the colour of white light passing a birefringent plate between a polariser and an analyser, as a thin section shows it under the microscope

Syntax

rgb = rI.spectralTransmission(vprop, thickness)

Polariser at 45 degree to the fast wave.

rgb = rI.spectralTransmission(vprop, thickness, polarizationDirection=p)

A polariser direction.

rgb = rI.spectralTransmission(vprop, thickness, tau=30*degree, phi=90*degree)

The angles given.

r, g, b = rI.spectralTransmission(thickness, bandwidth=64)

Functions of the propagation direction.

Description

The light propagates along vprop through a plate of the given thickness. The two waves the refractive index tensor allows along it leave with a retardation, the birefringence times the thickness, and the analyser lets through what their interference leaves of every wavelength.

The transmitted spectrum is weighted with the CIE 1931 colour matching functions and given as Adobe RGB, one colour per direction. The values are not clipped: a channel may lie slightly below 0 or above 1.

With the thickness alone the three channels are S2FunHarmonic of the propagation direction, which plot draws as the interference colours of every direction. MATLAB returns them as one vector valued function.

Input

`rI`	refractiveIndexTensor
`vprop`	vector3d or Miller, the propagation direction of the light, in the frame of rI
`thickness`	the thickness of the plate in nanometres (30 micrometre = 30000)

Keywords

keyword	default	description
`polarizationDirection`	`None`	vector3d, the direction of the polariser; the angle between it and the fast wave replaces tau
`tau`	`45*degree`	the angle between the polariser and the vibration direction of the fast wave
`phi`	`90*degree`	the angle between the polariser and the analyser; 90 degree for crossed polarisers
`bandwidth`	`32`	the bandwidth of the three functions when no direction is given

Output

`rgb`	(…, 3) array, the colour of every direction
`r, g, b`	S2FunHarmonic, the channels as functions of the propagation direction

Used on

BirefringenceDemo

MATLAB’s refractiveIndexTensor.spectralTransmission

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/refractiveIndexTensor.spectralTransmission_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

refractiveIndexTensor.spectralTransmission