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<section>
<h1 class="noindent">Photometry Calibrated File</h1>
<p class="abstract">
The description of a FITS file with fully calibrated data.
</p>
<p>
The file is result of run of <samp>munipack phcal</samp> action.
</p>
<p>
The specification has been created for internal use in Munipack.
Any backward compatibility is not guarantied.
</p>
<h2>Introduction</h2>
<p>
Raw frames contains an array of counts, the array of digitised
amount of electrical charges due to dropped photons. The detected signal
is proportional of quality of detector, area of telescope and fluency
of many additional things appears.
</p>
<p>
To by able to compare, the raw data, we needs combine observed
quantities with calibrated ones. The dirty job is provided by
<samp>phcal</samp> action. And results of calibration are stored
in this kind of FITS file.
</p>
<p>
Crucial properties:
</p>
<ul>
<li>The array of observed data is converted from counts to photons (or another
physical quantity).</li>
<li>The quantities as additional tables are converted too.</li>
</ul>
<p>
Note that the calibration requires knowledge of both filter and photometric system.
</p>
<h2>Primary Array</h2>
<p>
The primary array has modified header with items:
</p>
<div class="table">
<table>
<caption><a href="http://www.stsci.edu/hst/HST_overview/documents/datahandbook/">Keywords compatible to HST</a> added by Photometry Calibration in primary image</caption>
<tr><th>Keyword</th><th>Description</th><th>Units</th></tr>
<tr><td>PHOTSYS</td><td>Photometric system</td><td></td></tr>
<tr><td>BUNITS</td><td>Physical units of array values, always 'photons'</td><td></td></tr>
<tr><td>PHOTFLAM</td><td>flux for 1 photon/s/cm2</td><td>erg/s/cm<sup>2</sup>/Å</td></tr>
<tr><td>PHOTZPT</td><td>magnitude zero-point for fluxes</td><td>erg/s/cm<sup>2</sup>/Å</td></tr>
<tr><td>PHOTPLAM</td><td>effective wavelength</td><td>Å</td></tr>
<tr><td>PHOTBW</td><td>passband FWHM</td><td>Å</td></tr>
</table>
</div>
<p>
All pixels of result image are converted to a required quantity.
</p>
<p>
The key conversion is from observed counts <i>c</i> to photons <i>n</i> (see BUNITS)
for every pixel in the image. For one-filter approximation, the relation
is used:
</p>
<p><i>n = r c</i></p>
<p>
where <i>r = 1/η</i> is photon to counts ratio.
<i>η</i> is coded in FITS header by CTPH keyword.
</p>
<p>
The conversion is more complicated in case of multi-filter observation.
Every pixel in a standard photometric system is computed as the linear
combination of pixels in an instrumental photometric on the same position.
This is main reason for creation of this kind of photometric calibration file.
</p>
<p>
The conversion from counts to photons will probably not visible on the first
sight due to algorithms used for scaling of high-range images, ones suppress
simple linear scaling in intensity.
</p>
<h2>Photometry Table</h2>
<p>
This PHOTOMETRY extension contains a photometry which would be used for
further processing.
</p>
<h3>Header Keywords</h3>
<div class="table">
<table>
<caption>Keywords</caption>
<tr><th>Keyword</th><th>Description</th><th>Units</th></tr>
<tr><td>EXTNAME</td><td>PHOTOMETRY as the identifier of this table</td><td></td></tr>
<tr><td>ORIGHDU</td><td>APERPHOT</td><td></td></tr>
<tr><td>APER</td><td>aperture radius<td>deg</td></tr>
<tr><td>ANNULUS1</td><td>inner sky annulus radius<td>deg</td></tr>
<tr><td>ANNULUS2</td><td>outer sky annulus radius<td>deg</td></tr>
<tr><td>CTPH</td><td>counts per photons<td></td></tr>
<tr><td>CTPHERR</td><td>Statistical Error of CTPH<td></td></tr>
<!--<tr><td>FWHM</td><td>standard FWHM of objects<td>pix</td></tr>-->
</table>
</div>
<p>
The parameters ANULLUSes an APER are directly copied from instrumental
table and with known astrometry calibration converted to degrees.
</p>
<p>
The photometry calibration is summarised in the comments
of this table.
</p>
<pre>
COMMENT === Photometric Calibration by Munipack ===
COMMENT Reference photometric sequence: UCAC5 Catalogue (Zacharias+, 2017)
COMMENT Number of objects used = 10
COMMENT Counts rate per photon rate = 1.1420 +- 7.9E-03
COMMENT Catalogue RA,DEC [deg] Photons [ph/s/m2] Rate [cts/s/m2] rel.err.
COMMENT 58.45428950 0.04279090 145.975E+03 59.052E+03 -0.00040
COMMENT 58.26729090 0.04719370 54.135E+03 21.358E+03 0.01220
COMMENT 58.36659530 0.10020920 25.089E+03 10.164E+03 -0.01539
COMMENT 58.32388300 0.07288640 20.058E+03 7.913E+03 -0.00444
COMMENT 58.32013680 -0.04973250 9.143E+03 3.632E+03 -0.03498
COMMENT 58.29327650 -0.11260250 13.611E+03 5.616E+03 -0.03224
COMMENT 58.38659270 0.07895420 5.104E+03 1.940E+03 0.01366
COMMENT 58.36115270 -0.04099480 4.532E+03 1.791E+03 0.00234
COMMENT 58.38704450 0.09433840 2.199E+03 810.295E+00 0.02770
COMMENT 58.28163680 0.01965840 3.141E+03 1.217E+03 0.01977
COMMENT Description: http://munipack.physics.muni.cz/dataform_photometry.html
COMMENT === End of Photometric Calibration by Munipack ===
</pre>
<p>
The table is designed likely of the <a href="dataform_astrometry.html">astrometry</a>
residual page. First and second
columns identifies calibration star, the third is photon flux in given filter
computed from catalogue magnitude of star, the fourth is counts rate
and last the ratio of [(3) - CTPH *(4)]/(3) as an analogy of residuals.
</p>
<h3>Table</h3>
<div class="table">
<table>
<caption>Photometry table of calibrated frame</caption>
<tr><th>Column</th><th>Description</th><th>unit</th></tr>
<tr><td>X</td><td>Horizontal coordinate</td><td>pix</td></tr>
<tr><td>Y</td><td>Vertical coordinate</td><td>pix</td></tr>
<tr><td>SKY</td><td>Mean sky level</td><td>photons per square arcsec</td></tr>
<tr><td>SKYERR</td><td>Statistical error of SKY</td><td>photons per square arcsec</td></tr>
<tr><td>PHOTON</td><td>Star photon count</td><td>photons</td></tr>
<tr><td>PHOTONERR</td><td>Statistical error of PHOTON</td><td>photons</td></tr>
</table>
</table>
<p>
The structure is perfectly same as structure of PHOTOMETRY
table in Processing file except that COUNTs are replaced by PHOTONs.
</p>
<h1 id="phquantities" >Available Photometric Quantities</h1>
<table>
<caption>Table of available photometry quantities for non-calibrated data</caption>
<tr><th>Quantity</th><th>Description</th><th>Units</th></tr>
<tr><td>COUNT<sup><a href="#count">[α]</a></sup></td><td>Counts <i>c</i></td><td>count</td></tr>
<tr><td>RATE<sup><a href="#rate">[β]</a></sup></td><td>Count rate</td><td>count/s/m<sup>2</sup></td></tr>
<tr><td>MAG<sup><a href="#imag">[γ]</a></sup></td><td>Instrumental magnitude <i>m</i></td><td></td></tr>
</table>
<div class="notes">
<p id="count">
<sup><a href="#count">[α]</a></sup>
Counts means number of detected electrons by captured photons. Ones are derived
from raw data <i>d</i><sub>n</sub> (data number (DN)) in relative units (ADU)
with help of gain <i>g</i> (photo-electrons per ADU): <i>c = g*d</i><sub>n</sub>.
</p>
<p id="rate">
<sup><a href="#rate">[β]</a></sup>
Counts rates are counts per area <i>A</i> of a detector per a time period <i>T</i>.
<i>A</i> is derived from AREA, <i>T</i> from EXPTIME header keyword
as <i>c/(A T)</i>.
</p>
<p id="imag">
<sup><a href="#imag">[γ]</a></sup>
Instrumental magnitudes are derived from rates. Theirs shift
against to right magnitudes is given by optical system attenuation.
Magnitudes are derived as <i>m</i> = 25 - 2.5 log<sub>10</sub> <i>c/(A T)</i>.
Note, that an instrumental shift has been chooses as 1 cts/s/m<sup>2</sup>
for magnitude 25 (see -2.5 log<sub>10</sub> 10<sup>-10</sup>).
</p>
</div>
<div class="table">
<table>
<caption>Table of available photometry quantities for fully calibrated data</caption>
<tr><th>Quantity</th><th>Description</th><th>Units</th></tr>
<tr><td>PHOTON<sup><a href="#photon">[a]</a></sup></td><td>Photon counts <i>n</i></td><td>photon</td></tr>
<tr><td></td><td>Photon flux <i>Φ</i></td><td>ph/s/m<sup>2</sup></td></tr>
<tr><td>PHOTNU<sup><a href="#photnu">[b]</a></sup></td><td>Photon rate per frequency n<sub>ν</sub></td><td>ph/m<sup>2</sup>/Hz</td></tr>
<tr><td>PHOTLAM<sup><a href="#photlam">[c]</a></sup></td><td>Photon rate per wavelength n<sub>λ</sub></td><td>ph/m<sup>2</sup>/nm</td></tr>
<tr><td>FLUX<sup><a href="#flux">[d]</a></sup></td><td>Energy flux in a band <i>f</i></td><td>W/m<sup>2</sup></td></tr>
<tr><td>FNU<sup><a href="#fnu">[e]</a></sup></td><td>Energy density flux per frequency <i>f</i><sub>ν</sub></td><td>W/m<sup>2</sup>/Hz</td></tr>
<tr><td>FLAM<sup><a href="#flam">[f]</a></sup></td><td>Energy density flux per wavelength <i>f</i><sub>λ</sub></td><td>W/m<sup>2</sup>/nm</td></tr>
<tr><td>MAG<sup><a href="#mag">[g]</a></sup></td><td>Magnitude <i>m</i></td><td></td></tr>
<tr><td>ABMAG<sup><a href="#abmag">[h]</a></sup></td><td>Magnitude per 1 Hz of frequency <i>m</i><sub>AB</sub></td><td></td></tr>
<tr><td>STMAG<sup><a href="#stmag">[ch]</a></sup></td><td>Magnitude per 1 nm of wavelength <i>m</i><sub>ST</sub></td><td></td></tr>
</table>
</div>
<div class="notes">
<p id="photon">
<sup><a href="#photon">[a]</a></sup>
Photon count <i>n</i> and photon flux <i>Φ</i> are the core of calibration.
The fitting routines estimates ratio of detected <i>c</i> and expected
<i>n</i> photons and derive quantity (efficiency by mean) <i>η = c / n</i>
(0 ≤ <i>η</i> ≤ 1). The typical values are between
0.1 — 0.5. The <i>η</i> is included in header keywords as CTPH and its
dispersion as CTPHERR. Photon count is derived from original data as
<i>n = c / η</i>.
The reference photon count in a band <i>B</i> is derived from a known (catalogue)
star magnitude <i>m<sub>B</sub></i><br>
<i>Φ = (f<sub>νB</sub> Δν<sub>B</sub> / h ν<sub>B</sub>) 10<sup>-0.4 m</sup> =
(f<sub>λB</sub> Δλ<sub>B</sub>) (h c / λ<sub>B</sub>) 10<sup>-0.4 m</sup></i>,<br>
where <i>f<sub>νB</sub></i> and
<i>Δν<sub>B</sub></i> are spectral density flux and passband FWHM (in this order)
defined by <a href="dataform_photosys.html">photometry system</a>.
Count of photons is <i>n = Φ A T</i>.
Note that product <i>f<sub>νB</sub> Δν<sub>B</sub></i> has meaning of
energy flux and <i>h ν<sub>B</sub></i> is the mean
energy of photon in the given band.<br>
The photon flux is also frequently is used quantity defined as <i>ϕ = n / A T</i>.
<p id="photnu">
<sup><a href="#photnu">[b]</a></sup>
Photon rate per unit frequency defined as
<i>n<sub>ν</sub> = n / Δν</i>.
</p>
<p id="photlam">
<sup><a href="#photlam">[c]</a></sup>
Photon rate per 1nm of wavelenght defined as
<i>n<sub>λ</sub> = n Δλ c / λ</i><sub>eff</sub><sup>2</sup>.
</p>
<p id="flux">
<sup><a href="#flux">[d]</a></sup>
Energy flux in given band (filter) defined as
<i>F = ϕ h ν</i><sub>eff</sub><i> = ϕ h Δλ c / λ</i><sub>eff</sub><sup>2</sup>.
</p>
<p id="fnu">
<sup><a href="#fnu">[e]</a></sup>
Spectral energy flux density per unit frequency defined as
<i>f<sub>ν</sub> = ϕ<sub>ν</sub> h ν</i><sub>eff</sub><i>
= ϕ h ν</i><sub>eff</sub><i> / Δν</i>.
</p>
<p id="flam">
<sup><a href="#flam">[f]</a></sup>
Spectral energy flux density per 1nm of wavelength defined as
<i>f<sub>λ</sub> = ϕ<sub>λ</sub> Δλ c / λ</i><sup>2</sup><sub>eff</sub><i>
= ϕ h c / λ</i><sup>2</sup><sub>eff</sub><i> /</i> 10<sup>-9</sup>.
</p>
<p id="mag">
<sup><a href="#mag">[g]</a></sup>
Magnitudes in the given filter are computed as
<i>m</i> = -2.5 log<sub>10</sub> <i>F / (f<sub>0ν</sub> Δν)</i> =
-2.5 log<sub>10</sub> <i>F / (f<sub>0λ</sub> Δλ)</i>.
Undefined values are marked 99.999.
</p>
<p id="abmag">
<sup><a href="#abmag">[h]</a></sup>
Magnitudes in the given filter are computed as
<i>m</i> = -2.5 log<sub>10</sub> <i>f<sub>ν</sub> / f<sub>AB</sub></i>,
where <i>f</i><sub>AB</sub> = 3.631 .10<sup>-23</sup> [W/m2/Hz] is
spectral flux density for star of magnitude zero in V (545nm) band for AB system.
Undefined values are marked 99.999.
</p>
<p id="stmag">
<sup><a href="#stmag">[ch]</a></sup>
Magnitudes in the given filter are computed as
<i>m</i> = -2.5 log<sub>10</sub> <i>f<sub>λ</sub> / f<sub>ST</sub></i>,
where <i>f</i><sub>ST</sub> = 3.6335 .10<sup>-10</sup> [W/m2/nm] is
spectral flux density for star of magnitude zero in V (545nm) band for ST system.
Undefined values are marked 99.999.
</p>
</div>
<div class="table">
<table>
<caption>Photometry table for fully calibrated data</caption>
<tr><th>Column</th><th>Description</th><th>units</th></tr>
<tr><td>RA</td><td>Right Ascension</td><td>deg</td></tr>
<tr><td>DEC</td><td>Declination</td><td>deg</td></tr>
<tr><td>SKY</td><td>Sky intensity</td><td><sup><a href="#usky">[-]</a></sup></td></tr>
<tr><td>SKYERR</td><td>Sky intensity error</td><td><sup><a href="#usky">[-]</a></sup></td></tr>
<tr><td>Q</td><td>A selected quantity<sup><a href="#uq">[+]</a></sup></td><td></td></tr>
<tr><td>QERR</td><td>The quantity standard error<sup><a href="#uq">[+]</a></sup></td><td></td></tr>
</table>
</div>
<p>
Note that for fully calibrated data, keywords TUNITn are presented in the
header.
</p>
<div class="notes">
<p id="usky">
<sup><a href="#usky">[-]</a></sup>
Units of sky intensity are the same as quantity Q, but, in addition,
they are related to the cone 1 arcsec<sup>2</sup>.
</p>
<p id="uq">
<sup><a href="#uq">[+]</a></sup>
There is many of possible related quantities, which can be directly
derived from calibrated photons.
</p>
</div>
<h2>Magnitudes Are Considered As Obsolete</h2>
<p>
Please, have in mind.
The photometry calibration is designed for a photon counting detector, eg.
a device that can detect an incoming single photon. CCD, CMOS and
many modern detectors are that photon counting devices. Ones are extremely sensitive
with linear response. The calibration naturally take the advantage.
</p>
<p>
The magnitude scale is considered as obsolete in this framework and
provided just for backward compatibility.
This approach for the photometry has many advantages for modern
astronomy for following reasons:
</p>
<ul>
<li>Simple, physical and powerful mind framework which is compatible
with astronomical photometry in non-optical bands.</li>
<li>There is new point of view onto many of classical astronomy problems, as light
attenuation in a media like Earth's atmosphere or the interstellar extinction.</li>
<li>
Magnitudes are used just only by optical astronomers and the data
are difficult to compare and understand for non-optical astronomers.</li>
<li>
Moreover, all modern detectors (photo-multiplier tube, CCD, ...) are strictly
linear, not logarithmic as human eye is supposed (note that modern
measurements of eye response shows dependency of response on flux
as ∝flux<sup>1/3</sup> in limited light ranges of modern digital devices
(<a href="https://en.wikipedia.org/wiki/CIELUV">CIE 1976 (L*, u*, v*) colour space</a>).
</li>
<li>A relative photometry (differential magnitudes) can be easy replaced
by ratio of fluxes (intensities).</li>
<li>An easy manipulation with wide range data can be replaced by (decadic)
logarithm over creepy 2.5*log<sub>10</sub>.</li>
<li>The normalised photon flux can be mutually converted to
spectral (density) fluxes (or intensities).</li>
</ul>
<h2>See Also</h2>
<p>
<a href="man_aphot.html">Aperture Photometry</a>,
<a href="man_phcal.html">Photometry Calibration</a>
</p>
</section>
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