conorect.stack: Conoscopy of uniaxial multilayer stacks: image calculation
In uniaxialOptics: Modelling multilayer anisotropic stacks

Description Usage Arguments See Also Examples

View source: R/conof.R

Computes a complete rectangular conoscopy image for given minumum and maximum angles of incindence

A conoscopy figure is formed when a cone of linearly polarized light passes through a sample (which should be uniform across the whole beam spot) and then, following collimation, through a second, crossed polarizer onto a screen. Provided the beam spot is some distance from the focus, the cone can be built up from rays, each of which strikes a differnt point on the screen. The trajectory of these rays can be computed by matrix methods for inifinite plane waves, such as the Jones or Berreman methods. A coordinate sytem x,y is defined such that r = x^2 + y^2 = sin(angle of incidence), phi = tan(y/x) = angle between plane of incidence and stack y-axis.

A list l is returned, including an nx x ny x nl array l$crossed, of which the element l$crossed[,,l] is a matrix if pixel values. Pixels outside. Pixels outside the annulus defined by pmin,pmax are set to 0.

Be warned: it is easy to ask for a lot of pixels, in which case the function will take a long time to evaluate. When trying out new code using it, keep the resolution down.

1 2	conorect.stack(lambda, depth, tilt, twist, eo, ee, nx, ny, pmin, pmax, az0 = pi/4,method = "ko")

`lambda`	vector of wavelengths, in metres, length = l
`depth`	vector of layer depths, length n
`tilt`	vector of tilt angles between optic axis and z-axis, length n
`twist`	vector of twist angles between optic axis and y-axis, length n
`eo`	ordinary relative permittivity. Either a complev vector, length = n, or an n x l complex matrix if dispersion is to be included
`ee`	extraordinary relative permittivity. See eo.
`nx`	number of horizontal pixels
`ny`	number of vertical pixels
`pmin`	minuimum angle of incidence
`pmax`	maximum angle of incidence
`az0`	scalar, angle between the polarizers transmission axis and the x-axis
`method`	which underlying method to use. Currently "ko" for Berreman 4x4 treatment, and "lien" for Jones treatment

conopix.stack, conorect.lc

#compute a conoscopy figure of a uniaxial, homeotropic
#layer between ito coated glass

depth <- c(0,.03,15,.03,0) * 1e-6
glass <- 1.52^2 + 0.0i
ito <- 3.8 + 0.08i
eo <- c(glass,ito,glass,ito,glass)
ee <- c(glass,ito,(sqrt(Re(glass)) + 0.2)^2 + 0i,ito,glass)
tilt <- c(0,0,pi/20,0,0)
twist <- rep(0,length(tilt))

angle <- seq(0,pi/3,l=100)
azimuth <- rep(pi/4,length(angle))
lambda <- 633e-9

numap <- .55/1.52 # numerical aperture, in glass, of ~50X lens
n <- 96 #horizontal and vertical resolution

rko <- conorect.stack(lambda,depth,tilt,twist,eo,ee,n,n, 0, numap, method="ko")


#define image plotting function 
imp <- function(r,l,bright,...){
  image(t(r$crossed[,,l]),
        col=colorRampPalette(c("black",bright),bias=1/2.2)(64),
        axes=FALSE,...)
}
imp(rko,1,bright="red",main=paste(lambda[1]*1e+9," nm, ko"))