convolve.psf: 2D Convolution

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

2D Convolution

Description

Perform the 2D convolution of two 2D arrays of equal dimension, using Fast Fourier Transforms (fft). This function is designed to be used for convolutions of Point Spread Functions (PSFs) with object apertures in photometric measurements. As such, the positional information of the first array (or more accurately the phase information of the first array's fft) is discarded.

Usage

convolve.psf(arr1, arr2, normalise = TRUE, renorm.arr2 = FALSE,
zapdig = NULL)

Arguments

arr1	(n,n) dimensional array; Usually will contain the PSF function. Phase information of this array is discarded in convolution
arr2	(n,n) dimensional array; Phase information of this array is retained in convolution. Magnitude information is optionally included/excluded
normalise	logical; if TRUE, the normalised Fourier Transform will be calculated
renorm.arr2	logical; if TRUE, then the magnitude information of arr2 is removed prior to FFT via normalisation
zapdig	integer; the precision to be used in a call to ‘zapsmall’. Used for removing (unwanted) small variations in near-zero areas of the array return by the FFT. If zapdig is NULL, getOption("digits") is used.

Value

(n,n) dimensional array containing the convolved & ‘zapped’ image.

Author(s)

Angus H Wright ICRAR [e-mail]

See Also

measure.fluxes, zapsmall

Examples

#Load LAMBDAR
library(LAMBDAR)

#Generate a 2D Gaussian PSF
#Stamp size (in pix)
n<-100
#Sigma
sigma.pix<-4
#Centre
x0<-y0<-n/2
y<-matrix(1:n,n,n)
x<-t(y)
psf<-exp(-(((x - x0)^2/(2 * sigma.pix^2)) + ((y -
            y0)^2/(2 * sigma.pix^2))))

#Make a Delta Function
ap<-matrix(0,n,n)
ap[n/2,n/2]<-1

#Show the convolution
layout(cbind(1,2,3))
image(x=1:n,y=1:n,z=psf,col=grey.colors(1E3),useRaster=TRUE,xlab='X (pix)',
ylab="Y (pix)",main="PSF Function",asp=1)
image(x=1:n,y=1:n,z=ap,col=grey.colors(1E3),useRaster=TRUE,xlab='X (pix)',
ylab="Y (pix)",main="Aperture Function",asp=1)
image(x=1:n,y=1:n,z=convolve.psf(psf,ap),col=grey.colors(1E3),useRaster=TRUE,
xlab='X (pix)',ylab="Y (pix)",main="Convolved Aperture Function",asp=1)

#Make an Aperture Function
#Pixel Grid
ap.pix<-expand.grid(seq(1,n),seq(1,n))
#Generate Aperture Pixel values
ap.pix.vals <- generate.aperture(x=ap.pix[,1],y=ap.pix[,2],xstep=1,ystep=1,
xcen=n/2,ycen=n/2,majax=10,axrat=0.5,axang=45)
#Construct Aperture Matrix
ap<-matrix(ap.pix.vals[, 3], ncol = n)

#Show the convolution
layout(cbind(1,2,3))
image(x=1:n,y=1:n,z=psf,col=grey.colors(1E3),useRaster=TRUE,xlab='X (pix)',
ylab="Y (pix)",main="PSF Function",asp=1)
image(x=1:n,y=1:n,z=ap,col=grey.colors(1E3),useRaster=TRUE,xlab='X (pix)',
ylab="Y (pix)",main="Aperture Function",asp=1)
image(x=1:n,y=1:n,z=convolve.psf(psf,ap),col=grey.colors(1E3),useRaster=TRUE,
xlab='X (pix)',ylab="Y (pix)",main="Convolved Aperture Function",asp=1)

#Phase information in the PSF-matrix is discarded during convolution,
#meaning that the PSF can be arbitrarily placed on its stamp:
#Big PSF, located in the stamp corner
big.psf<-matrix(0,n*3,n*3)
big.psf[1:n,1:n]<-psf
#A Big Aperture
big.ap.pix<-expand.grid(seq(1,n*3),seq(1,n*3))
big.ap.pix.vals <- generate.aperture(x=big.ap.pix[,1],y=big.ap.pix[,2],xstep=1,
ystep=1,xcen=n*3/2,ycen=n*3/2,majax=30,axrat=0.5,axang=45)
big.ap<-matrix(big.ap.pix.vals[, 3], ncol = n*3)

#Show the convolution
layout(cbind(1,2,3))
image(x=1:(n*3),y=1:(n*3),z=big.psf,col=grey.colors(1E3),useRaster=TRUE,
xlab='X (pix)',ylab="Y (pix)",main="PSF Function",asp=1)
image(x=1:(n*3),y=1:(n*3),z=big.ap,col=grey.colors(1E3),useRaster=TRUE,xlab='X (pix)',
ylab="Y (pix)",main="Aperture Function",asp=1)
image(x=1:(n*3),y=1:(n*3),z=convolve.psf(big.psf,big.ap),col=grey.colors(1E3),
useRaster=TRUE,xlab='X (pix)',ylab="Y (pix)",main="Convolved Aperture Function",asp=1)

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