Which formula correctly expresses geometric unsharpness in radiography, and which factors influence it?

• A. U = FSS × (SOD / OID); factors: focal spot size, OID, SOD.
• B. U = FSS × (OID / SOD); factors: focal spot size, object-image distance, source-to-object distance.
• C. U = FSS + OID + SOD; factors: none.
• D. U = FSS × OID × SOD; factors: focal spot size only.

Answer: (B)

Geometric unsharpness, or penumbra, arises from the finite size of the focal spot projecting rays onto the image plane. The expression that captures how this blur scales is U = FSS × (OID / SOD). This shows that blur grows with the focal spot size and with the distance from the object to the image receptor (OID), but decreases as the distance from the source to the object (SOD) increases. In practice, sharper images come from a smaller focal spot, smaller OID, and larger distances between the source and object (relative to the object-to-image geometry). The factors at play are the focal spot size, the object-image distance, and the source-to-object distance. The other formulations misrepresent how blur scales with geometry: placing OID in the numerator or denominator differently or adding the distances together does not reflect the true relationship of penumbra to these distances.