The development of an optical particle sizer for aerosols is described which is based on the principle of light scattering by single particles. The instrument is appropriate for simultaneous measurements of broad particle size distributions and allows applications in hot gases. The main topic concerns the evaluation of the particle size distribution from measured data, i.e. a mathematical correction for the influence of inhomogeneous illumination and of particle shape. Irregularly shaped and randomly orientated particles which also might be illuminated inhomogeneously (laser light, border zone) deliver different signal amplitudes, which finally results in a spreading of the measured particle size distribution. Assuming a specific distribution of signal amplitudes related to every particle size and shape, the spreading of the measured data can be corrected. The mathematical procedure requires the solution of a Fredholm integral equation, i.e. the inversion of a linear equation set whose coefficients are based on a correction function to be determined by a preceding calibration. A new inversion method combining the well known regularization according to Phillips and Twomey and the non-negative least-squares method according to Lawson and Hanson.