Inverse Mie Theory Functions¶
Contour Intersection Inversion Functions¶
For more details on the contour intersection inversion method, please see Sumlin BJ, Heinson WR, Chakrabarty RK. Retrieving the Aerosol Complex Refractive Index using PyMieScatt: A Mie Computational Package with Visualization Capabilities. J. Quant. Spectros. Rad. Trans. 2017. DOI: 10.1016/j.jqsrt.2017.10.012 There’s also a good example here.

ContourIntersection
(Qsca, Qabs, wavelength, diameter[, n=None, k=None, nMin=1, nMax=3, kMin=0.00001, kMax=1, Qback=None, gridPoints=100, interpolationFactor=2, maxError=0.005, fig=None, ax=None, axisOption=0])¶ Computes complex m = n+ik from a particle diameter (in nm), incident wavelength (in nm), and scattering and absorption efficiencies. Optionally, backscatter efficiency may be specified to constrain the problem to produce a unique solution.
Parameters
 Qsca : float or listlike
 The scattering efficiency, or optionally, a list, tuple, or numpy.ndarray of scattering efficiency and its associated error.
 Qabs : float or listlike
 The absorption efficiency, or optionally, a list, tuple, or numpy.ndarray of absorption efficiency and its associated error..
 wavelength : float
 The wavelength of incident light, in nm.
 diameter : float
 The diameter of the particle, in nm.
 n : float or listlike, optional
 An assumed real refractive index. Can be used in case scattering data is not available. If specified as a list, it must have only two elements. The first is the assumed n and the second is an uncertainty, such as a standard deviation.
 k : float or listlike, optional
 An assumed imaginary refractive index. Useful if only considering nonabsorbing aerosols, so you can set k=0. If specified as a list, it must have only two elements. The first is the assumed k and the second is an uncertainty, such as a standard deviation. **Note: when specifying this in the function call, input it as a real number. Omit the imaginary unit.
 nMin : float, optional
 The minimum value of n to search.
 nMax : float, optional
 The maximum value of n to search.
 kMin : float, optional
 The minimum value of k to search.
 kMax : float, optional
 The maximum value of k to search.
 Qback : float or listlike, optional
 The backscatter efficiency, or optionally, a list, tuple, or numpy.ndarray of backscatter efficiency and its associated error.
 gridPoints : int, optional
 The number of gridpoints for the search mesh. Defaults to 200. Increase for better resolution but longer run times.
 interpolationFactor : int, optional
 The interpolation to apply to the search fields, artificially increasing their resolutions. This is applied after calculations, so some features may be lost if interpolationFactor is too high and gridPoints is too low.
 maxError : float, optional
 The allowed error in forward calculations of the retrived m.
 fig : matplotlib.figure object, optional (but recommended)
 The figure object to send to the geometric inversion routine. If unspecified, one will be created.
 ax : matplotlib.axes object, optional (but recommended)
 The axes object to send to the geometric inversion routine. If unspecified, one will be created.
 axisOption : int, optional
Dictates the axis scales. Kind of useless since version 1.3.0. It’s still around until I get rid of it. Acceptable parameters are:
 ‘0’ for automatic detection of best axis scaling
 ‘1’ for linear axes
 ‘2’ for linear x and logarithmic y
 ‘3’ for logarithmic x and linear y
 ‘4’ for loglog
Returns
 solutionSet : list
 A list of all valid solutions
 ForwardCalculations : list
 A list of scattering and absorption efficencies produced by forward Mie calculations using the derived refractive indices
 solutionErrors : list
 The relative errors of the efficencies in ForwardCalculations.
 fig : matplotlib.figure object
 The figure object now associated with the inversion calculations.
 ax : matplotlib.axes object
 The axes object now associated with the inversion calculations.
 graphElements : dict
A dict of all artists necessary to fully manipulate the appearance of the output. The keys will depend on the options passed to the inversion function itself (i.e., errors specified, backscatter specified). Maximally, it will contain:
 ‘Qsca’, ‘Qabs’, ‘Qback’  the major contours;
 ‘QscaErrFill’, ‘QscaErrOutline1’, ‘QscaErrOutline2’  the error bound contours;
 ‘QabsErrFill’, ‘QabsErrOutline1’, ‘QabsErrOutline2’  the error bound fills;
 ‘SolMark’, ‘SolFill’  the circle thingies at each solution;
 ‘CrosshairsH’, ‘CrosshairsV’  solution crosshairs;
 ‘LeftSpine’, ‘RightSpine’, ‘BottomSpine’, ‘TopSpine’  graph spines;
 ‘XAxis’, ‘YAxis’  the individual matplotlib axis objects.

ContourIntersection_SD
(Bsca, Babs, wavelength, dp, ndp[, n=None, k=None, nMin=1, nMax=3, kMin=0.00001, kMax=1, Bback=None, gridPoints=100, interpolationFactor=2, maxError=0.005, fig=None, ax=None, axisOption=0])¶ Computes effective complex m = n+ik from a measured or constructed size distribution (in cm^{3}), incident wavelength (in nm), and scattering and absorption coefficients (in Mm^{1}). Optionally, backscatter coefficient may be specified to constrain the problem to produce a unique solution.
Parameters
 Bsca : float or listlike
 The scattering coefficient, or optionally, a list, tuple, or numpy.ndarray of scattering coefficient and its associated error.
 Babs : float or listlike
 The absorption coefficient, or optionally, a list, tuple, or numpy.ndarray of absorption coefficient and its associated error..
 wavelength : float
 The wavelength of incident light, in nm.
 dp : listlike
 The diameter bins of the size distribution, in nm.
 ndp : listlike
 The number of particles per diameter bin corresponding to dp, in cm^{3}. Must be same length as dp.
 n : float or listlike, optional
 An assumed real refractive index. Can be used in case scattering data is not available. If specified as a list, it must have only two elements. The first is the assumed n and the second is an uncertainty, such as a standard deviation.
 k : float or listlike, optional
 An assumed imaginary refractive index. Useful if only considering nonabsorbing aerosols, so you can set k=0. If specified as a list, it must have only two elements. The first is the assumed k and the second is an uncertainty, such as a standard deviation. **Note: when specifying this in the function call, input it as a real number. Omit the imaginary unit.
 nMin : float, optional
 The minimum value of n to search.
 nMax : float, optional
 The maximum value of n to search.
 kMin : float, optional
 The minimum value of k to search.
 kMax : float, optional
 The maximum value of k to search.
 Bback : float or listlike, optional
 The backscatter coefficient, or optionally, a list, tuple, or numpy.ndarray of backscatter coefficient and its associated error.
 gridPoints : int, optional
 The number of gridpoints for the search mesh. Defaults to 200. Increase for better resolution but longer run times.
 interpolationFactor : int, optional
 The interpolation to apply to the search fields, artificially increasing their resolutions. This is applied after calculations, so some features may be lost if interpolationFactor is too high and gridPoints is too low.
 maxError : float, optional
 The allowed error in forward calculations of the retrived m.
 fig : matplotlib.figure object, optional (but recommended)
 The figure object to send to the geometric inversion routine. If unspecified, one will be created.
 ax : matplotlib.axes object, optional (but recommended)
 The axes object to send to the geometric inversion routine. If unspecified, one will be created.
 axisOption : int, optional
Dictates the axis scales. Kind of useless since version 1.3.0. It’s still around until I get rid of it. Acceptable parameters are:
 ‘0’ for automatic detection of best axis scaling
 ‘1’ for linear axes
 ‘2’ for linear x and logarithmic y
 ‘3’ for logarithmic x and linear y
 ‘4’ for loglog
Returns
 solutionSet : list
 A list of all valid solutions
 ForwardCalculations : list
 A list of scattering and absorption coefficients produced by forward Mie calculations using the derived effective refractive indices
 solutionErrors : list
 The relative errors of the coefficients in ForwardCalculations.
 fig : matplotlib.figure object
 The figure object now associated with the inversion calculations.
 ax : matplotlib.axes object
 The axes object now associated with the inversion calculations.
 graphElements : dict
A dict of all artists necessary to fully manipulate the appearance of the output. The keys will depend on the options passed to the inversion function itself (i.e., errors specified, backscatter specified). Maximally, it will contain:
 ‘Bsca’, ‘Babs’, ‘Bback’  the major contours;
 ‘BscaErrFill’, ‘BscaErrOutline1’, ‘BscaErrOutline2’  the error bound contours;
 ‘BabsErrFill’, ‘BabsErrOutline1’, ‘BabsErrOutline2’  the error bound fills;
 ‘SolMark’, ‘SolFill’  the circle thingies at each solution;
 ‘CrosshairsH’, ‘CrosshairsV’  solution crosshairs;
 ‘LeftSpine’, ‘RightSpine’, ‘BottomSpine’, ‘TopSpine’  graph spines;
 ‘XAxis’, ‘YAxis’  the individual matplotlib axis objects.
Surveyiteration Inversion Functions¶
The surveyiteration inversion algorithm is discussed in detail in the Supplementary Material of the JQSRT paper. It is a strictly numerical two phase algorithm. First, a lowresolution survey of nk space is conducted and values of efficiencies or coefficients close to the inputs are located. From this survey, candidate m values are determined. The iteration phase is best described by this flowchart:

SurveyIteration
(Qsca, Qabs, wavelength, diameter[, tolerance=0.0005])¶ Computes complex m=n+ik for given scattering and absorption efficencies, incident wavelength, and particle diameter.
Parameters
 Qsca : float
 Measured scattering efficiency.
 Qabs : float
 Measured absorption efficiency.
 wavelength : float
 The incident wavelength of light, in nm.
 diameter : float
 The particle diameter in nm.
 tolerance : float, optional
 The maximum error allowed in forward Mie calculations of retrieved indices.
Returns
 resultM : listlike
 The retrieved refractive indices. Be sure and scrutinize this list for repeat entries.
 resultScaErr : listlike
 The relative error in scattering efficiency for each retrieved m.
 resultAbsErr : listlike
 The relative error in absorption efficiency for each retrieved m.

SurveyIteration_SD
(Bsca, Babs, wavelength, dp, ndp[, tolerance=0.0005])¶ Computes complex m=n+ik for given scattering and absorption coefficients, incident wavelength, and particle diameter.
Parameters
 Qsca : float
 Measured scattering coefficient.
 Qabs : float
 Measured absorption coefficient.
 wavelength : float
 The incident wavelength of light, in nm.
 dp : listlike
 The particle diameter bins in nm.
 ndp : listlike
 The particle concentrations (in cm^{3}) corresponding to each of the bins in dp.
 tolerance : float, optional
 The maximum error allowed in forward Mie calculations of retrieved indices.
Returns
 resultM : listlike
 The retrieved refractive indices. Be sure and scrutinize this list for repeat entries.
 resultScaErr : listlike
 The relative error in scattering coefficient for each retrieved m.
 resultAbsErr : listlike
 The relative error in absorption coefficient for each retrieved m.