3  LMie Inputs

calc_pf

Flag indicating whether or not to compute the elements of the scattering phase matrix.

calc_gc

Flag indicating whether or not to compute the coefficients for the expansion of the scattering phase matrix in terms of generalized spherical functions.

calc_lc

Flag indicating whether or not to compute the coefficients for the expansion of the scattering phase matrix in terms of Legendre polynomials.

dist_type

The particle size distribution to use. Currently seven size distributions are supported. Distributions 2 - 6 are given here as in chapter 5 of Mishchenko et al. [2002]

1. mono:
   

   n(r) = 1

   (1)
2. gamma:
   

   n(r) = C r(1 − 3b) / b exp ⎛ ⎝ − r ab ⎞ ⎠ , b ∈ (0, 0.5)

   (2)
3. modified gamma:
   

   n(r) = C rα exp ⎛ ⎝ − αrγ γr γc ⎞ ⎠

   (3)
4. power law:
   

   n(r) = ⎧ ⎪ ⎨ ⎪ ⎩ Cr−3 if r1 ≤ r ≤ r2 0 otherwise

   (4)
5. modified power law:
   

   n(r) = ⎧ ⎪ ⎨ ⎪ ⎩ C if 0 ≤ r ≤ r1 C(r/r1)α if r1 ≤ r ≤ r2 0 if r2 ≤ r

   (5)
6. log normal:
   

   n(r) = C r−1 exp ⎡ ⎣ − (lnr − lnrg)2 2 ln2σg ⎤ ⎦

   (6)
7. modified bimodal log normal:
   

   n(r) = C r−4 ⎧ ⎨ ⎩ exp ⎡ ⎣ − (lnr − lnrg1)2 2 ln2σg1 ⎤ ⎦ + γexp ⎡ ⎣ − (lnr − lnrg2)2 2 ln2σg2 ⎤ ⎦ ⎫ ⎬ ⎭

   (7)

where C is the normalization constant, r is particle radius, r₁ and r₂ are the minimum and maximum radii in the size distribution (input parameters r1 and r2), and the other size distribution parameters are input via inputs a1 - a5.

n_int1

The number of subintervals from 0 to r₁ for the integration of size distribution. Only used for the power law size distribution.

n_int2

The number of subintervals from r₁ to r₂ for the integration of size distribution.

n_quad

The number of quadrature points to use per subinterval for the integration of size distribution.

n_angles

The number of scattering angles at which to compute the elements of the scattering matrix. Only used if input flag calc_pf is set.

n_derivs

The number of derivatives to be computed.

lambda

Wavelength of incident radiation, the units of which must be consistent with the input size distribution parameters a1 - a5.

mr

The real part of the complex index of refraction of the particle medium.

mi

The imaginary part of the complex index of refraction of the particle medium. Must be positive.

a1 - a5

Size distribution parameters, the units of which must be consistent with the wavelength of incident radiation lambda. The number of parameters used and their definition depend on the size distribution selected by input dist_type. The unused parameters are ignored.

1. mono:

   a1 = r
2. gamma:

   a1 = a a2 = b
3. modified gamma:

   a1 = αa2 = r_c a3 = γ
4. power law:

   a1 = r_eff a2 = v_eff
5. modified power law:

   a1 = α
6. log normal:

   a1 = r_g a2 = (lnσ_g)²
7. modified bimodal log normal:

   a1 = r_g,1 a2 = (lnσ_g,1)² a3 = r_g,2 a4 = (lnσ_g,2)² a5 = γ

r1, r2

Minimum and maximum radii (r₁ and r₂) in the size distribution. In theory, r1 and r2 should be equal to zero and infinity, respectively. In practice, the user should extend their range until the calculated scattering characteristics converge to within a prescribed numerical accuracy. Unused for the mono (disperse) and power law size distributions.

accuracy

The numerical accuracy at which to compute the coefficients for the expansion of the scattering matrix in terms of generalized spherical functions (flag calc_gc) and/or Legendre polynomials (flag calc_lc).

lambda_l, mr_l, mi_l, a1_l - a5_l, r1_l, r2_l

Linearized inputs indicated by a "_l" appended to the name for the associated input base value. These inputs are one dimensional arrays of size n_derivs where each element is associated with one of n_derivs derivatives. As a simple example, if we have a log normal size distribution and we are interested in derivatives with respect to m_r, m_i, r_g, and (lnσ_g)², in that order, for a total of 4 derivatives, the inputs would be set as

lambda_l	=	{0, 0, 0, 0}
mr_l	=	{1, 0, 0, 0}
mi_l	=	{0, 1, 0, 0}
a1_l	=	{0, 0, 1, 0}
a2_l	=	{0, 0, 0, 1}
r1_l	=	{0, 0, 0, 0}
r2_l	=	{0, 0, 0, 0}

More complex inputs, with values other than unity and where more than one linearized input is set to nonzero for a particular derivative index, are possible if one has derivatives of the inputs with respect to parameters further up the chain and is interested in Mie results with respect to these parameters.