generate.aperture: Elliptical Aperture Creation

In AngusWright/LAMBDAR: Measure galaxy fluxes from an arbitrary FITS image using input aperture locations and dimensions

Elliptical Aperture Creation

Description

The generate.aperture() procedure creates a single elliptical aperture on a finite grid, which is designated by the values of {x,y}. The aperture is created with properties determined by the input parameters. In order to improve the accuracy of the aperture integral, the accuracy of the pixel values at the aperture boundary are improved by increasing the resolution of the grid at the boundary, calculating the subpixel values, and summing over subpixels. The functions checkgrid(), inap(), and reexpand.grid() are low level functions called internally by generate.aperture().

Usage

generate.aperture(x, y, xstep, ystep, xcen = 0, ycen = 0,
axrat = 1, axang = 0, majax = 1, deg = TRUE, resample.upres = 2,
resample.iterations = 9, pixscale = FALSE, peakscale = FALSE,
peak = 1)
checkgrid(x, y, xstep, ystep, xcen = 0, ycen = 0,
axrat = 1, axang = 0, majax = 1, deg = TRUE)
inap(x, y, xcen = 0, ycen = 0, axrat = 1, axang = 0,
majax = 1, deg = TRUE)
reexpand.grid(x, y, xstep, ystep, id, resample.upres = 2)

Arguments

x	numeric vector; The x coordinates associated with every point on the grid that the aperture will be placed upon
y	numeric vector; The y coordinates associated with every point on the grid that the aperture will be placed upon
xstep	numeric; The interval between each x coordinate
ystep	numeric; The interval between each y coordinate
xcen	numeric; x value that aperture will be centred on
ycen	numeric; y value that aperture will be centred on
axrat	numeric; ratio of minor-to-major axis of aperture: 0 < axrat < 1
axang	numeric; angle that the major axis makes with the y axis (i.e. N0E90)
majax	numeric; length of the major axis in pixels/grid-units
deg	character;
id	character; id of parent pixel
resample.upres	numeric; exponent used to increase resolution of boundary pixels. Must be > 1.
resample.iterations	numeric; number of iterations performed when increasing the resolution of boundary pixels. If resample.iterations=0, no increase in resolution of boundary pixels occurs.
pixscale	logical; if TRUE - values are scaled to reflect pixel area, rather than pixel fraction if FALSE - pixels are not scaled, and reflect piel fraction rather than area
peakscale	logical; if TRUE - aperture is scaled so that maximum pixel value is ‘peak’. if FALSE - aperture is normalised such that volume of aperture is equal to unity
peak	numeric; the value used to rescale the peak

Details

The function, at its most rudimentary, creates an eliptical aperture on a pixel-grid. The input values to the function are largely just the parameers needed to describe the eliptical aperture we wish to generate. There are additional paramaters (resample.upres, resample.iterations, pixscale) that are used specifically to improve the aperture generation for use in photometric measurements.

As the procedure is designed for use in high precision photometric measurements, the aperture integral can be improved significantly by determining the values of the pixels at the boundary at high resolution. For this reason, the function takes two inputs (resample.upres and resample.iterations) which increase the resolution of the boundary pixels. After the last iteration, the resolution of pixels on the aperture boundary will be (resample.upres)^(resample.iterations) higher than the original pixel size.

Value

array; The procedure returns an array similar to that generated by the expanded.grid() function; it has dimension [n,3] where n is the number of points on the input grid. The three columns of this matrix are: 1 - x coordinates of each point on the grid (i.e. same as the input variable ‘x’) 2 - y coordinates of each point on the grid (i.e. same as the input variable ‘y’) 3 - the pixel value corresponding to this x and y position

Author(s)

Aaron Robotham ICRAR [e-mail]

Angus H Wright ICRAR [e-mail]

See Also

measure.fluxes, flux.measurements

Examples

#Load LAMBDAR
library(LAMBDAR)
## Example 1: Simple Placement of an aperture
#Generate a random grid radius
grid.width<-floor(runif(1)*100)
#Define a grid onto which we will place the aperture
grid<-expand.grid(seq(-grid.width,grid.width), seq(-grid.width,grid.width))
#Generate random elliptical aperture parameters
majax<-runif(1,min=0.2,max=0.8)*grid.width
axrat<-runif(1,min=0.2,max=1)
axang<-runif(1)*180
#Place the aperture using binary Placement
aper_expanded<-generate.aperture(x=grid[,1],y=grid[,2],xstep=1,ystep=1,
axrat=axrat,axang=axang,majax=majax,resample.iterations=-1)
#Convert return back into matrix
aper<-matrix(aper_expanded[,3],nrow=(grid.width*2+1))
#Plot Aperture
layout(cbind(1,2,3,4))
image(x=seq(-grid.width,grid.width),y=seq(-grid.width,grid.width),z=aper,
xlab='X (pix)',ylab='Y (pix)',asp=1)

## Example 2: Quarternary Placement
#Place the aperture using quarternary Placement
aper_expanded<-generate.aperture(x=grid[,1],y=grid[,2],xstep=1,ystep=1,
axrat=axrat,axang=axang,majax=majax,resample.iterations=0)
#Convert return back into matrix
aper<-matrix(aper_expanded[,3],nrow=(grid.width*2+1))
#Plot Aperture
image(x=seq(-grid.width,grid.width),y=seq(-grid.width,grid.width),z=aper,
xlab='X (pix)',ylab='Y (pix)',asp=1)

## Example 3: Improve aperture edge-pixel determination
#Using the same parameters as in Example 1, just improve edge determination
aper_expanded<-generate.aperture(x=grid[,1],y=grid[,2],xstep=1,ystep=1,
axrat=axrat,axang=axang,majax=majax, resample.upres=3, resample.iterations=4)
#Convert return back into matrix
aper<-matrix(aper_expanded[,3],nrow=(grid.width*2+1))
#Plot Aperture
image(x=seq(-grid.width,grid.width),y=seq(-grid.width,grid.width),z=aper,
xlab='X (pix)',ylab='Y (pix)',asp=1)

## Example 3: Quantifying improvement of aperture integral
#Generate the grid
grid.width<-2
grid<-expand.grid(seq(-grid.width,grid.width,by=0.1),
seq(-grid.width,grid.width, by=0.1))
#Using a simple elliptical parameters, create basic aperture
aper_expanded<-generate.aperture(x=grid[,1],y=grid[,2],xstep=0.1,ystep=0.1,
axrat=0.5,axang=-45,majax=2,resample.iterations=0)
#Convert return back into matrix
aper<-matrix(aper_expanded[,3],nrow=length(seq(-grid.width,grid.width,by=0.1)))
#Plot Aperture
image(x=seq(-grid.width,grid.width,by=0.1),y=seq(-grid.width,grid.width,by=0.1),
z=aper,xlab='X (pix)',ylab='Y (pix)',asp=1)
#This aperture should integrate to 2pi, so we can use this to
#quantify the improvement of our integral by plotting the integral vs iteration
residual<-array(0,11)
for (i in 1:11) {
  aper_expanded<-generate.aperture(x=grid[,1],y=grid[,2],xstep=0.1,ystep=0.1,
  axrat=0.5,axang=-45,majax=2,resample.upres=2,resample.iterations=(i-1),pixscale=TRUE)
  residual[i]=abs(sum(aper_expanded[,3])-2*pi)
}
#Plot the residuals
magplot(x=seq(0,10), y=residual, xlab="Number of descent iterations",
ylab="Aper. Area - Expected Area",log='y',type='b')

AngusWright/LAMBDAR documentation built on Sept. 19, 2024, 10:26 a.m.