What is the geometric magnification of an x-ray system?

The geometric magnification of an x-ray system is the ratio of the (distance between the x-ray tube focal point and the system detector) to the (distance between the x-ray tube focal spot and the sample), as shown in the diagrams. So the closer the sample can get to the x-ray tube focal spot the greater the geometric magnification a system can achieve. Therefore, the thinnest samples will always be able to achieve the highest geometric magnifications in an x-ray system. With this in mind, being able to move the sample as close as possible to the x-ray tube without the danger of sample collision or damage becomes very important. The x-ray tube focal spot is the position within the tube where the x-rays are actually produced and this is not the same place as the outer cover of the tube from where the x-rays emerge.

With the above ratio in mind it could be assumed that by increasing the distance between the x-ray tube focal point and the system detector, or A in the diagram, then larger and larger magnification could be achieved. Whilst this is true in principle, the laws of physics unfortunately do not allow this luxury. This is because although the magnification will increase linearly with distance, the intensity of the x-rays coming from the x-ray tube decrease at the inverse square rate at the same time. In other words, doubling the distance A will double the geometric magnification but at the same time the intensity of the x-rays reaching this longer distance has decreased by a factor of 4. So it will take 4 times as long to acquire the same number of x-ray photons at this larger distance to produce the same quality image at the closer distance. Therefore, a compromise must be reached in real x-ray inspection systems to balance image quality, speed of use and realistic magnification.

Geometric magnification should not be confused with the system, or total, magnification. The system magnification is a product of the geometric magnification and the magnification of the imaging chain, as shown in the diagram. It is the ratio of (size of the object on the operator screen) to the (actual size of the object).

The system magnification provides a larger number than the geometric magnification. However, if the detector area used upon which the image is captured and/or an increasingly large operator display is provided, then the system magnification can be raised to very high numbers without actually providing any more meaningful magnification of the actual object under examination. Some image intensifiers, for example, can be operated in what is called double or triple-field mode and this will increase the system magnification values dramatically, but do not change the geometric magnification.

Further information on geometric magnification with open and closed x-ray tubes, and their effects on the capabilities of an x-ray inspection system, can be found in the following technical paper Differences Between Open And Closed Tubes presented by Dage in the Proceedings of SMTA International, Chicago, September 2002.