PRELOAD IMAGE UTILITY (BIAS OR OFFSET)

The Bias is included in the Black. If the Black was taken with the same exposure time as the deep sky image, it do not not use the Bias in the preprocessing of raw deep sky images. Otherwise, it must be used. It is important to understand this fact well so as not to use the Bias unnecessarily in the preprocessing of raw images because each preprocessing image is not perfect and retains a certain level of noise which is added to the image of the deep sky.

To fully understand this fact, we will take as an example what happens on a single pixel. Let's say the Bias on this pixel is worth 20 units. Black with an exposure time of one minute is worth for example 200 units. With an exposure time of 2 minutes it is equal to 400 units (it should be noted that in reality increasing the exposure time does not have a perfectly linear effect on the pixels but, to simplify the example we will apply it linearly). If the Black and the deep sky image were taken with an exposure time of 2 minutes, the pixel of the Black image will have the value of 420 units (400 for Black and 20 for Bias). When subtracting Black from the raw deep sky image, the Bias will be perfectly subtracted (20 units in the raw image - 20 units in the Black image). So if the black was taken with the same exposure time as the raw image, the Bias should not be used.

Now let's take a look at what happens when the black and the raw image were not taken with the same exposure time. Black was taken with an exposure time of one minute and the raw image 2 minutes. The Black image is therefore worth 220 units (200 for Black and 20 for Bias). When the preprocessing software uses this Black to preprocess the raw image, it will increase the Black by 200 units to match the exposure time of 2 minutes. It will also increase the value of the Bias by 20 units which will give a total value of 440 units for the Black image (400 for the Black and 40 for the Bias). Considering that the Bias always has a constant value regardless of the exposure time (20 units in this example), when subtracting Black, the Bias will not be correctly subtracted (20 units in the raw image - 40 units in Black image).

To correct this problem, we are going to subtract the Bias from the Black image. The Black image is then worth 200 units (220 units - 20 units for the Bias). The Black therefore no longer contains the Bias. When the preprocessing software uses this Black to preprocess the raw image, it will increase the Black by 200 units to match the exposure time of 2 minutes. Black is therefore worth 400 units. After the subtraction of the Black, the preprocessed image therefore still contains the Bias. You will then have to use the Bias to subtract it from this preprocessed image (20 units in the preprocessed image - 20 units in the Bias image). So if the black was not taken with the same exposure time as the raw image, the Bias must be used in the preprocessing.

To avoid any confusion in the preprocessing of deep sky images, here are the formulas to use in the two possibilities mentioned above:

If the Black was not taken with the same exposure time as the deep sky image :

  • Calibrated image = (Raw image - (Black - Bias) - Bias) / (PLU - (Black - Bias) - Bias)

If the Black was taken with the same exposure time as the deep sky image

  • Calibrated Image = (Raw Image - Black1) / (PLU - Black2)

Black1 = Same exposure time as each of the raw images

Black2 = Same exposure time as each of the PLU images

By examining the two formulas, we realize the interest of taking blacks with the same exposure time as each of the deep sky images, because each preprocessing image is not perfect and retains a certain level of noise which s' adds to the image of the deep sky. Indeed, by using the first formula, we use 4 times the Bias, while in the second formula, we do not use any Bias. The calibrated image will therefore be less noisy by using blacks with the same exposure time as the deep sky images (and other blacks with the same exposure time as the PLU images).

Richard Beauregard

Sky Astro - CCD

Revised 2021/01/04

reference:

The New CCD Astronomy, Ron Wodaski, New Astronomy Press, pages 244 and 245.