In this final episode of our three-part series, Join Dr. Bill Cardoso as he combines the previous equations to enhance our understanding of X-ray image resolution.
Because when we explore the mechanics of X-ray imaging, we have to talk about image resolution. Three crucial elements drive it: focal spot size, pixel dimensions, and magnification. This interaction between focal spot size and source magnification also impacts image quality. Attaining impeccable image quality requires a balance of these factors, vital for precise diagnostics and analysis. For more information, also see how we achieved the perfect X-ray Image.
Welcome to another episode of X Ray University. This is the third of three parts where we’re talking about the image resolution for x-ray systems. The third parts were put it all together. Parts one, we dealt with a real X resource and an ideal detector. On part two, we looked at image resolution with an ideal X resource and a real detector.
So now we’re going to bring all those equations together to the final image, the resolution of an x-ray imaging system. Right. So let’s get into it. Part one We talked about what happens when you have an ideal detector. And by ideal detector we mount to detect with when pixels are really, really small. So zero size pixels, you end up with an infinite number of pixels on an actual detector.
And we determined that the resolution in that case is equal to F, which is the size of the focal spot size on the X resource times magnification minus one. So that resolution, we want the resolution to be a small number because we define a resolution as the size of this big number here onto the detector. So the smaller the AR, the better the image quality is going to be.
The sharper image are going to be. On the other hand, when we have an ideal X resource with where our physical, which is zero, and when we have a real detector that has pixels of a specific size, right, the not zero size pixels. So we have a detector with a finite number of pixels. You end up with a resolution that’s a function of p, and p is the size of each pixel divided by magnification.
So the larger the magnification rate, the better the resolution is going to be. Why? Because a larger representation of the sample is going to be shown by a larger number of pixels. And the more pixels you have, the better resolution is going to be. And the same way, the smaller the pixel size, the better the resolution is going to be, right?
Because the more, again, the more pixels you’re going to have to represent a specific size or a specific area of your sample. So all of those things make sense. So let’s finally bring it all together. That’s all we’ve been waiting for for so long now. So I’m super excited we’re here. Ideal detector we have that resolution is equal to B, which is the pixel size divided by magnification.
Ideal source. We’re going to have that the resolution is equal to F, which is the focus plus size on the source times magnification when there’s one and put it all together. Edit All resolution is going to be f mag minus one plus p divided by magnification. So what does that look like in a real system? So what we did here, we were showing you three results at the same time in orange, you have an ideal detector, right?
Where f equals to mag minus one, which is that straight line that we’ve seen before. There represents a system where you have infinite pixels. On the other hand, in silver we show you and when you have an ideal X resource, right where resolution is driven by the size of the pixel and magnification, and that’s the inverse plot that we’ve seen before, where the higher the magnification, the better resolution, the smaller the number is in.
The smallest resolution you can achieve is when you have magnification equal to one, which means that that pixel size is indeed the resolution of the system. Now, when you put it all together, what we see is that in that two-hour blue line here, what we see is that for small mag, you know, for small magnification, the detector drives the resolution.
Right. As we increase magnification, your resolution gets better and better and better. Right? Keeps getting better right now because we follow this great curve here gets better until the focal spots take over. And then we are back in this guy where magnification gets large enough that takes over and drives the resolution up. So decreases the image quality.
So in this case, just a guy. So he gets to have the numbers. We have a focus port of five microns with a pixel size of 100 microns. Pretty cool, right? So here, let’s play a little bit more with the numbers so you can see different equations and different impacts. This is a situation where we have a pixel size where we know detecting with 100-micron pixels and three different sources, two-micron spot size five, microscope size and 50-micron spot size.
And you can see the drastic difference. So this is 15, this is five and this is true microns, right? So right at the beginning when you have a little mag like we saw before, like intuitively you already know this. If you’ve seen the previous two videos and if you have and please go check them out. But if you’ve seen the two previous videos, intuitively, you knew that with a low mag doesn’t really matter what focus 47 is Source because your sample’s really close to the detector, right?
That’s what you see here as we’re really close to the detector, Max, low enough. There’s the impact of these focus spots is not as pronounced, but as we increase magnification, that’s when you see the huge impact that the focus port has on the image quality. So let’s do the opposite. Let’s now go ahead and pick one x-ray, one focal spot for the x resource employed play with different pixel sizes.
Right? So we have pixel size. Blue is 50 micro oranges. One of my crew and gray is 150 microns just like we saw before in a lot of these things all come together intuitively, the pixel size has a deep impact on low mag and not a major influence when you have high mag. Exactly, which shows here the influence of pixel size shows up in the low mag and as increased magnification they converge toward each other and there’s not much difference.
So here’s the final equation. R is equal to f, F is the focus spot size five microns, 50 microns, 33 microns, half a micrometer like front. And then a focal source’s magnification is a function of how the distance between the sample and the actual resource in the sample in the detector P is the pixel size on your detector in magnification shows up again.
And you know, we discussed this in a previous video and Tony is going to show us a link here where we talk about the quality of an x-ray image is a short blanket, right? You can improve in one area and something else is going to get worse. So magnification shows up in the denominator and the numerator.
So it’s a straight line and an inverse function. And that’s exactly what we see here, depending where you’re going to be, you have to pick specific features of the actual imaging system to optimize a specific application. There’s no one-size-fits-all, right? That’s why if you’re doing LEDs and you need low magnification because you want x-ray a bunch of LEDs in the panel at once, pixel size has more impact than necessarily the spot size and source because you’ve got to be working at low mag.
Now, if you want to look at the water board of a specific video or a wearable of a specific bear dye, well now you’re going to be working at high mag, which means that the spot size of your source really, really matter. So I hope these three videos have been interesting and informative. If you have any questions, please let us know.
We’ll be more than happy to address them here in future videos. Thanks for watching. And if you haven’t, please sign up for x-Ray University. I’ll talk to you later.
Dr. Bill Cardoso