The mie_derivs.pro procedure performs single particle
Mie scattering calculations, providing the distribution of scattering
radiation, various particle cross sections and the analytically
derived derivatives of all calculated quantities.
A the derivation of expressions for the analytical derivatives
of Mie scattering terms is covered by:
Grainger, R.G., J. Lucas, G.E. Thomas, G. Ewan, "The Calculation
of Mie Derivatives", Appl. Opt., 43(28), 5286-5393, 2004.
mie_derivs.pro is an IDL procedure and can be called with the following
command line from the IDL prompt (as long as the source file lies within your
IDL_PATH environment variable):
x: The particle size parameter(s). This must be a scalar float/double
quantity and must always be greater than zero.
Cm: The complex refractive index of the particles. Only one refractive
index value can be used in each call to the procedure and must take the
form complex(a,-b) (where a is the real part of the refractive index,
and b is the imaginary (or absorpative) part, and is either zero or
negative).
Dqv: The cosine of the scattering angles at which to calculate the
amplitude functions and phase function. This must be a float/double vector.
The output parameters are:
Qext: The extinction efficiency.
Qsca: The scattering efficiency.
dQextdx: Derivative of the extinction efficiency with respect
to the particle size parameter.
dQextdRem: Derivative of the extinction efficiency with respect
to the real part of the refractive index.
dQextdImm: Derivative of the extinction efficiency with respect
to the imaginary part of the refractive index.
dQscadx: Derivative of the scattering efficiency with respect
to the particle size parameter.
dQscadRem: Derivative of the scattering efficiency with respect
to the real part of the refractive index.
dQscadImm: Derivative of the scattering efficiency with respect
to the imaginary part of the refractive index.
Note: All of the above output variables are scalars of type double.
i1: The first intensity function - intensity of light
polarized in the plane perpendicular to the directions of incident light
propagation and observation.
i2: The second intensity function - intensity of light
polarized in the plane parallel to the directions of incident light
propagation and observation.
di1dx: Derivative of the first intensity function with respect
to the particle size parameter.
di2dx: Derivative of the second intensity function with respect
to the particle size parameter.
di1dRem: Derivative of the first intensity function with
respect to the real part of the refractive index.
di1dImm: Derivative of the first intensity function with
respect to the imaginary part of the refractive index.
di2dRem: Derivative of the second intensity function with
respect to the real part of the refractive index.
di2dImm: Derivative of the second intensity function with
respect to the imaginary part of the refractive index.
Note: All of these output variables will be vectors of type double, with
the same number of elements as Dqv.
