"1994 Elsevier Science B. V. All rights reserved. Optical methods in biomedical and environmental sciences. H. Ohzu and S. Komatsu, editors. Volume diffraction by, and imaging of striated muscle fibres J.T. Sheridan' and C.J.R. Sheppard b 31 a Angewandte Optik, Phys. Inst., Univ. Erlangen-Niirnberg, Staudtstr. 7, D-91058, Gennany. b Dept. of Phys. Optics, School of Physics, Univ. of Sydney, Sydney, NSW, 2006, Australia. INTRODUCTION '\ For over one hundred years the diffraction of light by striated muscle fibres, SMFs, has been known to the biology communityl. Striated muscle is composed of cylindrical fibres in which a fine striated pattern appears. Although most of the research carried out has been empirical, the existence of constructive interference, or Bragg effect, within the striation pattern was identified by biologists. All such empirical attempts, including the use of scalar theory based on Fourier transmittance theory fail, because the dimensions of the striation are close to the wavelength of the incident light. In this case multiple scatter occurs which necessitates the use of volume diffraction theory to analyse the diffraction effects. Recently it has been proposed to apply rigorous electromagnetic theory to analyse this problem 2 • 3 .4,5. Much of this work bears strong similarities to work carried out in physical optics in modelling holographic 6 and surface relief gratings 7 . In these areas approximate and rigorous electromagnetic models have been derived and applied for many years. These models give accurate infonnation regarding the variation of the diffraction orders as the depth, angle of incidence and polarisation of the incident light are changed. They also allow variations of the striation pattern inside the volume to be modelled. Comparisons of the rigorous and approximate models show that first-order coupled wave theory can be successfully applied to analyse striated muscle fibres. This can be well understood using the so-called optical thickness and thinness parameters 5 • In Ref. 5 rigorously calculated coherent dark-field and bright-field images were presented. Here we discuss the generalisation of the methodology presented in Ref.s 3 and 4 to deal with TM polarised light and conical incidence. Confocal transmission images are calculated, and the posibility of calculating fluorescent images is indicated. RIGOROUS ELECTROMAGNETIC THEORY OF DIFFRACTION In Ref. 4 a rigorous numerical methodology to rigorously deal with a grating illuminated by TE-polarised light classically incident (in the plane of the grating) was presented. Using the notation of this paper we now present the corresponding equations for TM polarised light. The two polarisation cases can be simply compared as follows TE(s), H-mode E(x,z) = ye,(x,z): H(x,z) = xhx(x,z) + zh,(x,z) (1) TM(p), E-mode H(x,z) = yh,(x,z): E(x,z) = xex(x,z) + ze,(x,z) (2) The plane of the grating is the x-z plane. The cross-sectional pennittivity is given by - 1 A . Er(X) = E rO + exp(jnKx] where En = - J Er (X) exp[ - jnKx]dx (3) n=-- A 0 which can take any form necessary, and the following notation also appears