Welcome to the second part of this captivating trilogy at X-ray University, where we embark on a deeper exploration into the world of X-ray imaging resolution. In this enlightening journey, we unravel the intricate relationship between an ideal X-ray source and a real detector. Our focus is on understanding how the size of the X-ray beam and the level of magnification influence the quality and resolution of the resulting images.
Let’s dive into these factors with close attention and get some deep insights into how pixel size, magnification, and the sharpness of the images all come together. Join us as we continue this captivating series and reveal the final equation in the upcoming third part. Get ready to uncover the exciting culmination of our fascinating exploration!
Welcome back to X-ray University. Today, we’re going to be discussing the second part of this trilogy about X-ray imaging resolution. Today, we’re going to in this video, we’re going to talk about an idea which we source with a real detector. In part one, we discussed a real X resource, and this ideal detector didn’t pass through. We were going to combine those two equations to formulate the final equation for an X-ray imaging resolution.
So again, if you want to just get the result, jump to part three. But for now, we’re going to discuss what happens when you have an idea which resource with a real detector. Now, in the previous video, part one, we discussed what happens when you have a real X-ray source that has a finite spot size. As you can see here, decorate the X-ray.
Photons are going to cross each other like that. Creating this penumbra I want you to detect or in that penumbra is what causes an issue or reduction of the resolution of your image. Right. We also found out that the lower the magnification, the Lauder impact is going to be because the source is going to be farther away from the sample and the sample is going to be closer to the detector.
So that penumbra is going to get smaller and smaller as the sample gets closer to the detector. Right. And we saw that the relationship is a function of the focal spot size given by F multiplied by M minus one, where MAG is the magnification of the system, which is your geometric magnification. Right. So the closer the object is or the sample we use to the source, the higher magnification, the larger this number, the larger is the resolution.
Right. So the worse off your image is going to be. As you can see here on the images, if you have a large spot size, the higher the magnification, the lower the quality is going to be. When you have a smaller spot size, you end up with the same effect. Right. With magnification reduces the quality of the image, but is more spot size is going to give you an ability to increase magnification while keeping some level of image resolution.
And that’s why when you have where we need higher magnification, we have to go with as more spot size, either a microphone because or and then a focus should be able to give you the sharp edges that you’re looking for in the image. In this analysis we’re going to do in this part to now is look at an idea x ray tube and a real detector, an idea x ray to like we discussed last time.
But one is one where the focus spot size is zero. So it’s a perfect x ray tube, which means that all the x ray photon tracks coming out of the source do not intersect each other. There’s no cross on that beam. All the traces are perfectly. There are parallel to each other because it’s a combined right, but they don’t cross each other, which is critical.
And here’s the detector. A real detector is one where the pixels have a finite size. So instead of infinite pixels like we saw last time, these attacks are actually has a finite number of pixels and the pixels have dimension, right? So each square here in the detector is representing a pixel, much like we saw last time. As we move the sample closer to the source, the projection of that sample onto the detector gets bigger.
In other words, more pixels are going to be representing. That same object does increase in magnification. So you can see magnification as a projection of our increased sample on to the detector. So we have a low magnification, low resolution, high magnification, and then we end up with a high resolution way because more pixels are looking at a specific or the same area or the same region of the sample.
Let’s look at it all the way. Imagine this corner of your sample in in a low resolution over a low magnification. That portion of your sample is being represented by a couple of pixels. If you look now at that same portion of your sample under magnification or higher magnification, you can see that it’s now being represented by a much larger number of pixels, thus increasing the resolution of your image, right, in such a way that the resolution of the image of the x ray image in the detector cells is equal to P, which is the size of your pixel divided by magnification.
The larger the magnification, the smaller irresolution number is going to be. The sharper image is going to be right. And that’s why if the image look cool, this is if the sample is right on top of the detector with no magnification. Right, Megs, you go to one you are resolution ends up being P, which is the size of the pixel, which makes a lot of sense.
So what we’ve done here is with the horizontal axis, we have magnification, the vertical axis, we have the resolution in on the detector. Right. Again, it’s an idea which is a resource here. And so the focus plot size is zero. And we looked at three different different pixel size that are somewhat typical into the text that we use.
Blue is 15 microns, orange is 100 micrometers and gray is 150 micrometer pixels. And as you can see, as you increase magnification, the resolution sharply drops where it gets better and better and better because more and more pixels are going to be representing that smaller portion of the sample. And when magnification is equal to one, right, as we know, magnifications equal to one, the resolution is equal to P, which is that point right there at the beginning with magnification is one.
The resolution is p as we would expect. Now what happens when you have a real x ray source in a real detector? Well, that’s a topic for the next part of this trilogy. So check out part three where we combine all the equations into the final x ray image resolution equation.
Dr. Bill Cardoso