Aerosol extinction spectroscopy has been used to determine optical constants since the pioneering works by [Avery, R. K.; Jones, A. R. Journal of Physics D-Applied Physics 1982, 15, 1373].  and [Milham, M. E.; Frickel, R. H.; Embury, J. F.; Anderson, D. H. Journal of the Optical Society of America 1981, 71, 1099].  The refractive indices of ice at lower temperatures were obtained using the extinction spectra of ice aerosol particles [Clapp, M. L.; Miller, R. E.; Worsnop, D. R. Journal of Physical Chemistry 1995, 99, 6317].  Neither the "small particle spectra” method nor the thin film technique is, however, applicable to metastable liquids. In case of the thin film technique, the difficulties arise from  the large volume of a sample, which makes deep supercooling unachievable. In the case of the aerosol approach, it is very difficult to prepare samples of particles less than 0.3 mm.  These difficulties have been overcome  with the invention of a new method to correct the imaginary part of the refractive index, starting with approximate values as a first guess [Dohm, M. T.; Potscavage, A. M.; Niedziela, R. F. Journal of Physical Chemistry A 2004, 108, 5365].

The computer code that was used to determine the optical constants of supercooled water [Zasetsky, A. Y., A. F. Khalizov, M. E. Earle, and J. J. Sloan, , Journal of Physical Chemistry A, 109(12), 2005] from extinction measurements is based on the following algorithm. 

do while ()

         do while ()

                     ,                              !scale absorption coefficient

                     ; i=1,N^ext        !perform KK transform

                     ; i=1,N, j=1,M     !compute extinction efficiency (Mie)

                     ; i=1,N, j=1,M         !normalize to the particle volume

                     , subject to    !solve linear system

                                                !compute 1-norm

end do while !

for i=1,N

;

;

;

  !correct imaginary part of refractive index

end for

end do while !

is the aerosol extinction cross section at the frequency n_i normalized to the volume of a sphere with radius r_j; Q^ext and Q^scat are the extinction and scattering efficiency coefficients, respectively; is the complex refractive index; r is the particle radius, and is the frequency. The vector I is the (observed) extinction spectrum and 1 is the identity matrix.  The solution vector P gives the volume size distribution after normalization by the total volume of aerosol particles. The matrix K is an N´M matrix column, in which N is the number of frequencies (~6000), M is the number of discrete radii, and N^ext is the number of points used in the discrete Kramers-Kronig integration, which is different from N as an extended frequency range is used. The quantity is the refractive index at infinite frequency, k' is the scaling coefficient, and is the norm. The quantities e₁ and e₂ are small numbers that are used to specify the stop criterion.  The details on solving the least squares can be found in [Zasetsky, A. Y.; Khalizov, A.; Sloan, J. J. Applied Optics 2004, 43, 5503 ].