Geometric FactorsGeometric Factors

FocalSpot

Object

Film

a b c h---- = --- = --- = --- A B C H

Film

B A

H

CObject

b a

h

c

size of image--------------------

size of object

Magnification DefinedMagnification DefinedFocalSpot

ObjectFilm

(image)

focus to film distance HMagnification = ---------------------------------- = --- focus to object distance h

Using Similar TrianglesUsing Similar TrianglesFocalSpot

ObjectFilm

(image)

h

H

size of imageMagnification = --------------------

size of object

focus to film distance Hmagnification = ---------------------------------- = --- focus to object distance h

Using Similar TrianglesUsing Similar TrianglesFocalSpot

ObjectFilm

(image)

h

H

size of image

Magnification = --------------------size of

object

focus to film dist.size of image = size of object X ---------------------------------

focus to object dist

Optimizing Image QualityOptimizing Image Quality

• Minimize magnification• Minimize object-film distance• Maximize focal-film distance

FocalSpot

Object

Film(image)

h

H

focus to film distance Hmagnification = ---------------------------------- = --- focus to object distance h

*

Distortion TypesDistortion Types

X-RayTube

Film Image

Shape Distortion

X-RayTube

Film Image

Relative Position Distortion

minimal distortion when object near central beam & close to film

PenumbraPenumbra

• Latin for “almost shadow”– also called edge gradientedge gradient

• region of partial illumination

• caused by finite size of focal spot

– smears edges on film

– zone of unsharpness called» geometric unsharpness

» penumbra

» edge gradientFilm Image

Line sourcefocal spot

True MagnificationTrue Magnification

• Function of ratio of focal spot to object size (f / d)

• true & geometric magnification equal only when object very large compared to focal spot

a

b

f

d

M=m + (m-1) X (f / d)

m = geometric magM = true mag

Penumbra CalculationPenumbra Calculation

Line sourcefocal spot

Object

F

P

SOD

OID OIDP = F x ------- SOD

SID

Minimizing Penumbra

•Minimize object-film distance (OID)

•Maximize source-object distance (SOD)

•Makes focal spot appear smaller

•Minimize focal spot size

MagnificationMagnification

m = geometric magM = true mag

a

b

f

d

m = (a+b) / a

M=m + (m-1) X (f / d)

Finite sized focal spot

M = m = (a+b) / a

Infinitely small focal spot

Geom = True

For general radiography purposes the geometric For general radiography purposes the geometric unsharpeness dominates the other components unsharpeness dominates the other components

Therefore the unsharpeness will increase with increasing Therefore the unsharpeness will increase with increasing magnification. To keep magnification small (close to m=1) requires magnification. To keep magnification small (close to m=1) requires the image receptor to be as close as possible to the patient and the the image receptor to be as close as possible to the patient and the focus patient distance to be large. focus patient distance to be large.

Typical conditions are: Typical conditions are:

a a 1mm 1mm

dd11 1 m 1 m

dd22 10 cm 10 cm

110cm = =1.1 100cm

m

1 =1mm 1- =0.091mm

1.1gU

Motion UnsharpnessMotion Unsharpness

• Caused by motion during exposure of

– patient– tube– film

• Effect– similar to penumbra

• Minimize by– immobilizing patient– short exposure times

Absorption UnsharpnessAbsorption Unsharpness• Cause

– gradual change in x-ray absorption across an object’s edge or boundary

» thickness of absorber presented to beam changes

• Effect– produces poorly defined margin of solid objects

X-RayTube

X-RayTube

X-RayTube

Inverse Square LawInverse Square Law

• intensity of light falling on flat surface from point source is inversely proportional to square of distance from point source

– if distance 2X, intensity drops by 4X

• Assumptions– point source– no attenuation

• Cause– increase in exposure area with distance

Intensity 1/d2

d

Trade-offGeometry vs. Intensity

Trade-offGeometry vs. Intensity

• maximize SID to minimize geometric unsharpness

but• doubling SID increases mAs by

X4– increased tube loading– longer exposure time

» possible motion

• going from 36 to 40 inch SID requires 23% mAs increase

F

P

SOD

OID

SID

Magnification TypesMagnification Types

• Geometric Magnification– assumes point source

– calculated from similar triangles

• True Magnification– takes into account finite size of focal spot

» focal spot is area (not point) source

FocalSpot

Object

Film

h

H

Automatic ArtifactAutomatic Artifact

• Occurs whenever we image a 3D object in 2D

• Work-around– Multiple views

?? ??

Film ConstructionFilm Construction

• Radiographic Film has two basic parts.

• Base

• Emulsion

• Most film has two layers of emulsion so it is referred to as Double Emulsion Film

EmulsionEmulsion

• The emulsion is the heart of the film. The x-rays or light from the intensifying screens interact with the emulsion and transfer information to the film

• The emulsion consists or a very homogeneous mixture of gelatin and silver halide crystals about 3 to 5 µm thick.

Silver Halide CrystalsSilver Halide Crystals

• 98% Silver Bromide

• 2% Silver Iodide

• Tabular shape used most commonly for general radiography.

• About 1µm thick for screen film exposure.

Silver Halide CrystalsSilver Halide Crystals

• The differences in speed, contrast and resolution depend upon the process by which the silver halide crystals are manufactured and by the mixture of these crystals into the gelatin.

• Size and concentration of crystals have a primary influence on speed.

Producing the Latent Image

Producing the Latent Image

The resulting silver grain is formed.

Silver halide that is not irradiated remain inactive. The irradiated and non-irradiated silver halide produces the latent image.

Types of X-ray FilmTypes of X-ray Film

• Two main types:

• Screen film used with intensifying screens.

– Single emulsion- emulsion on one side of base.

– Double emulsion used with two screens.

• Direct exposure film or non-screen film.

• Special purpose: Duplication, Cine, Dental

Film Dosimeters

Dose (log)

OD)density icalopt OD , logOD

t

0

L

L

Optical densityOptical density

• X-ray film is a negative recorder – increased light (or x-ray) exposure causes the developed film to become darker

• Degree of darkness is quantified by the OD, measured with a densitometer

• Transmittance and OD defined as:

I

I

TT

I

IT

0101010

0

log1

loglogOD

OD examplesOD examples

T OD Comment

1.0000 0 Perfectly clear (does not exist)

0.7760 0.11

Unexposed film (base + fog)

0.1000 1 Medium gray

0.0100 2 Dark

0.0010 3 Very dark; requires hot lamp

0.00025

3.6 Maximum OD used in medical radiography

ContrastContrast

• Contrast of a radiographic film is related to the slope of the H&D curve:

– Regions of higher slope have higher contrast

– Regions of reduced slope (e.g., the toe and shoulder) have lower contrast

• A single number, which defines the overall contrast of a given type of radiographic film, is the average gradient

Average gradientAverage gradient

• OD1 = 0.25 + base + fog

• OD2 = 2.0 + base + fog

• Average gradients for radiographic film range from 2.5 to 3.5

110210

12

logloggradient Average

EE

ODOD

Scattered radiationScattered radiation

• For virtually all radiographic procedures except mammography, most photon interactions in soft tissue produce scattered x-ray photons

• Detection of scattered photons causes film darkening but does not add information content to the image

Effect of collimationEffect of collimation

• As the field of view is reduced, the scatter is reduced

• An easy way to reduce the amount of x-ray scatter is by collimating the x-ray field to include only the anatomy of interest and no more

Antiscatter gridAntiscatter grid

• An antiscatter grid is placed between the patient and the screen-film cassette

• The grid uses geometry to reduce the amount of scattered reaching the detector

Antiscatter grid (cont.)Antiscatter grid (cont.)

• Antiscatter grid is composed of a series of small slits, aligned with the focal spot, that are separated by highly attenuating septa

• Primary x-rays have a higher chance of passing through the slits unattenuated by the adjacent septa

• Septa (grid bars) are usually made of lead; openings (interspaces) between the bars can be made of carbon fiber, aluminum, or even paper

Bar Phantom SetupBar Phantom Setup

                                                    

The Rise & Fall of Joe CamelThe Rise & Fall of Joe Camel

Focal Spot Size Varies with Technique

Focal Spot Size Varies with Technique

• Electron beam focuses more poorly at high mA or low kV

• BloomingBlooming– increase of focal spot size with increasing mA

» more of a problem at low kV’s

» more blooming perpendicular to cathode-anode axis

• kilovoltage effects– size decreases slightly with increasing kVp

• size always measured & specified at particular technique

Off-Axis VariationOff-Axis Variation

• focal spot measurements normally made on central ray

• apparent focal spot size changes in anode-cathode direction

– smaller toward anode side

– larger toward cathode side

– less effect in cross-axis direction

Focal Spot SizeFocal Spot Size

• Trade-off– heat vs. resolving power

– exposure time vs. resolving power

• Focal Spot Size most critical for– magnification

– mammography

Modulation Transfer Function (MTF)

Modulation Transfer Function (MTF)

• How well information reproduced (fraction of contrast retained) at various input spatial frequencies

Modulation Transfer Function(MTF)

Modulation Transfer Function(MTF)

• Fraction of contrast reproduced as a function of frequency

RecordedContrast

(reduced by blur)frequency

MTF

1

0Contrast provided

to film

Freq. =line pairs / cm

50%

MTFMTF

• If MTF = 1– all contrast reproduced at this frequency

RecordedContrast

Contrast providedto film

MTFMTF

• If MTF = 0.5– half of contrast reproduced at this frequency

RecordedContrast

Contrast providedto film

MTFMTF

• If MTF = 0– no contrast reproduced at this frequency

RecordedContrast

Contrast providedto film

Modulation Transfer Function (MTF)

Modulation Transfer Function (MTF)

• value between 0 and 1¤ MTF = 1 indicates all information reproduced at this

frequency

¤ MTF = 0 indicates no information reproduced at this frequency

Component MTFComponent MTF• Each component of imaging system has its

own MTF– each component retains a fraction of contrast as function of

frequency

• System MTF is product of MTF’s for each component.

Modulation Transfer Function (MTF)

Modulation Transfer Function (MTF)

• Since MTF is between 0 and 1, composite MTF <= MTF of poorest component

1/2 * 1/3 * 1/4 * 1/5 = ?

? < 1/5

Film MTFFilm MTF

• Resolves 10-20 line pairs per mm

• MTF ~ 1 for clinical applications

Focal Spot MTFFocal Spot MTF

• Function of magnification

• Deteriorates with increased magnification

– all clinical imaging involves some magnification

• The larger the focal spot, the more deterioration of MTF with increased magnification

Imaging Screen MTFImaging Screen MTF

• improves with magnification

• Why?– magnification of an object of given

frequency reduces frequency seen by screen

Focal Spot & Screen MTFFocal Spot & Screen MTF• focal spot MTF degrades with magnification

• screen MTF improves with magnification

• film MTF unaffected with magnification

• best system resolution– detail screens

– minimize magnification

– BUT detail screens decrease speed» increase exposure time

» more potential for motion

Imaging Physics Wrap UpImaging Physics Wrap Up

Object MotionObject Motion

• independent of magnification

• depends on– exposure time

– velocity

• If motion < 0.1 mm usually doesn’t contribute to unsharpness

• If motion > 1 mm, it generally dominates

Quantum MottleQuantum Mottle

• statistical fluctuation in # of x-ray photons used by imaging system to form image

• quantum mottle independent of geometric (radiographic) magnification

– for a given density the same # of photons must strike a given area of screen/film

Quantum MottleQuantum Mottle

• quantum mottle directly affected by photographic (optical) magnification

» less photons per unit area of image

Quantum MottleQuantum Mottle

• influences perception of low-contrast objects with poorly defined borders

– not well addressed by MTF» measures sharp high contrast borders

• geometric (radiographic) magnification may improve visibility of low contrast objects

– quantum mottle noise does not increase

Skin Exposure & MagnificationSkin Exposure & Magnification

• Patient closer to x-ray tube– Increases exposure

• grids not used with magnification work because of air gap

– Decreases exposure

– No bucky factor loss (3-6)

FilmGrid

Skin Exposure & MagnificationSkin Exposure & Magnification

• Increase is less than calculated by inverse square law

• for 2X mag skin not twice as close– routine radiography also involves some magnification

• smaller volume of patient exposed• high speed screen/film sometimes used for

magnification

FilmGrid

You Must Remember ThisYou Must Remember This

Ilse, we’ll always have

physics.