A ■wave sca ttered or radiated from a moving ob ject w ill su ffer a s h if t in frequency proportional to the instantaneous v e lo c ity o f the o b ject. This phenomenom, f ir s t explained by
C hristian Doppler in 1842, has been w idely used for the measurement, o f r e la tiv e v e lo c ity . One o f i t s o ld e st a p p lica tio n s has been in the
f ie ld o f astronomy, in which spectrom eters have long been used for the determ ination o f large recessio n r a te s o f d ista n t lig h t sources. U nfortunately, sin ce the fra ctio n a l frequency s h if t o f e le c tr o magnetic waves i s in the order o f 10~^ tim es the v e lo c ity in m/s the reso lv in g power o f o p tic a l spectrom eters i s q u ite in s u ffic ie n t
for measuring r e la tiv e v e lo c it ie s below approximately 10^ m /s. The
development o f heterodyning techniques enabled d etection o f Doppler s h if t s o f very small fra ctio n a l va lu es. The technique, however, i s r e s tr ic te d to coherent waves and u n til recen tly only sig n a ls in the radio-frequency portion o f the electrom agnetic spectrum were 'V g v a ila b le to f u l f i l th is requirement. Within these .-lim itation s radar Doppler .instrum ents allow the measurement o f o b jeo ts moving w ith a wide range o f v e lo c it ie s .
The introduction o f la se r s removed the main o b sta cle in the path o f the O p tic a l1 measurement o f low r e la tiv e v e lo c it ie s . A la se r ca v ity may be considered to be a high-gain o s c illa t o r o f extrem ely narrow band width. Only a small portion o f the energy i s em itted, but t h is i s very in ten se compared with the em ission w ithin
a comparable frequency range from a conventional source. In short,
la s e r s are intense^ sou rces-of highly monochromatic lig h t and as such are id e a lly su ited to the ap p lication o f heterodyning techniques. Before continuing w ith an account o f the development o f la se r anemometry i t may be worthwhile to consider the Doppler e f fe c t in s lig h tly more d e ta il.
A2 The DDppler E ffect
An observer on a p a r tic le moving away from a fix e d source o f lig h t would see lig h t at a lower frequency than the source
frequency and, to the station ary observer, the lig h t sca ttered from the p a r tic le s would also su ffer an apparent frequency s h ift. The geometry o f th is situ a tio n i s shown in fig u re jU lj-^ e^ 1 and , os l are u n it vecto rs in the d irectio n s o f the in cid en t and scattered lig h t
waves r e sp e c tiv e ly and ,v* i s the v e lo c ity o f any sp e c ifie d p a r tic le . The frequency rela tio n sh ip between the sca ttered lig h t waves and the lig h t wave i t o r ig in a te s from i s given according to the vector
+ 4
(8l).
equation I
+ V . . . (a.i )
where, f - frequency o f sca ttered lig h t - frequency o f in cid en t lig h t
§ - u n it vector in sca tterin g d irectio ns 2 u n it vector in in cid en t d irectio n = wavelength o f in cid en t lig h t and v * v e lo c ity vector
The frequency s h ift i s equal to the Doppler frequency, f^ •
f D “ f s “ f i (A. 2)
thus, = j v (e s - . . . (A .3)
I t may be seen from t h i s .equation that the Doppler frequency i s
d ir e c tly proportional to the p a r tic le frequency. The la se r anemometer, then, measures the Doppler frequency, f^ , obtained by way o f
p a r tic le s in the flow . The p a r tic le diameter may w ell be as small as the la se r lig h t wavelength and, .thus, the p a r tic le s have approximately the same lo c a l v e lo c ity as the flow medium even in a high frequency turbulent stream.
A3 The Development o f Laser Anemometry
In the early s ix t ie s the f e a s ib ilit y o f measuring steady flu id v e lo c it ie s from the Doppler s h ift in frequency o f sca ttered
( 8 2 )
rad iation was demonstrated by Teh and Cummins . Using a la s e r - Doppler spectrometer they measured the v e lo c ity p r o file in a liq u id flow and obtained r e s u lts which agreed remarkably w ell w ith
Incident light
Scattered x. light .Flo.w