An analytic inversion method, based on the anomalous diffraction approximation for nonabsorbing spherical particles, was developed to retrieve the size distribution from the optical turbidity or extinction spectrum. This method makes use of a differential Fourier cosine transform approach and provides a simple and fast inversion by means of fast Fourier transform and the Savitzky–Golay filter. The applicability of this algorithm was tested on the extinction data generated by the Mie solution. The effects of noise, modality, band limits, and data set size were analyzed by comparison with simulated data. This method can be used to reconstruct the original monomodal and bimodal distributions from 10% noise-corrupted data. The peak position and ratio of peak heights can be recovered with 10% or less deviation. The experiments with latex spheres showed that the inversion result from this method compares favorably with that from the dynamic light scattering measurement.
© 1996 Optical Society of America
Original Manuscript: March 20, 1995
Revised Manuscript: July 10, 1995
Published: January 1, 1996
Jianhong Wang and F. Ross Hallett, "Spherical particle size determination by analytical inversion of the UV–visible–NIR extinction spectrum," Appl. Opt. 35, 193-197 (1996)