Production of X-Rays

Bremsstrahlung/”braking”/general/continuous radiation = e passing through matter, deflected and loses energy that is emitted in each of several interactions or all energy released at once if head on collision with nucleus; >99% of energy dissipated as heat

characteristic radiation = ejection of an inner shell electron with subsequent electrons dropping shells; if tube kVp > K-shell binding energy of W = 70keV up to 4 K-shell characteristic X-rays; usually 10-30% of total tube intensity

intensity = N x E; N = number of photos and energy E

intensity of XR flux anode Z, tube current (↑ all energies) and more than kVp2

filtration with Al, Cu preferentially removes lower energy XRs with rare earth metals also higher energy XR

during acceleration to anode electrons repel each other, greater with ↑current and ↓kVp

space charge effect = kVp and electron cloud around filament repels e back

saturation = when all electrons boiled from filament reach the anode

most tubes are operated betw space charge and saturation and generator must include kVp-mA compensation; when operated at low mA, operation is near saturation and tube current dictated by filament current alone

spectrum of intensity vs photon energy with mean photon energy ≈ ⅓ to ½ max/endpoint energy

X-Ray Tubes

evacuated glass or metal (better cooling due to higher heat conduction, additional earthing for stray electrons) envelope

cathode = 0.2 dia W filament coil to form vertical spiral in shallow focussing cup; heated to white heat with current and boil electrons off by thermionic emission

focussing cup (negative) concentrates electrons on focal spot of anode

anode focal spot/track material can be W (or rhenium[10%]-W alloy for physical and thermal resistance) or Mo-Rh (kVp always ≤ 32)

when focussing cup is substantially negative cf filament electron cloud is contained and tube is off

external window is Pyrex glass, Bakelite or Be (beryllium in mammo)

line focus tube (stationary anode) = effective focal spot smaller than the actual focal spot area due to an angle of 6-15°; smaller in CT and XII as can tolerate smaller field from anode cut-off

rotating anode: actual focal spot area = 2πR x ab; R≈ 60mm; W-Rh anode bonded to Mo (high melting point, poor heat conductor) disc at 3000-8500 rpm; axle may be ceramic and single or double bearing; bearings may be liquid metal for direct conduction cooling

dual focus tubes have two filaments that may be focussed on the same track or tracks of different angles for diff focal spot sizes

CT tubes have oil or cooled water heat exchangers to remove head from tube housing

heel effect

XRs that are produced at depth in anode are self-absorbed (hence reduced intensity, higher average energy), greater at the anode side of the beam, smaller angle, large field size, smaller focus-image distance

total anode cut-off = when small anode angle with large FOV chosen

tube failure

pitting of the anode due to electron bombardment increases scattering and self absorption

vaporisation of the filament over time

vaporisation of the anode target causes metal plating the inner side of the tube, when tube is hot  out-gassing inferior vacuum with a gassy tube causing reduced output; tube will eventually arc (making high kVp difficult) and puncture of the envelope causes it to fill with oil

bearing failure increases noise and friction (rotor unable to reach operating speed)

tube shielding

tube housing is lined with Pb, and to prevent tube from being earthed mineral oil fills the gap between the tube and housing which also removes heat via convection and conduction

leakage radiation at 1m from focal spot shall not exceed 1mGy/h (preferred < 100μGy/h) at maximum continuous rated current and kVp; more strict for mammography and dental units

collimator = light beam diaphragm = beam restrictor

can be adjusted from 0 to 40 x 40cm @1m, and usually incorporates a light source

the further the collimator leaves are from each other, the less off-focal radiation there is

tube specifications

include max exposure time for given kVp and mA, anode heat storage capacity and how long at certain input rates to reach these levels, anode cooling rate, tube housing specs

HU = heat unit = amount of energy deposited in anode = kVp x average mA x time (s)

for single phase units energy = 0.75 x HU; for 3-phase/constant potential units energy = HU

kW rating = max power that can be applied to the tube for 0.1s

X-Ray Generators

supplies current to filament via step-down transformer with precise control of filament heating, high V across tube via step-up transformer


primary coil causes changes of magnetic field with time, induces current in secondary coil (alternating current); coils around a central closed core

Faraday’s law of induction: Np/Ns = Vp/Vs; VpIp = VsIs; N = number of coils

rectification = ACDC; self-rectified with XR tube does this (anodecathode inhibited; inefficiency as exposure times twice as long and anode heats and electrons may boil off)

single-phase generators

AC cycle in Australasia = 20ms = 50Hz

half-wave rectifier = one pulse generator = only the positive half of the wave used

full-wave rectifier = two pulse generator = diode bridge using 4 rectifiers = full AC cycle utilised

low V part of the wave generates low energy electrons, less XRs with lower energy causing higher dose and heat

minimum exposure time of one pulse = 10ms

three-phase generators

industrial power source with 3 wires, 3 separate power sources in different phases

ripple = how much V varies with time from max to min (single-phase = 100%)

six rectifier-six pulse = 6 pulses per cycle = 13.5% ripple

12 rectifier-6 pulse; 12 rectifier-12 pulse (3.5% ripple)

minimum exposure time of 1-2ms

medium and high frequency generators = constant potential generator

V f.n.A; f = AC frequency; n = number of turns in secondary coil; A = cross-sectional area of core

rectification & filtering, chopping (inverter) before transformer to increase f thus making generator smaller and V higher; output is rectified and smoothed to produce 13% (medium f) and 4% (high f) ripple

compact (can be housed in XR tube), temporal stability, higher XR output per mAs (thus reducing exposure time), can undergo rapid switching (negates need for grid controlled switching)

capacitor discharge generator

transformer and rectified output charges bank of capacitors (takes several seconds) before discharge across tube with exposure time controlled with grid-controlled tube

one microfarad (μF) capacitor has 1kV drop in V for every mAs of charge drawn

may be operated from rechargeable batteries but reduced mAs capability with drop in V

Exposure Switching and Timing

primary switching controlled in primary coil of transformer

secondary switching expensive as needs with withstand high V

grid-controlled switching controlled by increasing cup negativity thus turning tube off

timing performed by time required to charge a capacitor through selected resistance or by counting pulses with high frequency quartz oscillator under microprocessor control (limited by cable capacitance)

AEC = automatic exposure control = photo-timing

detects radiation responding w a pulse that can be used to terminate exposure when reference signal obtained

photomultiplier, parallel plate ionization chamber or solid state detector (must be transparent to XR) placed betw grid and imaging device (except mammography where AEC behind film-screen)

for chest, 3 AEC elements/fields placed over each lung and mediastinum; correct alignment required and size of field must be sufficient to produce meaningful average signal

Interactions with Matter

attenuation = reduction in intensity from absorption of scattering

-ΔN (N XR removed from 1y beam) = μ.N.Δx; μ = linear attenuation coefficient for monochromatic beam, N = intensity, Δx = thickness; N = N0e-μx

HVL = half value layer = thickness for K to reduce to half = ln2/μ (for monochromatic beam) ≈ few mm Al ≈ few cm of tissue

mass attenuation coefficient = μ/ρ; ρ = density; same for liquid, solid and gas

polychromatic beams are hardened (lower energy photons preferentially absorbed)

due to filtration/attenuation

generally ↑kVp by 10keV, need to 2x exposure

Ionization and Excitation

ionization = loss of electron causing imbalance in electronic and nuclear charges

de-excitation = when inner electron shell not full the rest of electrons usually drop one level (but may drop more at once) releasing characteristic X-rays

excitation = valence electron elevated to higher level which is unstable and reverts releasing photon in visible/UV spectrum; some organic crystals remain in these metastable states for several days

conduction band = band above valence band where electrons may move freely along the inorganic crystal lattice; separated by a forbidden energy region, a gap of a few eV

positive hole = gap left (and can move freely) when electron is excited from valence to conduction band

electron trap = from variations in the energy bands from lattice defects or impurities, in the forbidden region

fluorescence = excitation then de-excitation back to valence band in <10ns with emission of light

phosphorescence = when electron in a superficial trap receives enough thermal energy at room temp to escape and drop back to valence band

photostimulable luminescence (PSL) and thermoluminescence (TL) when e in deeper trap and need visible light/IR or heat to be released then de-excite releasing visible/UV light

Coherent Scattering

unmodified scattering = change in direction without loss of energy

  • Thomson/classical scattering = with single unbound electron
  • coherent/Rayleigh scattering = bound electrons set vibrating with photons from electrons in the same atom combining to be emitted with same λ

mainly at low kVp and large Z; contribution <5% of total interactions (except for mammography)

PE = Photoelectric Effect

photon absorbed by electron (usually K-shell) and ejected with de-excitation of electrons cascading inwards emitting characteristic XRs

EK = K-shell binding energy: Mo 20keV, Rh 23, I 33, Ba 37, La 39, Gd 50, W 70

μ/ρ Z3/E3 (once E ≥ binding energy); since Z3 it magnifies tissue contrast at expense of high D (from low E)

K-edge = when E=EK rapid change in attenuation due to PE which decreases

important for breast imaging hence need to keep kVp < 20 keV

Compton/Incoherent Scattering

if E binding energy electron (usually outer shell) ejected with kinetic E and photon released

E’ (scattered photon) = ; θ = scattering angle (preference for forward or backward scattering), m = electron rest mass

μ/ρ electron density and independent of Z; more important than PE above 30keV hence image essential one of electron density; slowly reaches max scattering with E then slowly drops

Pair Production

when E > 1022keV and photon passes near nucleus it is absorbed with creation of positron and electron; positron later annihilates with free electron to produce two 511keV photons 180° to each other

E = 2mc2 + E+ + E; E± = kinetic E of positron/electron

μ/ρ Z2


at E >8MeV a photon may eject a neutron, proton or α particle


primarily arises from Compton events and increases with higher kVp, thickness and field size (reaches plateau at ≈ 30 x 30 cm)

BSF = back scatter factor = factor that skin D is increased from scatter alone

5cm away from 1y beam, D ≈ 10% from scatter

scatter fraction = ratio scatter to primary K

scatter @1-2m is ≈ 1/1000 of primary beam ESD

scatter received by radiographer/radiologist <1% of ESAK


absorber/filter placed in polychromatic beam to preferentially attenuate certain E

inherent filtration = from glass/metal envelope, insulating oil, exit window, cassette cover etc

added filtration usually in collimator housing, may have rotating disk for easy of interchange, may be controlled by microprocessor

  • traditional low Z filters: Al, Cu
  • K-edge filters = higher attenuation just above K-edge = rare earth (La, Er, Gd), Mo, Rh; not usually used in general or CT XRTs
  • compound/combination filter = Cu for most attenuation and Al to absorb characteristic XR from Cu (second filter required for any heavy metal filter)

total filtration = inherent + added specified in mm of Al (minimum 0.5mm Al [or 0.03mm Mo] for <50kVp, 1.5mm for 50-70kVp, 2.5mm for >70kVp)

wedge filters = thickest part at thinnest part of patient for uniform density in image (similar effect to heel effect)


preferentially remove scattered radiation (apart from few° Compton or septal penetration) thus improve contrast, but requires higher mAs (from loss of 1y radiation, reduced total radiation), may cause grid cut-off or aliasing (when grid lines parallel to raster or digital image lines)

shouldn’t be used for thin parts, grid ratio should increase with pt thickness

lead strips interspersed in substrate (organic, Al, paper, air): parallel, focussed (strips oblique to surface), crossed (strips 90° to each other) or honeycomb (interspaced material air)

r = grid ratio = h/D = height/width of transparent substrate ≈ 4-6

N = pitch = number of lines per centimetre (lowvisible lines; high↓contrast) ≈24-60 lines/cm

primary transmission = ; D = substrate width, d = septal thickness; less than expected due to substrate absorption

B = Bucky factor =incident/transmitted radiation or = intensity without grid/intensity with grid; increases with kVp due to more scatter

K = CIF = contrast improvement factor = contrast with grid/contrast without lead content (areal ρ, g/cm2)

grid cut-off increases with high r, short focus-grid distance, moving grids; from:

  • upside-down focussed grid with central strip the only part visible
  • lateral decentring causing uniform loss over image (same as if grid is tilted); fraction of primary radiation lost = ; f = focal distance, b = amount of lateral decentring
  • focus-grid distance decentring (worse when too near), loss of density worse laterally; L = ; f’ = actual focus-grid distance, c = distance of image point from symmetry axis of grid
  • combination of lateral and focus-grid distance decentring, density gradient across image; ; c is positive when point is same side of symmetry axis as the focus

moving grids are moved 1-3cm to blur shadows caused by grid lines but causes lateral decentring and must be asynchronous with pulses of generator

Air-Gap Technique

reduces scatter and magnifies image (esp mammography); if magnification is not wanted then SID increased to ~3m (also restores image sharpness) for air gap of 30cm

decreases patient dose, but increases tube loading, increases magnification and image unsharpness (due to finite size of focal spot)

Inverse Square Law

inverse square law for point source from principle of conservation of energy with surface are of sphere = 4πr2

flux density/intensity = number of rays/quanta passing through a unit area

DAP = dose-area-product (Gy.m2) measured with ion chamber at exit of tube housing and is constant


luminescence = stimulated emission of light

fluorescence if <10ns, when electrons in traps are released immediately

phosphorescence if delayed, when release from electron traps after absorption of own thermal energy

conversion of XR photons to large amount of light photons predominantly due to PE of high Z

reduces patient dose, tube and generator loading, motion artefact (from reduced mAs); but reduces spatial resolution (from isotropic light emissionlateral diffusion, increases with screen thickness; reduced with light-absorbing dyes)

consists of protective layer (2μm), phosphor in low Z matrix (100-300μm), TiO2 reflecting layer (1μm, not always present) and plastic base (200-300μm)

two asymmetric screens may be used on either side of double emulsion film with back screen thicker

phosphors: CaWO4 (calcium tungstate), (BaSr)SO4:Eu (celestobarite:europium)

phosphor particle size ~4-8μm (silver halide grains ~2μm)

Rare-Earth Screens

phosphors: Gd2O2S:Tb (gadolinium oxysulphide:terbium), LaOBr (lanthanum oxybromide)

K-edges matched to XR energy (25-50keV), with Gd preferentially detecting primary radiation (has higher average keV, which is above Gd EK); however as keV increases beyond EK, secondary emission of characteristic XR from screen with subsequent reabsorption reduces spatial resolution


QDE = quantum detection efficiency = absorption efficiency = fraction of incident XRs captured

conversion/intrinsic efficiency = fraction of the absorbed XR energy converted to light that the film is sensitive to (3-5% for CaWO4, 10-20% for rare-earth); rest converted to heat

screen efficiency = fraction of light that escapes screen to interact with film

speed = intensification factor = K without screen/K with screen

efficiency for CaWO4 falls below 80kVp (due to EK, is stable above 80kVp) and rare-earth screens peak at 80-100kVp

Emission Spectrum

inorganic phosphors (except CaWO4) need to be doped with an activator to increase light emission efficiency and spectrum to match film response

CaWO4 has with broad emission spectrum peaking at 430nm = violet, matched to silver halide film

rare earth screen emission dominated by Tb at 544nm=green extending to 630nm=red, hence require orthochromatic (sensitive to blue/green) or panchromatic (sensitive to all visible light) films


X-ray film or laser (copied via laser printer) film


supercoat (5-10 μm, gelatine to protect from mechanical damage), emulsion, adhesive, film base (170-200μm, glass, cellulose nitrate, cellulose triacetate or polyester)


  • photographic gelatine made from bone, prevents clumping of grains and allows processing chemical penetration
  • silver halide grains = 1-10% AgBr and 90-99% AgI; 1 billion Ag ions per a 2μm grain, billions of grains per mL

grains sensitised by heating with sulphur reducing agent to form sensitivity speck (AgS at surface of crystal to trap electrons)

tabular grains have large surface area to increase absorption

AgBr absorbs UV and blue; sensitisation broadened with addition of dyes to create orthochromatic (green sensitive) and panchromatic (red sensitive) film

stabilisers added to prevent deterioration

double emulsion film (most uses) have screens on either side of the film

single emulsion film (in mammography) has less quantum mottle and better spatial resolution due to absence of crossover exposure (from opposite screen)

Image Formation

Gurney-Mott hypothesis = AgBr + photon  Ag+ + Br atom (=hole) + e (mobile until encounters imperfection/sensitivity speck where it gets trapped)

nucleation = Ag+ + eAg = mobile Ag+ attracted by trapped electron, with growth of Ag at the sensitivity speck; at least 4 atoms required for stability to form latent image centres; Br taken up by the gelatine

reciprocity law = density in developed film intensity x time

low intensity reciprocity failure = flux too low to permit stable Ag clumps

high intensity reciprocity failure = production of e too fast for Ag+ migration, with recombination in places other than latent image sites hence not processed

solarisation = very large exposures causing reduction in latent image due to recombination

film duplication = duplicate film pre-exposed to max optical density so further exposure through originally developed film reduces the latent image

direct absorption of XR result in energetic free electrons with thousands of Ag formed, but only account for 3-10% of latent image as exposure sensitivity (500-1500μGy) much less than film-screen (1-100μGy)

Film Processing

development = reducing agent (hydroquinone and phenidone) + AgBr in alkaline solution  Ag, where latent image is catalyst and increases with dwell time and temperature; unexposed grains creating fog

  • increased Br limits life of developing solution
  • preservative = sodium sulphite; restrainer = KBr (to reduce rate of fog formation)

fixing = ammonium thiosulphate forms complexes with Ag thus dissolving AgBr (for chemical equilibrium); chemical hardeners toughen the gelatine

washing removes fixing chemicals and thiosulphate (which causes film to brown with age)

replenishment – ~60mL of developing solution is removed and replaced with replenishment solution for each film to maintain chemical balance

Film Photographic Characteristics

D = optical/photographic density = log10; I0 = incident light intensity on film, I1 = transmitted intensity; useful densities are 0.25-2.0; unexposed film 0.1-0.2 (base + fog); log due to response of eye to light is logarithmic; total density = sum of individual densities

characteristic/H&D (Hurter and Drifield) curve = D vs log(relative exposure)

  • toe = low gradient at low exposure (underexposed), shoulder = low gradient at high exposure (overexposed)
  • Γ = film gamma = max gradient
  • average gradient = betw 0.25 and 2.0 above base+fog; if >1 then film will enhance subject contrast
  • latitude = dynamic range of film = range of log(E) for acceptable D (betw 0.25-2.0 above base+fog)
  • Dmax = max possible density on film

increasing developer temperature or dwell time increases average gradient, film speed and fog

storage of film must not be in cassettes and in a dark shielded room with lifetime exposure <2μGy to reduce fog

speed of film-screen K that gives D of 1 above base+fog, where nominal speed of 100 represents K of 11.1μGy

Computed Radiography (CR)

CR = photostimulable luminescence (PSL) = digital luminescent radiography (DLR)

ionising radiation excites electrons from valence to conduction band (indirectly or via excitation), with some trapped in impurity centres (electron traps)

thermoluminescence = released of electrons in traps after application of heat

photostimulable luminescence = released with exposure to visible or infrared light

phosphors: BaFX:Eu (europium-activated barium-fluoro halide; X = Br:I 85:15), CsBr (improved resolution)

stored signal does not fade appreciably, high emission sensitivity (blue 300-500nm) when stimulated by red 600-680nm

plate scanned (scan direction) in raster pattern (line-by-line, sub-scan direction) with focused He-Ne or GaAs laser, with emitted light collected by fibre optic coupling to PM tube; or directly by array of 5 PM tubes

PM tube output amplified and compressed, digitised (ADC)

plate flooded with high intensity Na discharge lamp (orange) to erase remnants (bright and correct λ matching)

scan times 30s-4min

pre-read stage – small fraction of signal read with low power laser to determine how many images and which have areas have been exposed to primary radiation with pixels outside collimated regions excluded, and gain of PM tubes adjusted

relative intensity of emitted light directly proportional to log K on plate over at least 4 orders of magnitude, ie large linear dynamic range with window and levelling adjusted to access different regions

histogram analysis limits dynamic range for display with lowest useful K pixel value 0, highest = 1023; some units offer larger range of pixel values; raw data 16bit  10 or 12 bit

further image processing with smoothing, edge enhancement, grid removal (Fourier analysis), collimation detection

low bandpass filter used as high freq may undergo aliasing from sub-sampling in laser sub-scan direction

tonal processing – contrast scaling to sigmoidal H&D curve for printing or viewing of monitor

Image Quality

resolution limited by phosphor plate thickness (thin↑D), diameter of laser beam (100μm, with divergence of laser from scatter in the body of the phosphor layer), readout time (detector sampling rate)

more sensitive to scatter than Gd2O2S rare earth screens, hence recommend moving grids with lines perpendicular to CR scan lines

aliasing can occur when spatial frequency higher than sampling frequency (2.5lp/mm), reduced with low bandpass spatial filtering along axis perpendicular to scan line

lower absorption efficiency compared to film-screen, hence higher or comparable K required for given noise

plates should be erased when not irradiated for ≥8h

Flat Panel Image Receptors = Digital Radiography (DR)

active-matrix liquid-crystal flat panel displays (AMLCDs) – large integrated circuit (=active matrix array) of millions identical semiconductor elements on substrate material

dell = detector element

each pixel has switch (off during exposure) connected to switching control so they are operated in individual rows with output connected to a pre-amplifier in each column before digitisation (ADC); image acquired row/line by row/line; in fluoroscopy mode array is scanned continuously

mounted on device replacing XR cassette, operation controlled by digital image processor

digital image processing with logarithmic transformation (to correct for exponential XR attenuation), contrast enhancement, optimisation for displayed grey values

corrections for flat-field (spatial sensitivity variations), median filtering (remove effects of bad pixels)

pixel size is 100-200μm

are either counters (each event counted separately, independent of energy; low noise) or integrators (total charge collected and measured, dependent on energy which increases with kVp; noise collects over time)

well = total charge that a capacitor can collect, limits dynamic range

fill factor – percentage of pixel area sensitive to signal, with need to accommodate conductors (~10μm); in direct photons striking over switching electronics still hit photoconductor and attracted to capacitor which lies betw switches; indirect receptors photons striking screen over switching electronics are not detected

large linear dynamic range (better than PSL), superior MTF and DQE, better detection efficiency (>65%, compared to ~30% with CR and film)

worse resolution than CR, but not noticeable

Indirect Image Receptors

screen (Gd2O2S:Tb or CsI:Tl [grown in needles]) coupled to AMLCDs of photodetectors (a-Si amorphous silicon) that generate charge proportional to amount of light, stored until read-out

small lag, can be used for fluoroscopy

Direct Image Receptors = Direct Radiography

photoconductor (a-Se amorphous selenium, PbI2, PbO, TlBr or CdTe) coupled to AMLCDs of electrode and capacitors, with charge stored until readout

charge of 5,000V applied to photoconductor surface electrode so electrons attracted to pixel electrode

an electron and hole pair (electron cloud) are produced from ionisation which drift in opposite directions to corresponding electrodes

significant lag (from drift of charge cloud), so cannot be used for fluoroscopy

improved resolution due to lack of screen phosphor

higher absorption efficiency due to ~100% fill factor

CCD (Charged Coupled Device)

lighta-Si photodetectorcharge stored in capacitors until readout; 25μm pixels in max 5x5cm area

limited FOV – conventional phosphor screen coupled to CCD using lenses or fibre optics; size limited to stereotactic biopsy with time delay of only a few seconds

full FOV integrates subassemblies with CCDs/lenses focussing on individual CCDs and may be utilise repositioning

scanning equalisation radiography uses 22x1cm collimated fan beam with gantry (tube and 4 CCD array receptor) moving with acquisition time 5sec, reduced scatter (no grids required), but artefacts from irregular movement, increased load on tube (may require W tube)

inefficiencies in minification due to loss of light in optical coupling

alternatively 4 exposures taken with mosaic collimator and CCD pattern imaging different quadrants before stitching the image together and also has reduced scatter

Image Quality

ability of imaging device to record each point in object accurately; includes contrast, noise, blur, artefacts, distortion

Radiographic/Image Contrast

subject/object contrast = due to differential attenuation = C = IS/IL = lnIA – lnIB of XR intensities through segments of tissue; Is = I through small/thin segment, IL = through large/thin segment; depends on difference in anatomical thickness, density, Z, and radiation quality (kVp, HVL) with low kVp ↑C due to PE but has small exposure latitude

film contrast influenced by H&D curve and gamma, film density, screen or direct exposure and film processing (gamma, speed and fog with increased dwell time or temperature)

contrast sensitivity = relationship betw subject and radiographic contrast, with film usually amplifying subject contrast

fog from prolonged/improper film storage, excessive developer T, dwell time of poor chemistry causes reduction in film contrast (thus radiographic contrast), high speed film (highly sensitised grains)

exposure fog = accidental exposure of film to light/XRs

scatter (mainly Compton scattering) increases with thickness, FOV and kVp and lowers radiographic contrast; SPR = ratio of scattered to primary radiation

  • contrast in presence of scatter = C = C0 x contrast reduction factor ; s = scatter, p = primary beam

Noise = Radiographic Mottle

noise = random + structured/systematic noise

non-uniformity of density from film graininess (only important with high magnification of film), structure (defects in screen) and quantum mottle; screen mottle = structure + quantum mottle

random noise = quantum mottle (refers to film-screen or XII) = statistical fluctuation in N of photons per unit area absorbed by screen/detector in a Poisson distribution with standard deviation =noise = = ; to reduce noise by 10x, N/area or K needs to increase by 100x

reduced with screen thickness, absorption efficiency, increased with conversion efficiency

Blur = Unsharpness

in digital imaging is mostly due to pixel size; reduces noise by smoothing

how much the film-screen degrades an edge; UT2 = Ug2 + Um2 + Ua2 + Ur2; when patient close to receptor blur dominated by receptor, when close to focus it is dominated by focal spot size

geometric unsharpness = focal spot blurring = penumbra

geometric magnification (if from ideal point source) = m =

umbra = central density; penumbra = peripheral lighter density from finite sized focal spot

true magnification = M = = umbra + penumbra = ; f = focal spot size, o = object size

effect of geometric unsharpness reduced with low f, large o, reduced m

blooming = increase in size from space charge effects with electrons repelling each other at high mA

XRs emanating from focal spot not uniform and has edge-band or Gaussian/normal distribution or elongated in direction of tube axis

motion unsharpness

the magnitude of which depends on magnification

absorption unsharpness

due to anatomical ill-defined edges and round objects

screen/receptor unsharpness

from lateral diffusion (increased with phosphor thickness, usually ~0.15-0.6mm), light crossover, poor film-screen contact, parallax (two images separated by width of film base in double-emulsion films), halation (backscatter from surfaces of screen)

Resolution = resolving power

ability to record close objects as separate, determined by blur; measured with high contrast (Pb or Cu) grids

resolution limit = cut-off resolution = number of line pairs (lp) per mm or cycles that can be seen

Measurement of Image Quality

dynamic range = range of signal I that image is acquired; range of signal A that can be handled by system without distortion of image

LSF = line spread function

single emulsion film-screen exposed from narrow slit (10μm) in opaque material (Pt/Pb), with density extending out for several hundred μm due to receptor unsharpness

FWHM = full width half maximum = width of profile at half the maximum peak height

spatial resolution (lp/mm) =

PSF = point spread function

MTF = modulation transfer function

Fourier transform of the LSF

large objects/ill-defined borders have lower spatial frequencies and small objects/sharp borders higher f components

measurement of object contrast and resolution

MTF = = ; where contrast is from a line pair phantom and is plotted against spatial frequency (lp/mm)

resolving power = point where MTF = 0.1; the human eye can resolve ~2-4lp/mm

total MTF = product of individual component MTFs

for digital images, the MTF in the diagonal direction has a drop-out region due to aliasing before increasing again at higher spatial frequency

Wiener spectrum

Fourier transform of an exposed blank film with noise power vs spatial frequency

white noise = incident XR flux with equal noise at all frequencies, but screen cannot transmit all frequencies equally, hence curve slops down with frequency (gradient depends on MTF)

magnitude at 0 lp/mm = quantum/screen + film grain noise; magnitude at high lp/mm = film grain noise

DQE = detective quantum efficiency

complete performance of imaging chain; DQE (at certain lp/mm) = (SNROUT/SNRIN)2; SNR = signal to noise ratio where SNRIN from quantum noise and SNROUT from quantum and system noise

DQE ≈ 50-80% of absorption efficiency (due to system noise); if no noise in imaging chain then DQE = absorption efficiency

focal spot size measurement

effective focal spot size > nominal size

pinhole and slit camera methods

lead star resolution pattern = line pair pattern

  • feq = focal spot size of equivalent rectangular spot
  • star pattern placed below focus with m=2 using 2-10mAs@75kVp with diameter of pattern where there is loss of resolution/blurring measured
  • diameter parallel to tube = resolution limit; diameter perpendicular to axis = focal spot dimension

magnification reduces effective MTF for focal spot size, but increases effective MTF for receptor; and apart from mammography focal spot size is the limiting factor hence magnification kept as low as possible