"The Process For Examining Pluto Images"

Marc Buie - April 20, 1996
Planet Advocate for Pluto

    Ed note: the text for this messages comes largely from Marc Buie's homepages at:

http://www.lowell.edu/users/buie/pluto/analysis1.html

This story is much better understood with pictures, so if you have Web access we suggest you go straight there. We are reprinted the gist of the story here without pictures for those without Web access. Anything between XX and XX is a description of the image that goes with the story.

GETTING STARTED
The first step in checking out these new pictures of Pluto is to first figure out what we're looking at. We can calculate what part of Pluto is visible. We can calculate where Pluto's satellite, Charon, will be and how far apart they are. We can also figure out how big we expect them to be in the image. Once we know what to expect for Pluto, we then need to understand the actual images. HST is a spacecraft and doesn't know anything about "up" or "down" like we do here on Earth. That means the pictures can be rotated to just about any orientation. These steps of predicting and then understanding the pictures is called navigating. It is the first thing that must be done to examine our data.

PLUTO AT THE TIME OF THE IMAGES
From what we know about the orbit of Pluto around the Sun and the orbit of Charon around Pluto, here are a few details: 


        Distance from Sun          29.887 AU   (4,471,000,000 km)
        Distance from Earth        29.689 AU   (4,441,000,000 km)
        Pluto diameter              0.107 arc-seconds   (2300 km)
        Charon diameter             0.055 arc-seconds   (1180 km)
        Pluto-Charon separation     0.852 arc-seconds (18,335 km)
        Sub-Earth latitude         19 degrees  
        Sub-Earth longitude       201 degrees
The unit arc-seconds is a measure of the angular size of an object. When you're standing outside where you can see the horizon, from one horizon to the other through the point directly overhead, that is 180 degrees or half a circle. Our own moon appears to be 0.5 degrees in diameter. The degree scale is chopped up into smaller bits just like time is. There are 60 arc-minutes in one degree and there are 60 arc-seconds in one arc-minute. That means our moon is 1800 arc- seconds in diameter, nearly 17,000 times as big as the apparent size of Pluto! Of course, our moon isn't really that much bigger. It only looks bigger because it is much, much closer.

The sub-Earth latitude and longitude are coordinates on the surface of Pluto. 0 degrees latitude would be on Pluto's equator. At 0 degrees longitude, Charon is directly overhead. If you were standing on Pluto at these coordinates, the Earth (and Sun) would be directly overhead We can only see one half of the planet at a time and these coordinates tell us which half is visible.

STARTING TO EXAMINE THE PLUTO IMAGES
The camera we are using takes pictures with little square picture element detectors called pixels. The format we used is a 512 by 512 pixel array. Each of these pixels measures 0.01435 arc-seconds across. Here's some more information about what we see in the images: 

Full image width and height  7.4 arc-seconds

          Pluto diameter               7.5 pixels
          Charon diameter              3.8 pixels
          Pluto-Charon separation     59.4 pixels
You can see from this that the area of the image we care about is only a tiny fraction of the entire image. So, we're looking for two small spots of light in the full image and that's just what we see.

XX There is a photo of Pluto and Charon taking up just a small part of the overall picture on Marc's Web page; there are also a lot of tiny dots throughout the image. XX

You can see Pluto and Charon in these images, Pluto is the brighter of the two. The rest of the image is just noise, which just looks like random speckles.

THE VISIBLE IMAGE OF PLUTO
The image I start with is a 31x31 pixel extraction from the original image that is centered on Pluto. The outer parts of the image are all black (corresponding to the space which surrounds Pluto), so I concern myself only with a 13x13 pixel grid corresponding to just Pluto data.

I've also drawn a figure of a globe which matches exactly the known size of Pluto. When I put the figure with the Pluto data, the images from the actual HST data extend past the edges of the figure (the known size of Pluto).

Are you surprised at this? I bet you would have thought that the size of Pluto and the size of the image we took would be the same. But if you look closely at our image, you see that there are pixels outside the edge of the wire-frame globe that are not black. Where's the light coming from for these pixels? This light does not come from Pluto's atmosphere. It also isn't from an incorrect size for Pluto.

The answer is that the image is blurred by the finite resolution of the Hubble Space Telescope. Does that mean HST is not working right? Not at all. Every telescope has some limit beyond which it cannot be pushed and HST is no exception. That limit is known as the diffraction limit and is governed by fundamental properties of light. What you see in this picture is that Pluto is just barely bigger than the diffraction limit of HST. As a result, Pluto is blurred out, ever so slightly. The next step will be to remove the effects of this blurring.

WHAT IS A PSF?
The acronym, PSF, stands for Point-Spread Function. The name comes from what it does. If you put a point source image into the telescope, you never get a single point out the back end. What's a point source? Well, it's one of these special mathematical constructs that doesn't really exist. A point source is something that is infinitely small but of finite brightness. We usually use stars as point sources. They aren't infinitely small, but they are so far away that they are usually indistinguishable from a point source.

So you put a point source into the telescope and you get out..., that's right, a point-spread function. Another way to think of this is that a telescope (or any camera for that matter) will blur the image it sees. The blurring function is the PSF. Here, take a look at the PSF for HST with its Faint Object Camera.

XX It looks like a bright pixel surrounded by less bright pixels, surrounded by even darker pixels, surrounded by blackness. XX

The image on the left is a "normal" view of the PSF. I say normal because I haven't played any image processing tricks to change how it looks. You can see the one pixel in the center is the brightest and its nearest neighbors are considerably fainter and the rest appear black. The image on the right is a stretched version that brings out detail in the darker areas. This PSF show the blurring that is present in the Pluto image that keeps it from looking like a nice sharp disk. The next step in processing the Pluto data is to remove this blurring from the image.

REMOVING THE PSF
The process of removing the PSF is easy to visualize but harder to do. If you write the problem like one of those 1st grade math problems it looks like this:

Pluto BLURRED_BY psf = Image

"BLURRED BY" is similar to an operation like addition or subtraction (its formal term is "convolved with"). "Image" is the image of Pluto that we got from HST. "Pluto" is the image of Pluto that we want to get. We know "psf", "Image", and how to blur the image. All we need to do is fill in the blank and find the Pluto image that satisfies this equation.

I have a program developed for the 1994 Pluto observations that allows me to solve this equation. This program takes many hours to run and get the answer. I also discovered a minor flaw in my older program when running these new images through. These two things when put together meant this step took over four days for me to get the answer out.

The following pictures show the above equation as images:

XX Three images are shown of Pluto, PSF and the Image XX

If you look really careful, you will notice that the Image on the right is not the original image earlier on this page. It is very, very close to the same image but not exactly.

CONVERTING TO A MAP
What we really want to know is where on Pluto's surface are all these light and dark patches. Let's zoom in on the Pluto picture from the previous step. I'll also draw the wire frame globe on top of the image so you can see where things are. Remember, the yellow line is the equator and the orange line is 180 degrees longitude.

XX Picture of the images overlaid with grid of planet XX

The next step is to unwrap the image of the sphere and re-display the image as a flat map. You can almost see how you could read off the brightness at a given latitude and longitude using the gridlines as a guide, then on the map you put down that brightness. The rectangular image below is the result of reprojecting the image onto a map.

XX Flat map; this map has changes in contrast with jagged, pixelated edges) XX

All the black areas (just over half this map) are regions that are on the back side of Pluto when the picture was taken. You can see now why we would have needed all three of the LHST orbits to make a complete map. Now, I bet you're thinking this map (and the above image) look pretty strange. These light and dark patterns look something like farm plots would here on Earth. (Ed note: Marc is referring to the jagged edges). This apparent structure is caused by how I set up the computer programs and not by anything on Pluto itself. The next step is to turn this into a more realistic portrait of the surface. The next image comes from smoothing out the blocky map to remove these artificial edges.

XX A similar image appears but without the jagged edges XX

This is about as far as we can go with our new data by itself. The next step is to compare this against the map from 1994.

HAS PLUTO CHANGED SINCE 1994?

In case you're getting lost, this is where we've been trying to get to all along. We took a picture of Pluto to see if it is still the same or different than when we looked in 1994. We need to start with a review of the 1994 results.

In 1994, Dr. Alan Stern (Southwest Research Institute), Dr. Laurence Trafton (University of Texas, Austin), and myself teamed up to create a global map of the surface of Pluto. We took a total of 12 images at 4 distinct longitudes in visible light and 8 images in the ultraviolet. Our results were announced in March 1996 and you may have seen some news report on the maps.

XX Pictures of the entire map of Pluto (1994) and also the new halfmap from 1996 (darker then 1994 map) XX

Take a moment to look at these two maps. Are you confused yet? At my first look I was really confused too. At first glance, these two maps don't really look all that much alike, do they? Did we just discover something changing on Pluto? If you haven't been reading all my journals, you might want to review how I attack problems like this. Although we are looking for change, these photos reveal that there is an enormous difference and I just don't believe it.

Before we get too far, let's look at the data in a different way. These images show the maps wrapped onto a "globe" at the orientation as when the new image was taken.

On the left, is the 1994 map image and on the right is the 1996 map image. This still looks confusing, maybe even more confusing. The 1996 image looks really dark. Why? Well, to display an image, I usually set the display to show the brightest area as bright white. In the 1996 the brightest area is a very small region pointed to on the lower left part of the image (at the very edge of the sphere).

Now, here's where my judgment comes into play. The process of pulling out the "perfect" image of Pluto works best in the center of Pluto. Near the edge of the planet, the extraction is not as accurate. So I want to adjust the map to make those really bright areas near the south pole a little darker so they aren't as prominent. XX The new image is adjusted to be much brighter then before XX

I think this looks much better. The change I made was relatively small but it let's us see the other areas of the map much more clearly. Here's where it gets interesting. The basic appearance of the maps is similar. Both maps show a cluster of three bright regions near the center. Just left of center both maps show a dark region. In fact, the similarities are pretty strong. However, there are differences. The north pole is darker in the new map, the south pole is brighter. The change in the south is quite strong, especially considering that I made two small areas darker in the previous step.

CONCLUSIONS
The question now is: "Has Pluto changed?" Or, is this process of getting maps from HST images not entirely repeatable? These questions can be addressed by examining how we got these images and by looking at past work on Pluto.

At the north pole, there are quite a few previous maps that predict its brightness. Half of them say the north pole is dark and half of them say the north pole is bright. All the work was well done but the answer still eludes us. The lack of agreement between previous work means we shouldn't get too excited about a lack of agreement in the HST maps.

The south polar area is more interesting. I'm still not entirely convinced that these differences are due to a real change on Pluto. However, this new map does makes me wonder. This is an area where I'd expect to see change. If we repeat this experiment and see it continue to brighten then I'd say we are finally seeing a change in the surface. If a repeat shows a dark area again, then I'd say that we have the same problem in the south as everyone has had with the north pole.


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