A Two-Colour CCD Survey of the North Celestial Cap: I. The Method
ABSTRACT We describe technical aspects of an astrometric and photometric survey of the North Celestial Cap (NCC), from the Pole (DEC=90 deg) to DEC=80 deg, in support of the TAUVEX mission. This region, at galactic latitudes from ~ 17 deg to ~ 37 deg, has poor coverage in modern CCD-based surveys. The observations are performed with the Wise Observatory one-meter reflector and with a new mosaic CCD camera (LAIWO) that images in the Johnson-Cousins R and I bands a one-square-degree field with subarcsec pixels. The images are treated using IRAF and SExtractor to produce a final catalogue of sources. The astrometry, based on the USNO-A2.0 catalogue, is good to ~ 1 arcsec and the photometry is good to ~ 0.1 mag for point sources brighter than R=20.0 or I=19.1 mag. The limiting magnitudes of the survey, defined at photometric errors smaller than 0.15 mag, are 20.6 mag (R) and 19.6 (I). We separate stars from non-stellar objects based on the object shapes in the R and I bands, attempting to reproduce the SDSS star/galaxy dichotomy. The completeness test indicates that the catalogue is complete to the limiting magnitudes. Comment: 31 pages, 15 figures, Accepted for publication in Astrophysics & Space Science
- SourceAvailable from: arxiv.org[show abstract] [hide abstract]
ABSTRACT: We present empirical color transformations between the Sloan Digital Sky Survey (SDSS) ugriz photometry and Johnson-Cousins UBVRI system and Becker's RGU system, respectively. Owing to the magnitude of data that is becoming available in the SDSS photometric system it is particularly important to be able to convert between this new system and traditional photometric systems. Unlike earlier published transformations we based our calculations on stars actually measured by the SDSS with the SDSS 2.5-m telescope. The photometric database of the SDSS provides in a sense a single-epoch set of 'tertiary standards' covering more than one quarter of the sky. Our transformations should facilitate their use to easily and reliably derive the corresponding approximate Johnson-Cousins or RGU magnitudes. The SDSS survey covers a number of areas that were previously established as standard fields in the Johnson-Cousins system, in particular, fields established by Landolt and by Stetson. We used these overlapping fields to create well-photometered star samples on which our calculated transformations are based. For the RGU photometry we used fields observed in the framework of the new Basel high-latitude field star survey. We calculated empirical color transformations between SDSS photometry and Johnson-Cousins UBVRI and Becker's RGU system. For all transformations we found linear relations to be sufficient. Furthermore we showed that the transformations between the Johnson-Cousins and the SDSS system have a slight dependence on metallicity. Comment: 11 pages, 7 figures, Accepted for publication in A&AAstronomische Nachrichten 09/2006; · 1.40 Impact Factor
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ABSTRACT: Selected results obtained in major observational sky surveys (DSS, 2MASS, 2dF, SDSS) and deep field observations (HDF, GOODS, UHDF, etc.) are reviewed. Modern surveys provide information on the characteristics and space distribution of millions of galaxies. Deep fields allow one to study galaxies at the stage of formation and to trace their evolution over billions of years. The wealth of observational data is altering the face of modern astronomy: the formulation of problems and their solutions are changing and all the previous knowledge, from planetary studies in the solar system to the most distant galaxies and quasars, is being revised.Physics-Uspekhi 11/2005; 48(11):1109. · 1.87 Impact Factor
arXiv:0912.2355v1 [astro-ph.IM] 11 Dec 2009
A Two-Colour CCD Survey of the North Celestial Cap:
I. The Method
Evgeny Gorbikov1, Noah Brosch1, and Cristina Afonso2
1The Wise Observatory and the Raymond and Beverly Sackler School of Physics and Astronomy,
the Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
2Max Planck Institute for Astronomy, K¨ onigstuhl 17, 69117 Heidelberg, Germany
December 11, 2009
We describe technical aspects of an astrometric and photometric survey of the
North Celestial Cap (NCC), from the Pole (δ = 90◦) to δ = 80◦, in support of the
TAUVEX mission. This region, at galactic latitudes from ∼ 17◦to ∼ 37◦, has poor
coverage in modern CCD-based surveys. The observations are performed with the
Wise Observatory one-meter reflector and with a new mosaic CCD camera (LAIWO)
that images in the Johnson-Cousins R and I bands a one-square-degree field with sub-
arcsec pixels. The images are treated using IRAF and SExtractor to produce a final
catalogue of sources. The astrometry, based on the USNO-A2.0 catalogue, is good to
∼ 1 arcsec and the photometry is good to ∼0.1 mag for point sources brighter than
R=20.0 or I=19.1 mag. The limiting magnitudes of the survey, defined at photometric
errors smaller than 0.15 mag, are 20.6 mag (R) and 19.6 (I). We separate stars from
non-stellar objects based on the object shapes in the R and I bands, attempting to
reproduce the SDSS star/galaxy dichotomy. The completeness test indicates that the
catalogue is complete to the limiting magnitudes.
The North Celestial Cap Survey (hereafter NCCS) is compiled from digital imaging obser-
vations of the Northern Celestial Cap region (δ ≥ +80◦) performed at the Wise Observatory
from February 13, 2009 with the 1-meter Boller and Chivens telescope and the Large Area
Imager at Wise Observatory (LAIWO) digital camera. The NCCS is a photometric and
astrometric catalogue in the Johnson-Cousins R and I bands (Johnson & Morgan, 1953;
Cousins, 1974) and is expected to contain more than 1,500,000 distinct objects. This paper
presents technical details of the project and a brief discussion of the quality of the first
The NCCS catalogue of point and extended objects supports the TAUVEX project.
The TAUVEX space telescope array, constructed by ElOp (Electro-Optic Industries Ltd.),
a division of ELBIT Systems, for Tel Aviv University with funding from the Israel Space
Agency (Ministry of Science, Culture, and Sport), consists of a bore-sighted assembly of
three 20-cm telescopes imaging in the vacuum UV the same ∼one-degree field of view from
geosynchronous orbit. Satellites in such orbits and, in particular, those used for telecommu-
nications, are normally not used for astronomy since they do not point-and-track celestial
objects. To allow the observation of various objects in the sky TAUVEX is mounted on the
side of the Indian Space Research Organization (ISRO) GSAT-4 satellite on a Mounting Deck
Plate (MDP) that can aim the TAUVEX line of sight (LOS) to different declinations, from
δ=+90◦to δ=-90◦. As GSAT-4 orbits the Earth on its geo-synchronous orbit, the TAUVEX
LOS scans a sky ribbon. The data transmitted to the ground station are reconstructed into
a set of UV images of the sky ribbon scanned by the experiment.
The scanning mode of observation used by TAUVEX implies that the motion of objects
through the TAUVEX field of view is done at the sidereal rate. Because of this, the exposure
times for each source vary with declination δ as
without requiring numerous re-scans of the same sky ribbon, the TAUVEX observations will
cosδ. In order to reach very deep exposures
mostly be restricted to the circumpolar regions and, for the first half-year of the mission,
the area to be observed will mainly be 90◦≤ |δ| ≤ 80◦; the northern sky patch covered by
TAUVEX in survey mode uses its three principal filters SF-1, SF-2 and SF-3. These
filters span the spectral region from somewhat longer than Lyman α to 320 nm with three
well-defined bands. Three filters define two color indices in the UV that can be combined
with optical (e.g., V-R or R-I) and eventually infrared color indices to characterize the nature
of detected sources.
The availability of visual and near-infrared photometric digital sky surveys from 1990’s,
such as DSS, SDSS and 2MASS, made the process of retrieving astronomical data easy as
never before and contributed greatly to the development of modern astronomy. Reshetnikov
(2005) presented a very good review of sky surveys and deep fields. Yet, very few high-
quality photometric data are available for the Northern Celestial Cap region. The NCCS
aims to produce a catalogue of positions and R-I color indices to complement the UV colours
obtained by TAUVEX.
The first high-quality digital sky survey, the Digitized Sky Survey (DSS), was produced
by scanning the plates of photographic surveys (POSS-I, POSS-II, ESO/SERC) with specific
photometric calibrations. Although the DSS and its extension DSS-II are both all-sky surveys
and cover the North Celestial Pole region, they are based on photographic observations and
suffer from photographic emulsion shortcomings, such as low sensitivity, limited dynamic
range and non-linearity.The limiting magnitude of the survey also differs for different
directions, depending on which photographic survey was used to retrieve the data (Blim∼=
20.m0 for POSS-I,∼= 22.m5 for POSS-II and∼= 18.m5 for ESO/SERC).
Another great ccontribution of these photographic surveys (POSS-I, POSS-II, ESO/SERC)
was to provide high-precision astrometry used in catalogues such as USNO-A1.0, USNO-
A2.0, USNO-B1.0, etc. The USNO-A and USNO-B catalogues were all-sky high-precision
astrometric catalogues including also photometric data. USNO-A included two-color (B and
R) one-epoch data, while the USNO-B catalogue included three-color (B, R and I) and two-
epoch data. The USNO-B1.0 catalogue included photometric data with an accuracy of 0.3
mag and astrometric data with an accuracy of 0.2 arcsec for more than a billion individual
objects as faint as V= 21.m0 (Monet et al., 2003). The catalogue provided separation with
85% accuracy of stars and non-stellar objects with internal magnitudes 14 ≤ MV ≤ 20.
The USNO-B1.0 catalogue was released at the same time that the SDSS early data release
became available. Monet et al. (2003) compared the two data sets and found “systematic
offsets as large as 0.25 arcsec ... taken as evidence for distortions of the USNO-B1.0 as-
trometric calibration”. Moreover, when transforming the catalogue magnitudes to SDSS
magnitudes and comparing common objects, systematic photometric errors as high as 0.20
mag and dispersions up to 0.34 mag were found, which can be explained probably by the
photographic nature of the catalogue.
Another digital sky survey is the Two Micron All Sky Survey (2MASS). 2MASS was
performed in the near-infrared (NIR): J (1.25 µm), H (1.65 µm) and Ks(2.17 µm) with two
robotic telescopes in the USA and Chile in 1997-2001. The NIR was chosen to minimize the
influence of galactic and extragalactic dust on the photometric data. 2MASS is not suitable
as a reference survey for the TAUVEX project by itself, since it is NIR only and is not
sufficiently deep, with limiting magnitudes J = 15.8, 15.0 mag, H = 15.1, 14.3 mag and Ks
= 14.3, 13.5 mag for point and extended sources respectively (Skrutskie et al., 2006).
The Sloan Digital Sky Survey (SDSS) covers about 10,000 square degrees of the sky and
provides high-precision photometric data in five Sloan bands with limiting magnitudes of
ulim= 22.m0, glim= 22.m2, r = lim = 22.m2, ilim= 21.m3, zlim= 20.m5 for point objects
and an astrometric accuracy of < 0.′′1 RMS per coordinate (Abazajian et al., 2009). SDSS
is not suitable as well for the TAUVEX project purposes, since it does not cover the North
Celestial Cap, but will be used here for comparison, as a commonly accepted standard.
The NCCS is essential for the TAUVEX project since no available survey completely
satisfies the requirements to support TAUVEX in this sky region. Here we describe the
method, the achieved accuracy, and provide a comparison with SDSS. In a following paper
we will present some preliminary results.
The observations were performed at the Wise Observatory, Israel, from February 13, 2009
in runs of 3-9 nights per month. The 1-meter telescope and the LAIWO camera were
used. LAIWO is a mosaic CCD camera built at the Max Planck Institute for Astronomy,
Heidelberg. The telescope and camera parameters are listed in Table 1.
The technical parameters of LAIWO determined during its construction were described
by Baumeister et al. (2006). For a more detail description of LAIWO and its performance see
Afonso et al. 2010, in prep. Nevertheless, we dedicate the following subsection to describe
its characteristics and performance for a better understanding of the potential and adequacy
of LAIWO for the NCCS survey.
The LAIWO camera consists of four Lockheed CCD486 4096×4096 pixel frontside-illuminated
devices, refered to as the science CCDs. The LAIWO observation manual and some techni-
cal details can be found in Kaspi (2009) and Afonso (2007). At the f/7 focus of the Wise
telescope each pixel subtends 0.43 arcsec and each CCD images a 29.5×29.5 arcmin2field.
The CCDs are mounted on a single heat sink cooled by liquid nitrogen (lN2) to -105±5◦C
and are individually connected to the lN2dewar with flexible copper bands. The chips are
not contiguous, but are spaced ∼26 arcmin apart. Each science CCD is connected to four
output channels to reduce the read-out time of the entire mosaic. Figure 1 shows the layout
Table 1: The Telescope and Camera Parameters:
∼4.9 square degrees
4 science + 1 guider
∼0.′′44 per pixel
∼40% between 600 and 850 nm
9 <RON< 19 e−
Focal length (f/7)
Secondary mirror diameter
Field of view
Number of CCDs
Nimber of pixels
Field of view
Peak quantum efficiency
of the LAIWO 16 quadrants in North-East orientation. The resultant image of an exposure
is a mosaic FITS file (Hanisch et al., 2001) consisting of 16 extensions.
The science CCDs exposures are binned 2×2 to match the typical seeing, reducing the
number of pixels to 16 Mpixel sampled to ∼ 0.′′87 arcsec per binned pixel. The read-out
time of the entire mosaic in 2×2 binning is only ∼28 sec.
A guider CCD is located at the center of the science CCDs mosaic. This is a back-
illuminated e2V CCD47-20 device with 1024×1024 13µm pixels, corresponding to 0.38 arcsec
pixel−1, with maximal quantum efficiency of ∼80% and covering a 6.′4 × 6.′4 field of view.
The science and the guider CCDs can be exposed separately and/or simultaneously. The
guider CCD usually takes continuous short exposures of a small region including a guiding
star. The image is compared to the previous one and, if the shift of the star photocenter
exceeds certain limits, the telescope pointing is corrected via a LAIWO-telescope interface.
The guider CCD images are not stored by default at the end of the night.
LAIWO has no dead or hot pixels, however all the flat field images taken with the camera
have all the pixels in column X=1 and in row Y=1 saturated in each quadrant. Row Y=2 in
each quadrant shows sometimes a few saturated pixels. Fig. 2 shows the World Coordinate
show LAIWO CCD layout. A clear-filter flat field imaged with LAIWO guider CCD on July
5, 2009 is shown at the center of the image. The relative sizes and distances are preserved.
I band flat field imaged with LAIWO science CCDs on June 12, 2009 used to
System specific to each LAIWO quadrant. Note that the saturated columns X=1 and rows
Y=1 in each LAIWO quadrant are the edge columns and the edge rows of each CCD; this
saturation feature is not observed in science images. For this reason, sources located near
the image edges are not extracted.
The entire LAIWO CCD array detects 1090±30 cosmic rays (CR) during a 300-sec ex-
posure (∼3.6 CR*sec−1). Most CRs produce ∼100-300 counts above the background, with
only ∼7% of the CRs produce more than 1,000 counts above the background. Table 2 shows
the average numbers of the CRs detected in each CCD from four 300-sec exposures of the
same field taken on May 14 and June 13, 2009.
Figure 2: WCS defined for each LAIWO quadrant. The relative sizes and distances are not
preserved here. The CCD identification and orientation are like in Fig. 1.
The edge-to-center (EC) flat field (FF) ratio of LAIWO is about the same for the R and I
bands and is ∼ 86%. Table 3 shows the EC values for each quadrant, extracted from twilight
FF images from June 14, 2009. The center FF value was extracted as the mean value of
the 16 pixels of the particular quadrant located near the CCD center. The edge value was
extracted as the mean value of the 16 pixels furthest from the CCD.
The LAIWO camera FFs exhibit different obscuration patterns, which are divided into
two groups: ring-shaped dust diffraction patterns (“donuts”) and irregular patterns (“fila-
ments”). Fig. 3 shows examples of these patterns, observed on FFs from June 12, 2009.
The donuts are produced by dust particles located on the filter or on the CCD window and
affect the exposure level at a ∼1% level. Their location and number may vary from filter to
filter and from night to night. The filaments are produced probably by dust particles or tiny
debris located on the CCDs themselves. They dim the light by ∼20% and their location is
Table 2: LAIWO CR Sensitivity:
> 1,000 counts
Table 3: Edge-to-Center Flat Field Ratio of the LAIWO Camera:
I-band Flat Field
R-band Flat Field
Figure 3: LAIWO dust difraction patterns. Panel (a) shows a donut pattern in I band flat
field. Panel (b) shows a filament pattern in R band flat field.
constant for all the filters, but their number may change from night to night. These features
are observed also in science images. We eliminate their influence by using FFs taken in the
same night and by imaging the same sky field three times with dithering of ∼15′′, to prevent
the appearance of the features on the final, debiased, FF-subtracted and median-combined
A 0-sec exposure of LAIWO camera shows a bias level of ∼ 400 ± 20 counts pixel−1
(hereafter 1 count = 1 ADU). A 300-sec dark exposure produces an additional dark level
of 3 ± 3 counts pixel−1(∼0.01 counts pixel−1sec−1). Bias/dark exposures taken at the
beggining and at the end of a night show the same bias/dark levels.
Using SExtractor (Source-Extractor, SE; Bertin & Arnouts 1996), we obtained Kron
(1980) aperture parameters for all the objects 2σ above the background noise from an image
of the Landolt (2009) standard field SA107 taken on June 14, 2009 at an airmass of 1.175. The
Kron aperture is an elliptical aperture fitted individually to every object. The parameters
of Kron aperture are a, b and θ, the semi-major and semi-minor axes and the position angle
of the main axis, respectively. The a and b parameters of the Kron aperture are analogs of
the FWHM of circular aperture.
By exposing this image at a low airmass we eliminate the effect of atmospheric dispersion
which is further reduced by the filter bandpass restriction. The ellipticity of the objects may
arise from an optical distortion, from some CCD tilt, from inaccurate tracking/guiding or
from a combination of these factors. We divided every quadrant into 3×3=9 regions and
calculated the mean value of a, b and θ of the objects in them. The results are plotted
in Fig. 4. In a number of quadrants the major axes are directed mostly from the camera
center outwards. The exception is CCD2 (upper-right corner) where the ellipses seem to be
directed almost randomly. Note that the ellipse elongation on the X axis is greater than that
on Y axis.
Figure 4: LAIWO distortion picture. The grey circle at the center is for scaling and shows
an ideal circular object with FWHM 2”. The quadrant layout is as shown in Fig. 1.
2.2 Observational Strategy
The NCCS observational strategy is to obtain three 300-sec exposures of each field in the
two Johnson-Cousins filters R and I, with a small ∼15′′dithering between the exposures.
The three 300-sec exposures are then registered and median-combined to allow the detection
of fainter objects and to reduce random noises such as sky and object Poisson noise, dust
interference patterns, cosmic rays, satellite tracks, etc. Biases, 300-sec darks and twilight
FFs are also taken at the beginning of each night. Landolt (2009) photometric standard
stars are observed, usually during one night of the run, whenever the weather conditions
allow. For runs when no Landolt standards are observed, the photometric calibrations are
derived from the overlapping regions of the particular run and other runs.
The fields are chosen using two selection criteria. The first is that they should be as
close to the meridian as possible and they should be higher than the North Celestial Pole to
be observed at the lowest possible airmass. We try to follow the meridian during the night,
however the hour angle deviation from the meridian may sometimes be up to 3h. The second
criterion is that the following field should have a small overlap region with the previous field
to provide a contiguous coverage of the NCC region, filling in the “empty” spaces between
the CCDs in LAIWO array.
3 Data Reduction
The reductions are done using a fully-automated pipeline written in IRAF (Image Reduction
and Analysis Facility; Tody 1986) script. The pipeline uses the SE program (Bertin & Arnouts,
1996) to obtain object fluxes from the images, and the WCSTools (World Coordinate Systems
Tools) package of programs (Mink, 2002) to extract astrometric standards from USNO-A2.0
catalogue (Monet, 1998). The pipeline input consists of all the images of a particular night.
The pipeline output is a list of objects containing the parameters defined in Table 4. Most
of the data are extracted automatically by the SE routines. The pipeline runtime (including
reductions, photometric and astrometric calibrations) is about 6 hours for one observing
The pipeline median-combines all the bias and dark exposures to obtain master bias and
master dark frames. The master bias is subtracted from the FFs and the debiased FFs are
median-combined with mode scaling to obtain master flat frames for the R and I bands. The
master flats are normalized, each quadrant to its median. The master dark is subtracted
from the science images and the dark-subtracted science images are then normalized by the
master flats. The normalized science images are then split into 16 separate images, one per
CCD quadrant, keeping the common WCS aligned (East to the left, North up).
All the images are grouped by the sky imaged field, by the number of the quadrant
and by the filter. Each group contains three 300-sec debiased, dark-subtracted and flat-
Table 4: Pipeline Output Parameters:
Object position along X
Object position along Y
Corrected isophotal flux
RMS error for ISOCORR flux
RMS error for Kron flux
RMS error for Petrosian flux
SE internal flags
of Kron apperture
of Kron apperture
of Kron apperture
of Kron apperture
of Kron apperture
fielded exposures of the same quadrant in the same field, taken with the same filter. For
each image in the group the shifts produced by dithering are calculated. The earliest taken
image between the three is used as the reference frame. The images are then registered to
cover exactly the same field. The images in each group are then median-combined to obtain
one less noisy 300-sec exposure, as explained above. The resultant image contains only the
overlapping region of the three original images; rows and columns out of the overlapping
region are filled by the median value of the overlapping region.
The combined science images are scanned with SE. We prefer SE photometry to IRAF
photometry since it is very fast and robust. We define the scanning threshold of the SE to be
2σ above the noise fluctuations, which corresponds to a point-object detection probability
We use Kron (1980) aperture photometry to determine the flux of the objects, which uses
an elliptical adaptive aperture, for a number of reasons:
1. LAIWO produces elongated objects even at low airmass as shown in Fig. 4.
2. The survey area is relatively close to the horizon (Alt = 20◦− 40◦, airmass∼= 2.0),
therefore all point sources will be slightly elongated by the atmospheric dispersion. For
point sources, this seems preferable to that of a circular aperture.
3. Elliptical apertures are natural for extended sources. Moreover, galaxy Kron fluxes
can be easily transformed into Petrosian fluxes (Graham & Driver, 2005), which are
used in the SDSS.
4. The Kron photometry is flexible, since the aperture is fitted individually to each object.
5. The Kron photometry provides additional parameters of the detected objects, such as
semi-major and semi-minor axes, inclination angle, ellipticity and elongation. These
parameters are very useful for star/galaxy separation and for field distortion estimation.
The SE subtracts the sky counts from the object counts. We set the background sub-
traction parameters of the SE to local background fit and subtraction. For each saturated
object, or one that overlaps with another, has poor photometry, is truncated, etc. the SE
ascribes an internal flag. The SE defines as truncated an object that is close to the edge
of a quadrant, that may not necessarily be the edge of the common region of the three
initial 300-sec exposures. The source lists need therefore to be cleared from false detections
produced by objects located only partly in the common region of the combined image. The
pipeline ascribes the truncation flag to all the objects located closer than 10 pixels to the
edge of the common region of the combined images.
The pipeline also calculates the airmass of the image and the effective airmass of the
combined 300-sec exposure, which we define as the mean airmass of the three initial expo-
sures. The airmass that appears in the output lists is the effective airmass of the combined
4 Photometric calibration
The photometric calibration is relative to Landolt (2009) standards. Currently the photo-
metric calibration program is not a part of the pipeline. Some modified parts of the pipeline
and an adittional program written in MATLAB are used for photometric calibrations. If
the standard data for a run are missing, we derive calibration equations from objects in the
overlapping region between a particular run and another run when standards were observed.
The following calibration equations were obtained from the June 14, 2009 night. The
Landolt SA107 field, which contains stars with R and I magnitudes of about 10m−15mand
R - I colours from −0.m5 to +1.m4, was observed at 11 airmasses from 1.17 to 3.16 with
120-sec exposures. The calibration coefficients were obtained from the Kron fluxes of 18
standard stars. The following calibration equations were derived:
R = −2.5log(NR/t) − (0.155 ± 0.006)X + (0.001 ± 0.042)(R − I) + (20.952 ± 0.023)
I= −2.5log(NI/t) − (0.092 ± 0.004)X + (0.349 ± 0.029)(R − I) + (19.743 ± 0.016)
where N/t is the object flux in ADU sec−1and X is the airmass.
We define as ‘grey’ magnitudes mIand mRthe object magnitudes obtained from equa-
tions (1) without including the colour term. We also define the instrumental colour mR−mI
as the difference between the grey magnitudes of the object in the respective filters. Using
calibration equations (1), the relation between the instrumental and Landolt colours is:
R − I= 0.742(mR− mI)
∆(R − I) = 0.742?∆m2
I+ (mR− mI)2(0.0422+ 0.0292)
Equation (2) allows the transformation of fluxes to magnitudes in two stages, since the R
and I images of the same field would not necessary be of exactly the same field due to small
changes in telescope pointing and image dithering. The detected objects would not have
exactly the same X and Y, and some would possibly miss I or R exposures till later stages
of the survey. Moreover, one needs to know the true (R - I) colour of each object to perform
the correction of magnitudes in equation (1) for the colour term, and the object true (R - I)
colour is usually not known beforehead. Therefore, the photometric transformation needs to
be done in two stages: first, to obtain the grey magnitudes from the fluxes, and second, after
the astrometric solution for the field is found, to correct the grey magnitudes for the colour
terms, using colours obtained from equation (2). This yields the true R and I magnitudes of
Fig. 5 shows the Landolt colours vs. the calculated instrumental colours and the line
predicted from equation (2). The fit of the photometric solution in equation (1) to the
magnitudes ofthe Landolt standards has a root-mean-square error σ = 0.047 mag and σ =
0.033 mag in the R and I bands respectively.
Figure 5: Landolt colour vs. Instrumental colour. The black solid line shows the relation
predicted by the equation (2).