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<title>Munipack ‒ Averaged bias frame</title>
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<h1>Averaged Bias Frame</h1>

<p class="abstract">
An average bias frame of a set of bias frames.
</p>

<h2>Synopsis</h2>

<code>
munipack bias [.. parameters ..] file(s)
</code>

<h2>Description</h2>

<p>
A bias frame is a zero-time exposure with no light. The exposure with the shortest
possible exposure time provided by a device. One maps a pre-amplifier bias (offset)
of readout electronics. This routine creates an average bias frame,
sometimes named as a masterbias.
</p>

<p class="indent">
Because bias exposure times are really short (1/100s or less), it is
recommended to acquire and average a lot of exposures (>10).
</p>

<p>
An output bias <i>B<sub>ij</sub></i> is computed as the average of every pixel of
input images <i>(I<sub>k</sub>)<sub>ij</sub></i>:
</p>

<p>
<i>B<sub>ij</sub></i> = 〈 <i>I<sub>k</sub></i> 〉<i><sub>ij</sub></i>,
</p>
<p>
where <i>i,j</i> is an index of a pixel and <i>k</i> is an index of an image.
</p>

<p class="indent">
Two methods of averaging are implemented. An arithmetical mean
is fast and memory conserving while a robust mean is significantly slower and requires
much more memory. Use of the robust mean is preferred because random defects (cosmics,
interferences) are greatly suppressed.
</p>

<p class="indent">
Both chip temperatures or exposure times are checked to be nearly the same
during processing when FITS_KEY_TEMPERATURE and FITS_KEY_EXPTIME
<a href="man_env.html">environment variables</a> are set to values of
corresponding quantities.
</p>

<h2>Input And Output</h2>

<p>
On input, list of frames representing the bias is expected.
</p>

<p>
On output, the only one file as mean bias frame is created.
</p>

<h2>Parameters</h2>

<dl>
  <dt><samp>--arith</samp></dt><dd>use arithmetical mean instead of
    default robust mean</dd>
  <dt><samp>--tol-temp temp</samp></dt><dd>limit for nearby temperatures
    (default = 1K)</dd>
  <dt><samp>--tol-exp exptime</samp></dt><dd>limit for nearby exposure times
    (default = 1 μsec)</dd>
  <dt><samp>-B bitpix</samp></dt><dd>set numerical type of output images,
    see <a href="man_com.html">Common options</a> (default -32)</dd>
  <dt><samp>-o filename</samp></dt><dd>save to the output file,
    see <a href="man_com.html">Common options</a></dd>
</dl>

<p>Also see <a href="man_com.html">Common options</a></p>

<h2>Examples</h2>

<code>
$ munipack bias -o bias.fits bias_*.fits
</code>


<figure>
<img class="figure" src="arithmetical_mean.png" alt="arithmetical_mean.png" title="Arithmetical mean">
<figcaption>
Arithmetical mean (duration 0.2 sec)
</figcaption>
</figure>

<figure>
<img class="figure" src="robust_mean.png" alt="robust_mean.png" title="Robust mean">
<figcaption>
Robust mean (duration 3.5 sec)
</figcaption>
</figure>


<h2>See Also</h2>
<p>
<a href="lctut.html">Light Curve Tutorial</a>,
<a href="phcorrtut.html">Photometric corrections tutorial</a>,
<a href="man_dark.html">Averaged dark frame</a>.
</p>

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