02 Imaging

Geometric unsharpness

Focal-spot blur from effective spot size and distances.

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Simulation

Geometric unsharpness — Change the numbers; the scene follows.

Where it works

Radiography room

X-ray tube

At the focal spot in the tube housing — spectrum, output, SID geometry, and unsharpness start here.

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Formula

U_g = f \cdot \frac{\mathrm{OID}}{\mathrm{SOD}}

Variables

f · Effective focal spotmmOID · Object-to-image distancecmSOD · Source-to-object distancecm

Results

U_g
Geometric unsharpness
0.2118mm

Explanation

U_g = f \cdot \frac{\mathrm{OID}}{\mathrm{SOD}}

What it means

Geometric unsharpness (focal-spot blur) U_g = f × OID/SOD. Large foci, large object-to-image gaps, and short SOD all blur the image. This is why a small focal spot is used for magnification mammography. This is a working relation in Diagnostic imaging.

Where it is used

Clinically it sits on the Radiography room — X-ray tube. At the focal spot in the tube housing — spectrum, output, SID geometry, and unsharpness start here. Diagnostic equations live on the tube, the detector, and the patient: magnification, air kerma, CTDI, and why bone lights up at 70 kV. They turn a technique chart into physics you can defend.

Radiography room · Open this machine

How to use it

Enter effective focal spot (mm), OID and SOD. Compare U_g with detector pixel size — the larger of the two limits spatial resolution. Change one input and watch the curve and the simulation follow.

Symbols

fEffective focal spot1.2 mm
OIDObject-to-image distance15 cm
SODSource-to-object distance85 cm

Worked example

A typical case from the default values: f = 1.2 mm (Effective focal spot); OID = 15 cm (Object-to-image distance); SOD = 85 cm (Source-to-object distance). Substituting into the relation gives U_g = 0.2118 mm. These are teaching numbers — align them with your machine.

Typical values give

U_g = 0.2118mm

Where it comes from

The displayed formula is the working relation. Focal-spot blur from effective spot size and distances. Usual reference: Bushberg. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg

Assumptions & limits

Geometric only. Motion unsharpness and detector MTF add in quadrature in a full resolution budget. ‘Effective’ focal spot already includes anode angle (line-focus principle).

Pitfalls

kVp is not the same as effective energy. CTDI is not patient dose — SSDE and organ dose come after. Do not quote DLP as if it were effective dose without a k-factor. Geometric only. Motion unsharpness and detector MTF add in quadrature in a full resolution budget. ‘Effective’ focal spot already includes anode angle (line-focus principle).

Keep this

Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. Geometric only. Motion unsharpness and detector MTF add in quadrature in a full resolution budget. ‘Effective’ focal spot already includes anode angle (line-focus principle).

In this specialty

Diagnostic imaging