Interpret Read Noise Frame FFT
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Interpret Read Noise Frame FFTs
Now with a basic understanding of how to visually interpret FFTs lets go back and take a look again at our read noise frames. We know that a Fourier transform of purely random, Gaussian, noise will show a smooth variation of pixels throughout the FFT with one bright pixel at the center. Recall that you must first subtract the average of multiple bias frames from the target bias frame in order to isolate just the read noise in a read noise frame.
We also know that a line in an FFT represents a pattern in the original image perpendicular to the line in the FFT. Here again is a representative read noise frame from a QSI 504 camera cooled to ‑20C and its FFT.
QSI 504 Read Noise Frame QSI 504 Read Noise frame FFT
Compare the read noise frame above with the frame of mathematically generated Gaussian noise below.
(The histogram of the Gaussian noise frame below has been adjusted to approximately the same range of pixel values present in the QSI 504 Read Noise Frame)
Gaussian Noise Gaussian Noise FFT
The QSI 504 Read Noise Frame appears very similar to the frame of Gaussian noise but more importantly, their FFTs are almost identical . Both FFTs display a smooth range of pixels across the image with a single bright pixel at the center. This supports our earlier finding that the histogram of the QSI 504 bias frame displayed a smooth Gaussian distribution. The FFT of the read noise frame shows that the QSI 504 camera introduced no measurable periodic read noise.
Here again is Read Noise Frame 3 with its FFT to the right:
Read Noise Frame 3 Read Noise Frame 3 FFT
With our knowledge of visually interpreting FFTs, we can now reach some conclusions about the read noise in Bias Frame 3. It was shown earlier that Bias Frame 3 had a non-Gaussian distribution of pixel values, but the histogram alone couldn’t tell us anything about the nature of the noise.
Compare Read Noise Frame 3 to the QSI 504 Read Noise Frame. You can see that Read Noise Frame 3 isn’t as smooth. There are brighter and darker pixels scattered throughout the image. This is likely the result of the non-Gaussian distribution “shoulders” seen in the histogram of Bias Frame 3, but other than some extra dark and light pixels, the structure of the noise is difficult for the eye to see. The structure of that noise becomes easily visible in the frequency domain. The FFT of Noise Frame 3 reveals a series of strong vertical lines running through the image. These vertical lines indicate horizontal noise of various frequencies in the original image.
Recall from the sine wave FFT examples that dots or lines further from the center indicate periodic noise of higher and higher frequencies. The type of noise seen in Bias Frame 3 can often be seen as a series of visible lines running horizontally through images. Most importantly, this non-Gaussian noise won’t be reduced by combining multiple images.
Reducing Noise by Stacking Images
The way astronomers typically deal with noise in their images, after calibrating the raw images with dark frames, flat fields and bias frames, is by “stacking” multiple images. Stacking multiple images with a pixel-by-pixel average or median combine tends to increase the signal to noise ratio (SNR) of the combined image. This is because random variations in pixel values tend to cancel each other out when multiple images are combined, resulting in a smooth background, while non-random pixels, the bright objects in the night sky you’re trying to take a picture of, reinforce each other getting you closer to a true representation of the patch of sky you’re imaging.
The benefits of stacking images can be clearly seen by comparing an individual bias frame to a pixel-by-pixel average of multiple bias frames. Below left is an individual bias frame from a QSI 504 camera. To the right is an average of three bias frames taken at the same time.
QSI 504 Bias Frame QSI 504 Bias Frame (Avg stack of 3)
The pixel values in the individual bias frame range from 93 to 139 with a standard deviation of 5.0. The pixel values in the average combined image are reduced to a range of 101 to 128 with a standard deviation of only 2.9. Adding more bias frames would further smooth the results allowing you to get arbitrarily close to the true bias of the camera. In some cases, doing a “median combine” rather than an “average combine” may yield better results. This will be discussed in the section on "How to Obtain a Proper Bias Frame."
The fundamental problem with periodic noise, as seen in the FFT of Read Noise Frame 3 (repeated to the right), is that, by definition, it isn’t random. Unlike random noise, periodic noise won’t be reduced by combining multiple images. When multiple images with periodic noise are combined, the noise patterns are reinforced, exactly like signal. Image processing can’t completely eliminate this type of non-random noise without simultaneously eliminating some of the information you want, the signal.
Any noise added to a CCD image reduces the signal to noise ratio and the dynamic range in your final images. Periodic noise, not only limits the dynamic range, producing lower contrast images, it also adds visible patterns that are almost impossible to remove from your images in subsequent image processing. The more periodic noise present in an image, the more visible it becomes and the harder it is to remove.
Producing the best final images always begins with the very best, lowest noise, source images.
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