The transmission function for neutron scattering instruments is developed using acceptance diagrams. This formalism clarifies why some optimisations (eg HRPD) work. This talk develops the formalism for a Three Axis Spectrometer. Scan profiles are the convolution of two 2D shapes corresponding to the neutrons scattered by the sample and the secondary spectrometer transmission. An optimised scan matches these shapes to each other and to the slope of any dispersion surface in the scattering. Ideally the shapes are narrow in the scan direction and broad perpendicular to that direction. Simple calculations show some surprising results. Principal among these are that collimator widths and crystal mosaic should be considerably larger in the secondary spectrometer than in the primary spectrometer for a normal scan (E>0 and kF fixed) and that the plough or long-chair configurations are superior to the W at sample scattering angles less than about the monochromator take-off angle. The reflecting Soller collimators developed at ILL are described. It is shown that the gains from such collimators should be a factor of 3 on a HRPD and 5 on a TAS not the factor of 2 previously expected. This may make them viable competitors to horizontal focussing monochromators

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