This work is concerned with the determination of polydisperse particle size distribution (PSD) function n(r) for aerosols from measurements of the radiation intensity of scattered light. A new mathematical model is proposed to find the unknown function n(r) from a simulated data measurement of differential volume angular scattering coefficient, volume extinction coefficient, volume scattering coefficient, and volume backscattering coefficient for various valuesof scattering angles 0=0° (1° ) 10°, 170° ( 1" ) 180" for bislatic system and twelve lidar wavelengths λ = 0.35, 0.53 , 0.55 , 0.6238 , 0.694 , 1.06 , 3.5 , 4 , 7, 9.1, 10.6 , and 11 μm for bistatic and monostatic systems. It is assumed in our study that the particle is spherical and the wavelength is comparable with particle size ranges; consequently.Mic theory is used. A new modified method is introduced to determine the domain of definition of particle size distribution using a solution of the poolynomial equation. These methods, involve matching the optical data with simulated data obtained from the direct solution of the problem. For optimizing the solution, Hooke & Jeeves unconstrained optimization method is used to determine the coefficients of polynomial function of PSD that yield the best agreement with the measured optical data; where the objective function is the sum of the squared deviations. Different cases are presented for the inversion of a narrow monomodal PSD function, a broad monomodal PSD function, and Bimodal PSD function. The accuracy of the solution is depending on the system of lidar used, how many wavelengths used for detection, and the degree of polynomial for the inverted PSD function.