}

If both scattered waves are superimposed on the detector, the resulting signal frequency is:

{\ displaystyle {\ begin {aligned} & f_ {S} = f_ {1} -f_ {2} = f_ {L} \, \ left (1 - {\ frac {\ vec {v}} {c}} \ cdot ({\ vec {e}} _ {L1} - {\ vec {e}} _ {D}) \ right) -f_ {L} \, \ left (1 - {\ frac {\ vec {v} } {c}} \ cdot ({\ vec {e}} _ {L2} - {\ vec {e}} _ {D}) \ right) \\ & = f_ {L} {\ frac {\ vec { v}} {c}} \ cdot \ left ({\ vec {e}} _ {L2} - {\ vec {e}} _ {L1} \ right) = f_ {L} {\ frac {{\ vec {v}} \ cdot {\ vec {n}}} {c}} \\ & = v_ {x} {\ frac {2 \ sin \ phi} {\ lambda}} \ end {aligned}}}

This corresponds to the relationship between signal frequency and speed perpendicular to the interference fringes given above for the interference fringe model. The advantage of the two-beam arrangement is that the signal frequency does not depend on the direction of observation, only the angle of intersection and the wavelength are included in the constant of proportionality for determining the speed and a defined speed component is recorded. This means that the two-beam method does not have to be calibrated.

A typical measurement volume in laser Doppler anemometry has a length of one millimeter and a diameter of a few tenths of a millimeter.

Since the flow direction of the particles in a static interference fringe pattern is not clear, the individual laser beams are frequency-shifted with the help of an optoacoustic modulator and thus a movement is induced in the interference fringe pattern, so that the determination of the speed direction becomes clear. To put it simply, the acousto-optical modulators called Bragg cells consist of a crystal through which the laser beam is passed. By means of piezoelectric excitation of the crystal in the ultrasonic range from 25 MHz to 120 MHz, density differences, i.e. H. Refractive index fluctuations, induced at which the incident laser beam in the Bragg cell bends at the Bragg angle . The frequency of the laser and that of the acoustic waves are added to a total frequency of the exiting laser beam, i.e. H. when leaving the Bragg cell, the frequency of the laser beam is shifted by the amount of the Bragg cell frequency. If only one of the laser beams has experienced a frequency shift, the interference fringe pattern in the measurement volume moves with the frequency of the Bragg cell used. The bursts of individual particles flowing through the measurement volume are recorded by a photodetector. For evaluation, the signal is still bandpass filtered so that it is symmetrical with respect to a zero line; the direct current component of the original LDA burst signal is eliminated here. A processor receives the measurement signal via an A / D converter. By evaluating the burst signals (counter) and the signal time, the frequency f is finally obtained . As an alternative to the counter method, the measurement signal can be directly subjected to a Fourier transformation using appropriate devices (e.g. a transient recorder ).

The photodetector can be constructed in a forward scattering arrangement or in a backward scattering arrangement. If the photodetector is installed in the forward scattering direction, the signal scattered by the particle is picked up by receiving optics in the direction of propagation of the light. In the backscattering arrangement, the detector is arranged in the opposite direction to the propagation of both laser beams. In the case of the backward scattering arrangement, the transmission optics can be constructed in such a way that they also take up the reception optics at the same time, so that complex adjustment between the transmission and reception unit is not necessary. However, the intensity of the scatter signal in this arrangement is an order of magnitude smaller than in the forward scatter arrangement ( Mie scatter ), so that backward scattering was only made possible by the development of powerful lasers and photodetectors.

For scientific and especially commercial use, i. H. with frequently changing measuring operations, LDA systems in so-called backscattering arrangements have established themselves as these are more flexible and easier to adapt. Nowadays, LDA systems with probes that contain backscatter optics are used almost exclusively.

literature

F. Durst, A. Melling, JH Whitelaw: Principles and Practice of Laser-Doppler Anemometry. Academic Press, London, 1976.
LE Drain: The Laser Doppler Technique. John Wiley & Sons, 1980, ISBN 0471276278 .
Jochen Wiedemann: Laser Doppler Anemometry. Heidelberg: Springer, 1984, ISBN 3540134824 .
Bodo Ruck: Laser methods in flow measurement technology. AT-Fachverlag, Stuttgart, 1990, ISBN 3921681014 .
H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea: Laser Doppler and Phase Doppler Measurement Techniques. Springer, 2003, ISBN 3540678387 .
CI Moir: Miniature laser doppler velocimetry systems. SPIE Conference Proceedings, Optical Systems, 2009, vol. 7356.