Lightmeter calibration
For calibration of your instrument send measurments from a few clear days and night, preferably also with some Moon together with your coordinates to Lightmeter@astronomy2009.at or upload the data to the Lightmeter-database where they are also calibrated. --GuentherWuchterl 18:29, 14. Jan. 2010 (UTC)
For the preferred calibration with Sun and twilight see the Calibration example Linz.
Below approximately / Unterhalb von ca 1 Lux ... the Lightmeters are linear and a factor of the order of a few 10^-7 is sufficient to convert from counts to Lux / ... sind die Luxmeter linear und es reicht ein Faktor im Bereich von einigen 10^-7 zur Umrechnung von counts auf Lux.
Above approximately/ Oberhalb von ca 1 Lux ... is a slightly different daytimemeasurement. An experimental, non-linear part has been added for a qualitative day/night comparison / ... wird für den Tag anders gemessen. Es ist ein experimenteller, nichtlineare Teil hinzugefügt um Tag/Nacht qualitativ vergleichen zu können.
Below are a few experimental calibrations for the entire (day and night) range that are worth a try. / Folgende experimentelle Kalibrationen sind für den gesammten Bereich einen Versuch Wert;
Faustregel: 1 Lux entspricht 1 000 000 counts.
Umschaltpunkte Tag/Nacht und Messbereiche
Die Umschaltung erfolgen bei AD-Wert >30000 in den nächst größeren (unempfindlichen) und bei 1000 in den nächst kleineren (empfindlicheren). Meßbereiche
Meßbereich OV Verst. OV Faktor AD-Faktor Gesamt Empfindlichkeit
1 3,2 1 1 120 minimal
2 48 15 1 8
3 48 15 2 4
4 48 15 4 2
5 48 15 8 1 maximal */
d.h. in die letzte "Nachtstufen" 2-5 werden bei 240000 verlassen und bei 120000 wird wieder in die Nacht eingetaucht. Wenn sich hier ein Zusammenhang feststellen lässt - müssen wir nochmal an die Hardware.
Kalibrationsbeispiele
Luxmeter 3: Die Grobkalibration für das Linzer Luxmeter (#3), zB, sollte sein: Lux = 2E-6 * counts für < 1 lux
Bis mindestens 20 000 lx ist folgendes (bei #2) auf ca 10% genau: Lux = 2E-6*( counts +exp( counts/8.7E4 ) )
Luxmeter 7: Lux = 2.0E-7*counts+0.7E-5*exp(counts/0.90E5) fittet bis 20 000 Lux mit sigma 27%.--GuentherWuchterl 22:47, 21. Sep. 2008 (UTC)
Luxmeter 12: Lux = 2.65E-7*counts für < 0.2 Lux; Lux = 2.65E-7*counts+2.5E-5*exp(counts/1.0E5) bis mindestens 10 000 Lux. (Kalibration 25. Sept 2008)
Luxmeter 12 (in Libelle 2 Glas): Lux = 4.0E-7*counts für < 1 Lux; Lux = 4.0E-7*counts+0.7E-5*exp(counts/0.90E5) passt bis mindestens 10 Lux. --GuentherWuchterl 21:59, 23. Sep. 2008 (UTC)
Daylight calibration and comparison to a Sky Quality Meter to 21.15 mag/arcsecond²
On September 18th and 25th I did experimental calibrations of the L12 luxmeter that is installed on the roof of the main building of the Thüringer Landessternwarte in Tautenburg. Since September 22nd L12 is installed on the same mast and at the same height within a distance of 30 cm of the "old" Libelle 2 and thus the two could be directly compared for the first time.
As calibration reference I used the handheld Voltcraft Luxmeter as usual and did quasi-simultaneous measurements with a Sky Quality Meter (SQM,#2816) borrowed from Thomas Posch. Measurements were taken as follows:
- Libelle 2: Automatically every 10s (first Tautenburg Luxmeter),
- L12: every second (new prototype series),
- Voltcraft handheld luxmeter: typically every minute down to its limit at 0.02 Lux,
- Sky Quality Meter: within a minute, usually 30s of the Voltcraft readings and in regular intervals. Up to three measurements were taken with the SQM after a first one that was ignored because I have been told that the first SQM-values shown after pressing the button are not reliable. I can confirm this, in particular once the SQM was integrating (beeping) below 0.02 lx.
I used the mag/square arcsecond to Lux conversion as given by Schlyter, in the form Lux = 10.0**(-0.40195*mag-5.5917) to convert from the SQM readings to Lux values. The conversion was checked by a similar fit due to André Müller.
To fit the so derived values from the SQM to the measurements of Libelle 2 and L12 as calibrated with the shown Voltcraft measurements I had to add 0.6 mag on the 18th of September and 1 mag on the 25th. The calibration on 18th September was done with the L12-cell in the housing of Libelle 2. The difference in the calibration factors, 4.0E-6 Lux/count for Sept 18th, inside the housing and 2.65E-6 Lux/count on Sept 25th, free on the mast, corresponds to 0.45 magnitudes. Thus the difference in offsets is likely due to the glas-housing of Libelle 2, see picture above.
The 1 mag offset between the SQM-readings converted to Lux (the difference in opening angle is accounted for) and the Luxmeter-values are likely due to the different spectral responses of the SQM and the Luxmeter. E.g. the SQM sensitivity extends further to the blue, see the section on spectral response below.
Measurements started in the afternoon with overcast (100%) sky. Clouds started to open up with the first stars shining through at 18h50 UTC and the sky started to clear rapidly from 20h30 to 20h50 UTC when no clouds remained and the visual limiting magnitude reached 6 mag as determined in UMi, with the http://sternhell.at method.
For the new L12 Luxmeter, two calibrations are shown: (1) in blue which just uses a factor to convert from counts to Lux and (2) an experimental experimental calibration that takes care of the logarithmic behaviour that was added for daylight measurements. The transition between the linear "night"-range and the "logarithmic" daylight behaviour was intentionally set near the full moon value to (1) use as much of the dynamic range of the A/D converter as possible in a linear way for the low light levels and have convenient access to light levels below 100 ulx, and (2) cover all daylight values without switching in the electronics. This feature is an intentional non-linearity in the A-D conversion and not due to the solar cell that behaves linearly.
The Luxmeters were covered near 19h10 and 19h50 UTC to check the distance to the detection limit which is beyond the bounds of the figure, deep in the mikro-Lux domain.
Overall the Luxmeters and the SQM are giving consistent results from 1 000 lx to the lowest values measured at about 1 mlx that correspond to the lowest SQM-readings of 21.15 mag/square arcsecond.
Note: The SQM above ist an SQM-L, with a full width half maximum opening angle of 20 degrees. It has to be distinguished from the original SQM with a full with half maximum opening angle of about 84 degrees, see http://unihedron.com/projects/darksky/
SQM offset and comparison to measurements with Johnson V filter
Quantitatively the offset to be expected to the SQM may be estimated from the difference of the plain cell to one with a Johnson-V-filter (1.7 mag, see Fig on the right) and the difference between SQM and Johnson V. In his Darksky Vienna 2008 talk, slide 16 Andreas Hähnel gives differences SQM-V between 0.5 and 0.6 mag for the sky and polluted sky. Assuming V as fainter we arrive at an expected offset of 1 mag between the Luxmeter and the SQM, consistent with the comparison presented here. In summary:
- L13 with V - L13 = 1.7 mag,
- SQM - V = 0.5 - 0.6 mag,
- L12 - SQM = 1 mag,
all to +/- 0.1 mag.
Models / Sources
This section provides links and sources of models and other useful data for calibration purposes of the Lightmeter.
- Reference Solar Irradiance Spectra (ASTM E490): http://rredc.nrel.gov/solar/spectra/
- Air mass: Fritz Kasten and Andrew T. Young, Applied Optics, Vol. 28, Issue 22, pp. 4735-4738 (1989), Revised optical air mass tables and approximation formula
- Extinction model: Hayes, D. S. and Latham, D. W., Astrophysical Journal, vol. 197, p. 593-601 (1975), A rediscussion of the atmospheric extinction and the absolute spectral-energy distribution of VEGA
- Wavelength dependent extinction coefficients for La Silla observatory: http://www.eso.org/sci/observing/tools/Extinction.html
- Photopic and Scotopic functions: http://cvision.ucsd.edu/
- Radiometry and photometry in astronomy with examples: http://www.stjarnhimlen.se/comp/radfaq.html
- Lunar Irradiance model: http://www.moon-cal.org/index.php, see also: Kieffer et al., The Astronomical Journal, Volume 129, Issue 6, pp. 2887-2901, The Spectral Irradiance of the Moon