Geometric Unsharpness Calculator

What is geometric unsharpness?

In radiography, we want the image of a part to show edges and small details clearly. If an edge is sharp, it changes from light to dark over a very short distance. If an edge is unsharp, it changes gradually across a wider band. That blurred band is called the penumbra.

A useful way to picture it is a shadow on a wall. A tiny torch makes a fairly sharp shadow. A wide lamp makes a softer shadow because light comes from different parts of the lamp. Industrial X-ray tubes and gamma sources are not perfect mathematical points, so their shadows can also have soft edges.

Key point: geometric unsharpness is not caused by the material being inspected. It is caused by the geometry of the exposure setup.

f = effective focal spot size  |  a = source to front of subject  |  b = front of subject to film (gap + thickness)

Reading the formula

The formula says the blur gets larger when the focal spot size f gets larger, or when the object is farther from the film or detector. The blur gets smaller when the source is farther away from the object.

At Year 10 maths level, read Ug = f × b / a as: multiply the source size by the object-to-film distance, then divide by the source-to-object distance.

Worked example

Question: A setup has a 2 mm focal spot. The source is 400 mm from the front of the part. The front of the part is 20 mm from the film. What is the geometric unsharpness?

• Write the values: f = 2 mm, a = 400 mm, b = 20 mm.
• Use the formula: Ug = f × b / a.
• Substitute the values: Ug = 2 × 20 / 400.
• Calculate: 40 / 400 = 0.10 mm.
• Answer: The estimated geometric unsharpness is 0.10 mm.