Would it be possible to include a "year" entry in bibtex?

Code

miepython.mie_S1_S2(1.507-0.002j , 0.7086 , -1)

Output

In [8]: miepython.mie_S1_S2(1.507-0.002j , 0.7086 , -1)

TypeError Traceback (most recent call last)
in
----> 1 miepython.mie_S1_S2(1.507-0.002j , 0.7086 , -1)

~/opt/anaconda3/envs/Bo_Chen_Research/lib/python3.8/site-packages/numba/core/dispatcher.py in _explain_matching_error(self, *args, **kws)
654 msg = ("No matching definition for argument type(s) %s"
655 % ', '.join(map(str, args)))
--> 656 raise TypeError(msg)
657
658 def _search_new_conversions(self, *args, **kws):

TypeError: No matching definition for argument type(s) complex128, float64, int64

Hello there,
In example 04_gold you name and use the variable radius=0.1. But for the plots, you use the title "Gold Spheres 100nm diameter".
I compared the results of your code to the one nanocomposix uses, and conclude that only the title should be renamed to 100nm radius.

I'd like to calculate physical differential cross-sections from the normalized parameters and not sure how. This would have units of area per unit solid angle. https://en.wikipedia.org/wiki/Cross_section_(physics)#Differential_cross_section

I can square the amplitudes S₁ and S₂ and see that they give iper and ipar, but I still don't see how to recover actual differential cross-sections; they always integrate to 1.0 for any size particle (any reasonable x and m).

It seems it all boils down to the following sentence in 03_angular_scattering.ipynb:

Now if P₀ of light is scattered by a sphere then the scattered power on the detector will be...

I can imagine that P₀ might be the incident power over the geometrical cross-section πr² but I'm not sure if it's that, or it's related to one of the four values returned from mp.mie().

Example of what a differential cross-section plot with physical units would look like: See Figure 4. http://plaza.ufl.edu/dwhahn/Rayleigh%20and%20Mie%20Light%20Scattering.pdf

When I use your online calculator or this python module with following settings:

wavelength = 1500e-9
r = 4.710E-07
k = 2*3.14/wavelength
x = k * r             # dimensionless Mie size parameter = 1.9719
m = 1.4100 - 0.0080j  # index of refraction of sphere

qext, qsca, qback, g = miepython.mie(m,x)

print("The qext efficiency  is %.3f" % qext)
print("The scattering efficiency  is %.3f" % qsca)
print("The backscatter efficiency is %.3f" % qback)
print("The scattering anisotropy  is %.3f" % g)

then I get the following results:

The qext efficiency  is 1.155
The scattering efficiency  is 1.090
The backscatter efficiency is 0.097
The scattering anisotropy  is 0.658

With the script of Maetzler (bottom of page https://omlc.org/software/mie/), if I do:

mie(complex(1.410E+00, -8.000E-03), 2*pi/1500e-9*4.710E-01*1e-6).'

I get:

ans =

    1.4100
   -0.0080
    1.9729
    1.0879
    1.1556
   -0.0677
    0.1161
    0.6533
    0.1005

where ans(4) = qext = 1.0879 and ans(5) = qsca = 1.1556.

So it seems that the values of the extinction coefficient and of the scattering coefficent are interchanged.

I digged deeper in your code and found that the Python Mie coefficients an and bn are different to that of Maetzler:

Maezler (an):

  0.310171419307873 - 0.473671739481655i
  0.037432108684527 - 0.200893621373526i
  0.000067151985416 - 0.021297737932288i
 -0.000019924584511 - 0.001285929209167i
 -0.000000825241069 - 0.000050906381267i
 -0.000000022452476 - 0.000001402834546i
 -0.000000000449367 - 0.000000028342714i
 -0.000000000006890 - 0.000000000437321i
 -0.000000000000083 - 0.000000000005320i

Python (an):

  0.317746891588117 + 0.454752059193760i
  0.045298858385873 + 0.197467459081684i
  0.000838661081755 + 0.021263464324966i
  0.000023228420817 + 0.001285707362372i
  0.000000830332704 + 0.000050900760559i
  0.000000022453522 + 0.000001402654704i
  0.000000000449301 + 0.000000028338490i
  0.000000000006889 + 0.000000000437247i
  0.000000000000083 + 0.000000000005319i

Most numbers are equal but the signs are different. Same is true for bn values.

I also tried this Java Applet (http://www.lightscattering.de/MieCalc/eindex.html), which is really hard to get it running and it provides confusing results. Sometimes it provides the same results as the Python script, sometimes it there are clearly wrong values. Therefore I also tried "bhmie Matlab" from this site: http://scatterlib.wikidot.com/mie

With this script, I get the same results as with the script of Maetzler.

This is very confusing. Do you know more about this issue?

Thanks
Apollo3zehn

The following code gives results which I didn't expect:

import numpy as np
import matplotlib.pyplot as plt

# if miepython is missing, do `pip install miepython`
import miepython as mp

m = 1.5 - 0.01j
x = np.logspace(-1, 5, 20)  # also in microns

qext, qsca, qback, g = mp.mie(m,x)
plt.plot(x, qext, 'b+-', label="Q_ext")
plt.plot(x, qsca, 'r+:', label="Q_sca")
plt.plot(x, qback, 'g+:', label="Q_back")
plt.plot(x, g, 'r+-', label="<cos>")
plt.plot(x, qext - g * qsca, 'kx-', label="Q_pr")
plt.xscale('log')
plt.yscale('log')
plt.xlabel("size parameter")
plt.legend()
plt.grid()

The resulting figure:

At size parameter larger than ~ 5000, all coefficients except for qext (expected to be ~ 2) deviate largely, and qpr becomes negative.

As I am not so familiar with scattering theory, I couldn't understand/interpret this result. Is this an expected behavior?

Thanks for your work on miepython. I am seeing different results in this program based off of the bhmie.f program from what I see in miepython.
https://github.com/cfinch/Mie_scattering/blob/master/Mie_scattering_results.txt

For instance,

Case 14
Refractive index = 1.5000-1.0000j
Size parameter = 1.0000

bhmie, Python implementation:
Angle  Cosine              S1                        S2             Intensity         Polzn
0.00   1.0000  -8.38663e-01 -8.64763e-01  -8.38663e-01 -8.64763e-01     TBD             TBD
                (-1.43587)   (-4.53907)    (-1.43587)   (-4.53907)
0.52   0.8660  -8.19225e-01 -8.61719e-01  -7.21779e-01 -7.27856e-01     TBD             TBD
                (-1.44816)   (-4.60321)    (-1.44309)   (-4.99863)
1.05   0.5000  -7.68157e-01 -8.53697e-01  -4.19454e-01 -3.72965e-01     TBD             TBD
                (-1.48429)   (-4.78415)    (-1.45662)   (-9.08475)
1.57   0.0000  -7.03034e-01 -8.43425e-01  -4.44461e-02  6.94424e-02     TBD             TBD
                (-1.54059)   (-5.04542)    (-1.22683)   (-1.12318)
2.09  -0.5000  -6.42983e-01 -8.33904e-01   2.90109e-01  4.67297e-01     TBD             TBD
                (-1.60661)   (-5.32360)    (-1.65895)   (-3.80045)
2.62  -0.8660  -6.02066e-01 -8.27386e-01   5.11402e-01  7.32909e-01     TBD             TBD
                (-1.66244)   (-5.53839)    (-1.67298)   (-5.09510)
3.14  -1.0000  -5.87707e-01 -8.25093e-01   5.87707e-01  8.25093e-01     TBD             TBD
                (-1.68473)   (-5.61943)    (-1.68473)   (-5.61943)

The same angles, refractive index, and size parameter in miepython

import numpy as np
import miepython as mp
import pandas as pd

x=1.0
m=1.5-1.0j
theta=np.array([0.0,0.52,1.05,1.57])
#these are already in radians, just take the cosine
mu = np.cos(theta)
S1, S2 = mp.mie_S1_S2(m,x,mu)
d = {'Radians':theta,'mu':mu,'S1': S1, 'S2': S2}
pd.DataFrame(d)

	Radians	mu			S1											S2
0	0.00	1.000000	(0.21559134761827634+0.07032158696589161j)	(0.21559134761827634+0.07032158696589161j)
1	0.52	0.867819	(0.2088975313282614+0.06911399542780117j)	(0.1850220959903823+0.053959935270422095j)
2	1.05	0.497571	(0.19091059968083227+0.06584447573080125j)	(0.10580127368584931+0.014929002269445686j)
3	1.57	0.000796	(0.1684751305292149+0.06170965784286728j)	(0.013508092940547764-0.02277315059600813j)

I'm probably doing something wrong but if you have any ideas please let me know.

I am working on a theoretical approach for modelling reflectance spectra in blood.

Using the following parameters:

x(size parameter) = 2pir/lambda

For erythrocytes, r = 2.8 um and lambda = 0.450 um, I obtained x as 39, which was used to compute the a_n and b_n coefficients.

To be exact, I am passing refractive index and x (size parameter) to the "mie_An_Bn" function to obtain a_n and b_n values

I have two questions:

1. I see that the number of a_n, b_n coefficients varies as a function of size parameter(x). Since I am modelling a spectra(array of wavelengths in the range(450nm - 850nm)), do I need to compute the size parameter and subsequently a_n, and b_n for each of the wavelengths individually. Or Can I use a fixed wavelength (say 450nm).

2. Is there a way or set of standard values using which I can verify that the computed a_n, b_n coefficients are valid and can be used to model whole blood?

Hello, thank you for an excellent Python library!

I noticed that in 02_efficiencies.ipynb, the plot of the absorption, scattering, and extinction cross sections shows a unit of 1/microns^2. However, if I am not mistaken, it should instead be microns^2.

One then gets the absorption coefficient as number_density * cross_section, which is microns^-3 * microns^2 = 1/micron, as it should be.

Hi Scott, thanks for this very helpful tool!

When looking at the introductory documentation page in a browser (Chrome, Internet Explorer), the formulas are displayed in a strange way (see the following snippet).

I think this is a bit confusing, as one could read the second line as x = 2 pi r / lambda / n, while it is actually x = 2 pi r / (lambda / n), right?

Hi @scottprahl and thank you for a very useful Python package!

I noticed a method, mie_S1_S2, to compute the scattering amplitude functions, but no method to compute the scattering phase matrix (perhaps I miss it?) and I was wondering if this would be a feature that you'd be willing to have included in miepython?

In my application (radiative transfer for Earth observation), the knowledge of the scattering phase matrix lets one take polarisation into account, which is a significant improvement compared to unpolarised computations. But I don't know if this is something relevant for your application? From my understanding, deriving the scattering phase matrix from the scattering amplitude funtions is straightforward (e.g. with eqs. 5.2.105-6 in K. N. Liou (2002) - An Introduction to Atmospheric Radiation, Second Edition). If you are interested, I could prepare a pull request. 😃

Would be great if you put this on conda-forge

problem:

extinction is smaller than backscatter at certain size parameters

import numpy as np
import miepython
import sys

for i in np.arange(1.01, 10, 0.01):
    qext, qsca, qback, g = miepython.mie(i, np.pi)
    if qback>qext:
        print(i)
        sys.exit()

Is there a good paper to cite if using miepython in a publication? If so, it might be helpful to include in the README or read-the-docs.

This seems very easy to use and I can plot stuff, but I'm not sure how to understand and use the Scattering Amplitude outputs. With a plane wave intensity (W/m^2) on a single plarticle I'd like to know for example the scattered intensity at a given angle in W/sr).

help(miepython.mie_S1_S2) returns

...The amplitude functions have been normalized so that when integrated over all 4pi solid angles, the integral will equal the single scattering albedo. The units are weird, sr**(-0.5)

What exactly is the "single scattering albedo" is that the geometrical cross-section? I think I can understand the units (inverse radians) if this is assumed to be integrated over d phi (the azimuthal angle).

Is there a paper or source where I can read further?

Thanks!

update: I've just seen https://github.com/scottprahl/miepython/blob/master/doc/03_angular_scattering.ipynb and will have a look now, and update further, but a published reference would be handy as well.