Defocusing is a technique used to capture photometry data by researchers to achieve a higher signal-to-noise ratio and therefore a smaller error in data. Since the light is spread over a much larger area of pixels on the CCD chip, the exposure time can also be increased, which helps to “smear out” the images and gather more photons. My research group wanted to try and quantify this, as well as do some observations of exoplanet transits. The theory is that when the light is only on a few pixels, variance and distortion on any of those pixels has a large effect on the data but with defocusing, the light is spread over a much larger pixel area so that if a few pixels are varying in any given image, the data set as a whole isn’t effected that much. Exoplanets are great for this type of observation since we are looking purely at the amount of light and no visual resolution is needed.
Our research was done at the Cal Poly State University observatory, a 14 inch Meade LX-600 ACF telescope and an SBIG CCD camera. We were able to get three data sets: one for WASP-59b (13th magnitude host star) that was in focus, and two for WASP-33b (8th magnitude host star), one in focus and one out of focus. PyRAF was used for the data reduction and differential photometry process, but some custom tools were written to deal with the data sets. A tool called “daofind” creates lists of stars that meet certain criteria in each image of the data set so that you can use these stars to calculate photometric values such as magnitude and SNR. Unfortunately, it is not very good at keeping “found stars” consistent between images. Star #1 in image #1 is not necessarily star #1 in image #2, and so on. This is not a good problem when there are hundred or thousands of images. The tool I wrote compares all of the stars found in a given image against the stars from the previous images and if the x, y, and magnitude all change less than a certain threshold, it considers it to be the same star. This aligns the data that gets dumped and makes it easy to complete photometry.
These are some of our resulting light curves along with the binned curve that was used to estimate the transit start/stop times (marked with the yellow lines) and depth of the magnitude delta.
We obtained some great measurements of the transiting exoplanets. The defocused data was much easier to reduce and we did not throw out a single data point. With the other two focused runs, many data points were missing for comparison stars or the primary target and had to be omitted. Keep in mind, these graphs look differently because the data from WASP-33b focused contained about 2500 images since they had to be taken at 2.5 second exposure times. Focusing all of the star’s light onto a few pixels means that saturation is reached quickly, so this was the maximum exposure time that we could use. Defocusing allowed us to increase the exposure time to 15 seconds, so the data is naturally less noisy and there are far fewer data points in the graph. Defocusing also increased the SNR by a factor of 12.5 to 20.
While we could not draw a direct conclusion about the defocusing technique being the factor that made the data much better, the defocused data set was much less variant over the period of the transit than either of the two focused data sets and had a much larger SNR. We need to get more telescope time in order to draw a better and more quantitative result, but so far this looks very promising.