Basic Imaging Theory

Hurter and Driffield (H & D) Curves

plot of optical density versus log of the exposure
aka characteristic film curve

H & D curves

Optical Density formula

OD = log(I_0 / I )

Fog

Darkening of film due to background radiation

Base

natural attenuation of completely unexposed film

speed

is a term that is related to the amount of radiation required to give an OD of 1 above the base and fog

fast films

require little radiation
diagnostic films are fast

slow films

require a lot of radiation
used in therapy

gradient

slope of the curve in the linear portion and measure of the contrast of the film

high gradient

means strong contrast

linear portion

where you want to be for imaging and dosimetry tests

latitude

refers to range of exposures a film can accept and still produce contrast in the image (darkest to lightest)

Contrast to noise ratio (CNR) Formula

CNR = (A - B) / σ

Contrast

difference in value between two objects on an image
could take the form of OD or HU
A and B in CNR formula

Noise

defined as the amount of fluctuation in an image due to statistical uncertainties and can be measured by looking at the standard deviation in pixel value over a uniform area
May come from photon counting or from electrons
σ

CNR

directly related to being able to see an object
lots of noise = need lots of contrasts to visualize

Modulation transfer Function (MTF)

measure of perceived contrast versus object size
as an object becomes smaller (increasing spatial frequency), it becomes harder to visualize (decreasing contrast)

limit of perceivable contrast

MTF of 0.1

MTF

Nyquist Frequency

minimum frequency an object must be sampled to be visualized (needs to be sampled twice to be seen)

aliasing

occurs when a high-frequency signal is sampled at a lower frequency

pixel binning (type of aliasing signal)

Quantum Detection Efficiency (QDE)

measure of how efficient your detection system is
defined as the ratio of number of photons detected to the number incident
Goal: as high as possible, to keep patient dose low and achieve low noise
- why we use phosphor screens and build up materials

Detective Quantum Efficiency (DQE)

measure of whole imaging system’s efficiency in forming an image (lumps electronic system noise in with errors from counting photons)

Used to track for QA because its a direct metric for the dose efficiency of the system

SNR

signal to noise ratio

DQE Formula

DQE = (SNR_out)² /(SNR_in)²

Phosphor screens

used in film radiography
Function to amplify the number of photons striking a film
Made of scintillating materials, take energy from x-ray and splits into many photons which strike film
Placed in front and behind films
accounts for 95% of x-rays striking film

Magnification

can be varied on an image by changing the location of source, object or detector

defined as ratio of size of object in image to true size

Magnification formula

M = image size / object size = SID/SOD

SID

source to image distance

SOD

source to object distance

How do you increase magnification

• move object closer to source

• move detector farther away

Penumbra

increases with magnification
Balance between penumbra blurring and image resolution

Image dose

increases with magnification

Scatter Grids

used to reduce amount of scatter reaching a detector
in order to remove attenuation from the bars, the grid can be rapidly shifted during acquisition (performed by the Bucky)

Receiver Operating Characteristic Curves (ROC curves)

used to assess usefulness of a test for detecting something

True Positive Fraction (TPF)

TPF = TP / (TP +FN)
Calling something positive when it is

sensitivity of the test

true positive fraction

False Positive Fraction (FPF)

calling something positive when its not
FPF = FP / (FP + TN)

Specificity

calling something normal when it is
Specificity = TN / (TN + FP)

Accuracy

calling something what it truly is
Accuracy = (TP + TN) / (TP + TN + FP + FN)

kV imaging

best contrast between soft tissue and bony anatomy
significant Compton interaction, large proportion of interactions are still photoelectric and the effective Z of bone is nearly 2x that tissue
cannot penetrate thick person’s anatomy

MV imaging

exhibit nearly no photoelectric interactions
only measure attentuation due to compton interactions
MV can penetrate thick

Beam Shape

scatter degrades images (compton scatters will ideally scatter away from detector)
beam geometry changes amount of scatter degrading image

Scatter grid only works for kV imaging

pencil beam

1st gen of Ct

no scatter, any scattering events send photon away from detector

fan beam

scan faster but have scattered components that degrade image

cone beams

scan fastest but have scatter in both dimensions that degrades image quality
- most modern CT machines - size of cone is important