• August 26, 2013

    Measuring the Size of ISON's Nucleus: Pixelization

    by ISON Blog Guest

    Welcome to guest poster Dr. Jian-Yang Li. Dr. Li is a research scientist at the Planetary Science Institute and a comet expert. His interests include photometry of asteroids and cometary nuclei, physical properties of cometary nuclei, and the connection between comets and asteroids. His expertise is in photometric analysis, especially from high-resolution data obtained from the ground and returned by spacecraft. He is one of the first few astronomers who applied disk-resolved photometric analysis to cometary nuclei, and found possible connections between the photometric properties and cometary activities. Dr. Li has been actively involved in Deep Impact and Dawn missions.


    We observed Comet ISON with the Hubble Space Telescope on April 10. One important goal of our observations was to measure the size of its nucleus. We need to know the size in order to predict what will likely happen this Thanksgiving when the comet goes through the extremely hostile environment near the Sun, baked by the Sun’s heat to thousands of degrees and tossed by the Sun’s strong gravity.

    It is relatively straightforward to measure the size of an asteroid. By gauging the brightness of an asteroid in an image, one can calculate how large the asteroid has to be by assuming its reflectivity and using some simple physics laws. For comets, however, the presence of their comae significantly complicates the problem. To understand the process, we need to understand two key concepts: pixelization and point spread function. Today we will take a look at pixelization, and in next week's post we will look at point spread function.

    Almost everyone uses digital cameras nowadays, and everyone knows what a pixel is. Let’s take one step forward and see what that means for astronomical objects in astronomical images.

    Astronomical images are no different than any other images. So let’s take an image as an example. This is a picture of a beautiful lawn in front of mountains and blue sky. There is a rock on the grass. Our task is to measure the size of the rock.



    Everyone knows how to measure the size of the rock — if you know how large the view is. But what if the rock is small and you cannot see it clearly, as in the image below?



    I put a box around the rock so you know where it is. Can’t see it well? Let’s blow it up.



    I also took away the color, because astronomical images are always taken in a single color at a time. Now everyone sees pixels! Great. Still not a problem to measure how big the rock is as long as you know that 1 pixel = 10 centimeters, for instance. In this case, the rock will be about 200 centimeters, or 2 meters, across. A huge one. But now we have a little bit of a problem: we can’t see the edge of the rock clearly, because any details smaller than a pixel are lost in the pixelization. So the actual size of the rock can’t be measured to be more accurate than at least 2 pixels, or 20 centimeters.

    Now what if it is an even smaller rock, say, 8 centimeters across, so it is smaller than 1 pixel. Then it will look like this image:



    Does it look anything like a rock? No. It is just a bright pixel with the brightness of the rock against the darker background. In this case, we can only say its size is less than 10 centimeters, the size of 1 pixel. And we don’t know anything about the rock’s shape. This is what we get when we look at cometary nuclei, which are almost always smaller than 1 pixel in any astronomical images taken either from the ground or from Hubble Space Telescope. In our images of ISON, 1 pixel = 123 kilometers.

    What happens if the nucleus is smaller? The image will look like this:



    You can see that the brightness of the center pixel is getting darker and closer to the background — blending into the background. Still smaller? Look at this:



    Now the rock is so small that the brightness of the center pixel is so close to the background pixels that we cannot tell whether the slight brightness of the center pixel is noise or from the tiny rock. At this point, the rock is lost in the noise.

    This is exactly what happens when imaging a cometary nucleus. The rock is the nucleus, and the grass background is the coma. If the nucleus is big, then we can see its brightness above the background coma. If the nucleus is too small, it will be lost in the background coma.

    But then how can we still measure its size? You guessed it — from how much brighter the center pixel is than the background.

    First, we need to know how bright the background is in the center pixel. Using our example of a rock on grass, we look at the image and say: the brightness of the grass doesn’t change across the image, so let’s assume that the background has the same brightness in the center pixel. For comets, the coma never has constant brightness, as you can see from the beautiful images of ISON. So we look at the coma, and generate a model to best describe the brightness distribution of the coma based on some physical assumptions and laws. Then, based on the model, we estimate how much brightness in the center pixel is due to coma, and how much brighter the center pixel actually is. The difference is the total brightness of the nucleus.

    As you can see from the example of a rock, the accuracy of size measurement is limited by how large the object is compared to the size of a pixel, how noisy the image is, and how accurately we can predict the contribution from the coma in the center pixel. While every comet is different, we cannot control the last factor. But we can use a camera with very high resolution (i.e., very small pixel size) and very low noise. This is exactly why we used the Hubble Space Telescope for our observations.

    Join us next Monday for my explanation of point spread function, and how it further affects our observations of ISON’s nucleus.