Linespread-, Pointspread- and Modulation Transfer Function
Calculations with Mathematica

In imaging the linespread function (LSF), the pointspread function (PSF) and 
the modulation transfer function (MTF) are used to characterize the spatial 
resolution of an imager. 
Similar to electronics, the PSF is the response to a point illumination or a 
2-dimensional delta-function; the LSF is the response to a 1-dimensional 
delta-function and the MTF is the spatial frequency response to sinusoidal 
functions. These three functions are related to each other by integral 
transforms:

LSF	--->	MTF	by Fourier Transform
PSF	--->	MTF	by Hankel Transform
PSF 	---> 	LSF	by Abel Transform.

Since often only one of these functions is measured or can be measured easily, 
the others can be calculated by means of these transforms.

Programs

Three programs, written in Mathematica, have been designed to carry out the 
above conversions. They read and store ASCII files of x,y values 

1.) 'lsf_to_mtf_to_psf', input: LSF, output: MTF, PSF
2.) 'psf_to_mtf_to_lsf', input: PSF, output: MTF, LSF
3.) 'mtf_to_psf_to_lsf', input: MTF, output: LSF, PSF


Environment

Access is needed to a computer that holds a Mathematica licence.


Literature

Danty and Shaw, Image Science, Academic Press