Night Sky Photometry with Sky Quality Meterfirst draft, ISTIL Internal Report n. 9, v.1.4 2005, c© 2005 ISTIL, Thiene

Pierantonio CinzanoDipartimento di Astronomia, Vicolo dell’Osservatorio 2, I-35100 Padova, Italy

Istituto di Scienza e Tecnologia dell’Inquinamento Luminoso, Via Roma 13, I-36106 Thiene, Italyemail:cinzano@lplab.it

ABSTRACT

Sky Quality Meter, a low cost and pocket size night sky brightness photometer, opens tothe general public the possibility to quantify the quality of the night sky. Expecting a largediffusion of measurements taken with this instrument, I tested and characterized it. I analyzedwith synthetic photometry and laboratory measurements the relationship between the SQMphotometrical system and the main systems used in light pollution studies. I evaluated theconversion factors to Johnson’s B and V bands, CIE photopic and CIE scotopic responses fortypical spectra and the spectral mismatch correction factors when specific filters are added.

Subject headings: light pollution – night sky brightness – photometry – instruments – calibration

1. Introduction

Measurements of artificial night sky brightnessproduced by light pollution are precious to quan-tify the quality of the sky across a territory, thepossibility of the population to perceive the Uni-verse where is living, the environmental impact ofnighttime lighting and their evolution with time.However accurate mobile instruments do not fit re-quirements for wide popular use. They are expen-sive and, even if designed to be set up rapidly andto map the brightness on the entire sky in few min-utes like WASBAM (Cinzano & Falchi 2003), theyrequire transport, pointing, tuning, computer con-trol. Compact mobile radiometers, like LPLAB’sIL1700 (Cinzano 2004), require at least to carryaround a 2.5 kg bag and to spend thousands of dol-lars. Unfriendly, bothering and time-consumingoperations prevent frequent measurements by notprofessional users (and sometimes by professionalusers too) and high cost prevent purchases by in-dividuals. As a result, so far many amateurs as-tronomers, activists of organizations against lightpollution, dark-sky clubs, educators, environmen-talists and citizens were unable to face with thequantification of the quality of the sky of their

territory.Unihedron Sky Quality Meter (thereafter SQM),

a low cost and pocket size night sky brightnessphotometer, opens to the general public the pos-sibility to quantify the quality of the night sky atany place and time, even if with different accuracyand detail from professional instruments. Expect-ing that measurements taken with SQM be widelydiffused, I tested and characterized the instru-ment in order to well understand how they relateto usual measurements. I studied the effects ofthe instrumental response on the measurements oflight pollution based on synthetic photometry andlaboratory tests carried out with the equipmentsof the Light Pollution Photometry and Radiome-try Laboratory (LPLAB). I evaluated for typicalspectra the conversion factors to photometric sys-tems used in light pollution studies, like Johnson’s(1953) B band, V band, CIE photopic and CIEscotopic responses. I also checked the spectralmismatch correction factors when specific filtersare added.

Results presented here should be taken only asan indication because LPLAB equipments werenot made to check instruments with uncommonlylarge aperture angle and response under 400 nm.

1

Fig. 1.— Measurement of the acceptance angle.

Residual background ambience light could con-taminate some data and the sensitivity of the re-sponse calibration equipment is low under 400 nm.

2. Acceptance angle

I checked the acceptance angle of the SQM se-rial n.0115 v.1.09 mounting it, both in horizontaland vertical position, on a rotation table (accuracy0.01 degrees) placed at 1.289 m from a circularaperture with diameter 3.2 mm in front of LPLABSpectral Radiance Standard (lamp 7) powered bythe LCRT-2000 radiometric power supply (radi-ance stability 1% at 550 nm)(Cinzano 2003c, e).The set up is shown in fig. 1. Room temperaturewas maintained at 24.5±0.5 C. Background lighthas been subtracted.

The readings of the instrument at each angleare shown in fig. 2 in magnitude scale with arbi-trary zero point. Open squares are data along thevertical plane, filled squares are data along thehorizontal plane. Angles are positive below themiddle plane and at right, like in the data tablesof the detector manufacturer (TAOS 2004).

Fig. 3 shows the same readings in a linear scalenormalized to its maximum. The figure also showsthe normalized output frequency of the detectorat each angle provided by the detector manufac-turer (vertical is dashed, horizontal is dot-dashed).This quantity is proportional to the measured ir-radiance because the detector is a Light Intensity

Fig. 2.— Angular response of SQM in magnitudes.Angles are positive downward and rightward.

to Frequency Converter. The larger attenuationof light incident on the filter with increasing an-gle makes the SQM angular response slightly nar-rower than the detector angular response at largeangles. The Half Width Half Maximum (HWHM)is ∼42 degrees. A factor 10 attenuation of a pointsource is reached after 55 degrees. Optical inspec-tion shows that screening of the detector begins atabout 60-65 degrees.

When comparing SQM measurements withmeasurements taken with small field photome-ters it should be taken into account that night skybrightness is not constant with zenith distance. Inparticular, artificial night sky brightness usuallygrows with zenith distance with large gradients.The brightness measured pointing the SQM to-ward the zenith will be the weighted average ofbrightness down to a zenith distance of 60 degrees,and then it will be greater (lower magnitude persquare second of arc) than the punctual zenithbrightness:

I =

∫ 2π

0

∫ π/2

0I(θ, φ)D(θ) sin θ dθ dφ

∫ 2π

0

∫ π/2

0D(θ) sin θ dθ dφ

, (1)

where I is the measured average radiance, D(θ) isthe angular response given in fig. 3 and I(θ, φ)

2

Fig. 3.— Angular response of SQM in a linearscale. Lines show the normalized output frequencyof the detector at each angle provided by the de-tector manufacturer, along the vertical (dashed)and horizontal (dot-dashed) planes.

is the radiance of the night sky in the field ofview of the SQM. Fig. 4 shows the weight func-tion D(θ) sin θ for each angle of incidence θ. It ispeaked at about 30 degrees because going from 0to π/2 the angular response decrease and the inte-gration area grows. The effect is still more impor-tant when pointing the SQM to zenith distances ofabout 30 degrees because the instrument will col-lect light from the zenith area down to the horizon.As an example, fig. 5 shows an estimate of the dif-ference Db between the SQM average brightnessand the punctual brightness at each zenith dis-tance, based on a typical brightness versus zenithdistance relationship at a polluted site measuredby Favero et al. 2000 (in Cinzano 2000, fig.14) inPadova. It shows that at 30 degrees of zenith dis-tance the SQM average brightness is brighter thanthe punctual brightness of -0.4 mag/arcsec2. Mea-surements beyond 30-45 degrees of zenith distance(i.e. under an elevation of 60-45 degrees) shouldbe avoided if the contamination by light sourcesand by the luminous or dark landscape under thehorizon cannot be checked.

10 20 30 40 50 60zenith distance - degrees

0.2

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1

weightfunction

Fig. 4.— Weight of the radiance at each angle ofincidence in the measured average radiance.

5 10 15 20 25 30zenith distance deg

-0.4

-0.3

-0.2

-0.1

0Db

mag�arcsec^2

Fig. 5.— Difference between SQM average andpunctual brightness for a typical polluted site.

3. Linearity

I checked the linearity of our SQM analyzingthe residuals of a comparison with the IL1700 Re-search Radiometer over the LPLAB Variable Low-light Calibration Standard (Cinzano 2003c). Dataare shown in figure 6.

The standard error is 2σ = ±0.028 magarcsec−2 corresponding to 2.6%. Linear regres-sion has coefficient 0.0005. The uncertainty of theSQM due to deviations from linearity over a rangeof 12 magnitudes is likely smaller than 2.6%, be-cause measurements are affected by the stabilityof the standard source (1%), the linearity of thereference radiometer (1%) and the fluctuations of

3

Fig. 6.— Residuals of the comparison of the SQMwith a reference radiometer over a variable low-light calibration standard. They give an upperlimit to linearity.

the subtracted background. I did not check effectsof temperature on linearity but according to themanufacturer the detector is temperature com-pensated for the ultraviolet-to-visible range from320 nm to 700 nm (TAOS 2004).

4. Spectral response

I obtained the response curve of our SQM mul-tiplying the spectral responsivity of the TAOSTSL237 photodiode by the transmittance of theHoya CM-500 filter, both provided by manufac-turers, and renormalizing to the maximum value.Fig. 7 shows the normalized photodiode spectralresponsivity (solid line) and quantum efficiency(dashed line). The responsivity (response per unitenergy) is not flat like the quantum efficiency (re-sponse per photon) because photons at smallerwavelength have more energy. Fig. 8 shows theSQM normalized spectral responsivity (solid line),its normalized quantum efficiency and the Hoyafilter transmittance (dotted line).

I checked the calculated SQM responsivity withLPLAB’s Low-Light-Level Spectral Responsiv-ity Calibration Standard (Cinzano 2003c). Theequipment is composed by a standard lamp (lamp3) powered by an high-accuracy Optronic OL-

400 600 800 1000wavelength nm

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1

EnergyResponseandQE

Fig. 7.— Normalized photodiode spectral respon-sivity (solid line) and quantum efficiency (dashedline).

65-A radiometric power supply (source stability±0.05%), a collector lens which collect the lighton the entrance slit of a Fastie-Ebert monocroma-tor (wavelength accuracy ± 0.2%). A camera lensfocuses on the detectors the light coming fromthe output slit. At the moment at LPLAB weare mainly interested in checking the spectral re-sponse of our instruments rather than to obtainaccurate responsivity calibrations, so we use a ref-erence detector with known response rather thana certified spectral responsivity standard. Thereference detector was a Macam SD222-33 siliconphotodiode. Background stray light has been sub-tracted. Room temperature was maintained at23±0.5 C.

Fig. 9 shows the measured responsivity of theSQM (squares) compared with its calculated re-sponsivity (line). The measurements follow thecalculated responsivity quite well. The reason ofthe difference over 550 nm is unknown, but mainfactors could be an inclination of the filter in re-spect to the incoming light, a different laboratorytemperature, an uncertainty in the reference ra-diometer responsivity. Due mainly to light absorp-tion from collector and camera lenses, the specificirradiance produced on the detector from the LowLight Level Responsivity Calibration Standard be-come low under about 400 nm, as shown in fig. 10.As a consequence, measurement errors due to theresidual background stray light become large at

4

400 500 600 700 800wavelength nm

20

40

60

80

100

response,QE,

transmittance

Fig. 8.— SQM normalized spectral responsivity(solid line), quantum efficiency (dashed line) andfilter transmittance (dotted line).

these wavelengths.I checked changes in SQM spectral responsivity

due to the inclination of the incoming rays in re-spect to the normal to the filter. For inclined rayswith off-normal angle of incidence θ, the normal-ized filter transmittance is:

Tλ = (Tλ,⊥)tθ/t⊥ , (2)

where tθ is the effective filter thickness:

tθ =1√

1− sin2 θn2

t⊥. (3)

I assumed the index of refraction of the glassn=1.55. The Full Width Half Maximum (FWHM)of the normalized transmittance Tλ(θ) decreaseswith the angle of incidence and, consequently, thesame behavior is followed by the normalized spec-tral responsivity Rλ(θ) = SλTλ(θ), where Sλ isthe photodiode response. Due to the large fieldof view, the SQM collects light rays with a widerange of incidence angles. The effective spectralresponsivity Rλ is the average of the spectral re-sponsivity for each incidence angle Rλ(θ) weightedby the angular response D(θ) given in fig.3 and bythe angular distribution of the spectral radianceof the night sky in the field of view Iλ(θ, φ):

Rλ =

∫ 2π

0

∫ π2

0Rλ(θ)Iλ(θ, φ)D(θ) sin θ dθ dφ

∫ 2π

0

∫ π2

0Iλ(θ, φ)D(θ) sin θ dθ dφ

. (4)

Fig. 9.— Measured SQM responsivity (squares)and calculated SQM responsivity (line).

Fig. 10.— Response of the LPLAB’s Low-Light-Level Spectral Responsivity Calibration Standard.

5

550 600 650 700wavelength nm

20

40

60

80

100

response

Fig. 11.— Average spectral responsivity of theSQM for an uniform night sky brightness (dashedline), for light rays with 30 degrees incidence angle(dotted line) and for normal incidence (solid line)

Fig. 11 shows the average responsivity of theSQM for an uniform night sky brightness (dashedline), for rays with 30 degrees incidence angle (dot-ted line) and for normal incidence (solid line). TheSQM could slightly underestimate the brightnessof the sky when it is polluted from sources withprimary emission lines in correspondence of theright wing of the spectral responsivity, where theresponse is lower. However usual nighttime light-ing lamps distribute their energy on many lines,apart from Low Pressure Sodium (LPS) lampswhich, anyway, emit near the maximum of SQMresponse.

5. Relationship between SQM photomet-ric band and V-band

Fig. 12 shows for comparison the SQM nor-malized response (dotted line) and the standardnormalized responses of Johnson’s B band, CIEscotopic, Johnson’s V band and CIE photopic(dashed lines from left to right). These are someof the main photometric bands used in light pollu-tion photometry. The emission spectra of an HPLmercury vapour lamp (solid line) is also shown.Fig. 13 shows the same responses and the spectraof an HPS High Pressure Sodium lamp (solid line).It is evident that the SQM response is quite differ-ent from these standard responses. SQM responseis also quite different from the old-time visual andphotovisual bands and from the combination of

400 500 600 700wavelength nm

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1

normalizedresponse

Fig. 12.— SQM normalized response (dottedline), standard normalized responses of Johnson’sB band, CIE scotopic, Johnson’s V band andCIE photopic (dashed lines from left to right) andemission spectra of an HPL mercury vapour lamp(solid line).

scotopic and photopic eye responses. Its largerange recall the sensitivity of panchromatic films.These differences cannot be easily corrected withsimple color corrections like in stellar photometry,where sources have nearly blackbody spectra. Infacts, spectra of artificial night sky brightness typ-ically have strong emission lines or bands, so smalldifferences in the wings of the response curve canproduce large errors.

In order to avoid mistakes, it is more correctconsidering the SQM response as a new photo-metric system. It adds to the 226 known astro-nomical photometrical systems listed in the AsiagoDatabase on Photometric Systems (ADPS)(Moro& Munari 2000, Fiorucci & Munari 2003). Theconversion factors between SQM photometric sys-tem and other photometrical systems can be ob-tained based on the kind of spectra of the observedobject. Hereafter I will call ”SQM” the brightnessin mag arcsec−2 measured in the SQM passband.

The conversion between an instrument responseand a given standard response can be made multi-plying the instrumental measurement by the con-version factor FC between the light fluxes collectedby the standard response and by the instrumental

6

400 500 600 700wavelength nm

0.2

0.4

0.6

0.8

1

normalizedresponse

Fig. 13.— SQM normalized response (dottedline), standard normalized responses of Johnson’sB band, CIE scotopic, Johnson’s V band and CIEphotopic (dashed lines from left to right) and emis-sion spectra of an HPS High Pressure Sodiumlamp (solid line).

response:

FC =∫

fλRλdλ∫fst,λRλdλ

∫fst,λSλdλ∫fλSλdλ

, (5)

where fλ is the spectral distribution of the ob-served object, Rλ is the considered standard re-sponse, Sλ is the instrumental response and fst,λ

is the spectral distribution of the primary stan-dard source for calibration, e.g. an A0V star forthe UBV photometric system or Illuminant A forthe CIE photometric system. The error due to anuncorrected spectral mismatch is:

ε =1− FC

FC. (6)

I computed the conversion factors FC betweenSQM response and V band response for: (i) aflat spectrum, (ii) an average moon spectrum ob-tained assuming the lunar reflectance as given bythe Apollo 16 soil and a solar spectral irradiancespectrum from the WCRP model (see Cinzano2004 for details), (iii) a natural night sky spectrumfrom Patat (2003) kindly provided by the author,(iv) an averagely polluted sky spectrum obtainedwith a mix of spectra of natural night sky, HighPressure Sodium (HPS) lamps and HPL Mercury

Fig. 14.— Conversion factors from SQM responseto Johnson’s V band.

lamps (Cinzano 2004), (v) the CIE Illuminant A(Planckian radiation at 2856 K), (vi) spectra ofHPS lamp and HPL lamp taken with WASBAM(Cinzano 2002) and (vii) a series of blackbodyspectra at various temperatures. I adopted asthe standard response curve of Johnson’s (1953)BV bands those given by Bessel (1990, tab. 2), aslightly modified version of the responses given byAzusienis & Straizys (1969).

The conversion factors from SQM response toJohnson’s V band in magnitudes are shown in fig.14 (see also tab. 2, column 1):

SQM − V = −2.5 log10 FC (7)

Here I will continue to call them conversion ”fac-tors” even if SQM-V is an addictive constant. Iassumed here that both bands are calibrated overa primary standard AOV star spectra like alphaLyrae. As absolute calibrated spectrum I adopteda synthetic spectrum of alpha Lyrae from Kuruczscaled to the flux density of alpha Lyrae at 555.6nm given by Megessier (1995), as discussed in de-tail by Cinzano (2004).

The conversion factors are large, as expectedbecause of the large difference in the responsecurves. However, given that the SQM will be usedto measure light pollution and it will never be usedto measure stars or sources with flat spectra, theconversion factors for interesting sources lie in thenarrower range 0.35-0.6 mag arcsec−2. They canbe reduced using a calibration source inside the

7

Fig. 15.— SQM-V measured ¥ and calculated ¤.

Fig. 16.— SQM-V versus B-V is not linear.

same range, like Illuminant A or another lampfor nighttime lighting. As an example, referringthem to an Illuminant A lamp (SQM-V=0.48 magarcsec−2) these conversion factors would lie in therange ±0.12 mag arcsec−2. In fact Unihedron usesfor calibration a fluorescent lamp (their zero pointwill be discussed later). The argument is furtherfaced in the following discussion.

I measured the SQM-V conversion factors fora number of sources by comparing SQM measure-ments with V-band measurements made with theIL1700 research radiometer (accuracy of V bandcalibration ±4.9%, linearity 1%). Fig. 19 showsthe equipment used for some measurements. Fig.

Fig. 17.— Limited range of interesting SQM-V.

Fig. 18.— SQM-V for blackbodies (solid line).

15 shows the measured (filled squares) and calcu-lated (open squares) conversion factors from SQMresponse to the V band in magnitudes per squarearcsec in function of the B-V color index of thesource. I shifted the zero-point of calculated fac-tors to approximately fit the corresponding mea-sured ones. Fig. 16 shows that the sources do notfollow a simple B-V relation, as expected. Evenif a polynomial (dashed line) could give a veryrough fit to datapoints, a SQM-V versus B-V re-lation does not make sense because data pointsdepend on the spectra of the source which in gen-eral is not univocally determined by the color in-dex. Except few cases, lamps for nighttime light-

8

ing are discharge lamps or LEDs, which are verydifferent from blackbodies. Fig. 17 shows thatif we consider only sources related to light pol-lution, conversion factors lie in the range 0-0.25mag arcsec−2. As already pointed out, using anhigher zero-point or using an Illuminant A calibra-tion source, the range could be restricted to about±0.12 mag arcsec−2.

Fig. 18 shows the SQM-V versus B-V relation-ship for blackbodies (solid line). As expected, itfits Illuminant A, the Moon, a flat spectra and al-pha lyrae. The last is not fitted well because aA0V star spectra it is not a true blackbody due toabsorption lines and bands. A polynomial interpo-lation gives SQM−V = −0.162(B−V )2+0.599(B−V ) − 0.426. Linear regression gives SQM−V ≈0.25(B−V )−0.26 when based on datapoints reg-ularly distributed within 0.4 ≤ B − V ≤ 1.7 andSQM−V ≈ 0.28(B−V )−0.30 when based on dat-apoints within 0.5 ≤ B − V ≤ 1.7.

Two independent authors tested the SQM atthe telescope over standard stars finding a goodagreement with SQM − V ′ ≈ 0.2(B′ − V ′) (Uni-hedron, priv. comm.). The smaller angular co-efficient could be explained by the differences be-tween stellar and blackbody spectra, i.e. by thedifferent distribution of stellar datapoints in re-spect to blackbody datapoints on the plane SQM-V versus B-V. The different zero point is likely dueto the fact that the relation has been obtainedwith outside-the-atmosphere magnitudes V’ andB’. As an example, assuming an extinction of 0.35mag in V and 0.15 mag in B and replacing V’=V-0.35 and B’=B-0.15, where V and B are the ap-parent magnitude below the atmosphere, we ob-tain SQM − V = 0.2(B − V ) − 0.31 in agree-ment with my previous results. The zero pointof the current SQM calibration made by Unihe-dron gives SQM≈V’ for stars with B’=V’, abovethe atmosphere, and consequently the below-the-atmosphere SQM-V correction factor for the alphaLyrae spectrum come out different from zero. Fig.18 shows that for alpha Lyr is SQM-V=-0.35 magarcsec−2.

Given that the instrument is not used for mea-surements of stars at the telescope, this featureappears not necessary. On the contrary, by re-ferring the calibration to an Illuminant A andthe zero point to the condition SQM=V (belowthe atmosphere), the conversion factors for the

Fig. 19.— The Variable Low Light Level Calibra-tion Standard. From left to right are visible theSQM and the reference detector, the Uniform In-tegrating Sphere, the aperture wheel and a testlamp for road lighting (baffles removed). Spec-tral irradiance/radiance standard lamps with ra-diometric power supplies and optical devices areused in other configurations.

sources related to light pollution would have beenreduced to the range ≈ ±0.12 mag arcsec−2. Mybest calibration to Illuminant A, obtained withthe LPLAB Low Light Level Calibration Stan-dard, the spectral radiance standard lamp no. 7powered by the LCRT-2000 radiometric powersupply (radiance stability 1% at 550 nm) andthe IL1700 reference radiometer (accuracy of Vband calibration ±4.9%, linearity 1%), providesV = SQM − 0, 108± 0.054 mag arcsec−2. The er-rorbar includes both the measurement uncertaintyand the V band calibration uncertainty of the ref-erence photometer. The condition SQMnew=Vfor Illuminant A is satisfied increasing the currentSQM zero point of 0.108 mag arcsec−2 or sub-tracting this number from current measurements.Given the many uncertainty factors playing whencomparing instruments, before an official changeof zero point a wider comparison should be car-ried, better if also including measurements overthe night sky. The SQM-V conversion factors af-ter the adjustment are listed here:

9

Fig. 20.— SQM-V conversion factor (magarcsec−2) for a night sky model spectrum, in func-tion of its V brightness and B-V color index.

source SQM-VHPS lamp +0.11HPL lamp +0.00illuminant A +0.00sky natural +0.06sky polluted +0.08moon ab. atm. -0.13

I finally explored the relation between the con-version factor SQM-V for the night sky spectrumand its V brightness and B-V color index. Follow-ing Cinzano (2004), I constructed a very simplemodel spectra for polluted sky assuming that thenight sky brightness spectrum fsky is given by thesum of a natural night sky spectrum, an HPS lampspectrum and an HPL mercury vapour lamp spec-trum, each of them multiplied by a coefficient kn,independent by the wavelength:

fsky = fnat + k1 (k2fHPS + (1− k2)fHPL) (8)

With this spectrum I calculated the functionSQM − V (Vsky, (B − V )sky). Fig. 20 shows theconversion factor SQM-V of the night sky in mag-nitudes per square arc second in function of the Vbrightness and the B-V color index. The conver-sion factor is referred to the natural sky, i.e. itsadds to the SQM-V of the natural sky (+0.48 magarcsec−2 if calibration refers to alpha Lyr or +0.06mag arcsec−2 if calibration refers to Illuminant A).

6. Addition of filters for CIE photopic,CIE scotopic, V-band, B-band

I also calculated with eq. 5 the spectral mis-match correction factors between SQM responseand the CIE photopic, CIE scotopic, V-band, B-band responses, when specific filters are added. Iconsidered addition of filters rather than replace-ment of the existing filter because more on linewith the SQM philosophy of simple and fast mea-surements. Anyone can add a filter in front of theinstrument whereas replacement requires specificwork. Calculations assume that the instrument isproperly calibrated over an Illuminant A for theCIE photometric system and over an AOV star,like alpha Lyrae, for Johnson’s B and V (or prop-erly rescaled to it). I choose for these tests anOptec Bessell V filter, an Optec Bessell B filter,an Oriel G28V photopic filter and a scotopic fil-ter.

Fig. 21 shows the standard response (solid line)and the SQM+filter response (dashed line) for CIEphotopic (top) and CIE scotopic responses (bot-tom). The SQM response is also shown for com-parison (dotted line). The spectral mismatch cor-rection factors for the photopic and scotopic re-sponses are presented in tab. 1. The standard re-sponses of the CIE photometric system are givenin CIE DS010.2/E where they are called ”spectralluminosity efficiency functions”. The instrumentis assumed to have been calibrated over an Illumi-nant A spectrum. Tab. 1 shows that after the ap-plication of the filter the spectral mismatch correc-tion factors became quite small, so that correctioncould be neglected. The match to the CIE pho-topic response could be further improved choosinga filter with the left wing at larger wavelengths.The match of scotopic response is adequate.

Fig. 22 shows the standard response (solid line)and the SQM+filter response (dashed line) for Vband (top) and B band (bottom). The SQM re-sponse is also shown for comparison (dotted line).The spectral mismatch correction factors in mag-nitudes per square arcsec for the Johnson’s B andV bands are presented in tab. 2. The instrumentis assumed to have been calibrated over an AOVstar spectra, like alpha Lyrae, or properly rescaledto it. The match of V band response is adequate.The match to the B band could be further im-proved choosing a filter with the left wing at lower

10

400 450 500 550 600 650 700 750wavelength nm

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1

normalizedresponse

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0

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1

normalized

response

Fig. 21.— Top panel: CIE photopic response(solid line) and SQM + G28V filter (dashed line).Bottom panel: CIE scotopic response (solid line)and SQM + scotopic filter (dashed line).

wavelengths.

7. Further notes on measurement compar-ison

When comparing SQM measurements withmeasurements made with other instruments, itshould be taken also into account that:a) SQM, like the other photometers, radiome-ters, luminancemeters and WASBAM, correctlymeasures the night sky brightness ”below the at-mosphere”, the way it was. On the contrary,measurements made with instruments applied totelescopes are ”below the atmosphere” when the

450 500 550 600 650 700wavelength nm

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normalizedresponse

375 400 425 450 475 500 525 550wavelength nm

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1normalizedresponse

Fig. 22.— Top panel: V band response (solid line)and the SQM+ Optec V filter (dashed line). Bot-tom panel: B band response (solid line) and theSQM+ Optec B filter (dashed line).

calibration factor and extinction are properly eval-uated with the Bouguer method but are wronglygiven as ”above the atmosphere” when countsfrom standard stars and sky background are com-pared without accounting for extinction from thetop of the atmosphere to the ground.b) SQM includes all stars whereas measurementsof sky background made with telescopes usuallyexclude field stars more luminous than a givenmagnitude. When the artificial brightness is notpredominant, the contribution of these stars tothe night sky brightness should be added beforecomparing telescopical measurements with SQMmeasurements (table 3.1 of Cinzano 1997 could be

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source Photopic Scotopicno filter filter no filter filter

HPS lamp 0,78 1,01 1,70 1,00HPL lamp 1,02 1,06 1,22 1,06illuminant A 1,00 1,00 1,00 1,00sky natural 0,96 1,05 0,79 1,02sky polluted 0,85 1,02 1,37 1,02moon ab. atm. 1,20 1,08 0,79 1,02flat 1,35 1,08 0,84 1,03

Table 1: Spectral mismatch correction factors forCIE photopic and scotopic responses.

source V band B bandno filter filter no filter filter

HPS lamp +0,59 -0,05 -2,26 +0,10HPL lamp +0,48 +0,04 -0,63 -0,01illuminant A +0,48 +0,04 -1,37 +0,20sky natural +0,54 +0,02 -0,57 +0,04sky polluted +0,56 -0,02 -1,34 +0,03moon ab. atm. +0,35 +0,01 -0,59 +0,07flat +0,23 +0,01 -0,43 +0,02alpha Lyrae +0,00 +0,00 +0,00 +0,00

Table 2: Spectral mismatch correction factors forV and B responses in magnitude per square arcsec.

used). When the night sky brightness is referredto naked eye, only stars to magnitude 6 should beincluded. However the contribution of stars moreluminous of mag 5 (included) is only 6% of thenatural night sky brightness.

8. Conclusions

Sky Quality Meter is a fine and interestingnight sky brightness photometer. Its low cost andpocket size allow to the general public to quan-tify the quality of the night sky. In order to un-derstand the measurements made by it, I checkedacceptance angle, linearity and spectral responsiv-ity. I analyzed the conversion between SQM pho-tometric system and Johnson’s B and V bands,CIE photopic and CIE scotopic responses and de-termined for some typical spectra both the conver-sion factors and the spectral mismatch correctionfactors when specific filters are added.

Comparing SQM measurements with measure-ments taken with other instruments it should betaken into account that:

a) conversion factors from SQM photometric sys-tem to Johnson’s V band are in the range 0-0.25mag arcsec−2 when considering only main sourcesof interest for light pollution. They are presentedin fig. 15.b) conversion factors for the polluted sky differsfrom the factor for the natural sky less than ±0.05mag arcsec−2 and can be related to the sky Vbrightness and B-V color index (fig. 20).c) quick conversion factors to obtain V bandbrightness from SQM measured brightness withcurrent factory calibration are proposed here be-low for further testing. They are chosen to mini-mize the expected uncertainty ∆V .

Conversion for V ∆VNatural & polluted sky SQM-0.17 ±0.07Lamps, sky, moonlight SQM-0.11 ±0.14

First line is for typical natural or polluted sky,the second line is for surfaces lighted by artificialsources (HPS, HPL, Illuminant A), natural nightsky, polluted night sky or moonlight. The uncer-tainty of the V band calibration of the referencephotometer used in test measurements is includedin ∆V . Units are V mag/arcsec2.d) SQM gives the average night sky brightness,weighted for the angular response inside an ac-ceptance area which has a diameter of 55 degreesdown to 1/10 attenuation. Due to the gradientsof the night sky brightness with zenith distance,the SQM average brightness is larger (smaller magarcsec−2) than the brightness measured by a nar-row field photometer pointed in the same direc-tion, as shown e.g. in fig. 5. In order to roughlyestimate the punctual V band brightness, add toSQM measurements 0 to 0.3 mag/arcsec2 at zenithor 0 to 0.4 mag/arcsec2 at 30 degrees of zenith dis-tance, depending on the pollution level.e) SQM correctly gives the brightness ”below theatmosphere” whereas telescopical measurementscalibrated on standard stars give ”below the at-mosphere” brightness only when the extinction isproperly evaluated and accounted for.f) SQM correctly fully includes the stellar compo-nent in the measured brightness whereas telescop-ical measurements frequently exclude stars moreluminous than a given magnitude.g) addition of commercial Johnson’s B band, Vband, CIE photopic or CIE scotopic filters infront of the SQM with proper calibrations, makes

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the spectral mismatch correction factors very low.This allows reasonably accurate multiband mea-surements, including B-V color indexes and sco-topic to photopic ratios.

ACKNOWLEDGMENTS

LPLAB was set up as part of the ISTIL project‘Global monitoring of light pollution and nightsky brightness from satellite measurements’ sup-ported by ASI (I/R/160/02). Some instrumen-tation has been funded by the author, the Inter-national Dark-Sky Association, Tucson, the BAACampaign for Dark-Sky, London, the AssociazioneFriulana di Astronomia e Metereologia, Remanza-cco and Auriga srl, Milano.

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