We present a new design of hygroscopic tandem differential mobility analyser (HTDMA) capable of rapidly switching between measurement at constant humidity and the determination of humidograms. Both technical aspects of the instrumental setup and the software control are discussed. The optimal estimation method (OEM) developed by Rodgers (Rev. Geophys. 14 (1976), J. Geophys. Res. 95 (1990), Inverse Methods for Atmospheric Sounding, World Scientific, Singapore 2000) for solving atmospheric data inversion problems has been successfully developed to retrieve measurements of hygroscopic particle growth using the tandem DMA. The technique makes no assumptions about the shape of the hygroscopic growth distribution and is able to determine the resolution and shape of the retrieved distribution. The technique has been shown to be robust throughout extensive tests and a thorough error analysis has been performed. The largest source of error arises from the under-sampling of the measurements, the so-called 'smoothing error'. However, the uncertainties in the measurements and error in the forward model are also significant. The technique allows hygroscopic growth measurements to be retrieved under a variety of atmospheric conditions and over an extended time period in a reliable and consistent manner. A comparison is made between the OEM routine and the well-documented TDMAfit method of data analysis, showing the limitations and subjectiveness of TDMAfit in certain situations. The OEM data retrieval process is a transferable routine that could also be used in other applications, such as the volatility tandem DMA instrument. © 2004 Elsevier Ltd. All rights reserved.