Calibration frames explained: bias, darks, flats, dark flats and the math that combines them

What each frame records

Every raw light frame carries three signals besides the sky. The Siril documentation and the AAVSO photometry guide describe one calibration frame for each.

• Bias (offset). An electronic offset that keeps the analog-to-digital converter’s input positive. You shoot bias frames with the shutter closed at the shortest exposure the camera allows; Siril cites 1/4000 s on a modern DSLR. Siril recommends a synthetic bias for modern sensors, whose offset is very uniform: a constant level typed as an expression, such as =2048 or =64*$OFFSET when the FITS header contains an OFFSET keyword. Siril notes that this saves disk space and minimizes noise in the final image.
• Darks. The thermal signal, which Siril describes as proportional to temperature and exposure time. Shoot them with the shutter closed at the same exposure and ISO or gain as the lights, at about the same temperature. Darks also contain the bias.
• Flats. Telescopes do not illuminate the sensor evenly, dust casts shadows, and photosites differ in sensitivity. Each light is divided by a master flat made from evenly lit, unsaturated frames.
• Dark flats. Siril’s model ignores the dark current that builds up during the flats’ own exposure. When that signal is not negligible, you need dark flats taken at the flats’ exposure, or at least a measurement of their level.

The calibration equation

Siril writes the whole operation as:

L_c = (L − D) ÷ (F − O)

L is the light, D the master dark (dark current plus offset), F the master flat and O the offset, from a master bias or a synthetic level. To show why that combination is the right one, Siril models a background pixel at position x across a frame of width W:

L = S(x) + d·t + o   D = d·t + o   F = K·S(x) + o   O = o,   with S(x) = a − b(x − W/2)²

S(x) is the vignetting profile, d·t the dark signal, o the offset and K the flats’ brightness factor. Substituting gives L_c = 1/K at every x: the spatial term cancels. Siril adds that no other combination removes it, and only the full equation also removes dust shadows.

Worked example with Siril’s numbers

Siril’s own parameters are a = 200 ADU, b = 0.0003 ADU/px², a dark rate of 1 ADU/s, a 10 s exposure, an offset of 2048 ADU and a 1000 px wide frame. The sky signal is then 200 ADU at the center and 125 ADU at the edge. Dividing the corrected edge value by the corrected center value shows how flat each method leaves the frame (computed; the results below do not depend on K):

Method	Edge ÷ center	Result
L − D (darks only)	0.625	edges 37.5 % darker, vignetting untouched
L ÷ (F − O) (flats, no darks)	1.547	edges 55 % too bright, inverse vignetting
(L − O) ÷ (F − O) (bias and flats)	1.029	nearly flat; the 10 ADU of dark signal remains
(L − D) ÷ (F − O)	1.000	flat

The second row is the trap Siril warns about: dividing by a flat without removing the offset from the light overcorrects, because the 2048 ADU pedestal in the light does not scale with the vignetting. The third row explains Siril’s practical advice: if you have no darks, subtracting the offset from the lights gets you close.

What has to match

Frame	Must match the lights in	Source
Bias	gain, offset, binning, readout mode; new set after a change of temperature setpoint or gain	AAVSO
Darks	exposure (or a scaled master), ISO or gain, offset, temperature, binning	Siril, AAVSO
Flats	focus and optical train, binning, gain, offset, temperature	AAVSO
Dark flats	the flats’ exposure, gain and temperature	Siril

Siril stresses the offset setting: it must be the same for darks and lights and for bias and flats, or flat-fielding will most likely fail. AAVSO asks for flats at the focus of the lights so the “dust donuts” match. When dark exposures differ from the lights, Siril can scale the master dark. In its example, a 600 s master calibrates 60 s subs with a computed coefficient of 0.110, close to the 60 ÷ 600 = 0.1 ratio of exposures. AAVSO calls this approach scaled darks and notes that some sensors behave too nonlinearly for it.

Flats need care at the top of the histogram too. Siril says an overexposed flat guarantees a failed calibration and suggests keeping the right tail of the histogram below 80 %. AAVSO, writing for photometry, targets 50–70 % of full well.

Noise and frame counts

Siril states that calibration never reduces noise; it increases it. Every master adds its own noise to every light, so both sources advise many calibration frames. AAVSO asks for “a lot” of bias frames, at least 5–7 flats per filter, and combining them with sigma clipping or a similar rejection method. The integration time guide covers how noise adds up, and the gain and read noise guide explains offset and gain settings.

How much disk space a library takes

A 16-bit FITS frame from a 6248 × 4176 IMX571 sensor is 52.19 MB (computed). That assumes two 2880-byte header blocks, as the storage calculator does, plus the image data at 2 bytes per pixel, padded to whole 2880-byte blocks as the FITS standard requires. Assume 30 frames of each kind, an example count rather than a recommendation:

Setup	Frames	Size (computed)
Color camera: darks, flats, dark flats, bias	120	6.26 GB
Mono camera, 7 filters: flats and dark flats per filter, darks at 3 exposure lengths, bias	540	28.18 GB
Same mono library with a synthetic bias	510	26.62 GB

Per-filter flats drive the mono total. The session storage calculator adds these frames to a night’s lights and processing copies, and the IMX571 camera page lists the cameras that share this sensor.