For an imaging setup with a 2 mm effective focal spot, 2-inch OID, and 40-inch SID, what is the focal spot blur?

For an imaging setup with a 2 mm effective focal spot, 2-inch OID, and 40-inch SID, what is the focal spot blur?

• A. 0.106 mm
• B. 0.210 mm
• C. 1.06 mm
• D. 0.0106 mm

Answer: (A)

Geometric unsharpness comes from projecting a finite focal spot size onto the image plane. The blur on the image is given by Ug = F × (OID / SOD), where F is the focal spot size, OID is the distance from the object to the image receptor, and SOD is the distance from the focal spot to the object. Here, the focal spot is 2 mm. The object-to-image distance is 2 inches, and the source-to-image distance is 40 inches, so the source-to-object distance is SOD = SID − OID = 38 inches. Convert to millimeters: OID ≈ 50.8 mm and SOD ≈ 965.2 mm. Compute Ug ≈ 2 mm × (50.8 / 965.2) ≈ 2 mm × 0.0526 ≈ 0.105 mm, which rounds to 0.106 mm. So the focal spot blur is about 0.106 mm.

Geometric unsharpness comes from projecting a finite focal spot size onto the image plane. The blur on the image is given by Ug = F × (OID / SOD), where F is the focal spot size, OID is the distance from the object to the image receptor, and SOD is the distance from the focal spot to the object.

Here, the focal spot is 2 mm. The object-to-image distance is 2 inches, and the source-to-image distance is 40 inches, so the source-to-object distance is SOD = SID − OID = 38 inches. Convert to millimeters: OID ≈ 50.8 mm and SOD ≈ 965.2 mm.

Compute Ug ≈ 2 mm × (50.8 / 965.2) ≈ 2 mm × 0.0526 ≈ 0.105 mm, which rounds to 0.106 mm. So the focal spot blur is about 0.106 mm.