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Canon Digital Rebel (300D) Noise Analysis

This document summarizes my attempt to characterize the noise of a Canon Digital Rebel (300D) as a function of ISO and Exposure Time. This is part of an ongoing attempt to answer the age-old question, "How long, and at what ISO, should each exposure be in order to maximize the Signal-to-Noise Ratio (SNR) of an astrophoto?".

Before going any further, please note that this entire analysis was carried out at room temperature (roughly 72F), and I fully expect that these results might be significantly different if carried out at colder temperatures. That's on my "to be investigated" list.

Here is the basic methodology. I took eight "dark" (lens cap and viewfinder cap in place) exposures at all ISO settings (100, 200, 400, 800, 1600, 3200) and at several representative exposure lengths (0sec, 15sec, 30sec, 1min, 2min, 4min, 8min). Note that the 0s exposure was actually a 1/4000'th of a second exposure, the shortest the Digital Rebel allows. This 0s exposure was meant as an ISO-specific "offset" frame, figuring that any noise generated at such a short exposure in complete darkness was the result of biasing of the sensor array and/or read noise.

The following graphs show the RAW noise as a function of exposure length and ISO. The first is the RAW frames straight from the camera, converted to a CFA file in IRIS where the sigma (standard deviation) was computed (as an average of the sigma of each of the eight sample frames). The second is after "dark frame calibration", using the following processing chain in IRIS:

  1. Compute an offset frame from the eight 0s exposures.
  2. Compute a dark frame from the eight Ns exposures, using the offset frame computed in #1.
  3. Subtract the offset and dark frames from the RAW frames, resulting in "Calibrated" frames.
  4. Compute and average the sigma of the Calibrated frames.

Here's before calibration:

Figure 1: Raw Noise, uncalibrated, unnormalized.

 

And here's after calibration:

Figure 2: Calibrated Noise, unnormalized.

 

My interpretation of Figures 1 and 2 is as follows:

Note that these first two graphs are un-normalized; i.e., there's no compensation for ISO setting or exposure length. More interesting is to normalize the Noise by ISO and Exposure length, since one assumes the "signal" will be proportional to ISO and Exposure due to linearity of the CMOS sensor, and what we really seek is the Signal to Noise Ratio (SNR). Here are the "before" and "after" calibration graphs, now normalized for ISO and Exposure Length (and normalized so that ISO 1600 at 480s would result in a value of "1"):

Here's before calibration:

Figure 3: Raw Noise, uncalibrated, normalized.

 

And here's after calibration:

Figure 4: Calibrated Noise, normalized.

 

My interpretation of Figures 3 and 4 is as follows:

Since one of the advantages of DSLRs is getting a full-color image in each frame, it's interesting to scale the noise sigma in proportion to the "scale factors" typically applied during image processing to see how that affects the total noise. I use factors of {1.96, 1.00, 1.23} for Red, Green, and Blue respectively, when processing, so I scaled the noise sigma's in those channels by those factors and then combined the result to get an "RGB Balanced" noise estimate. The result is shown in Figures 5 and 6.

Here's before calibration:

Figure 5: RGB Balanced Noise, uncalibrated, normalized.

 

And here's after calibration:

Figure 6: RGB Balanced Noise, calibrated, normalized.

 

My interpretation of Figures 5 and 6 is as follows:

I'm still struggling with how to compute "available dynamic range" at the various settings, but part of the answer would seem to lie in how much of the A/D converter's number space is taken up by noise, especially at higher ISO and longer exposure lengths. This next graph provides the "mean" of the pixel values of the (uncalibrated) dark frames at the various settings:

Figure 7: Mean pixel value, uncalibrated, unnormalized.

 

Figure 7 makes my brain hurt:

Comments? Please post them to the Yahoo digital_astro list (preferable) or .