A novel method is described for the calculation of the differential mobility analyser (DMA) transfer function in scanning mode, which is based on the derivation of an analytical solution for the non-diffusive particle trajectories inside the DMA, under exponentially varying electrical field and fully developed laminar flow. The scanning mode transfer functions can substantially improve the measurement accuracy of fast scanning mobility particle sizers (SMPS) as shown by Collins, Cocker, Flagan, and Seinfeld [(2004). The scanning DMA transfer function. Aerosol Science and Technology, 38, 833-850]. Compared to the Monte Carlo simulations described by Collins et al., the method developed here is much more accurate and sufficiently fast to be employed in advanced DMA inversion algorithms. (c) 2007 Elsevier Ltd. All rights reserved.