The issue of saturation effects due to limitations in the dynamic range of the COSMOS measuring machine has already been dealt with at length in Sect. 3.5 (click here). The other most common causes of systematic errors in photographic photometry include: differential de-sensitisation of photographic emulsions due to exposure to atmospheric oxygen and water-vapour, vignetting, uneven and/or inadequate hypersensitisation (these effects can prevent the sky density reaching the threshold necessary for a linear response on those areas of the emulsion affected) plate defects (such as scratches or spurious "images'' that are wholly artefact) and inadequacies in background-fitting, sky-subtraction and calibration procedures (which also depend on the accuracy of the reference measurements e.g. photoelectric aperture- [or simulated-aperture-] photometry measurements).
As can be seen from Fig. 13 (click here) and SFig. 14 (click here), for Fields A and B the mean
zero-point offset between the isophotal magnitudes generated from the different
plates is small:
, whilst
for Fields C and D it is quite substantial:
. Significant de-sensitisation of
Plate J4882 over most of Fields C and D was found to be the cause of this
disparity. J4882 was the inferior plate of the two, almost certainly because
it was taken before an important modification was made to the UKST plate-holder
in December 1982. This modification enabled the plate holder to be flushed with
dry nitrogen (which is inert as far as the emulsions are concerned) during
exposures, thus preventing de-sensitisation.
Note that as J4882 is quite a dark plate (i.e. emulsion densities
due to the sky are quite high) the problem in this case was not that the
differential de-sensitisation depressed the sky brightness below the threshold
for a linear response on the part of the emulsion, but rather that the relative
density-to-intensity calibration was based largely on that part of the
emulsion's characteristic-response curve between the linear portion and the
saturated portion. As the sky was very dense throughout Fields A and B, this
calibration was quite adequate for these fields. However, over large areas of
Fields C and D, the sky density was depressed onto the central part of the
characteristic curve's linear portion for which the adopted
relative-calibration polynomial was poorly determined.
As the magnitudes were based on both plates in the cases of Fields A and B,
but
by necessity just on Plate J9229 in the cases of Fields C and D
,
the errors are
higher for the latter fields.
Mean standard errors on those mean magnitudes that were derived from
two plates are tabulated
in Table 6 (click here), and were multiplied by
in
order to obtain values applicable to magnitudes derived from one plate.
Corresponding errors on the reduced
isophotal radii are
shown in Table 7 (click here)
.
magnitude range | two plates | one plate |
![]() | 0.06 | 0.08 |
![]() | 0.08 | 0.11 |
![]() | 0.10 | 0.14 |
|
magnitude range | two plates | one plate |
![]() | 4.9% | 6.9% |
![]() | 4.5% | 6.4% |
![]() | 4.0% | 5.7% |
|
Vignetting arises as a consequence of geometric shadowing effects inherent to
many telescope designs including that of the UKST. The net effect is that
off-axis light is not transmitted as efficiently to the image plane as is
on-axis light, with the fractional reduction in efficiency increasing
with off-axis distance.
In the case of the UKST, the fractional reduction in efficiency is
within
of the axis. As the survey area is
across and more or less centred on the plate centre, only four small
areas near to the corners of the survey area could possibly be affected,
if the sky density failed to reach the threshold for a linear response (on the
part of the photographic emulsion) within these regions. In Sect. 3.3 (click here),
it was mentioned that the skies were established to be flat. In order to
test for the significance of any apparent slope in the estimated sky as a
function of radial distance from a plate's centre, the sky values estimated for
the positions of those galaxies with published aperture photometry measurements
were plotted as a function of radial distance.
Although, in the case of the U9362 (see Fig. 17 (click here)) there does at
first sight appear to be a slight fall off in estimated sky brightness as a
function of off-axis distance, the size of the slope was found to be
. In other words, the uncertainty
on the slope is very much larger than the best estimate of the slope. In the
case of J9229, there is even less evidence for any radial variation as this
slope was found to be
. These
slopes were computed by means of bootstrap resampling with 10 000 realisations
in each case, and using as many data points for each galaxy as there were
individual aperture measurements for that galaxy; even though only
one data point (the mean sky estimate) is shown in Fig. 17 (click here) for each
galaxy's
position. In summary then, whilst more calibrating galaxies beyond the
limit would really be required to establish conclusively that
vignetting had been properly accounted for, no evidence has been found for
significant radial variation in the skies of Plates J9229 and U9362. This does
not of course rule out the possibility that there is significant radial
variation, but it does establish that the random disagreements between other
observers' aperture photometry measurements constitute a much larger effect.
The 1 ranges of sky density values for Plate J9229 in Fields A, B, C and D were
635-679, 660-690, 540-700 and 545-690 density units respectively. Ignoring
localised regions affected by prominent objects,
the sky density was subject to variation
of the order of 10% (625-690 units) over 95.8% of the scanned area of Plate
J9229. The remaining 4.2% corresponded to the corners of the combined area of
the four fields, where vignetting reduced the densities. The vignetting was
most severe in the outer corners of Fields C and D, where the densities were
reduced to about 550 units. Apart from the issue of how well vignetting has
been compensated for (which has already been dealt with) the accuracy to which
the sky could be determined depended on the noise associated with the
background measurements and any bias there may have been in the determination
of the mode sky density values to which the background fits were applied.
The bias in the estimation of mode densities was found to be of the order of
of a sky unit, in the sense that the sky brightness was slightly
overestimated. This figure of 0.06% was arrived at by comparing the adopted
estimate of the mode for each bin (containing 7225 pixels) with that mode value
obtained by interpolating a histogram of density values for that bin. As
described in Sect. 3.2 (click here), there were typically 2000+ bins not significantly
affected by extended objects. The interpolation process involved fitting a
Gaussian curve to the central portion of each histogram's modal peak,
using Starlink's ESP package.
The sample standard deviation in the sky values with respect to the background
fits was less than 0.25% in sky units (0.20%, 0.22%, 0.23% and 0.25% for
Fields A, B, C and D respectively). This is considerably larger than the
bias effect which will henceforth be neglected. The VPC's limiting
-isophote of
, was 5.6% of Plate J9229's sky
intensity. The random component of the uncertainty on the limiting isophote due
to background fitting errors is therefore at most
for Plate J9229.
Figure 17: The estimated surface brightness of the sky on Plate U9362 for the
positions of galaxies with published U-band aperture photometry, as a
function of radial distance from the plate centre. Note that the points
plotted are means for each galaxy, and that some points are very much more
significant than others due to either (1) being based on more aperture
photometry measurements and/or (2) because they are based on more
independent observers' measurements
One of the advantages of having a slight displacement between the different
J9229 and J4882 fields was that if an image happened to be truncated by the
edge of a field in one coordinate system, it was unlikely to be truncated in
the other system. It was therefore possible to base the magnitudes of
such galaxy images on the most suitable plate. As a result, edge-of-field
effects have been minimised, though Fig. 18 (click here) was plotted in order to
provide a check on the effectiveness of the background-fitting procedure at the
extremities of a field where interpolation was not possible. As can be seen
from this figure, the magnitude measurements do tend to be noisier at the field
edges than at the field centres, but the increase in noise with distance from
the field centres does appear to be quite gradual and without any very steep
increase near the edges.
Figure 18: Individual standard errors on those mean magnitudes that were
derived from both
plates (overlapping images excluded) as a function of
distance from the nearest field edge measured in 2.1 pixels
Overlaps between adjacent images could not always be resolved satisfactorily during the image segmentation. Magnitudes and indeed other photometric parameters are therefore less reliable for images with overlapping isophotes, and particularly so in cases where the brightest overlapping isophote approaches the mean (or even the peak) surface brightness quoted for the galaxy.
As the measured mean and peak surface-brightness parameters
(as opposed to the extrapolated ones)
quoted in the VPC have not been corrected
for effects that degrade image resolution;
namely diffraction, atmospheric seeing, sampling due to
the pixel size of the plate scans and the smoothing of the scans prior to image
segmentation; they tend to be slight over-estimates of the true values as
measured in . Unsaturated composite-stellar-profiles (as
described in Sect. 3.5 (click here)) were measured in order to estimate the degree to
which the resolution of each image had been degraded by smearing effects,
particularly the smoothing of the plate-scan data. The FWHM
of the unsaturated composite stellar profiles were found to be
in the case of U9362,
in the cases of the two
plates and
in the case of R2936.
Of the four plates reduced, R2936 (for which the limiting isophote adopted
corresponded to 10.4% of the sky) was the noisiest, followed by J4882 (7.7%),
J9229 (5.7%) and the least noisy U9362 (3.1%). It
was unfortunate that without such severe smoothing, limiting isophotes
brighter would probably have to have been adopted as noise peaks in the
plate-scan data would have degraded the images around their edges. The smoothing
was also very necessary to reduce image fragmentation (the segmentation of
individual galaxy images into two or more major components).
In order to investigate the extent to which the VPC's isophotal magnitudes
have been degraded by atmospheric seeing, sampling and smoothing; model-galaxy
profiles were convolved with a
FWHM Gaussian
distribution.
Only relatively small images were considered, as the significance of the
degradation decreases with increasing image size.
The results are tabulated in Table 8 (click here), in which the approximate changes
in isophotal radius,
, and isophotal magnitude,
,
are shown for a variety of different Sérsic profile
parameters (intrinsic index, n, and intrinsic central surface brightness,
,) and for a variety of small intrinsic isophotal radii,
. As can be seen from Table 8 (click here), even though
the effects on the isophotal radii can be quite significant, the errors
introduced to the isophotal magnitudes are typically of the order of several
percent (i.e. several hundredths of a magnitude) even for the small images
considered, and are in most cases insignificant compared to the other
sources
of error quantified earlier. Also, note that a coarse resolution function
can cause observed isophotal radii to be either larger or
smaller than their intrinsic values, in other words the effect is not
uni-directional.
n | ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() ![]() |
0.25 | 16.5 | +13 +0.16 >17.7 | +7 +0.06 >17.4 | +5 +0.03 >17.2 | +3 +0.01 >16.9 |
0.50 | 22.0 | [+3 +0.06 19.7]![]() | +3 +0.04 19.0 | +3 +0.03 18.4 | -1 -0.02 17.9 |
0.50 | 23.5 | [-1 -0.08 20.3]![]() | [+1 +0.00 19.4]![]() | +1 +0.00 18.8 | -5 -0.11 18.4 |
1.00 | 22.0 | [+5 +0.06 19.2]![]() | +5 +0.04 18.5 | +5 +0.03 17.9 | +3 +0.01 17.4 |
1.00 | 23.5 | [-1 -0.07 20.1]![]() | [+1 +0.00 19.2]![]() | +1 +0.00 18.6 | -3 -0.06 18.2 |
2.00 | 22.0 | +9 +0.03 18.8 | +9 +0.03 17.9 | +7 +0.02 17.3 | +5 +0.01 16.9 |
2.00 | 23.5 | [+1 +0.00 19.7]![]() | +1 +0.00 18.9 | +1 +0.00 18.3 | +1 +0.00 17.8 |
|
The standard error on each mean colour, as quoted in the VPC, is
based upon two colour values generated from either of the two following
plate combinations:
1) U9362 and J4882, U9362 and J9229
2) R2936 and J4882, R2936 and J9229.
Assuming that U9362
and R2936 are of similar quality to the plates, the standard
errors quoted in the VPC need to be multiplied by
in order to
obtain meaningful estimates of the standard errors on the quoted colours,
as tabulated in Table 9 (click here).
magnitude range | (![]() | (![]() | ||
2 plates | 1 plate | 2 plates | 1 plate | |
![]() | 0.18 | 0.20 | 0.19 | 0.22 |
![]() | 0.17 | 0.19 | 0.16 | 0.18 |
![]() | 0.16 | 0.18 | 0.16 | 0.18 |
|
Systematic errors must also be present due to differences between the resolution
functions inherent to different plate scans. Systematic differences between the equal-area
and total colours were however found to be very small in the case of the index,
though more noticeable in the case of the
.
The estimated random errors on the total magnitudes quoted in the VPC are
listed in Table 10 (click here). They are based on several assumptions and
approximations, and are therefore only intended as rough estimates. The
mean extrapolation from to
is 0.35 mag, and the
estimated standard error on a mean extrapolation was taken to be
magnitudes. This value was propagated with each of the mean standard
errors on
values listed in Table(s) 6 (and 10) to yield mean
standard-error estimates on
values. From Fig. 8 (click here)
it can be seen that the uncertainty on any estimate of
(B-V) based on a value of (
) is
mag. The
offset between the B and
systems is
, whence the mean
error in the
-to-
conversion
was taken to be 0.07 magnitudes. This was
increased to 0.1 magnitude in order to take into account uncertainties in the
colour-coefficient term, and propagated with the mean standard deviation
estimates for
values in order to obtain mean standard deviation
estimates on
values.
The mean extrapolations from U25 to
and from
to
were found to be 0.45 and 0.25 mag respectively. Therefore the random errors on the
colours can be expected to be considerably smaller than those on
the
ones. This was confirmed by intercomparisons between
the equal-area and total colours.
Magnitude range | ![]() | ![]() | ![]() |
Two plates: | |||
| 0.06 | 0.13 | 0.16 |
![]() | 0.08 | 0.14 | 0.17 |
![]() | 0.10 | 0.15 | 0.18 |
One plate: | |||
| 0.08 | 0.14 | 0.17 |
![]() | 0.11 | 0.16 | 0.19 |
![]() | 0.14 | 0.18 | 0.21 |
|
In the absence of alternative measurements for most of the objects suffering from saturation effects in the VPC, those sources listed in Sect. 5 (click here) have had to suffice. It is hoped that for the bright galaxies concerned, these sources are reasonably reliable.
An indication as to the accuracy of the astrometry is given by the residuals between the positions as quoted in the AGK3 catalogue and those calculated according to the plate solution adopted. The root-mean-squared residual was 2.28 (0.87 in right ascension and 2.11 in declination). As the segmentation software did not centroid the galaxy images, but assigned (x,y) coordinates to the brightest pixel within each image, this quantity is, as expected, quite similar to the pixel size of the segmented images: 2.148. The lack of a centroiding algorithm was not a problem for the saturated galaxies however, as RC3 positions were generally adopted for them.
These errors were taken from those sources of radial-velocities listed in Sect. 5 (click here) without modification. In the cases of the following VPC (VCC) objects, there are very large mutual disagreements between different sources in the literature, and the true errors may be very much larger than the values quoted: VPC 25, 424, 447, 502, 545, 624 and 810 (which correspond to VCC 325, 815, 870, 945, 1035, 1148 and 1355 respectively).
Owing to the small plate scale of the UKST plates, and the high degree of saturation exhibited by many of the galaxy images, even approximate typing was not always possible. The majority of those morphological types obtained from the VCC (see Sect. 5 (click here)) were presumed to be correct, but one mis-classification was noticed. Binggeli et al.'s (1985) VCC 500 was classified as an S0, instead of as a ringed-spiral. This has been corrected in the VPC. Note that the re-classifications listed in de Vaucouleurs & Corwin (1986) all concern spiral-galaxy subclasses, and are therefore beyond the scope of the broad classifications provided by the VPC.