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Update index.rst
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bsumlin committed Jul 24, 2017
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Expand Up @@ -44,30 +44,30 @@ You can install PyMieScatt from `PyPI <https://pypi.python.org/pypi/PyMieScatt>`
Returns Mie efficencies of a spherical particle in the Rayleigh regime (:math:`x=\pi d/\lambda << 1`) given refractive index *m*, *wavelength*, and *diameter*. Optionally returns the parameters as a dict when *asDict* is specified and set to True. Uses Rayleigh-regime approximations:

:math:`Q_{sca}=\frac{8x^4}{3}\left|{\frac{m^2-1}{m^2+2}}\right|^2`
:math:`Q_{sca}=\frac{8x^4}{3}\left|{\frac{m^2-1}{m^2+2}}\right|^2`

:math:`Q_{abs}=4x\:\text{Im}\left\{\frac{m^2-1}{m^2+2}\right\}`
:math:`Q_{abs}=4x\:\text{Im}\left\{\frac{m^2-1}{m^2+2}\right\}`

:math:`Q_{ext}=Q_{sca}+Q_{abs}`
:math:`Q_{ext}=Q_{sca}+Q_{abs}`

:math:`Q_{back}=\frac{3Q_{sca}}{2}`
:math:`Q_{back}=\frac{3Q_{sca}}{2}`

:math:`Q_{ratio}=1.5`
:math:`Q_{ratio}=1.5`

:math:`Q_{pr}=Q_{ext}`
:math:`Q_{pr}=Q_{ext}`

.. py:Function::`LowFrequencyMieQ(m, wavelength, diameter[, asDict=False])
Returns Mie efficencies of a spherical particle in the low-frequency regime given refractive index *m*, *wavelength*, and *diameter*. Optionally returns the parameters as a dict when *asDict* is specified and set to True. Uses :py:func:`LowFrequencyMie_ab` to calculate :math:`a_n` and :math:`b_n`.

.. py:Function:: LowFrequencyMie_ab(m,x)
Returns external field coefficients :math:`a_n` and :math:`b_n` based on inputs of *m* and :math:`x=\pi d/\lambda` by on limiting the expansion of :math:`a_n` and :math:`b_n` to second order:
Returns external field coefficients :math:`a_n` and :math:`b_n` based on inputs of *m* and :math:`x=\pi d/\lambda` by limiting the expansion of :math:`a_n` and :math:`b_n` to second order:

:math:`a_1=-\frac{i2x^3}{3}\frac{(m^2-1)}{m^2+2}`
:math:`a_1=-\frac{i2x^3}{3}\frac{(m^2-1)}{m^2+2}`

:math:`a_2=-\frac{ix^5}{15}\frac{(m^2-1)}{2m^2+3}`
:math:`a_2=-\frac{ix^5}{15}\frac{(m^2-1)}{2m^2+3}`

:math:`b_1=-\frac{ix^5}{45}(m^2-1)`
:math:`b_1=-\frac{ix^5}{45}(m^2-1)`

:math:`b_2=0`
:math:`b_2=0`

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