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@7of9

PyMieScatt > ScatteringFunction() > measureの式 | scattereing wave vector | phase difference

動作環境
GeForce GTX 1070 (8GB)
ASRock Z170M Pro4S [Intel Z170chipset]
Ubuntu 16.04.4 LTS desktop amd64
TensorFlow v1.7.0
cuDNN v5.1 for Linux
CUDA v8.0
Python 3.5.2
IPython 6.0.0 -- An enhanced Interactive Python.
gcc (Ubuntu 5.4.0-6ubuntu1~16.04.4) 5.4.0 20160609
GNU bash, version 4.3.48(1)-release (x86_64-pc-linux-gnu)
scipy v0.19.1
geopandas v0.3.0
MATLAB R2017b (Home Edition)
ADDA v.1.3b6
gnustep-gui-runtime v0.24.0-3.1

Reference

ScatteringFunction() > measure

  if _q:
    measure = (4*np.pi/wavelength)*np.sin(measure/2)*(diameter/2)
  return measure,SL,SR,SU

measureというのは
http://pymiescatt.readthedocs.io/en/latest/forward.html#ScatteringFunction
を見ると下記のthetaに対応するようだ。

Returns
theta :numpy.ndarray
An array of the angles used in calculations. Values will be spaced according to angularResolution, and the size of the array will be (maxAngle-minAngle)/angularResolution.

上記の実装は

measure = \frac{4\pi}{\lambda}sin(\frac{measure}{2})\frac{diameter}{2}

Sorensen, M. Q-space analysis of scattering by particles: a review. J. Quant. Spectrosc. Radiat. Transfer 2013, 131, 3-12
を購入しないとわからない式のようだ。

上記、Sorensen(2013)のAbstractに下記の記載がある。

This analysis involves plotting the scattered intensity versus the scattering wave vector q=(4π/λ)sin(θ/2) on a double log plot.

measureというのはscattering wave vectorというもののようだ。

論文の用語とReadTheDoc上の説明用語と実装変数がそれぞれ別にする必要はあるのだろうか?

以下の式が成り立つようだ。

measure = scattering vector * (diameter / 2)

phase difference

式についてBohren and Huffmanを眺めていて、下記の似たような式を見つけた (p106)。

\Delta \phi = \frac{2 \pi}{\lambda}2a(N1 - N) = 2x(m-1)

diameter/2=aなので、係数$4\pi a/\lambda$は同じではあるが、scattering wave vectorと関係があるのかは不明。

Bohren and Huffman (1983)
p106

For if we adopt the viewpoint of elementary optics, the phase difference $\Delta \phi$ between a ray that traverses a large transparent sphere wihout deviation (i.e., the forward-scattered or centray ray) and a ray that traverses the same physical path outside the sphere is ...

透明な球内部をdeviationなしで通過するray(前方散乱)と球外側を同じ物理距離通過するrayとの位相差ということのようだ。

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