Data Reduction with Skynet

Overview

In this exercise, you will learn about the basic steps of astronomical data reduction, the process by which digital images are calibrated for further analysis by removing sources of noise.

Submit the following via Blackboard:

  1. final_image your final image
  2. comp_image the comparison image
  3. your answers to the eight questions posed below (in red).

Part 1

Open and inspect the files in the following subfolders within one of your User Observations folders:

  • Raw Images: This is the preprocessed image, fresh off the telescope with no calibrations applied
  • Master Calibration Images: These are calibration images taken to remove sources of noise in the raw image. There are three calibration images,  corresponding to three different corrections made to the data:
    • bias image (or frame) corrects for readout noise, from the read-out amplifier electronics
    • dark frame corrects for thermal electrons in the image, i.e. counts that don’t come from photons but from thermal electrons in the conduction band
    • flat field corrects for differences in sensitivity across the chip, including obscuration by dust particles which look like big donuts because they’re out of focus!
  • Reduced Images: This is the final version of the image, processed for you by the Skynet algorithms, using the calibration images
  1. What is the typical counts in a pixel in the bias frame? 
  2. In the dark frame?
  3. In the flat field?
  4. What is the exposure time of the bias frame? 
  5. The dark frame?
  6. The flat field?
  7. What is the exposure time of the raw image frame?
  8. (See below)

Part 2

How to correct for the bias, dark, and flat using image math.

Image math refers to the fact that we can perform operations on the digital images on a pixel-by-pixel basis. The two basic types of operation we’ll work with are:

  1. Scalar:  A scalar operation is applied to all pixels in an image, e.g. every pixel value in an image is divided by 10 to create a resulting image.
  2. Image: Two images are involved in the operation, pixel-by-pixel, e.g. Image1 + Image2 means that the value of pixel (1,1) in the resulting image is the value of pixel (1,1) of Image1 plus the value of pixel (1,1) in Image2- same for pixel (1,2), pixel (1,3) and all other pixels.

Below, images (or “frames”) will be shown in boldface. Scalar values will be shown in italics.

For image reduction, we calculate:

final_image  =   (r – b – d*exp_scale)/(nflat)

where

  • r = raw_image
  • b = bias_frame 
  • d = dark_frame
  • exp_scale is a scalar = (exposure time of raw image)/(exposure time of dark current frame)
  • nflat = normalized_flat_field_frame = flat_field_frame/(mode of  flat field frame) Recall that the mode of a set of numbers (pixel values here) is the most frequently occurring value.

Step-by-step instructions

  1. Subtract the bias_frame from the raw_image using the Pixel Operations tool in Image mode.
  2. Check the exposure times of the raw_images and the dark_frame to determine if you need to scale the dark_frame to match the exposure time of the raw_frame. If your dark_frame is the same exposure time as your raw_frame, you do not need to scale it. If it is a different exposure time than your raw_frame, perform the scaling by multiplying the dark_frame by the appropriate factor, the exp_scale factor, using the Pixel Operations tool in Scalar mode.
  3. Subtract the (scaled if necessary) dark_frame from the result of step #1 using the Pixel Operations tool in Image mode.
  4. Inspect the flat_field_frame using the Display tool to determine the mode, the pixel value that is most common.
  5. Divide the flat_field_frame by the mode value using the Pixel Operations tool (Scalar mode).
  6. Divide the result of step #3 by the result of step #5 using the Pixel Operations tool in Image mode to get the Final image.

More information: A basic First-Aid procedure for CCD images

Compare this final_image (your reduced image) to the Skynet reduced image, by subtracting the two:

comp_image = final_image – Skynet reduced image (not the raw image)

8. Describe the appearance of the resulting image. What is the range of  count values in the pixels? (Hint: If it is not close to zero you should check your reduction process in the steps above.)