metrics Flashcards
spatial resolution
ability to detect contrast in high spatial frequency details
expressed by the MTF
function of line pairs per mm
(cycles/mm)
what spatial resolution depends on
source focal spot
magnification
detector resolution
MTF
modulation transfer function
expresses how spatial frequencies are transferred through system
a higher modulation value at higher spatial frequencies :
good for visualising higher frequencies
depends on lens
Some lenses are designed to be able to very accurately resolve lower spatial frequencies, and have a very low cut-off frequency (i.e. they cannot resolve higher spatial frequencies)
measuring the MTF
take a bar pattern test object and image it
start from a lower freq, assume mod of 1, measure other mod values and plot them against spatial frequency
disadv:
sampling at given frequencies, not full curve
using square instead of sinusoidal input, slight overestimation
measure IRF and fourier-transform it
point spread function
implies subdividing the pixel surface in small squares and expressing the relative efficiency of each
line spread function
implies subdividing the pixel surface in small stripes and expressing the relative efficiency of each
measuring PSF
one should have a pencil beam of negligible transverse direction and scan the pixel surface with it
measuring LSF
a ‘blade’ of radiation scanned in 1D only
impractical so ERF measured
LSF is derivative of ERF
fourier transform of LSF is MTF
ERF
edge response function
uses edge target images whose gray values are often affected by noise and other factors, decreasing its accuracy.
The edge response process requires taking the derivative of a well defined edge = LSF
graph is pixel intensity over distance from edge
slanted edge
tilted edge technique is more easily accomplished and gives superior results
/ slanted slit
ideal detector LSF
rectangular function
realistically edges will be rounded off
width wider than a single pixel
LSF effect on MTF
narrow LSF will generate a large MTF
(extending to high spatial frequencies)
most of the time
finding MTF of the entire imaging system
product of the MTFs of the individual components
(convolution in frequency domain)
components being:
focal spot
scintillator
detection layer etc
MTF(f.spot) broadened if object closer to detector
MRF(scint)&(det) are broadened if object is closer to source
noise types
quantum noise:
intrinsic, fluctuations, stochastic (random)
always present
electronic noise:
read noise, dark current, detector+readout electronics
film-grain noise
in films
structural noise
overlying and underlying anatomic structures
quantum mottle
number of photons contributing to image per cm^2
varies due to random fluctuations
proportional to 1/sqrt(N)
affected by preset exposure factors (mA)
comparing noise profiles
variance, mean
frequency dependence -> NPS
NPS noise power spectrum
(measure of how similar 2 signals are)
gives the variance (noise) of a system
noise power spectral density, expressing how power in a random signal distributed between frequencies
(indirect)
calculated as the FT of the autocorrelation function
-> spatial autocorrelation
or (direct)
directly calculating the square modulus of the fourier transform of the data itself
for digital detectors, discrete FT algorithms used, integrals replaced with sums
autocorrelation function
mathematical tool for finding repeat patterns
NPS white noise
white noise has the same power at all frequencies
flat noise profile = noise is uncorrelated
ideal:
noise in each pixel is independent to other pixels
real:
crosstalk
power
amplitude of the corresponding Fourier coefficient
NPS as a function of exposure
noise depends on number of quanta
higher sample exposure, lower NPS
NPS and MTF
both 2D function
pixel isotropy(identical) is assumed
high MTF, system can record noise at a high freq
low MTF, high frequency noise is blurred out
detection of xray photons process
(CCD camera)
- N x-rays impinge on the phosphor
- each x-ray creates many visible photons
- not all visible photons are collected by the fiber optics
- fiber optic transfer not 100% efficient
- phosphor spectrum and CCD camera sensitivity curve not perfectly matched
quantum accounting diagrams
lowest point defines SNR
SNR less than or equal to sqrt(lowest point)
detection efficiency
increased efficiency, lower spatial resolution
x-ray interaction in the sensor material for direct detection systems
in the phosphor for indirect ones
efficiency: number of photons stopped as a fraction of N0
