Scattering from Arbitrary Structures with DDA

The discrete dipole approximation (DDA) lets us calculate scattering from any arbitrary object by representing it as a closely packed array of point dipoles. In HoloPy you can make use of the DDA by specifying a general Scatterer with an indicator function (or set of functions for a composite scatterer containing multiple media).

HoloPy uses ADDA to do the actual DDA calculations, so you will need to install ADDA and be able to run:

adda

at a terminal for HoloPy DDA calculations to succeed.

A lot of the code associated with DDA is fairly new so be careful; there are probably bugs. If you find any, please report them.

Defining the geometry of the scatterer

To calculate the scattering pattern for an arbitrary object, you first need an indicator function which outputs ‘True’ if a test coordinate lies within your scatterer, and ‘False’ if it doesn’t.

For example, if you wanted to define a dumbbell consisting of the union of two overlapping spheres you could do so like this:

import holopy as hp
from holopy.scattering import Scatterer, Sphere, calc_holo
import numpy as np
s1 = Sphere(r = .5, center = (0, -.4, 0))
s2 = Sphere(r = .5, center = (0, .4, 0))
detector = hp.detector_grid(100, .1)
dumbbell = Scatterer(lambda point: np.logical_or(s1.contains(point), s2.contains(point)),
                     1.59, (5, 5, 5))
holo = calc_holo(detector, dumbbell, medium_index=1.33, illum_wavelen=.66, illum_polarization=(1, 0))

Here we take advantage of the fact that Spheres can tell us if a point lies inside them. We use s1 and s2 as purely geometrical constructs, so we do not give them indicies of refraction, instead specifying n when defining dumbell.

Mutiple Materials: A Janus Sphere

You can also provide a set of indicators and indices to define a scatterer containing multiple materials. As an example, lets look at a janus sphere consisting of a plastic sphere with a high index coating on the top half:

from holopy.scattering.scatterer import Indicators
import numpy as np
s1 = Sphere(r = .5, center = (0, 0, 0))
s2 = Sphere(r = .51, center = (0, 0, 0))
def cap(point):
    return(np.logical_and(np.logical_and(point[...,2] > 0, s2.contains(point)),
           np.logical_not(s1.contains(point))))
indicators = Indicators([s1.contains, cap],
                        [[-.51, .51], [-.51, .51], [-.51, .51]])
janus = Scatterer(indicators, (1.34, 2.0), (5, 5, 5))
holo = calc_holo(detector, dumbbell, medium_index=1.33, illum_wavelen=.66, illum_polarization=(1, 0))

We had to manually set up the bounds of the indicator functions here because the automatic bounds determination routine gets confused by the cap that does not contain the origin.

We also provide a JanusSphere scatterer which is very similar to the scatterer defined above, but can also take a rotation angle to specify other orientations:

from holopy.scattering import JanusSphere
janus = JanusSphere(n = [1.34, 2.0], r = [.5, .51], rotation = (-np.pi/2, 0),
                  center = (5, 5, 5))