GEOMETRY OF GEOMETRY OF RADIOGRAPHIC RADIOGRAPHIC

IMAGINGIMAGING

REQUIRED PRINCIPLESREQUIRED PRINCIPLES

X-rays Travel in Straight LinesX-rays Travel in Straight Lines X-rays diverge from source (focal spot)X-rays diverge from source (focal spot) Focal spot has finite size (not a point Focal spot has finite size (not a point

source)source)

ALSO:ALSO: Law of Similar TrianglesLaw of Similar Triangles

LAW of SIMILAR TRIANGLESLAW of SIMILAR TRIANGLES

INVERSE INVERSE SQUARE LAW:SQUARE LAW:

II22/I/I11 = (D = (D11/D/D22))22

Doubling distance Doubling distance from source reduces from source reduces intensity to 1/4intensity to 1/4

Intensity = Intensity = x-rays/areax-rays/areaDoubled distance = Doubled distance = 4x area covered by 4x area covered by beambeam

MAGNIFICATION FACTOR (M)MAGNIFICATION FACTOR (M)

MagnificationMagnificationand Distortion and Distortion

Distortion refers to Distortion refers to misrepresentation of misrepresentation of a structure or a structure or object’s size, shape object’s size, shape or position. or position. Distortion is Distortion is caused bycaused by unequal unequal magnificationmagnification of of different parts of the different parts of the same object.same object.

Size Distortion vs Position in BeamSize Distortion vs Position in Beam

Shape Distortion Position DistortionShape Distortion Position Distortion

Resolution (Blur): Detail VisibilityResolution (Blur): Detail Visibility

FOCAL SPOT BLUR: PENUMBRAFOCAL SPOT BLUR: PENUMBRA

Penumbra and Object-Image DistancePenumbra and Object-Image Distance

Focal Spot Blur:Focal Spot Blur:PenumbraPenumbra

P/F = h/H P/F = h/H P = F x (h/H)P = F x (h/H)

Minimizing Distortion and PenumbraMinimizing Distortion and Penumbra Minimum Magnif Minimum Magnif Minimum Minimum

DistortionDistortion– Small object-image distanceSmall object-image distance– Large Focal-image distanceLarge Focal-image distance

Minimizing Penumbra:Minimizing Penumbra:– Small object-image distanceSmall object-image distance– Large Focal-image distanceLarge Focal-image distance– Small focal spot sizeSmall focal spot size

Magnification and Screen ResolutionMagnification and Screen Resolution

Focal Spot vs Receptor BlurFocal Spot vs Receptor Blur Image receptor (e,g, screen) resolution (MTF) Image receptor (e,g, screen) resolution (MTF)

improvesimproves with increasing magnification with increasing magnification (objects appear larger to the image receptor)(objects appear larger to the image receptor)

Focal spot resolution (MTF) Focal spot resolution (MTF) worsensworsens with with increasing resolution (large penumbra)increasing resolution (large penumbra)

Optimum resolution will be a some Optimum resolution will be a some distance above image, depending on distance above image, depending on relative amounts of image receptor and relative amounts of image receptor and focal spot blurfocal spot blur

FOCAL SPOTSFOCAL SPOTS

Nominal vs Actual Focal Spot SizeNominal vs Actual Focal Spot Size

NEMA Tolernaces for Measured Focal Spot SizeNominal

Size (mm) Minus Plus

Less than 0.8 0% 50%0.8 to 1.5 0% 40%

Greater than 1.5 0% 30%

Measuring Focal Measuring Focal Spot Size:Spot Size:Pinhole CameraPinhole Camera

If pinhole placed If pinhole placed halfway between halfway between focal spot and film focal spot and film (SOD = OID), then (SOD = OID), then size of focal spot size of focal spot image will equal the image will equal the projected focal spot projected focal spot size size

Focal Spots: Pinhole CameraFocal Spots: Pinhole Camera

Focal Spot Size: Star Resolution Test Focal Spot Size: Star Resolution Test

Focal Spot Size vs kVp and mAFocal Spot Size vs kVp and mAkVp mA Measured FS Size (mm)

40 100 2.060 100 1.880 100 1.7150 100 1.7

kVp mA Foc Sp Size (mm)

40 100 2.040 300 2.380 100 1.780 300 1.8

Focal Spot BloomingFocal Spot Blooming Focal spot size Focal spot size increasesincreases with increasing with increasing

tube tube current (mA). This is called tube tube current (mA). This is called focal focal spot bloomingspot blooming. It is caused by electron . It is caused by electron repulsion while crossing x-ray tube, and is repulsion while crossing x-ray tube, and is most pronounced for for low kVpsmost pronounced for for low kVps

Focal spot size decreases slightly with Focal spot size decreases slightly with increasing kVp (less time for repulsion to act)increasing kVp (less time for repulsion to act)

NEMA:NEMA: Focal spots measured at 75 kVp Focal spots measured at 75 kVp using 50% of maximum rated mA using 50% of maximum rated mA