Non-uniform step, absorption & scattering: radiation_function.pyx

[MMoscheni]

Hi there, many thanks as usual for the amazing work! Below is our idea of implementation of non-uniform smapling along the ray direction, alongside absorption and scattering. Changes to the original code are marked by "MMM". More insights are provided in [A. Aimetta, M. Moscheni et al, "Forward modelling of Dα camera view in ST40 informed by experimental data", submitted to Fus. Eng and Des.]. If you have any feedbacks on this, that would be appreciated!

# Copyright 2016-2018 Euratom
# Copyright 2016-2018 United Kingdom Atomic Energy Authority
# Copyright 2016-2018 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
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from raysect.optical cimport Point3D, Vector3D, Spectrum, World, Ray, Primitive, AffineMatrix3D
from raysect.optical.material.emitter cimport InhomogeneousVolumeEmitter, NumericalIntegrator
from cherab.core.math.function cimport Function3D, autowrap_function3d
from libc.math cimport M_PI
import cython


cdef class RadiationFunction(InhomogeneousVolumeEmitter):
    """
    A general purpose radiation material.

    Radiates power over 4 pi according to the supplied 3D radiation
    function. Note that this model ignores the spectral range of the
    observer. The power specified will be spread of the entire
    observable spectral range. Useful for calculating total radiated
    power loads on reactor wall components.

    Note that the function will be evaluated in the local space of the
    primitive to which this material is attached. For radiation
    functions defined in a different coordinate system, consider
    wrapping this in a VolumeTransform material to ensure the function
    evaluation takes place in the correct coordinate system.

    Further parameters added to increase functionalities (e.g. non-uniform sampling).

    :param Function3D radiation_function: A 3D radiation function that specifies the amount of radiation
      to be radiated at a given point, :math:`\phi(x, y, z)` [W/m^3].
    :param float step: The scale length for integration of the radiation function.
    :param int use_step_function: If True (or 1) activates non-uniform sampling.
    :param Function3D step_function_3d: A 3D function that specifies the non-uniform sampling step
      at a given point, :math:`\Delta s(x,y,z)` [m^{-1}].
    :param int step_max: Maximum sampling step allowed in non-uniform sampling, :math:`\Delta s_{max}` [m].
    :param int use_absorption_function: If True (or 1) activates self-absorption.
    :param Function3D absorption_function_3d: A 3D function that specifies the macroscopic absorption
      cross section at a given point, :math:`\Sigma_{abs}(x,y,z)` [m].
    :param int use_scattering_function: If True (or 1) activates self-scattering.
    :param Function3D scattering_function_3d: A 3D function that specifies the macroscopic scattering
      cross section at a given point, :math:`\Sigma_{sct}(x,y,z)` [m].
    :param int collisions_max: Maximum number of self-scattering events (collisions).
    :param double scattering_probability: scattering probability for the material (= 1 - absorption probability). Assumed constant, i.e. independent from wavelength.

    .. code-block:: pycon

       >>> import numpy as np
       >>> from cherab.tools.emitters import RadiationFunction
       >>>
       >>> # define your own 3D radiation function and insert it into this class
       >>> def rad_function_3d(x, y, z):
               r = np.sqrt(x**2 + y**2 + z**2)
               if r == 0: return 0
               else:      return np.min([1E+00, r])
       >>>
       >>> # define your own 3D step function and insert it into this class
       >>> def step_function_3d(x, y, z):
               r = np.sqrt(x**2 + y**2 + z**2)
               if r == 0: return 1E-05
               else:      return 1E-02 * np.min([1E+00, r])
       >>>
       >>> # define your own 3D absorption function and insert it into this class
       >>> def abs_function_3d(x, y, z): return 1E-01 * rad_function_3d(x,y,z)
       >>>
       >>> radiation_emitter = RadiationFunction(radiation_function      = rad_function_3d,
                                                 step                    = np.inf,
                                                 use_step_function       = True,
                                                 step_function_3d        = step_function_3d,
                                                 step_max                = 1E-02,
                                                 use_absorption_function = True,
                                                 absorption_function_3d  = abs_function_3d,
                                                 sn_max                  = 1E+00,
                                                 use_scattering_function = False,
                                                 scattering_function_3d  = None,
                                                 collisions_max          = 0,
                                                 scattering_probability  = 0.44
                                                )
    """

    cdef:
        readonly Function3D radiation_function
        readonly Function3D absorption_function_3d   # MMM
        readonly Function3D scattering_function_3d   # MMM
        readonly Function3D step_function_3d         # MMM
        readonly int use_absorption_function         # MMM
        readonly int use_scattering_function         # MMM
        readonly int use_step_function               # MMM
        readonly int collisions_max                  # MMM
        readonly float step_max                      # MMM
        readonly float sn_max                        # MMM

    def __init__(self, radiation_function,                              # emission
                       use_step_function,       step_function_3d,       # non-uniform sampling
                       use_absorption_function, absorption_function_3d, # absorption
                       use_scattering_function, scattering_function_3d, # scattering
                       scattering_probability = 0.44,                   # default for Dalpha photons
                       collisions_max = 100,    step_max = 0.1,  step = 0.1, sn_max = 1E+100):

        super().__init__(NumericalIntegrator(step = step))
        # radiation emission
        self.radiation_function      = autowrap_function3d(radiation_function)
        # non-uniform sampling
        self.use_step_function       = use_step_function
        self.step_function_3d        = autowrap_function3d(step_function_3d)
        self.step_max                = step_max
        # absorption
        self.use_absorption_function = use_absorption_function
        self.absorption_function_3d  = autowrap_function3d(absorption_function_3d)
        self.sn_max                  = sn_max
        # scattering
        self.use_scattering_function = use_scattering_function
        self.scattering_function_3d  = autowrap_function3d(scattering_function_3d)
        self.collisions_max          = collisions_max
        self.scattering_probability  = scattering_probability

    @cython.boundscheck(False)
    @cython.wraparound(False)
    @cython.initializedcheck(False)
    cpdef Spectrum emission_function(self, Point3D point, Vector3D direction, Spectrum spectrum,
                                     World world, Ray ray, Primitive primitive,
                                     AffineMatrix3D world_to_local, AffineMatrix3D local_to_world):

        cdef int index
        cdef double wvl_range = ray.max_wavelength - ray.min_wavelength
        cdef double emission

        emission = self.radiation_function.evaluate(point.x, point.y, point.z) / (4 * M_PI * wvl_range)

        for index in range(spectrum.bins):
            spectrum.samples_mv[index] += emission
        return spectrum

[vsnever]

Hi @MMoscheni,

As a user, I find all three features mentioned in the topic useful and important. So, thank you very much for bringing this topic up. Below are my thoughts about the implementation.

First of all, I think that adaptive integration, inhomogeneous absorption and volumetric scattering must be considered and implemented separately.

1. Adaptive integration.

• I think that instead of modifying the NumericalIntegrator class, it would be more correct to define a separate AdaptiveNumericalIntegrator(VolumeIntegrator) class.

• Ideally, AdaptiveNumericalIntegrator should work with any InhomogeneousVolumeEmitter instant, and should not rely on special material methods such as step_function_3d(). Of course, the emission spectrum must be reduced to a single value in order to calculate the error required to correct the integration step. Some obvious options are the total intensity error and the maximum spectral intensity error. I think it would be nice to give the user the option to choose between several methods of spectrum reduction.

• In NumericalIntegrator you have the loop while length_traveled < length:. The user expects that length_traveled is equal to length when integration stops, and here length_traveled can be greater thanlength by the value lower than step. This potentially creates the debugging hell for the user, not to mention that the end point of integration lies outside the bounding primitive.

2. Inhomogeneous absorption.

• I think inhomogeneous emitter and inhomogeneous absorber are two different materials and should be implemented independently. If material combines both properties, it can be implemented using the Add() modifier with an emitter as the first argument.

• In general, absorption depends on wavelength, so material.absorption_function_3d() should return a SpectralFunction.

3. Volumetric scattering.

• Scattering changes the ray's direction. Therefore, the point at which the ray leaves the volume of the primitive is not known prior to scattering simulation. To be consistent with the rest of the Raysect API, this feature must be implemented in the evaluate_surface() method of the NullVolume material. However, the implementation will be tricky, because in addition to tracing the world, each daughter ray should be the subject of this Monte-Carlo scattering simulation inside the primitive, until the last of the spawned rays leaves it at some point.

I recommend that you create separate discussion threads in Raysect for each of these issues.

[MMoscheni]

Hi @vsnever ,

many thanks for the kind reply, and for understanding that I am something very far away from a software developer :') those advices are therefore much appreciated!

I will open separate issues regarding each topic, as you suggest.

Cheers, Matteo