Munipack ‒ Flat-field

# Flat-field

Overview of a general flat-fielding problem and description of its solution by Munipack.

Munipack implements its own flat-field algorithm on base of the standard photometry calibration rather than commonly used methods (they uses of median of scaled flat-fields). The presented approach enables to reach the maximal possible precision which is limited by only statistical noise of light. The approach is unique and has been not found in any available literature.

# Standing on the shoulders of flat-fields

Although a correct flat-field is the crucial tool for reaching suitable photometry precision of observations, the care of acquiring and processing of flat-fields is not appropriate. This is especially true for any flat-field post-processing.

A capacity of common semi-conductor detectors is limited on values, say, 100k counts per pixels. A good flat-field has its mean level about 50k counts which gives its relative precision on value √50k / 50k ≈ 0.004 per pixel, if Poisson distribution can by considered. So for a star which occupy about ten pixels (3×3), one will have a relative precision over 0.01 magnitude due to the flat-field. A small error in flat-field determination leads to measurable deviations of results.

To improve the precision, some increase of a capacity of detectors can help, but it have technical limitations. Also, it will not suppress different light sensitivity of pixels including all the optical path. In this case, the feasible way is averaging of frames as provides Munipack `flat` utility.

# The flat-fielding mystery revealing

Mean levels of flat-fields, captured using of an unstable light source (during twilight), are unequal. As a consequence, a direct average of that flat-fields is impossible.

A common solution of the trouble is normalisation of flat-fields on an unique intensity level preparatory to an averaging. The problem of the approach is determination of a mean level of every frame. Its values has no Normal distribution which is leading to a poor definition of the average level.

A distribution of values of flat-field shows an asymmetric histogram

The main difficulty comes due to the folded surface of flat-fields. While it is possible to compute a mean level, the estimate will not be optimal or accurate due to blending of statistical distributions: the light noise and the surface of flat-field itself.

The crucial point of Munipack approach is decomposition of flat-field frames on single, independent pixels. These pixels, with the same position but collected over all frames, can be considered as sources of light like stars and similar procedure as the star calibration can be used. Reference sources are initially unknown, but can be estimated by iterations.

A blended distribution of values as result of a folded surface of a flat-field

Munipack is using two-phase algorithm which determine a rough flat-field during the first phase (equivalent to common practice). The second phase determines the mean level against to the rough flat followed by averaging. The approach makes the second phase to be work with Normally distributed data giving precise and reliable results.

The final flat-field accepting folded (wrinkled) property. Resultant histogram of residuals of an single frame is near Normal distribution (only on per frame basis deviations).

The developed algorithm solves a non-linear implicit equation for both levels and all pixels of the resultan flat-field. The approach is a variant of photon calibration where the reference photon sources are iterative established during the computation.

# Flat-fielding rules

There is a list of rules, summarising of my long time experiences with flat-fielding, which I recommends for flat-fielding:

- The flat-field frame is very important, because a quality of the flat-field determines photometry precision of results.
- Only twilight flat-frames are acceptable (any light gadgets gives only poor results – please send me counter-example).
- The twilight flats can be acquired with this rules in mind:
  - acquire only on clear sky without any clouds,
  - additional light pollution by an artificial light or Moon is unacceptable,
  - use opposite directions on Sun,
  - choose fields in Earth's shadow,
  - acquire on field not too close to horizon,
  - keep polarisation due to Sun on minimum,
  - select a field with sparse and faint stars,
  - switch-off sidereal motion of telescope mount's,
  - use shorter minimal exposure to prevent changes of illumination during the twilight (but not such short to capture shutter speed),
  - prefer levels of flat-fields around half of its full range (capacity).

## See Also

Flat-field manual, Photometry corrections. Standing on the shoulders of giants.