Geometric Unsharpness (X-ray Penumbra)

Unsharpness in X-ray imaging is due to multiple components including: motion, detector and geometrical unshaprness due to the penumbra. In this video we cover the geometrical unsharpness and where the basic equation comes from that governs geometric unsharpness.
In Radiography an important consideration is the image sharpness. Here we will discuss the blurring in an x-ray radiograph that is due to the focal spot. This is sometimes referred to as geometrical unsharpness. We have a separate post which discusses the resolution limits due to a digital detector, and the quantification or measurement of image resolution. So here we will focus on the effect of the x-ray focal spot.
The system blurring is dependent upon the size of the focal spot, and the system geometry. The unsharpness (U) due to the penumbra is U=f*OID/SOD, where OID is the object to image distance and SOD is the source to object distance. Thus the unsharpness in the image directly relates to f (focal spot size) and the ratio of the object to image distance divided by the source to object distance.
We will define the unsharpness in the image due to the penumbra as ‘U’, and since it is dependent on the system geometry we will also define some important distances in this figure.
Unsharpness Formula X ray
As we mentioned above the focal spot has a finite size in both dimensions, but we show just one here in the figure for simplicity. We define the effective focal spot size as ‘f’ in this figure. Then SID is the source to the image distance and SOD is the source to the object distance (i.e. the portion of the patient being imaged).
The object to image distance OID is then the SID minus the source to object distance.
If we draw lines from the edge of the focal spot we can make similar triangles. From these triangles we can see that f/SOD = U/OID. If we solve for U we get U=f*OID/SOD. Thus the unsharpness in the image directly relates to f (focal spot size) and then we multiply by the ratio of the object to image distance divided by the source to object distance.
So, that gives us our geometric blurring or the level of the unsharpness due to the focal spot. You can do simple calculations if for instance, the focal spot has a size of 3 millimeters. Imagine that the object that were interested in, was halfway in between our x-ray tube and our imaging plane where our detector sits. So, if our object is halfway in between, then these two are going to be the same and if the focal spot that we said was three millimeters, then the unsharpeness of the detector is three millimeters.
As the object is moved closer to the source (leaving the source to image plane fixed) the penumbra becomes larger. Luckily, the rest of the image becomes larger as well.
The most important thing that controls the unsharpeness, in addition to the magnification term is the size of the focal spot itself. That’s why we discussed above that there is a desire to have a small focal spot.
But we know that in physical systems we want to have the acquisition done relatively quickly, so the patient doesn’t have a chance to move and we need to get enough x-rays going through the patient so that we can make a good image. There is the tradeoff between spatial resolution (better for small spot) and available x-rays (better for large spot), and this is why x-ray systems typically have multiple focal spot sizes.
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[@matthewleung3954]

Thank you for well explanation. Could you tech the theory behind the Star test pattern for measuring focal spot size?

[@UraniumGirl]

Great work!

[@HowRadiologyWorks]

Thanks Anna

[@dentoradiology3212]

very well expalined thank you

[@TheNettforce]

Thanks Dento Rad

[@SajjadAli-yk3no]

Thank you so much sir ❤️

[@HowRadiologyWorks]

You’re welcome Sajad

[@abdovitamins6331]

Good work

[@HowRadiologyWorks]

Thanks Abdo vitamins

[@petehall1900]

Thank you for radiation education. Maybe a video about how many x rays you should get a year max and min?

[@HowRadiologyWorks]

Thanks Pete, each scan should be considered on it’s own so there is not a given number to aim for but rather work with your clinicians to discuss the benefits of each exam before it is acquired