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Light source and geometrical requirements for the optimization of optical anemometry signals

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Abstract

The criteria for the design of optical arrangements for laser anemometry are formulated for reference-beam, two-beam and single-beam modes of operation. The dependence of useful light intensity upon optical path-length difference and number of axial laser modes is calculated. Laser power requirements are evaluated and the dependence upon band-pass filtering is quantitatively assessed. A new two-channel integrated-optical unit, with light-path compensation, and embodying the proposed design criteria, is described.

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Abbreviations

c :

velocity of light

D 1/e :

diameter of laser beam at 1/e-point

d :

half distance separating the beams leaving the lens

d m :

effective diameter of measuring control volume

d ph :

diameter of aperture in front of photo-multiplier

d r :

waist diameter of focused reference beam

d s :

waist diameter of scattering light beam

d l :

waist diameter of fucused light beam

F :

f-number of lens

χ :

scattering function introduced in Mie's theory

f :

signal frequency

Δf :

bandwidth of filter

Δf D :

Doppler line width of laser radiation

Δf G :

effective bandwidth of gain envelope of a laser

Δf M :

frequency difference between two adjacent axial modes

h :

Planck constant (6.6256×10−34J sec)

K 2π/λ :

wave number

L :

cavity length of laser

l m :

length of measuring control volume

m :

total number of axial modes of laser

M :

magnification (≡a/b)

N fr :

number of fringes in crossing region of the two light beams

N ph :

number of fringes seen by photomultiplier

N s :

number of photons scattered per particle passage

N e :

number of electrons leaving photo cathode per unit time

P l :

total light power emitted by laser

P s :

total light power scattered by particle

Q scat :

scattering coefficient

R :

distance from particle centre to point on plane of observation

r p :

radius of scattering particle

u :

velocity component perpendicular to fringe pattern

Δχ fr :

distance between fringes inside measuring control volume

η c :

efficiency of light collecting system\(\left( { \equiv \int {\int\limits_\Omega {IR^2 d\Omega /\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \bigcirc} {IR^2 d\Omega } } } } \right)\)

η q :

overall quantum efficiency of photodetector

g q :

coordinate measuring angle from the optical axis

φ :

half angle between wave fronts

λ :

wave length of light

υ :

frequency of incident light wave

∑e :

standard deviation of electron flux

τ :

transit time of scattering particle

Ω :

solid angle

dω :

solid angle element

References

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Author notes

  1. F. Durst

    Present address: University of Karlsruhe, Sonderforschungsbereich 80, Deutschland

Authors and Affiliations

  1. Department of Mechanical Engineering, Imperial College, London

    F. Durst & J. H. Whitelaw

Authors
  1. F. Durst
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  2. J. H. Whitelaw
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Durst, F., Whitelaw, J.H. Light source and geometrical requirements for the optimization of optical anemometry signals. Opto-electronics 5, 137–151 (1973). https://doi.org/10.1007/BF01414734

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  • DOI: https://doi.org/10.1007/BF01414734

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