DDA does not agree with Mie for a sphere

[tdimiduk]

sch = ImageSchema(shape=[100, 100], spacing=[0.10000000000000001, 0.10000000000000001], optics=Optics(wavelen=0.66, index=1.33, polarization=[1, 0], divergence=0.0), origin=[0.0, 0.0, 0.0]) sph = Sphere(n=1.59, r=0.5, center=(5, 5, 5)) hm = Mie.calc_holo(sph, sch) hd = DDA.calc_holo(sph, sch) hp.show(hm - hd)

These do not agree as well as they probably should. It appears there is a systemic offset in the center position.

[jeromefung]

Are you sure this isn't due to the non-far field r dependence being correctly captured by Mie while being ignored by DDA?

[tdimiduk]

Good chance that could be the case. I was just porting over all of the old bugs from launchpad to github, so I didn't actually look at this in any depth.

On Mon, Aug 11, 2014 at 5:09 PM, Jerome Fung notifications@github.com wrote:

Are you sure this isn't due to the non-far field r dependence being correctly captured by Mie while being ignored by DDA?

— Reply to this email directly or view it on GitHub https://github.com/manoharan-lab/holopy/issues/17#issuecomment-51841260.

[anna-wang]

The centroid offset introduced by voxellation also contributes.

On 11 August 2014 17:16, Tom Dimiduk notifications@github.com wrote:

Good chance that could be the case. I was just porting over all of the old bugs from launchpad to github, so I didn't actually look at this in any depth.

On Mon, Aug 11, 2014 at 5:09 PM, Jerome Fung notifications@github.com wrote:

Are you sure this isn't due to the non-far field r dependence being correctly captured by Mie while being ignored by DDA?

— Reply to this email directly or view it on GitHub https://github.com/manoharan-lab/holopy/issues/17#issuecomment-51841260.

— Reply to this email directly or view it on GitHub https://github.com/manoharan-lab/holopy/issues/17#issuecomment-51841989.

[vnmanoharan]

This is what we wrote in the DDA paper (Wang, Anna, Thomas G. Dimiduk, Jerome Fung, Sepideh Razavi, Ilona Kretzschmar, Kundan Chaudhary, and Vinothan N. Manoharan. 2014. “Using the Discrete Dipole Approximation and Holographic Microscopy to Measure Rotational Dynamics of Non-Spherical Colloidal Particles.” Journal of Quantitative Spectroscopy and Radiative Transfer 146 (October): 499–509):

We find that the best-fit x- and y-coordinates obtained by fitting the DDA model differ negligibly (0.3 +/- 0.1 nm) from those obtained from Lorenz–Mie, while the best-fit z-coordinates differ by 194 +/-1 nm, a significant offset. This difference in apparent axial position might arise from voxelation errors or the asymptotic approximation for the radial dependence of the scattered field. The Lorenz–Mie model includes non-asymptotic corrections for the scattered field, while the DDA model does not.

The x,y error likely arises from voxelation. The error in z probably depends on both.