Infographics / X-ray Physics

Geometric magnification and focal spot penumbra (macro radiography)

Two linked cutaways. Top: an angled anode target where electrons strike a long actual focal spot, whose projection toward the detector is a smaller effective focal spot (effective = actual times sine of the anode angle). Bottom: the finite effective focal spot acts as an extended source; rays past an object edge to the image receptor produce a full shadow (umbra) flanked by a partly lit penumbra. Penumbra width Ug equals focal spot size times object-to-image distance over source-to-object distance, so a larger focal spot or greater magnification gives more penumbra and blur.

Focal spot line-focus principle and geometric penumbra Two linked cutaways. Top: an angled anode target where electrons strike a long actual focal spot, whose projection toward the detector is a smaller effective focal spot (effective = actual times sine of the anode angle). Bottom: the finite effective focal spot acts as an extended source; rays past an object edge to the image receptor produce a full shadow (umbra) flanked by a partly lit penumbra. Penumbra width Ug equals focal spot size times object-to-image distance over source-to-object distance, so a larger focal spot or greater magnification gives more penumbra and blur. Line-focus principle: actual vs effective focal spot electrons actual focal spot θ (anode angle) effective focal spot (smaller) — acts as the source below effective = actual × sin θ smaller anode angle ⇒ smaller effective spot ⇒ sharper image Geometric penumbra: a finite focal spot blurs edges focal spot (finite source, width F) object edge image receptor umbra penumbra full exposure Penumbra grows when: • the focal spot F is larger • magnification M increases (object further from receptor, or closer to the source) Ug = F × OID / SOD = F × (M − 1) penumbra = geometric unsharpness Sharper: small F, low OID, long source–image distance
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