I am taking this week off from blogging to move across country. It’s an exciting and busy week, with lots of Physics involved, so I am sure traveling and moving will appear in the blog in some form in the coming weeks.
Someone I know had a CT scan last week. These scans are very commonplace these days, but I was wondering how many people know they work or even what CT stands for. I learned about this when was in graduate school and studying a method of imaging that is very similar to CT scans, but using laser light instead of x-rays.
These scans are usually called either CT (Computed Tomography) or CAT (Computed Axial Tomography) scans. The two terms seem to be used interchangeably. The ‘computed’ part is easy to understand – a computer is used to construct the final image. ‘Tomography’ refers to the method of taking multiple pictures of an object from different points of view in order to build up a two-dimensional image from one-dimensional pictures. ‘Axial’ means that these pictures are taken by rotating a camera in a circle around a center axis.
So how does this work in practice? While the method does not specify what type of light is used, doctors usually use x-rays for these scans. What are x-rays? They are part of the electromagnetic spectrum, which most of us just refer to as ‘light.’ We know all about the many colors of visible light because we can see them – from violet to red and everything in between. But as the wavelength of light gets shorter (and the frequency gets higher), the energy of the light increases. You can think of this as a wave on a string that oscillates faster and faster. As this happens, the wavelength (distance between peaks) gets smaller and smaller, like in the simple graphic below:
X-rays have shorter wavelengths & higher frequencies than the visible light we see. Much, much shorter. Here’s a graph of the different wavelengths of light and how they compare to visible light:
Light generally can not be used to measure things that are much smaller than the wavelength of that light (there are a few interesting exceptions). So x-rays can measure things that are much smaller, or with much better resolution, than microwaves or radio waves or even visible light. Of course, x-rays have wavelengths on the order of a nanometer – that is 100,000 times smaller than the width of a human hair! So that resolution probably is not needed for typical imaging in the body.
How do these x-rays interact with your body? A beam of x-rays is sent through the body, and some parts of your body absorb more of the light, and some absorb less. What you see on the camera on the far side is a shadow showing what parts of your body absorbed the light and which did not. Visible light is not good for this because it stops at your skin – you can see a shadow of your outside shape, but no features on the inside.
The fact that x-rays get absorbed throughout our bodies is one of the reasons that they can be so dangerous and why we should not be exposed to them too often. In addition to helping to diagnose cancer with CT scans, excessive exposure can cause cancer. Those high energy waves are absorbed by our cells and that energy can be used to alter and damage the cells. Short exposures of low doses are considered safe, but long term exposure can cause serious problems. Sadly, many of the early scientists who discovered and studied x-rays died of cancers caused by this research because they did not yet know of the dangers or how to protect themselves.
Now that we know what x-rays are, let’s get back to these multiple views. Why do we need to look at the body from different angles? This is the tomography part. If you have ever had a CT scan, you know that you need to lie still while an x-ray source and detector spin around you to get different views of your body. We know now that the pictures are basically shadows of your insides, so let’s look at some shadow pictures of some household objects to see how important it is to get multiple views.
Below are two pictures of two different objects in my house. The pictures were taken by shining a bright light on the object and then photographing the shadow created on the wall.
These two objects look to be almost exactly the same, and there is not a lot of information available on what the objects even are.
I then rotated the objects 90°, and these are the new shadows on the wall:
Now we can see that the object on the left is a paring knife and the object on the right is a serrated knife. Multiples views of the object give us more information about its shape and size in different dimensions.
Below are a few more fun shadow pictures from my house. As you look at the pictures, think about the following questions:
- Can you tell what the objects are?
- Do you need all the views to understand what you are looking at?
- Are some views more useful than others?
- How does having the multiple views help you better understand what you are looking at?
This last object is partially transmissive – light travels through the wings, but not the edges. This is similar to a picture of your body where the x-rays are not completely absorbed by some parts of your body. This gives us more information about the internal structure of the object being viewed.
So CT scans use x-rays, which are short wavelength light, and operate by taking multiple shadow pictures of our bodies at many different angles to reconstruct a full image. The picture below shows how this is done.
A computer adds up all the data on all those different lines, giving us a full circle cross section picture of the body. I will skip the details of the computer programming for now and just look at the results. I do not have any pictures myself of CT scans, but here is a really cool set of cross sectional scans of a human brain from Wikipedia’s page on Computed Tomography.
It’s really amazing that we can get so much information about how our body works from what are essentially shadow pictures. I frequently have students in my introductory Physics courses who are interested in being doctors. I think I should add a day on CT scans to the unit on light to see if I can convince them that Physics really is something useful for them to learn. If anyone out there has some more medical applications you would like me to explore in the future, I am all ears – there are tons of fun ones!
As Valentine’s Day approaches, I am reminded of all the people in my life that I love – my husband and daughter, my family and friends. While we do not generally participate in gift giving at this time of year, I know that some of you do and are probably wondering what the perfect gift would be for your loved ones. I have put together some suggestions of what people REALLY want for Valentine’s Day:
First, for pretty much anyone in your life that has any taste at all: Big Bang Theory, The Complete Fourth Season. This is the latest season of a great show about Physicists. But, who are we kidding, this came out last September, so we can only imagine that everyone you know and love already has this. But do they have:
For someone who likes practical gifts: A handheld sonic screwdriver for fixing things around the house.
For my family members out there who love to play cards: Great Physicists Playing Cards. One deck features great physicists from before 1960 and one the great physicists from after 1960. The set comes with a biographical booklet so you can learn about these great physicists while waiting for your partner to bid.
For those who light up your life, why not light up their life with a high power laser pointer? You can choose red, green, or violet laser light depending on your love’s favorite color. The green laser pointers are fantastic as pointers when out star gazing on clear night. (Note from the author: While these laser pointers are indeed very cool, they are also extremely dangerous and should definitely only be operated by a professional. For less dangerous, but equally cool green laser pointers, click here.)
And for those of you who prefer the more traditional gifts of flowers and chocolate, consider
- Eight Bit Flower Bouquet or
- Han Solo Carbonite Chocolate or
- Lindt Chocolate (If you’re going to get chocolate, at least get the good stuff!).
None of these ideas are perfect for your Valentine? Check out Think Geek’s Valentine’s Gift buying guide.
I love to watch my daughter’s eyes. She is so wide-eyed and expressive at this age. She also rarely blinks – my husband and I never noticed how seldom she blinks until we were out with some other kids around the holidays and the kids were having staring contests with her. I guess she just doesn’t want to miss anything.
Since I don’t normally stare into people’s eyes, I had never realized before what fantastic mirrors our eyes are, reflecting the world around us. There is something deep and metaphorical about seeing the world reflected in my little girl’s eyes, but I am going to concentrate on the more literal physical interpretation here.
My specialty in Physics is Optics – the study of light and the interaction of light with objects. This includes how images are formed in cameras and telescopes with lenses and mirrors. Eyes are really fascinating, as they can act as both lenses and curved mirrors.
While the eye’s main function is as a lens, imaging the world around us, they also act as partial mirrors. Mirrors reflect light back the way it came from, and lenses bend light as it travels through them. Eyes only reflect some light – most of the light travels through them to the back of the eye. This is good since my daughter uses this light to see the world! If you want to see a little more how the eye works as both a lens and a mirror, check out the picture below:
The three rays of white light hit the lens and most of the light travels through the lens, bending and crossing where an image is formed. A little bit of light bounces off and is reflected back towards the light source, though. This is the light we’ll concentrate on today.
So now that I’ve convinced you (I hope) that some light will reflect off our eyes, let’s look at how eyes work as mirrors. I will likely return to the eye as a lens (its main function) in a future post.
What happens when light hits a mirror? It reflects off the mirror, with the reflected angle the same as the incident angle. Below is the equation for the Law of Reflection and a picture to describe what that means, where is used to represent an angle (about 30° in the picture below).
The blue arrow represents light traveling toward the mirror, then reflecting back and off the mirror and traveling away.
Here is also a picture of rays of light – red laser beams in this case – bouncing off a piece of glass that is acting like a mirror.
So that is what happens when light hits a flat mirror. But my daughter’s eyes are curved, so when light hits the eye, it bounces off in different directions depending on what part of the eye it hits.
Images (what we see) are formed when light coming from an object like a light bulb hits the eye and reflects off. If the rays from the object come back together again somewhere, or seem like they do, we see an image. That probably does not make a lot of sense in words, so let’s look a picture (I like pictures today).
In this case the object is a red arrow. Light leaving the object and traveling directly to the right (the green arrow) bounces off the mirror and heads up and to the left. Light traveling from the object and hitting the center of the mirror/eye (blue arrow) bounces off and travels down and to the left. The green and blue rays of light never cross again, so no real image is formed.
But when I looked into my daughter’s eyes, I see images of the world around her. My eye sees these rays of light and thinks that they are coming from inside my daughter’s eyes. The dotted lines trace backwards where the light looks like it’s coming from and the dotted blue and green lines cross inside the eye. That’s where my eye thinks the image is. It looks like the world around my daughter is inside her eye.
You may also notice that the red arrow to the right of the mirror (inside the eye), is smaller than the original arrow. So, the world reflected in my daughter’s eyes looks smaller to me than the real world. Otherwise, how could it fit inside her eye?
So what do I expect to see in my daughter’s eyes? A picture of the world around her, but smaller.
Since her eyes only reflect some light, images of light bulbs (lots of light!) are the easiest to capture on camera. Really, capturing anything on camera is difficult since it is almost impossible to get an infant to stay still with her eyes open! Here are some pictures of reflections of the lights in our house in my daughter’s eyes, along with the light fixtures themselves for reference.
The bottom right picture has some other light reflections on the right side of her eye. Those are from the windows behind me, but are not as immediately recognizable as the chandelier.
Cool, huh? You can actually tell a lot about the shape of the eye just using these pictures. Eye doctors use the light that reflects off the front of our eyes to measure the curvature of the eye in order to get a good fit for contact lenses.
On a less physics-y note, as I was writing this, I was thinking of a song by Martina McBride…In My Daughter’s Eyes. You can listen to the song here if you’re interested. You can also find the lyrics on various websites online. It’s a lovely song for anyone with a little girl.