1 I n t r o d u c t i o n CONVENTIONAL methods of sperm motility assessment tend to be rather subjectiveand time-consuming procedures. Objective methods are very desirable. Laser light scattering provides one such method; the advantages of which for routine assessment have been discussed elsewhere (LEE, 1982; JOUANNET et al., 1977). This paper describes a light- scattering system capable of repetitivelyand automatically examining several samples over long periods of time. The tedious and repetitive nature of studies of changes in motility with time or sperm treatment have been eliminated. The motions of the sperm cause modulation of the scattered light. Whereas there is some discussion in the literature as to the specific motions of the sperm which are thus observable (CRAIG et al., 1979; FROST and CUMMINS, 1981), it is generally agreed that the interpretation outlined below is quite satisfactory for routine comparative studies. The spectrum (or, equivalently, the autocorrelation func- tion) of the light scattered by the sperm contains information on the swim-speed probability distribution P(v) charac- teristic of the sample, and the fraction c~ of the sperm which are swimming. 2 Correlation functions and motility 2.1 Theoretical background In this work we have observed the autocorrelation function of the scattered light, which is the Fourier transform of the optical spectrum. It contains contributions due to both the live (swimming) and the dead sperm, weighted by ct and ( l - a ) , respectively. The total field correlation function is thus g(1)(z) = o~gL(z ) + (1 -- ~)go(Z) . (1) First received 12th April and in final form 13th August 1984 (~ IFMBE: 1985 Medical & Biological Engineering & Computing May 1985 The forms of gL(z) and go(z) are given below. A single sperm swimming with instantaneous velocity v induces a Doppler shift in the scattered light: A ~ = k ' v where k is the scattering vector, the difference between t wave vectors of the incident and scattered light. If there is no preferred swim direction the correlation function for live sperm can be shown (NosSAL et al., 1971) to be f sin(kvz) gdz)= kvz 0 - - P ( v ) d v . (2) where P(v) is the probability distribution of the swim speed v. The motions of the dead sperm can be approximated as simple diffusion, characterised by a translational diffusion coefficient D: go(z) = e -~ (3) For an object of complex shape, such as a sperm, this is gross simplification, but the data uncertainties make any more detailed model unnecessary. Substitution of eqns. 2 and 3 into eqn. 1 yields the tota field correlation function. Assuming that the live sperm will also undergo Brownian motion, this is I isin(kvz) p(v)dv+(1-~)] (4) g(1)(z) = e -~ c~ kvz 0 It has been shown that data analysis is not sensitive to the postulated Brownian motion of the live sperm (FRosT and CUMMINS, 1981); the comparatively rapidly decaying gL(z) is 263