Optical particle counters (OPCs) are used regularly for atmospheric research, measuring particle scattering cross sections to generate particle size distribution histograms. This manuscript presents two methods for calibrating OPCs with case studies based on a Passive Cavity Aerosol Spectrometer Probe (PCASP) and a Cloud Droplet Probe (CDP), both of which are operated on the Facility for Airborne Atmospheric Measurements BAe-146 research aircraft. A probability density function based method is provided for modification of the OPC bin boundaries when the scattering properties of measured particles are different to those of the calibration particles due to differences in refractive index or shape. This method provides mean diameters and widths for OPC bins based upon Mie-Lorenz theory or any other particle scattering theory, without the need for smoothing, despite the highly nonlinear and non-monotonic relationship between particle size and scattering cross section. By calibrating an OPC in terms of its scattering cross section the optical properties correction can be applied with minimal information loss, and performing correction in this manner provides traceable and transparent uncertainty propagation throughout the whole process. Analysis of multiple calibrations has shown that for the PCASP the bin centres differ by up to 30% from the manufacturer's nominal values and can change by up to approximately 20% when routine maintenance is performed. The CDP has been found to be less sensitive than the manufacturer's specification with differences in sizing of between 1.6 ± 0.8 μm and 4.7 ± 1.8 μm for one flight. Over the course of the Fennec project in the Sahara the variability of calibration was less than the calibration uncertainty in 6 out of 7 calibrations performed. As would be expected from Mie-Lorenz theory, the impact of the refractive index corrections has been found to be largest for absorbing materials and the impact on Saharan dust measurements made as part of the Fennec project has been found to be up to a factor of 3 for the largest particles measured by CDP with diameters of approximately 120 μm. In an example case, using the calibration and refractive index corrections presented in this work allowed Saharan dust measurement from the PCASP, CDP and a Cloud Imaging Probe to agree within the uncertainty of the calibration. The agreement when using only the manufacturer's specification was poor. Software tools have been developed to perform these calibrations and corrections and are now available as open source resources for the community via the SourceForge repository.
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