# Photometry Calibrated File

The description of a FITS file with fully calibrated data.

The file is result of run of `munipack phcal` action.

The specification has been created for internal use in Munipack. Any backward compatibility is not guarantied.

## Introduction

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.

To by able to compare, the raw data, we needs combine observed quantities with calibrated ones. The dirty job is provided by `phcal` action. And results of calibration are stored in this kind of FITS file.

Crucial properties:

- The array of observed data is converted from counts to photons (or another physical quantity).
- The quantities as additional tables are converted too.

Note that the calibration requires knowledge of both filter and photometric system.

## Primary Array

The primary array has modified header with items:

Keywords compatible to HST added by Photometry Calibration in primary image
Keyword | Description | Units
--- | --- | ---
PHOTSYS | Photometric system |
BUNITS | Physical units of array values, always 'photons' |
PHOTFLAM | flux for 1 photon/s/cm2 | erg/s/cm2/Å
PHOTZPT | magnitude zero-point for fluxes | erg/s/cm2/Å
PHOTPLAM | effective wavelength | Å
PHOTBW | passband FWHM | Å

All pixels of result image are converted to a required quantity.

The key conversion is from observed counts c to photons n (see BUNITS) for every pixel in the image. For one-filter approximation, the relation is used:

n = r c

where r = 1/η is photon to counts ratio. η is coded in FITS header by CTPH keyword.

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.

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.

## Photometry Table

This PHOTOMETRY extension contains a photometry which would be used for further processing.

### Header Keywords

Keywords
Keyword | Description | Units
--- | --- | ---
EXTNAME | PHOTOMETRY as the identifier of this table |
ORIGHDU | APERPHOT |
APER | aperture radius | deg
ANNULUS1 | inner sky annulus radius | deg
ANNULUS2 | outer sky annulus radius | deg
CTPH | counts per photons |
CTPHERR | Statistical Error of CTPH |

The parameters ANULLUSes an APER are directly copied from instrumental table and with known astrometry calibration converted to degrees.

The photometry calibration is summarised in the comments of this table.

    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 ===

The table is designed likely of the astrometry 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.

### Table

Photometry table of calibrated frame
Column | Description | unit
--- | --- | ---
X | Horizontal coordinate | pix
Y | Vertical coordinate | pix
SKY | Mean sky level | photons per square arcsec
SKYERR | Statistical error of SKY | photons per square arcsec
PHOTON | Star photon count | photons
PHOTONERR | Statistical error of PHOTON | photons

The structure is perfectly same as structure of PHOTOMETRY table in Processing file except that COUNTs are replaced by PHOTONs.

# Available Photometric Quantities

Table of available photometry quantities for non-calibrated data
Quantity | Description | Units
--- | --- | ---
COUNT[α] | Counts c | count
RATE[β] | Count rate | count/s/m2
MAG[γ] | Instrumental magnitude m |

[α] Counts means number of detected electrons by captured photons. Ones are derived from raw data dn (data number (DN)) in relative units (ADU) with help of gain g (photo-electrons per ADU): c = g*dn.

[β] Counts rates are counts per area A of a detector per a time period T. A is derived from AREA, T from EXPTIME header keyword as c/(A T).

[γ] Instrumental magnitudes are derived from rates. Theirs shift against to right magnitudes is given by optical system attenuation. Magnitudes are derived as m = 25 - 2.5 log10 c/(A T). Note, that an instrumental shift has been chooses as 1 cts/s/m2 for magnitude 25 (see -2.5 log10 10-10).

Table of available photometry quantities for fully calibrated data
Quantity | Description | Units
--- | --- | ---
PHOTON[a] | Photon counts n | photon
| Photon flux Φ | ph/s/m2
PHOTNU[b] | Photon rate per frequency nν | ph/m2/Hz
PHOTLAM[c] | Photon rate per wavelength nλ | ph/m2/nm
FLUX[d] | Energy flux in a band f | W/m2
FNU[e] | Energy density flux per frequency fν | W/m2/Hz
FLAM[f] | Energy density flux per wavelength fλ | W/m2/nm
MAG[g] | Magnitude m |
ABMAG[h] | Magnitude per 1 Hz of frequency mAB |
STMAG[ch] | Magnitude per 1 nm of wavelength mST |

[a] Photon count n and photon flux Φ are the core of calibration. The fitting routines estimates ratio of detected c and expected n photons and derive quantity (efficiency by mean) η = c / n (0 ≤ η ≤ 1). The typical values are between 0.1 — 0.5. The η is included in header keywords as CTPH and its dispersion as CTPHERR. Photon count is derived from original data as n = c / η. The reference photon count in a band B is derived from a known (catalogue) star magnitude mB
Φ = (fνB ΔνB / h νB) 10-0.4 m = (fλB ΔλB) (h c / λB) 10-0.4 m,
where fνB and ΔνB are spectral density flux and passband FWHM (in this order) defined by photometry system. Count of photons is n = Φ A T. Note that product fνB ΔνB has meaning of energy flux and h νB is the mean energy of photon in the given band.
The photon flux is also frequently is used quantity defined as ϕ = n / A T.

[b] Photon rate per unit frequency defined as nν = n / Δν.

[c] Photon rate per 1nm of wavelenght defined as nλ = n Δλ c / λeff2.

[d] Energy flux in given band (filter) defined as F = ϕ h νeff = ϕ h Δλ c / λeff2.

[e] Spectral energy flux density per unit frequency defined as fν = ϕν h νeff = ϕ h νeff / Δν.

[f] Spectral energy flux density per 1nm of wavelength defined as fλ = ϕλ Δλ c / λ2eff = ϕ h c / λ2eff / 10-9.

[g] Magnitudes in the given filter are computed as m = -2.5 log10 F / (f0ν Δν) = -2.5 log10 F / (f0λ Δλ). Undefined values are marked 99.999.

[h] Magnitudes in the given filter are computed as m = -2.5 log10 fν / fAB, where fAB = 3.631 .10-23 [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.

[ch] Magnitudes in the given filter are computed as m = -2.5 log10 fλ / fST, where fST = 3.6335 .10-10 [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.

Photometry table for fully calibrated data
Column | Description | units
--- | --- | ---
RA | Right Ascension | deg
DEC | Declination | deg
SKY | Sky intensity | [-]
SKYERR | Sky intensity error | [-]
Q | A selected quantity[+] |
QERR | The quantity standard error[+] |

Note that for fully calibrated data, keywords TUNITn are presented in the header.

[-] Units of sky intensity are the same as quantity Q, but, in addition, they are related to the cone 1 arcsec2.

[+] There is many of possible related quantities, which can be directly derived from calibrated photons.

## Magnitudes Are Considered As Obsolete

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.

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:

- Simple, physical and powerful mind framework which is compatible with astronomical photometry in non-optical bands.
- 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.
- Magnitudes are used just only by optical astronomers and the data are difficult to compare and understand for non-optical astronomers.
- 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 ∝flux1/3 in limited light ranges of modern digital devices (CIE 1976 (L*, u*, v*) colour space).
- A relative photometry (differential magnitudes) can be easy replaced by ratio of fluxes (intensities).
- An easy manipulation with wide range data can be replaced by (decadic) logarithm over creepy 2.5*log10.
- The normalised photon flux can be mutually converted to spectral (density) fluxes (or intensities).

## See Also

Aperture Photometry, Photometry Calibration