Calibration Frames

Calibration frames consist of dark, bias and flat frames that are used to remove various sensor and OTA defects from the data.  The better job we do with calibration, the better our data is and the more we can stretch it in post-processing to reveal faint details.  First, some definitions of the calibration frames:
  • Dark: This is a frame that is exposed with the shutter closed for the same duration and at the same camera temperature as the light frame to which it will be applied.  Needless to say, this also means for the same camera.
  • Bias: This is a frame that is exposed with the shutter closed at the same temperature as any light frames to which it will be applied.  The exposure duration is 0 sec.  Thus a Bias frame is a 0 sec. exposure duration dark frame.
  • Flat: This is a light frame that is exposed to capture the pixel-to-pixel sensitivity variation for a given sensor and the overall light fall-off of the OTA.  It must be taken at a low enough signal level to insure linear operation.


    Dark frames are subtracted from the light frames.  This subtraction removes pattern noise, a fixed artifact of a given sensor and dark signal, a false signal that increases linearly with exposure time.  To avoid adding noise to the data, an appropriate number of dark frames must be combined to make a master dark frame.  This typically reduced the noise by the square root of the number of frames being combined.  Based on the sensor, the camera operating temperature and exposure duration, it is possible to calculate the number of darks to be combined to reach a desired noise contribution as a percentage of total noise.  CCDAutoPilot provides such a calculator on the Settings page, Tools tab.

    Bias frames are handled like dark frames - they are subtracted from the light frame we are trying to correct.  If exposure times are short enough, time-matched dark frames are not required for correction since little dark signal will accrue. Thus for short exposures, a zero-time-exposure dark frame, i.e. a bias frame, can be subtracted to remove pattern noise from the short-exposure light frame.  The principal noise component of a bias frame is read noise.  The noise contribution from read noise is reduced by the square root of the number of frames being combined.

    Flat frames are divided into the light frames.  Note that they are not subtracted.  Mathematically, if S is the signal, F represents the loss/change in going through the sensor and OTA and L is the resultant acquired light frame, then L = F * S.  since what we want is the unmodified signal S, then S = L/F.  That is why the flat frame is divided into the light frame.  Noise from this division behaves differently than subtraction.  Noise from division combines as the reciprocal as the sum of the reciprocals.  (For electrical engineers, this is like resistors in parallel.)  An example may make this more clear.

    Let's assume we have a camera with a gain (g) of 1.4 and have exposed a number of flats to a level of 20,000 ADU.  Each flat will have a signal of 1.4 * 20,000 or 28,000e.  The SNR of such a flat is the square root of the signal, 28,000 in this case, or 167.  Now, let's assume we have a light frame that has a faint area SNR of 3, generally considered a minimum level of SNR for a very faint region.  1/167 + 1/3  = 0.339.  1/0.339 = 2.95.  Thus, our original faint area SNR was very minimally degraded - in fact one would be hard-pressed to measure the degradation!  If we combine 4 flats, we get a SNR of 334.  The resultant impact on our faint area SNR is to reduce it to 2.97.  Where flat SNR becomes important is on high SNR areas, areas of bright signal.  Assume we have a galaxy core that is 8000 ADU.  Its SNR, using the above discussion, is 106.  Our 4 flats would reduce this SNR to 80.  This is a more significant issue but may or may not impact the appearance of the resultant processed image.  

    One occasionally hears you need "a million electrons" of flats.  Let's see what that means.  In the above flat example, this would correspond to 1,000,000/28,000 or 36 flats.  Properly combined, our master flat would have an SNR of 167*6 or 1000.  The impact on our faint area SNR is 2.99 and our galaxy core is 95.8.  Clearly more flats are better but how much is enough?  That is left to you to determine.  I suspect for aesthetic imaging, 4 flats are more than sufficient but for scientific purposes, i.e. milli-mag photometry, more are required.

    To maximize flat frame signal-to-noise ratio, the target ADU exposure should be as high as possible while staying within the linear range of the CCD. CCDAutoPilot has a wizard to help you determine that target ADU.


    A "suitable number" of dark and bias frames may be taken at any time, assuming the ambient light level is low enough.  Typical CCD cameras are very sensitive and not very light-tight so if care is not taken, the dark frames might have a gradient from light leakage.

    Flat frame acquisition is a subject of much debate, discussion and opinion, which is beyond the scope of this discussion.  There are basically two types of flats - sky flats and artificial flats.

    Sky flats are taken at twilight with the telescope pointing to a specific area in the sky that has a minimum light gradient.  The gradient is a function of the FOV of the imaging system, the larger the FOV, the larger the gradient.  Also, during twilight, the sky brightness is constantly changing so exposure times must be adjusted to maintain a desired signal level.  Lastly, since there is a limited amount of twilight available, both the number of flats and the filter sequence must be optimized to get the needed flats.  Further, if you use a rotator to acquire data on both sides of the meridian, you need to determine whether your OTA's light fall-off or vignetting is sufficiently symmetrical after rotation or not.  If not, you'll need to take flats at both rotations, i.e. PA's.   The number of flats is generally limited by exposure and download times as well.  So there is a lot that needs to be considered.  While experimentation on the number of flats that can be acquired during twilight is required, all of the other considerations are provided automatically by CCDAutoPilot.

    Artificial flats are taken with the telescope pointing to a uniformly illuminated light source.  The design and performance of such an artificial source is challenging.  Such flats can be taken at the end of the evening while the environment is still dark.  Here there is less of a limitation on the number of flats to be acquired since the light source can be on as long as necessary.


    For more details, background and analysis, the interested reader may want to review my papers on various image acquisition topics.