The invention relates to a method for measuring the rotary movement of objects, especially of the rotary velocity of a rotating body and of the vorticity in a flowing medium, by which method the object is irradiated by spatially coherent electromagnetic radiation from a raditation source and scattered radiation from two object elements are detected and the difference in Doppler shift in the radiation from the two object ' elements is measured. Measuring of the vorticity of a flowing medium is of great importance in the investigation of turbulent flows.

Such investigations are made within practically orientated research areas such as meteorology and oceanography and in the design of ship hulls, airplanes, airscrews, windmills, propellers, turbines, motorcars, pipe parts, gas- and fluid exhaust members, combustion chambers in internal combustion engines, nozzle buners etc. The measuring of the vorticity of flowing mediums can furthermore be used in the running of plans such as airports where the information gained thereby is of importance for the security of starting and landing ope¬ rations. The theories and mathematical models for tur¬ bulent flows elaborated until now are still comparative¬ ly incomplete and difficult to verify i.a. on account of problems with the measurement of the vorticity. Consequently, it has until now been necessary in practi- cal construction work to use timeconβuming and expensive

model experiments and testing of prototypes in wind- tunnels, tanks and the like.

It is therefore of both theoretical and technical interest to develop the theory of turbulent flow and in this connection to provide methods of mapping velocity fields and their development as a function of time, in¬ cluding the measurement of vorticity.

In recent years it has become usual to use Laser Doppler anemometry in the measurement of flow velocities in flowing media, which is inter alia due to the fact that this is a method in which no alterations in the flow are caused by the insertion of probes or the like in the medium.

The principle of Laser Doppler anemometry is that radiation scattered from a body moving in relation to a measuring instrument undergoes a change in frequency, the Doppler shift, which is proportional to the velocity of the body. If the body is carried by a flowing medium and if the influence of other forces on the body can be ignored, this Doppler shift is a measure of the flow ve¬ locity of the medium.

In the sample volume in which the measurement is carried out in practice, many particles will often move at slightly different velocities distributed about an average velocity and thus give rise to a frequency spec¬ trum of a certain extent. Hereby it is possible to mea¬ sure the average velocity and the degree of turbulence which reflects the velocity variations in the sample vo¬ lume. From an article by William Stachnik in SPIE, Vol. 208, Ocean Optics VI, page 216 (1979) a method is known for the measurement of vorticity and rotational veloci¬ ty, mainly based on the measurement of two orthogonal velocity components. By a conical scanning by means of a laser Doppler anemometer great vorticities are measu-

red which are defined as the dobble angular velocity of the measuring object. By the use of Stoke's theorem the integral of the tangential velocity is related to the rotation of the encircled area. In an article by Frish and Webb in J. Fluid Mech. (1981), vol. 107, page 173 a method is described by which the measuring objects are particles of the order of magnitude of 20 urn comprising plane crystal mirrors suspended in a fluid with an adapted refraction index and the voticity of which is to be measured. The partic¬ les are irradiated by laser pulses and by means of two detectors time differences are measured which are used in calculating the rotationel velocity of the particles which is half the local vorticity. Furthermore, methods for measuring velocity gra¬ dients by the combination of optics and laser anemometri are described in two articles by S. Hanson in Photon Co¬ rrelation Techniques in Fluid Mechanics, Springer Ver- lag, Berlin, Heidelberg, New York (1983), page 212 and Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon July 1984, paper 8.3 and in Danish accepted patent specification No. 148.334, in hich a method is described by which an op¬ tical element is used arranged in the radiation path 5 from the light scattering particles to a detector and having such optical characteristics that only scattered light from particle pairs having a given mutual distance determined by the optical element determins the electri¬ cal signal proportional to the velocity gradient. 0 In Technisches Messen tm, 52 Jahrgang, Hefte 3/1985, in an article by O. Wegner and M. Horstmann an optoelectronic system is described for measuring the ve¬ locity components on rotating solid surfaces by means of a circularly polarized laser beam made to pass through a $ Wollaston prism and splitting the beam into two beams

each passing through a pair of pivotally arranged wedges and in a so-called step prism deflected towards the rotating solid body the surface velocity of which is to be measured. Each of the two beams is divided in the step prism into two measuring beams. Backscattered ra¬ diation from the measuring points on the surface passes through a diaphragm and is deflected in the step prism towards a convex .lense sending the scattered radiation through a second Wollaston prisme after which it is re- ceived in the form of two returning beams by to detec¬ tors supplying two electrical signals to a differential amplifier to the output of which is connected a tracking processor or an FFT-analyser. By means of this apparatus tangential as well as radial velocity components can be measured together with velocity differences in the two measuring points.

In EP publication No. 0 103 422 Al a method is described in which laser radiation is divived by means of mirrors and diaphragms into two parallel beams de- fining two spots on the surface of a rotating shaft. Scattered radiation from the two irradiated spots is supplied to a detector producing a signal which is pro¬ portional to the rotational speed of the shaft. In this case no focusing of the laser radiation takes place, and the radiation intensity in the two spots is therefore rather small, resulting in a great noise sensitivity of the method.

A better signal-to-noise-ratio is obtained by a method described in an article by Watanabe et al in Op- tics Communications, Volume 43, No. 3, page 164, of 1 October, 1982. In this case two almost parallel laser beams are produced by means of mirrors and these laser beams are focused on the object, the rotational speed of which is to be measured, by means of a lens. Hereby a greater radiation intensity is obtained on the irradia-

ted object elements from which scattered radiation is supplied to a detector.

It is an object of the present invention to pro¬ vide a simple, effective and stable method by which the measuring result appears in the form of strong signals, which are fairly insensitive to the optically absolutely correct positions of the optical elements used for the measurement and to the possible variations of these positions during the measurements. To attain this the method as stated in the pre¬ amble of claim 1 is characterized, according to the in¬ vention, by the features as stated in the characterizing part of claim 1. Since the scattered radiation from the object elements passes on its way to the detector the radiation converging and the radiation dividing optical means, possible errors which might otherwise occur due to an optically not absolutely correct position of the optical elements will be compensated for. This is not the case in the method known from the above-mentioned article by Watanabe et al where the scattered radiation from the object elements does not pass the said optical means on its way to the detector.

By the expression radiation dividing optical means is to be understood, in this connection, a single or composed optical device having the characteristic that from an incomming beam it provides two nearly pa¬ rallel beams defining in connection with the radiation converging means, two relatively closely adjacent measu¬ ring points or object elements. The radiation dividing means may thus be an optical grating having a suitable grating constant and being of the absorption, phase or reflection type or intermediate forms thereon. Further¬ more is may be a Bragg-cell.

However, the radiation dividing means may also be of the birefringent type, such as a Wollaston or Rochon prism.

If the radiation source produces a linearly pola¬ rized electromagnetic radiation this radiation is expe¬ diently transformed into a circularly polarized radia¬ tion before it reaches the radiation dividing means. In an embodiment of the method the two object elements are irradiated with two beams being orthogonal¬ ly polarized and the two back scattered radiation beams from the object elements passing back through the bi¬ refringent optical element before they reach the detec- tor are sent through a polarizing filter turned 45° in relation to the main polarization direction of the ra¬ diation so that the two radiation beams are made to in¬ fluence each other and to provide a signal in the de¬ tector having a frequency which is proportional to the rotational velocity.

In another embodiment two birefringent optical elements are arranged in the radiation path from the source to the measuring object at right angles to each other whereby two vorticity components at right angles to each other can be measured at the same time, as two pairs of object elements are defined on the object each providing a signal to the detector representing one com¬ ponent and the other respectively.

The invention furthermore relates to an apparatus for carrying out the method according to claim 1,compri¬ sing a radiation source for spatially coherent elec¬ tromagnetic radiation which is focused on a measuring object from which scattered radiation is received and supplied to a detector for measuring the rotational mo- vement of the object on basis of an electrical signal supplied by the detector in which apparatus radiation dividing means splitting the radiation beam into two nearly parallel radiation beams and radiation converging means defining on the measuring object two object ele- ments are arranged in the radiation path from the

radiation source to the object, and the apparatus is characterized in that two beams of scattered radiation from the two object elements are sent back through the radiation converging means and the radiation dividing means towards a beam splitter arranged between the latter means and the radiation source and reflecting a substantial part of the radiation beams towards the de¬ tector.

An expedient embodiment of the apparatus compri- ses in the radiation path from a laser a diaphragm arranged in the radiation waist of the laser, a beam splitter, a lens the front focal plane of which is po¬ sitioned in the radiation waist of the laser and which defines the Fourier plane in which a beam dividing optical element is arranged, a diaphragm situated imme¬ diately behind the optical element, a second lens focusing the two radiation beams on the object and the radiation back scattered from the object elements on the optical element, and a detector receiving the back scat- tered radiation beams via the beam splitter.

The invention will now be further explained in the following with reference to the diagramatic drawing in which

Fig. 1 shows an embodiment of an apparatus accor- ding to the invention with a Wollaston prism as optical element,

Fig. 2 a ball shaped object,

Fig. 3 curves showing the result of measurements made at different rotational velocities, Fig. 4 curves showing measurements at different angles of incidence of the beams from the Wollaston prism, and

Fig. 5 curves showing the relative independence of the situation of the object elements on the rotating object.

In Fig.l 1 designates a laser from which is emitted a laser beam passing through a diaphragm 2 si¬ tuated in the waist of the beam, a λ/4 plate 3, a beam splitter 4, a lens 5 the front Fourier plane of which is situated in the plane of the diaphragm 2, an optical element which in this case is a birefringent prism 6 situated in the back Fourier plane of the lens 5, a diaphragm 7, a lens 8 and a rotating measuring object or measuring volume 9 situated in the back Fourier plane of the lens 8.

If the aperture of the diaphragm 2 is designa¬ ted θ2 and that of the diaphrahm 7 esη the apert res are expediently dimensioned so that:

where -λ is the wave length of the laser light and f - is the focal length of the lens 5. The reason for this dimensioning appears from the following. If it is supposed that the light in the beam from the laser is linearly polarized it is transformed on passage through the plate 3 into circularly polarized light when the plate is situated under an angle of 45° in relation to the direction of polarization of the incoming light.

The birefringent prism 6 divides the incoming laser beam into two beams the lights of which are pola¬ rized in two orthogonal directions which are at a little angle Ω to each other. The two beams irradiate two object elements 10 and 11 in the measuring volume 9 from which scattered light is received by the lens 8 and is sent back through the diaphragm 7, the optical element 6, the lens 5, and hit the beam splitter 4 which deflects the light so that after having passed a diaphragm 12 and a polarization filter 13 it is received by a detector 14.

The complex amplitude distribution in the plane of the optical element 6 is Fourier-transformed into a field distribution in the measuring volume situated in the back Fourier-plane of the lens 8. The original laser beam field distribution is thus convolved with the Fourier-transformation produced by the optical element 6. If a Wollaston-prism is e.g. used as the optical element the sum of two delta-functions will be produced representing the ordinary and extraordinary components respectively. The field distribution in the measuring volume will therefore consist of two orthogonally polarized Gaussian fields with the original beam width a , but separated in the x-direction (confer the coordinate system z-x indicated in Fig. 1) by a distance Δx determined by the expression

ΔX = flfg (2)

where Ω is the angle between the beams and fg is the focal lenght of the lens 8.

Light scattered from the object elements 10 and

11 in the measuring volume will be polarized in the same way as the incoming beam and will because of the movement of the object elements suffer a Doppler-shift Δω determined by

where λ is the wavelenght and vl. ,z is the velocity of the object element i in the direction of the z-axis.

The object elements have a certain extension determined by the width of the laser beam and the light distribution within the spot representing the object element is a Gaussian distribution. The light scattered

from the two object elements 10 and 11 is of mutually different polarization, namely corresponding to the po¬ larization in each of the incoming beams, and the fre¬ quency of the light will be shifted because of the move- ment of the object elements in relation to the frequency of the incoming laser light as well as mutually because the two object elements will normally move with diffe¬ rent velocities parallel to the direction of the laser beam and the scattered light will therefore have been subjected to different Doppler-shifts dependent on the object element from which it is coming.

Scattered light from both object elements 10 and 11 is collected by the lens 8 and transmitted as two plane waves of slightly different directions towards the birefringent prism 6 where they are transformed into two co-linear beams still of orthogonal polariza¬ tion and therefore unable to interfere in space or in time.

The diaphragm 7 in the Fourier-plane of the lens 8 filters the transmitted light before it is focused by the lens 5 via the beam splitter 4, the diaphragm 12 and the polarization filter 13 on the detector 14. The aperture of the diaphragm 12 is preferably of the same magnitude as that of the light spots on the object elements, that is as the waist width of the original beam and of the aperture of the diaphragm 2.

If the aperture of the diaphragm 7 is increased beyond the figure given in eq. (1) the amount of scattered light is increased proportional to the square of the width, but the illuminated object elements are divided into patches from which the light is added incoherently. Consequently, no improvement in the signal quality can be obtained by increasing the aperture provided that the signal is above the background light level.

The polarization filter 13 changes the polarization so that the scattered light from the two object elements can now interfere in time which means that a heterodyne frequency can be produced in the output signal of the detector.

A corresponding result can be obtained if instead of the birefringent optical element 6 a grating is used where the Fourier-transformation is the sum of the delta functions of each of the diffraction orders. In this case the plate 3 and the polarisation filter 13 are removed. The grating produces two similarly polari¬ zed beams with gaussion distribution og with a mutual angular diviation λ»g, where λ is the wavelength, and g is the grating constant. Experiments have proved that the optical configu¬ ration shown schematically in Fig. 1 can irradiate and coherently collect light from two spatially seperated object elements in the measuring volume, and that the detected frequency difference is proportional to the an- gular velocity in the measuring volume. The system is reasonably insensitive to optical turbulence and varia¬ tions of the reflexion characteristic of the optical path. The only instrument parameters which it is neces¬ sary to know are the focal length, the wavelength and the diffraction parameters of the prism or the grating. Neither the position of the beams on the object, the ra¬ dius of the scattering particles or the magnitude of the scattering eddy is of any significance.

As birefringent optical element can for example be used Wollaston or Rochon prisms or gratings of the absorption, fase or reflexion type as well as Bragg cells.

The method can for example be used to measure the vorticity of media such as liquids or gasses in the fol- lowing ways.

To the medium are added small scattering partic¬ les and the signals from particle pairs having the pre¬ determined correct mutual distance defined by the opti¬ cal element 6 and the lens 8 are analysed. Since the detected Doppler frequency depends only on the angu¬ lar velocity of the eddy, containing the particles, the instantaneous vorticity is obtained directly.

To the medium are added greater particles which are each irradiated with both beams and thus each comp- rise both scattering object element. In this case the distance between the beams must be a little less than the magnitude of the particles. The signals received by the detector then represents the rotational velocity of the single particles and thereby the vorticity. The spatial resolution of the system should be greater than the internal turbulens which is about 50urn in usual liquids.

The system may be used for measurements in the atmosphere. Convection eddies usually have comparatively small rotational velocities giving Doppler shifts under the MHz-area.

A system comprising one laser beam and two Wolla¬ ston prisms arranged at right angels to each other with an intervening retardation plate can be adapted to the simultaneous determination of two vorticity components at right angels to the optical axis.

It is also possible to determin the direction of rotation by detecting the Doppler shift and the corre¬ sponding quadrature signal. Since the electronic equipment for detecting the light signals and analysing the corresponding electrical signals is of a commonly known art it should not be ex¬ plained more in detail here.

Based on Fig. 2 the connection between the detec- ted Doppler frequency and the angular velocity of the

object in the measuring volume will now be explained mo¬ re in details.

The figure shows an object in the form of a ball shaped body having a radius R and a coordinate system with origo in center of the ball. The body is thought to rotate about the y-axis, and on the surface of the body are two points i and j, the paths of which are indicated as two circles of latitude. The points repre¬ sent two object elements irradiated by two laser beams and emitting scattered radiation.

The time-dependent positions of the particles can be written:

(t) = (/R ² -y ^Z _0i cosω ₀ t,y _0i , R ² -y ² _0i sinω ₀ t) (4)

X r_ (t) = = ( (/R - y:- _oj cos(ω ₀ t + Φ.), y _Qj ,

/R ² -Y ² _0j sin(ω ₀ t + Φ..)) (5)

where Φ _j is the angular distance between the positions of the particles projected in the x-z-plane.

The difference in velocity in the z-direction is therefore

(Ar _±j )'z = ω _Q (/R ² -y ² _Qi cosu> ₀ t -

/R ² -y ² _0j cos(ω _Q t + Φ )) (6)

which equals

(Δr _i; .)- = ω _Q • (Δr^'X) (7)

or if y _oi - y _oj « Δx

equals Δv ij,z = ω

O _' Δx (8)

where Δx is the distance between the objects in the x- direction.

The result shows that the difference in velocity in the z-direction is independent of the radius R and of the position of the object elements and depends only on the distance Δx in the x-direction between the object elements.

If the expression (3) for the Doppler shift is inserted, an expression for the measured frequency shift by use of a Wollaston prism is obtained:

Δω = (4τr/λ)'Ω'f ^« ω ₀ (9)

For an arbitrary angular velocity IDQ of the ob¬ ject is obtained

Δω = | 'Ksc ^x ω _Λ 0 x Δχ|' (10)'

where K is the scattering K-vector, ω _Λ is the an- gular velocity and Δx is the vector perpendicular to the K-vector between two illuminated object elements. If a diffraction grating is used instead of the birefringent prism, and if the quarter wave plate and the polarisation filter are omitted, the following ex¬ pression is obtained

Δω = 4»τr»f«g«ω_ (11)

This expression shows that the Doppler shift is independent of the wave length of the electromagnetic radiation and only depends _, the angular velocity OJQ ₀ f the rotating body and the chosen constants, namely the focal length f and the grating constant g.

As the system with the indicated diaphragm aper¬ tures is spatially coherent it is theoretically possible to use white light instead of laser light, although the result will be far from optimal. Compared to measurements using known laser Dopp¬ ler anemometers where the resultant scattering vector ^κ sc is usually small a Kg _C -vector having a maximum value is obtained by the method and the apparatus according to the invention leading to a great frequency shift. For instance, by using a rotational speed of one rotation pr. second and a He-Ne-laser and a Wollaston prism, whereby an ordinary beam and an extraordinary beam ha¬ ving a mutual angular deviation of 1°, and a focal

length of 1 meter, a frequency deviation of 348 kHz is obtained, when the line connecting the object elements is at right angels to the angular velocity vector.

In the following are indicated some measuring examples obtained by using an apparatus as shown schema¬ tically in Fig, 1, and having a 5 mW He-Ne-laser 1 with a linear polarization followed by a λ/4-plate 3 with its optical axis tilted 45°. The two lenses 5 and 8 each had a focal length of 10 cm, and the Wollaston prism 6 provided an angular deviation of 5° between the ordinary beam and the extraordinary beam. The vari¬ able diaphragm 7 was set to the same width as the in¬ coming beam with Gaussian distribution over the cross section. As object used was made of a ping-pong ball mounted on a shaft driven by a motor with variable speed.

The output signal from the detector 14, e.g. a photomultiplyer tube, was supplied to a band pass filter 15 filtering out the low frequency signals in order to avoid aliasing effects in the following signal processing. The upper cut-off frequency is preferably at least one order of magnitude higher than the lower cut¬ off frequency. The filtered signal is analyzed by means of an analog correlator 16 (HP 3721 A) and the autocor- related signal is Fourier-transformed in a corresponding spectrum analyzer 17 (HP 3720 A), the output signal of which is shown on an oscilloscope. In most of the ex¬ periments the Doppler-frequency could easily be recog¬ nised in the oscillogram of the unfiltered detector signal.

The results of three experiments are shown in Fig. 3, 4 and 5.

In Fig. 3 the energy spectrums of seven different values of the rotational speed of the object from 1,5 to 10,1 revolutions pr. minute are shown. The line connec-

ting the two object elements 10 and 11, Fig. 1, was at right angles to the z-axis, and the distance between the object elements was about 9 mm, and they were placed near the center of the object 9. The measuring results agree with equation (9). The relative spectral width is substantially constant. Only at the lowermost rotatio¬ nal speed there is an increased relative width caused by fluctuations in the rotational speed. By a reduction of the time interval over which autocorrelation is carried out, to e.g. 150 ms, "single-bursts" that is single pul¬ ses, can be analyzed. Hereby variations in the rotatio¬ nal speed can be revealed.

Fig. 4 shows the energy spectrums for different values from 90° to 30° of the angel between the Δx- vector and the angular velocity vector at a constant rotational speed of 6,5 revolutions pr. minute. The mea¬ surements confirm the sine-dependence predicted in eq. , (10). The absolute spectral width for the Doppler con¬ tribution to the energy spectrum is constant, causing the relative width to increase with decreasing angle, whereby the signal quality deteriorates. The angel was changed by turning the Wollaston prism.

Fig. 5 shows the energy spectrums for three dif¬ ferent positions of object element pairs a, b and c on the rotating object 9 shown schematically at the upper right corner of the figure. The three curves are desig¬ nated la, 2b and 3c. The curves illustrate that the Doppler shift is independent of the radius of the object and the position of the object element pairs on the sur- face of the object. It is seen that the signal quality is reduced as the element pairs are moved away from the central position a to the positions b or c. This is due to the fact that the intensity of the scattered light is reduced and that the intensities from the ob- ject elements of a pair become mutually different

causing a reduction of the modulation depth of the Dopp¬ ler signal.