An algorithm for inverting remote sensing measurements to determine particle concentration and size distribution, proposed by Nguyen and Cox in 1989, is described and evaluated. This determination uses extinction measurements at multiple wavelengths with the solution of the Fredholm integral equation. The solution represents the second derivative of the particle-size distribution as a linear combination of orthogonal functions chosen so that the resulting solution is smooth and positive everywhere. We used this algorithm to reconstruct concentrations and size distributions for simulated and experimental measurements of light extinction caused by different test aerosols. An “information content parameter” was used to measure how well each size distribution could be reconstructed from its corresponding measurements. For a wavelength range of 340–940 nm, aerosols in the accumulation mode (300 nm < d50 < 2500 nm) were reconstructed well. The algorithm was good at reconstructing moderately polydisperse aerosols (1.2 < σg < 2.0). Reconstruction quality was very sensitive to errors in the real part of the refractive index; however, the imaginary part of the refractive index did not have an important effect on reconstruction quality. The effect of adding different levels of random, normally distributed noise to the measurements was studied. The reconstruction algorithm was stable up to 10% noise in the measurements. With noise, the more measurements kept for analysis, the more oscillatory the solution became. Averaging multiple noisy measurements improved the quality of reconstruction. Increasing the measurement-wavelength range increased the range of particle sizes for which the reconstruction algorithm worked well, and also improved the stability of the solution against noise in the measurements. The algorithm is reliable for reconstructing multimodal distributions in the accumulation region. The method was also used to size manodisperse particles from laboratory measurements. Although the reconstructed frequency distributions had peaks that corresponded to the true size of the particles, a broadening of the distribution was observed.
Bibliographical noteFunding Information:
This research was partially supported by funding from the Kenan Foundation Fellowship at the University of North Carolina, and by the US. Environmental Protection Agency cooperative agreement CR815152 with the University of North Carolina. It has not becn subjected to Agency review and therefore does not ~iecessarily reflect the views of the Agency; thus no official endorsement should be inferred. We also thank Dr.