xopto.mcbase.mcpf.rayleigh module¶

class Rayleigh(gamma)[source]¶

Bases: xopto.mcbase.mcpf.pfbase.PfBase

The Rayleigh scattering phase function is defined as:

$\frac{3}{8}((1 + 3\gamma) + (1 - \gamma)*\cos^{2}(\theta))/(1 + 2\gamma)$

[Anthony Bucholtz, Applied Optics, Vol. 34, No. 15 Rayleigh-scattering calculations for the terrestrial atmosphere]. The scattering angle cosine is sampled/computed by using the Cardans formula to solve $x^3 + ax + b = 0$ , where:

$a &= 3 (1 + 3\gamma)/(1 - \gamma) b &= 4 (1 + 2\gamma)/(1 - \gamma)(1 - 2\xi)$

Jeppe Revall Frisvad, Journal of the Optical Society of America A, Vol. 28, Issue 12, pp. 2436-2441 (2011), Importance sampling the Rayleigh phase function.

For a special case when $\gamma = 1$ , i.e. isotropic scattering, the scattering angle cosine becomes $2\xi - 1$ , where $\xi$ is a random number from $[0, 1]$ . For gamma != 1 the solution ( $\cos(\theta)$ ) is defined in terms of Cardano formula:

$x = \cos(\theta) &= (-b/2 + (b^{2/4} + a^{3/27})^{1/2})^{1/3} + (-b/2 - (b^{2/4} + a^{3/27})^{1/2})^{1/3}$

Parameters: gamma (float) – Molecular anisotropy. Scattering is isotropic for gamma = 0.

static cl_declaration(mc: xopto.mcbase.mcobject.McObject) → str[source]¶: OpenCL declarations of the scattering phase function.

static cl_implementation(mc: xopto.mcbase.mcobject.McObject) → str[source]¶: OpenCL implementation of the scattering phase function.

cl_pack(mc: xopto.mcbase.mcobject.McObject, target: Optional[xopto.cl.cltypes.Structure] = None) → xopto.cl.cltypes.Structure [source]¶

Fills the OpenCL Structure (target) with the data required by the Monte Carlo simulator. See the cl_type() method for a detailed list of fields.

Parameters

mc (McObject) – Simulator instance.
target (cltypes.Structure) – Target OpenCL structure for packing.

Returns

target – Target structure received as an input argument or a new instance of ClRayleigh if the input argument target is None.

Return type

cltypes.Structure

static cl_type(mc: xopto.mcbase.mcobject.McObject) → xopto.cl.cltypes.Structure [source]¶

Returns an OpenCL structure that can be passed to the Monte carlo simulator.

Parameters

mc (McObject) – A Monte Carlo simulator instance.

Returns

struct (cltypes.Structure) – A structure type that represents the scattering phase function in the Monte Carlo kernel.
Fields
——
gamma (mc_fp_t) – Parameter of the Rayleigh scattering phase function,
a, b (mc_fp_t) – precalculated constants used to speed up the computation.

property gamma: float¶: Molecular anisotropy factor.

pf() → xopto.pf.rayleigh.Rayleigh [source]¶

Returns a new instance of the related utility scattering phase function class that can be used to compute Legendre moments and other scattering phase function quantifiers.

Returns: pf – Instance of the related utility scattering phase function.
Return type: xopto.pf.Rayleigh

todict() → dict[source]¶: Export object to a dict.