Hands-On Universe, Lawrence Hall of Science, University of California, Berkeley

Research

or Hands-On Universe explained

Locating Supernovæ using Image Comparison

with the Hands-On Universe Software

by Adam A. Bier

To locate a supernova in an area of space, two images are needed: one with the supernova in it, and one taken of the same area without the supernova. In this example, the following images shall be used:

* Normal - no supernova

* Fake - the same image with a supernova artificially added.

For this example, I will use two 6X6 images as shown below. The numbers in the image represent the brightness of each pixel, measured in counts. The first step is to find some reference point that appears in both images. Here, I am using the 2X2 square outlined by a box. In a real image, this might be a nearby star or other celestial body that is extremely bright.

After I have located a reference, I now must get the value for the sky of images, the amount of ambient light that corrupts the images due to terrestrial interference and other stars. This is accomplished by using the Sky tool in the Data Tools menu. Once I have this value, in the case of the Normal image 5, I use the Subtraction tool in the Manipulation menu to subtract that number of counts from the entire image. I repeat this procedure for the Fake image, using 7 as the sky value. I now have the images shown below.

Now that I have compensated for ambient light, I must adjust for differences in exposure time between the two images. Using the Auto-Aperture tool in the Data Tools menu, I measure the total brightness of the reference body in both images. This is calculated as the sum of the count values for all four pixels in the body. Using the examples below, I determine the Normal to be 280 and the Fake to be 56 counts. By dividing 280 by 56, it is shown that the Normal is 5 times brighter than the the Fake. I now use the Multiplication tool in the Manipulation menu to multiply the entire Fake image by 5 counts. The result of this operation is shown below.

By comparing the adjusted Normal and Fake images, it is now clear where the supernova is located. In a more complex image, however, it would not be so easy to detect. To show the exact location of the supernova, I will now correct for differences in vantage points between the two images. Using again the Auto-Aperture tool, I get the exact coordinates for the reference point in both images. In the example, I will use the top left pixel of the square, located at E4 in the Normal and at D3 in the Fake. From this measurement, I know that the reference in the Fake is 1 pixel up and 1 to the left of the one in the Normal. I use the Shift tool in the Manipulation menu to shift the entire Fake image using 1 for the x axis value and -1 for the y axis value, resulting in two images that are identical except for the supernova in the Fake, as shown below.

Finally, I use the Subtract tool to subtract the Normal image from the Fake, so that every pixel value in the Normal is subtracted from the corresponding value in the Fake. The resulting difference file shows only the supernova, and can be made more clear by adjusting the Max and Min settings for the image. The image is shown below.