Compute 2D diffraction limited optical transfer function
OTF2D = dlCore(rho,inCutFreq)
This routine calculates the 2D optical transfer function (OTF) of a
diffraction limited optical system.
The 2D OTF depends only a few parameters. These are the radial distance
(rho) of each spatial frequency from the origin, and the input cutoff
frequency (inCutFreq) at which wavelength. The inCutFreq, in turn, only
depends on the f# of the diffraction limited system.
The variable rho is a matrix defining the frequency of each entry (cycles
per meter). The vector inCutFreq is the incoherent cutoff frequency as a
function of wavelength.
A little more formally, an aberration-free diffraction-limited system
with a circular exit pupil can be described as:
di = distance between aperture and detector (meters)
A = aperture diameter (meters)
lambda = wavelength of incident light (meters)
rho = frequency (cycles per meter)
rho0 = (A/2*lambda*di) (cycles /meter)
The formula for the OTF at frequency rho and wavelength lambda is often
quoted as
H(rho,lambda)
=(2/pi)*(acos(rho/(2*rho0)) - (rho/2*rho0)*sqrt(1-(rho/(2*rho0)^2)))
=(2/pi)*(acos(rho/inCutF) - (rho/inCutF)*sqrt(1- (rho/inCutF))^2))
or 0 if rho >= 2*rho0, which is rho/inCutFreq >= 1
This can be simplified because 2*rho0 is the spatial cutoff frequency
inCutFreq = (A /(di * wavelength)) = 2*rho0
Define the normalized frequency, rho/inCutF.
normF = rho / (A/(di*wavelength))
In that case, the OTF formula becomes
H(normF,lambda) = (2/pi)*(acos(normF) - normF*sqrt((1-normF)^2))
In this form, we must convert normalized frequency OTF back to real units
Sources:
http://ao.osa.org/ViewMedia.cfm?id=38173&seq=0
Muralidhara Subbarao, APPLIED OPTICS / Vol. 29, No. 4 / 1 February 1990
Optical transfer function of a diffraction-limited system for polychromatic illumination
Also, http://www.microscopyu.com/articles/optics/mtfintro.html
See also dlMTF
Copyright ImagEval Consultants, LLC, 2003.