From erik Thu Feb 12 09:59:54 1998
Subject: CUO_26 APT photometry
To: gaia-sag@astro.estec.esa.nl (GAIA SAG)
Date: Thu, 12 Feb 1998 09:59:54 +0100 (MET)

Note on 20 Feb 1999:
===================
This is the design of NBP photometry that was updated today
by CUO_55, 56. The Sections 4 (Surface photometry) and 7 (Astrophysics)
may still be of interest. 
See discussion of CUO_26 in CUO_55, Section 2.
See CUO_53 for formulae and new notation.

A brief notation key is:
Feb. 98   Jan. 99
 ARVI      Spectro telescope
 APT       NBP
 PSM       ASM in Astro instruments
 FSM       BBP in Astro instruments


Estimation of background. APT photometry
========================================

E. Hoeg, J. Knude        12 February 1998            SAG_CUO_26


ABSTRACT:
Estimation of the sky background on-board the GAIA satellite is
required in the detection process of the sky mappers (SM) in the two
main telescopes and in the APT. It is also required for the photometry
in the APT in order to keep an acceptable data rate.
An algorithm is described and analyzed for APT photometry in the
Stromvil system.  It is shown that it gives reasonable values at 
all galactic latitudes.  The precision of multicolour photometry 
of the sky surface brightness and of stars with the APT is derived 
(see Tables 3-5 and 9). 

A main conclusion is that useful photometry of stars with 
10.0<V<16.0 can be obtained even if only two numbers per star, 
background and total flux, are transmitted to ground. Furthermore, 
observations of sky surface brightness are obtained as a by-product. 
Such observations from GAIA are to a higher degree free from 
contaminating star light than other observations of the sky surface.



1. Goal of study and basic assumptions
--------------------------------------
The ARVI Photometric Telescope (APT) is now the agreed name for which
we previously, e.g. in CUO_23, wrote 'ARVI photometer'.
The APT performance is studied with respect to star
photometry and to measurement of the sky background.
The sky background is determined by a median method and its sensitivity
to parasitic stars is evaluated. The star is detected in the APT SM 
(sky mapper) measuring in a wide V-band (Vw). The star is then 
integrated in six Stromvil bands as proposed in CUO_23. 
This system has recently become a provisional baseline
for APT photometry, i.e. a placeholder until further studies may show
something better. With these bands chosen it is appropriate to detect
in the Vw-band which is approximately centred on the Stromvil bands.

The star+background is estimated as the sum of some 
4*4 pixels = 2.0*2.0 arcsec^2 (see Table 1)
centred on the position of the star as obtained in the SM.
A more sophisticated estimation by fitting e.g. a two-dimensional 
profile to the counts of an area of pixels could be envisaged, 
but we have chosen to study the qualities of the simple sum.

The Table 1 contains parameters of the GAIA instrument from the
mid-term presentation by MMS in January 1998. 
Thus, the pupil of the main telescopes and the Airy ellipse 
(r_xA, r_yA) have changed with respect to Table 1 in CUO_23. 
The pixel sizes have changed for both instruments, now 
wpix*hpix=10*10 um^2 is assumed for the APT.

-------------------------------------------------------------------
Table 1. The GAIA photometric instruments, mid-term Jan. 1998. 
See also Table 7 with the photometric system.
 
                      2*FSM      APT
Pupil              1.7*0.7 m   0.7*0.75 m
A_pupil    [m^2]      1.190    0.525
f          [m]           50     4.17
scale [arcsec/mm]     4.125    49.46
scale      [s/mm]    0.0344    0.412
h_ccd      [deg]       0.66      1.0
l_ccd      [deg]      0.133      1.0
A_phot.ccd [deg^2]    0.088      1.0
Product [m^2 deg^2]   0.105    0.525
pixel      [um]        9*30    10*10
wpix       [mas]         37      500 along scan dimension
hpix       [mas]        124      500 cross scan dimension
r_xA       [mas]         85      206 at 700 nm
r_yA       [mas]        206      206 at 700 nm
-------------------------------------------------------------------
 
The following two sections are adapted from CUO_13.


2. Formulae for photometric precision
-------------------------------------
The following derives general formulae for the standard errors and
signal-to-noise ratio (SNR or F) related to CCD photometry carried 
out as described above. Thus the position of the star on the CCD is
known from the SM and the scan rates.

A peak is in the following defined as a peak in consecutive
one-dimensional readings from the CCD, or as a peak in the
two-dimensional image. In the latter case we shall e.g. assume that 
pixels in a 4*4 square contain all the star light of a star 
near the centre of the square. The sum of the counts of these
16 pixels consists of the star signal S [e-] and the background light
collected by the 16 pixels. This sum is subject to photon noise,
readnoise and disturbance from other (parasitic) stars.

Definitions and assumptions:
 
  n_c = number of pixels in a co-added sample 
  n = number of samples used to determine the peak
  t = integration time [s]
  S = star signal in n-sample peak, unit is [e-] 
  P = total counts in n-sample peak [e-] 
  b = sky background [e- per sample]
  r = readnoise [e- per sample or per pixel]
  F = signal-to-noise ratio (SNR)
  Flim = limit of SNR above which a peak is detected.
 
The peak amplitude derived from observation is called P 
consisting of a star signal contribution S, and
a background from the sky of size n*b, thus
 
P = S+n*b                               (1)
 
The variance of P is
 
sg_P^2=P+n*r^2=S+n*b+n*r^2              (2)
 
since P is assumed to have basically a Poisson distribution with the
variance P to which is added the Gaussian readnoise contribution 
from n samples.
 
The sky background b is estimated, e.g. by a median method, from a
number of pixels near to, or surrounding, the peak. This number 
should be several times n, say 5*n, so that the error of the 
estimated b can be neglected compared with the error of P. 
 
The signal estimate is obtained from the observed P and b as
 
S = P-n*b                               (3)
 
Its variance is accordingly
 
sg_S^2=sg_P^2 + (n*sg_b)^2              (4)
 
The signal-to-noise ratio of a signal S is generally defined 
as the ratio
 
F=S/sg_S                                (5)
 
We thus obtain a formula suited for performance prediction:
 
F=S / sqrt[S+n*b+n*r^2 + (n*sg_b)^2]    (6)
 
If N observed sky patches of the same star are superposed
the resulting F is obtained from Eq.(6) by multiplication with sqrt(N).
 
The simpler formula 

F=S / sqrt[S+n*b+n*r^2]                 (7)
 
may be used in cases where the sky background is low and well known
so that the last term in Eq.(6) containing sg_b can be neglected.
This is not usually the case as we shall see below because it contains
the factor n^2.
 
It is noted that the standard error of the magnitude m
estimated from a peak is 

sg_m = 1.086/F [mag]                    (8)

and that the standard error of F is

sg_F=1-0.5*F^2/S.                       (9)
 
The location of a peak has the approximate standard error

sg_xy=sg_PSF / F                        (10)

where sg_PSF is the standard deviation of a gaussian fit to
the PSF in respectively x or y directions. This follows from 
the location error of sg_g/sqrt(N) of a pure Gaussian with the 
sigma sg_g, without background and containing N electrons.
 
 
3. Estimation of the background for APT photometry
--------------------------------------------------
A median method is proposed for estimation of background and the 
resulting standard errors and systematic errors (bias) are given. The
following error sources are taken into account: Poisson noise,
readnoise, disturbance from other stars, here called parasites.
Other error sources are assumed to be negligible or can be calibrated
out: e.g. dark current, pixel-to-pixel sensitivity variations,
lumpiness of the sky surface.

The background is estimated as the median of the readings of k
consecutive pixels close to the point in the field where it shall be
used, i.e. within a few arcsec. A number of 20 to 40 pixels will give a 
sufficient precision and accuracy to match the accuracy of the 
estimate of the star light. The latter is obtained as the sum 
of 4*4 pixels in the APT. The following discussion takes the 
APT photometry as example, but can easily be adapted to the case 
of detection in the main telescopes (see Section 5). 

The standard error of the estimated median is, according to ESA SP-1200,
Volume 1, Equation 1.3.15

sg_b.med = sqrt(pi/2)*sg_b1/sqrt(N)         (11)

where N is the number of pixels and sg_b1 is the standard error of 
the single pixel value.  This is valid in case of pure Gaussian 
noise, as when the photon noise plus readnoise dominates. 

At high star densities the median would be disturbed by the stars close
enough to shed light on some of the k pixels. Such parasitic stars have
to be inside a rectangle centred on the line of pixels and having an
area

A_b= (2*wpix+2*r_xA)*(k*hpix+2*r_yA)        (12)

In case of k=20 we have A_b=14.7 arcsec^2.

The average number of stars in an area A is A*N(m) where N(m) is the
number of stars per deg^2 brighter than m. The number of times there
are approximately i stars brighter than m in the area is then derived 
from a Poisson distribution. This accounts for optical double stars, 
and the physical double stars generally act as one star at 
the magnitudes and pixel sizes we are concerned with. At e.g. m=15 
it is unlikely that pairs with separations beyond 0.6 arcsec 
are physical doubles.

A parasite can add light to one or two pixels, thus up to 2*i pixels are
affected. Consider now that the content were known for the N pixels
unaffected by parasites and that an unaffected 'old' median had been
determined. Each of the 2*i affected pixels will with 0.5 probability
be larger than the old median in which case the new median will not 
be changed. If it is smaller than the old median the result will 
be a higher new median value only in case the added light is 
sufficient to make the pixel content larger than the new (!) median. 
This will usually happen if the parasite gives a total signal
S >2*sg_b1. This takes tentatively into account the chosen size of 
A_b and the division of the star light often on 2 pixels.

We consider the case of the Stromvil v-band measured for 3s in the APT.
For V=15 we have S=880 e- (see Table 5). Assuming the readnoise
to dominate we have sg_b1=r=3 e-. A star of V=21 then gives S=4 e-, just
about the mentioned limit. Fainter stars will generally not give
individual disturbance of the median, but by the light from 
their large numbers they could influence the median background.

Thus, on average i values are changed to become higher than the 
new median. This increases the median by an amount

b_bias = i/N/0.40*sg_b1                (13)

where 0.40 is the ordinate phi(0) of the normalized Gaussian curve.
The formula is approximately valid for i/N<0.25. 

The probability p(i) of a given value of i is obtained from the Poisson
distribution and is given in Table 2. The average bias of the
median background from stars brighter than V=21 is

b_bias.ave= sum(b_bias * p(i))        (14)

It appears from the two cases in Table 2 that the average bias does
not depend on the number of pixels used in the background estimate. It
depends only on the average number of parasitic stars brighter than
some magnitude limit, but not on the brightness of these as long as
they are not very bright.  A similar table should be computed for the 
use of 4-pixel samples for the background estimation, as in Figure 1(d).

If the star+background signal is estimated as the sum of 4*4=16 pixels
the direct use of the estimated median background would give a signal 
with a bias up to 16*b_bias.ave=3.6 e- for the case considered, 
corresponding to 0.004 mag for a star of V=15 mag, still at the 
Galactic centre. This bias could be computed and be partly corrected 
on the ground when the stars become known from the survey.

The standard error of the estimated background will depend on the 
number of pixels as given by the Eq.(11), which is valid if there 
are only a small number of parasites in the area. The value to be used
in Eq.(6) is sg_b=0.59 e-/pixel=n_c*0.59 e-/sample for r=3e- 
and N=40 pixels. We assume the same readnoise for one pixel as for a
co-added sample. The contribution in Eq.(11) for n_c=4 is then 89, 
i.e. larger by a factor 2.5 than the preceding term n*r^2=36 if n=4, 
and will therefore dominate for the faintest stars. For the case of the
APT this term has been shown to be small enough even at V=17 if 
N=40 pixels.

Four possible arrangement of pixels for background estimation are shown
in Figure 1. (a) shows the simplest arrangement with background pixels
before and after the star. The median of all these gives a correct
background even in the presence of a linearly sloping sky background.
(b) The same is true here. The special advantage here would be that the
number of pixels to read slowly in each column is smaller so that a low
readnoise can more easily be achieved than in (a).

In the option (c) the background would be equally disturbed by 
parasitic stars in the single crossing as (a) and (b) because about 
the same number of independent pixels are used. But for the mission as
a whole with the various scan direction the disturbance would be larger
because a smaller total area is sampled.

In (c) is shown that 4*4 pixels are used for the star, with
co-addition of 4 pixels. Co-addition is recommended in order to reduce
the readnoise. The 4 pixel height is required to cope with up to 0.17
arcsec/s vertical motion, i.e. 0.5 arcsec during the 3 s required for
four of the Stromvil bands. Probably 5 pixel height is required for the
6.5 s integration of the u and P bands.

In all cases a sky background with a peak or valley near the star
would lead to a biased background. This could be taken into account
on the ground if two background values were transmitted, one from the
20 pixels closest to the star, the other from those further away.

Figure 1(d) shows 40 co-added background samples.
The background error sg_b is dominated by readnoise when single pixels
are used. This problem could be solved by using the same co-addition in
the background samples as for the star. This should be
further studied. This has in fact been done in Section 4 on surface
photometry, but not in Section 6 on star photometry, for lack of time.

---------------------------------------------------------------------
Table 2. Parasites with V<21 mag at the Galactic centre.
An area A_b=14.7 arcsec^2 centred on 20 pixels on a line contains
on average n=0.60 stars. p(i) is the probability that there are i
parasites in the area.

i              0     1     2     3     4     5  |  b_bias.ave

For N=20 pixels:
p(i)        0.55  0.33  0.10  0.02  0.003    -
b_bias      0.00  0.38  0.75  1.12  1.50  1.88    0.227 e-/pixel

For N=2*20=40 pixels:
p(i)        0.30  0.36  0.22  0.09  0.026 0.006
b_bias      0.00  0.19  0.38  0.56  0.75  0.94    0.227 e-/pixel
---------------------------------------------------------------------


---------------------------------------------------------------------
Figure 1. Four possible arrangements of samples for background 
estimation.  (a)-(c): 20+20 pixels are shown as an example, 
placed before and after the 4*4 or 4*5 pixels to be used for 
star signal estimation. With a pixel size of 500*500 mas^2 the 
background will be derived from about 70 arcsec^2 of the sky during 
the mission in the options (a) and (b), given the various scan 
directions.  (d): 40 co-added samples are used.

(a)  10 arcsec vertically          (b)  10 arcsec vertically

---> star motion
 _                 _                 _                       _
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|
|_|               |_|               |_|  _               _  |_|
|_|               |_|                   |_|             |_|
|_|               |_|                   |_|             |_|
|_|    _ _ _ _    |_|                   |_|   _ _ _ _   |_|
|_|   |_|_|_|_|   |_|                   |_|  |_|_|_|_|  |_|
|_|   |_|_|_|_|   |_|                   |_|  |_|_|_|_|  |_|
|_|   |_|_|_|_|   |_|                   |_|  |_|_|_|_|  |_|
|_|   |_|_|_|_|   |_|                   |_|  |_|_|_|_|  |_|
|_|               |_|                   |_|             |_|
|_|               |_|                   |_|             |_|
|_|               |_|                _  |_|             |_|  _
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|
|_|               |_|               |_|                     |_|



(c)

       5 arcsec            pixel=0.5*0.5 arcsec^2
<------------------->
 _     _                 _     _ 
|_|   |_|               |_|   |_|
|_|   |_|               |_|   |_|
|_|   |_|    _ _ _ _    |_|   |_|
|_|   |_|   | | | | |   |_|   |_|
|_|   |_|   | | | | |   |_|   |_|  5 arcsec vertically
|_|   |_|   | | | | |   |_|   |_|
|_|   |_|   |_|_|_|_|   |_|   |_|
|_|   |_|               |_|   |_|
|_|   |_|               |_|   |_|
|_|   |_|               |_|   |_|


(d)

       5 arcsec            sample=0.5*2.5 arcsec^2
<------------------->
 _ _ _ _ _ _ _ _ _ _ _ _ _ _
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
|_|_|_|_|_|_|_|_|_|_|_|_|_|_|
| | | |               | | | |
| | | |    _ _ _ _    | | | |
| | | |   | | | | |   | | | |
| | | |   | | | | |   | | | |  10 arcsec vertically
|_|_|_|   | | | | |   |_|_|_|
| | | |   | | | | |   | | | |
| | | |   |_|_|_|_|   | | | |
| | | |               | | | |
| | | |               | | | |
|_|_|_|_ _ _ _ _ _ _ _|_|_|_|
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
|_|_|_|_|_|_|_|_|_|_|_|_|_|_|
---------------------------------------------------------------------


4. Multicolour surface photometry with the APT
----------------------------------------------
The background measurement in an spot about 70 arcsec^2 centred on each
star provides the background required for the photometric reduction of
each star. It gives also a multicolour measurement of the surface 
brightness in the spot which may be of distinct scientific value.
The result would be spots centred on the 100 million brightest stars 
on the whole sky.  It appears from Table 3 that the mean sky with
brightness about V=22 mag/arcsec^2 could obtain multicolour photometry
with a precision about 0.02 mag/arcsec^2 in the Stromvil bands.

It would also be possible to acquire the multicolour surface
brightness with 10 arcsec resolution of all areas of the sky exceeding
a certain  brightness. For this purpose the APT sky mapper could 
be used to detect when the surface brightness in visual light 
exceeds a given limit, about V=19 mag/arcsec^2. This brightness 
could be detected with a SNR of about 4.0 (see Table 4). 

After a detection the action could be to sample the colour bands around
the position. The background, i.e. the surface brightness, in each 
band could then be computed onboard, or perhaps the pixel values 
should be transmitted. This possibility is discussed below in
connection with Table 4, and rejected on scientific grounds.

A surface photometry would, however, come as a by-product from APT
photometry. An expert in the field should discuss the expected 
scientific value of the photometry at the time it would become 
available some 15 years from now.

The measurement of the UV sky surface at 350 nm should be studied
since the origin of this radiation is still unknown, and the
observations may contribute to our understanding of the optical
properties of the dust grains.

We have considered whether measurements
of the surface brightness could perhaps be used to map the 
Halpha emission from the warm ionized component of the Galaxy 
interstellar medium.  About 10 per cent of the disk volume is 
occupied by this component.  A large fraction  of the sky area 
below 10 deg galactic latitude has a brightness from Halpha 
exceeding 1.0*10^-5 photons per (cm^2*s*arcsec^2).  This is derived 
from the numbers 3.5 - 6.8 photons per (cm^2*s*arcsec^2) obtained
from (5 - 10)/(4*pi) photons per (cm^2*s*sr^1) given by 
Reynolds (1984 = ApJ 282, 191).

The 1.0*10^-5 corresponds  to 0.025 e-/pixel=0.10 e-/sample
for a sample of 4 pixels in the Stromvil S-band. It could therefore 
*not* be measured with precision in a 5 year mission (see Table 3). 
We have supposed that the continuum could be subtracted by means of the 
background measured in the wide Sloan r'-band.  The contamination 
from [SII] at 671.7 nm is negligible since the ratio 
[SII]/Halpha=0.3 - 0.5 in the interstellar background, and 
since [SII] is reduced to 5 percent by suppression in the wing of
the S-band.

At higher latitudes the filling factor is larger that 10 per cent, but
the surface brightness is about 10 times lower and cannot be measured
by the APT.

The Halpha emission from localized HII regions (Stroemgren spheres)
is 100 - 1000 times higher, even 10000 times in the Orion nebula.
The 100 times means a brightness of 10 e-/sample in the 3s integration
of the S-band. But in the 0.2s integration of the Vw
detection band (APT-SM) only 0.2 e-/pixel would be measured. 
A detection requires about 10 e-/pixel, according to Table 4.  
Thus, only few bright regions would exceed the detection limit. 
And it is not worth while to initiate special data taking since 
the areas would anyway be sampled around every sufficiently 
bright star, and because they can be mapped by dedicated CCD 
exposures from the ground.

The detection in the APT-SM of stars in an area giving a background 
of V=15mag/sq.arcsec, i.e. 100 times the average background, is hampered
by about 1 mag, as appears from the precision given in Table 8.3.


---------------------------------------------------------------------
Table 3. Multicolour surface photometry with the APT.
The values are given as function of the sky surface brightness in V,
assuming a sky spectrum as a G2V star. The values are given for
measurement in the Stromvil S-band (at 656 nm, FWHM=20 nm, 3s
integration per crossing.) A sample of 4 co-added pixels was assumed
(cf. Figure 1(d)). A readnoise of r=2 e- was assumed.
The standard errors for the mission (last column)
are based on 100 crossings. 
Unit: m/a^2=mag/arcsec^2.

              | One crossing  | 100 crossings
Ssurf   Ssurf   sg_b1 sg_b.med  sg_b.mis 
   V
m/a^2  e-/pix  e-/pix  e-/pix      m/a^2

 15.0    1758    42.0     8.3
 16.0     700    26.5     5.3      
 17.0     279    16.8     3.3      0.001
 18.0     111    10.7     2.1       .002
 19.0    44.2     6.9     1.4       .003   
 20.0    17.9     4.6     0.9       .006  
 21.0     7.0     3.3    0.66       .010 
 22.0     2.8     2.6     .52       .020
 23.0     1.1     2.3     .45       .044   
 24.0    0.44     2.1     .42       .102  

---------------------------------------------------------------------


---------------------------------------------------------------------
Table 4. Detection of high surface brightness with the APT sky mapper.
The values are given as function of the sky surface brightness in V,
assuming a sky spectrum as a G2V star. The values are given for
observation in a wide visual Vw band and 0.2 s integration time per 
crossing, according to the value of b in Table 5 and the use of 
20 background pixels.  A readnoise of r=10 e- was assumed.
Unit: m/a^2=mag/arcsec^2.

              |    One crossing   |    
Ssurf   Ssurf   sg_b1 sg_b.med  F    
   V
m/a^2  e-/pix  e-/pix  e-/pix   -   

 16.0     170    16.4     4.6  >10
 17.0      68    12.9     3.6  >10
 18.0    26.9    11.3     3.2  8.5
 19.0    10.7    10.5     2.9  3.6
 20.0     4.3    10.2     2.9  1.5

---------------------------------------------------------------------

The following formulae were used for Tables 3 and 4, derived from 
Equations 2-9..

sg_b1^2 = Ssurf + r^2                    (15)

where Ssurf in [e-/sample] is derived from Table 5 for the S-band.
The rates for V=15.0 are about 1800 e-/0.2s in the wide band Vw and 
1800 e-/3s in Stromvil S-band. Readnoise of r=10 e- has been 
assumed for the fast reading of the sky mapper, and r=2 e- for the 
spotwise reading of the Stromvil bands.

The error of the median, sg_b.med, is obtained from Eq.(11) for N=40.
So, this number of independent pixels from the sky mapper is used to 
determine a median.

The error for the mission is given for the average of 100 crossings
by

sg_b.mission = 1.086*sg_b.med/10/Ssurf   (16)

The SNR for one crossing is

F = Ssurf/sg_b.med                       (17)


5. Sky mapper detection 
-----------------------
The idea is to detect the stars above a certain limit of SNR in the APT
SM. Find the centroid position of each star in the SM, and predict 
the position in the following CCDs by means of the known scan 
rates so that the samples shown in Figure 1 can be collected in 
each of the 6 Stromvil bands and be analyzed before transmission 
to the ground.

Since the SNR can only be computed if the background is known, the
first process with the SM pixels is to derive the background. We
propose to do so for every consecutive 20 pixels (=10 arcsec) by 
means of the median method.

The stars are found as peaks consisting of one pixel in the SM higher 
than its neighbours, as basically proposed by MMS. Such a pixel 
contains at least 26 per cent of the total star flux and this 
fraction of the flux is given in the following tables of performance
for the SM. The SM measures through a wide visual band Vw (see Table 7)
which will give a standard error about 0.2 mag at V=17.0 mag for all
spectral types (see Table 9), corresponding to SNR=5. 

The position of each peak is obtained by a centroiding using 9 pixels
centred on the peak; and *only* 3*3 pixels should be used. 
This should give a correct position within 0.2 pixels, sufficient 
for the subsequent sampling in the Stromvil bands.

If two detected stars are separated by less than 10 arcsec their
sampling patterns (Figure 1d) may overlap so that a decision must
be taken which star to be observed. At least two strategies could be
discussed. Only one of them should be used at any one time, 
but perhaps only for a part of the mission.
(1) Take the first star. The other one will then be measured at some
other directions of the scan.
(2) Take the brightest. The other one will then hardly ever be
measured.

The faintest stars will not be detected in every crossing due to
statistical fluctuations of photons and the star's position relative to
the pixels. The error from the last source of uncertainty can 
be diminished by computing a second SNR using the flux and a local 
background obtained from the centroiding. The flux will be based on
analysis of 3*3 pixels and therefore more accurate than the flux in
only one pixel used for the first SNR. The local background e.g. as in
Figure 3a will also be more accurate. Only stars with the
second SNR above a given limit should be observed in the bands.
This should give a sharp detection limit in Vw magnitudes thus
providing as many observations as possible for the stars above the
limit and as few as possible for those below. An average of 
100 observations for these stars is expected from a 5 year mission.

The detection method described here could be adapted for use in
the PSMs of the main telescopes. Perhaps 2*2 pixels should be coadded 
giving effective pixels of 18*60 um^2 = 74*248 mas^2, about 
equal to the radii of the Airy ellipse (see Table 1).


6. Photometry of stars
----------------------
The expected precision of APT photometry for stars of G2V and
interstellar absorption A_V=0 mag is given in Table 5.
Details at the bottom of the table should be understandable from the
preceding text. 

The sensitivity to two basic parameters, readnoise and number of pixels
used for background, is shown and discussed in Table 8 (see ANNEX)
to be compared with Table 5. It is essential for faint stars to have a
readnoise r=2 e- and to use 40 background samples as finally selected
for the Tables 5 and 9.

The sensitivity to the sky background is discussed in Table 8.

The precision for other spectral types and absorption are given 
in Table 9 and is commented in the following section.

------------------------------------------------------------------
Table 5. Precision of APT photometry for one field crossing. 
Division by 10 gives the precision for 100 crossings.

G2V   A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :  400-700 nm   
 
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 11.3      13    11    10     9     7     6     6
13.0 12.3      21    18    15    15    12    10    10
14.0 13.3      34    28    25    23    19    16    16
15.0 14.3      57    47    40    38    30    26    27
16.0 15.3     103    82    69    64    50    43    44
17.0 16.3     205   155   129   115    87    74    76
---------------------------------------------------------
V=15.0: S=    450   623   820   883  1394  1851  1769 [e-/n samples]
        t=    0.2   6.5   6.5   3.0   3.0   3.0   3.0 [s/star]
   ncoadd=      1     5     5     4     4     4     4 [pixels/sample] 
        n=      1     4     4     4     4     4     4 [samples/star]
Backgr: b=    1.7   3.1   4.1   3.5   5.6   7.4   7.0 [e-/sample]
    nback=     20    40    40    40    40    40    40 [pixels/backgr.]
     sg_b=    2.8   2.1   2.2   1.8   1.8   1.9   1.9 [e-/sample]
Rnoise: r=     10     2     2     2     2     2     2 [e-/sample]
---------------------------------------------------------


The bias in v about 0.004 mag for a star of V=15 mag at the Galactic 
centre due to parasitic stars in the background estimation was 
discussed in Section 3.

A parasitic star inside an area 

A_s= (5*wpix+2*r_xA)*(4*hpix+2*r_yA)      (18)

i.e. A_s=7.0 arcsec^2, centred on the 4*4 pixels in Figure 1
will bias the flux derived from these pixels. The bias will more or
less be repeated in all observations of the star. The bias may be
partly corrected lateron by means of the Sloan photometry known for the
parasitic star(s), if the proposal in CUO_22 is followed.
We may assume that the bias from a 3 mag fainter star can be
sufficiently corrected, i.e. within a few mmag on the main star 
magnitude.  If e.g. the magnitude difference is equal to 3 mag the
parasitic effect on the b-y index is less than 15 mmag which may easily
be corrected.

The average number of stars brighter than m within the area A_s is 
n=A_s*N(m). Table 6 gives the numbers for the Galactic centre.
Thus, even at such high star densities an accurate photometry for the
vast majority of stars of V=15 and brighter can be obtained. Stars with 
too bright parasites for a proper correction will be known from 
the sky survey obtained with the main telescopes.

A strategy could be to reject observations with parasites brighter than
V=18.0 in the star area, i.e. 2 per cent at the Galactic centre. 
Fainter parasites should be subtracted using multicolour photometry.
Parasites in the background area should also be taken into
account. For the final reduction this requires the results of the
multicolour survey in the main telescopes. 

I order to make a preliminary reduction it is proposed to transmit 
the SM information (x, y, total flux, background) for all detections, 
not only for those being measured in the bands. This would give a 
survey in visual light for all stars with Vw<17.5 without adding much
to the telemetry rate. It could be more quickly available than the
final multicolour survey.


Stromvil system:
The six bands given in Table 7 have been selected as proposed by V.
Straizys a few months ago. The Stroemgren y-band was been omitted since
it can perhaps be replaced by one of the Sloan bands. Should this not
be sufficiently accurate for the astrophysical utilization a fifth
filter could be inserted in the FFOV. If these filter are allocated
equal observing time they could obtain 2.2 s instead of the present 3 s.
The result would be that the tabulated standard errors in vbZS would
be obtained at 0.34 brighter magnitudes than given in the present
tables and the y-precision would be close to that of Z.


Area collected for the star:
An area of 4*4 pixels =2.0*2.0 arcsec^2 (see Table 1) will contain all 
light from a star, taking into account the Airy radius of 206 mas at 
700 nm, the TDI smearing, width due to stellar duplicity, optical 
aberrations, scan speed mismatch and a reasonable position uncertainty. 
This requires that the latter four error sources together contribute 
less than 300 mas.  This may be too tight, especially due to possible
duplicity. A solution could be to take 5 samples=2.5 arcsec along scan
instead of 4, which would have only few disadvantages. Another solution
would be to correct the star flux based on the later knowledge of
satellite attitude and stellar content at all magnitudes as obtained 
from the multicolour survey in main telescopes.

The longer wavelengths than 700 nm need not be taken into account 
since the longest Stromvil wavelength is the S-band at 656 nm. 
In the cross-scan direction a motion up to 0.17 arcsec/s gives a 
smearing up to 1.1 arcsec in the 6.5 s integration of the u and P bands 
and up to 0.5 arcsec in the 3 s integration of the other bands. 
Therefore, 5 pixels are collected across scan for u and P and 
4 pixels for the other bands. These must be co-added during 
readout in order to keep a low readnoise, assumed to be 2 e-.


Dynamic range:
A non-linear response is expected about 200.000 e- in a sample (TBC).
This would only occur for any spectral type in any band for a star
fainter than V=10.0 if the S-value given in Table 9 for V=15.0 is 
higher than 2000 e-. This happens only a few times and only in the 
u- and P-bands for B1V and in the S-band for highly reddened stars.  
Even for such cases the measurements would sometimes be in the linear 
regime, depending on where the star happens to be located relative 
to the pixels. It is therefore correct to say that all stars fainter 
than V=10.0 can be measured in all bands unaffected by non-linearity, 
and many stars brighter than V=10.0 can sometimes be measured, 
at least in some of the bands.


Cosmic hits:
MMS expects up to 4000 hits per second in the 1s PSM. This corresponds
to 182000 hits per sq.deg per second in the PSM and 1300 hits/sq.deg/s
in the APT due to the shorter focal length. This corresponds to 
1.7 hits/0.2s in the SM area which adds a negligible number of false
stars. It corresponds to 0.003 hits per 3s in the area of 
100 sq.arcsec containing the star and background for the typical 
Stromvil band, which is negligible for the APT accuracy. 
(The calculation on cosmic hits given in CUO_23 should be ignored.)


------------------------------------------------------------------
Table 6. Star densities at the Galactic centre. A_s=7.0 arcsec^2.
The number in V magnitudes, not in I, are relevant in relation to the
Stromvil system.

V      [mag]           18      19       20
N(V) [star/deg^2]   40000   85000   193000
n    [stars/A_s]    0.022   0.046    0.104
------------------------------------------------------------------


------------------------------------------------------------------
Table 7. The assumed CCD arrangement in the APT photometer.
 
APT photometry, preceding and followings fields:
 
PFOV:
SM  0.2s  detection , flux in 400-700 nm = Vw
    1s =2.4mm space
u   6.5s  flux, at 350 nm, FWHM=30 nm, Tmax=0.40
    1s =2.4mm space
P   6.5s  flux, at 374 nm, FWHM=26 nm, Tmax=0.42 (1)
   15.2s  =total
 
FFOV:
v   3s  flux, at 411 nm, FWHM=19 nm, Tmax=0.60
    1s =2.4mm space
b   3s  flux, at 467 nm, FWHM=18 nm, Tmax=0.70
    1s =2.4mm space
Z   3s  flux, at 516 nm, FWHM=21 nm, Tmax=0.80  (2)
    1s =2.4mm space
S   3s  flux, at 656 nm, FWHM=20 nm, Tmax=0.80
   15s  =total
 
Notes: 
(1) The Stromvil P at 374 nm, the Balmer jump, is included. It is
reddening sensitive while Hbeta is not. Hbeta may perhaps be
obtained from ARVI spectroscopy (see CUO_16).
(2) Possibly the y-band must be inserted (see Section 5):
y   2.2s  flux, at 547 nm, FWHM=23 nm, Tmax=0.80 
    1s =2.4mm space
------------------------------------------------------------------


7. Astrophysical comments
-------------------------
Following the tables with the expected errors in the uvbPZS photometry
and applying the accuracy of 10 muas in the parallaxes one might 
consider some applications of the astrometric/photometric combination.
The possible availability of radial velocities has *not* been included
in the following discussion. The comments are given separately for the
four spectral types in Table 9, resulting in some overlap of
scientific issues.

The K3III stars. The photometric metallicity can be determined with an
accuracy sigma_[Fe/H] <= 0.25 (V=15, A_V=0), <= 0.22 (V=14, A_V=0) and
<= 0.26 (V=12, A_V=5). Parallaxes might in fact be used to search for
better [Fe/H] determinations via the M_V,[Fe/H],u,b,y,P,Z relations.
In the galactic windows at (l,b) approximately (0,0) deg the kinematics 
of K3III stars may trace the velocities W and V over the distance range 
(R_sun,R_sun -5 kpc). In the anticenter direction data from (l,b) 
in the third quadrant close to l = 180 may similarly provide data for 
(R_sun,R_sun +5 kpc).  Obviously A_V = 0 also applies at high 
galactic latitudes where U and V may be studied in a volume complete 
sense for |Z| <= 5000 pc. With resulting density profiles one 
would be in the unique situation that the same type of tracer might 
be used in the disk and in the inner halo.  With A_V = 5 and the 
demand that sigma_[Fe/H] <= 0.20 the limiting magnitude rises to V=12 
and the K3III stars are confined to the volume within 200 pc. 
Since the K3III stars are rather frequent their photometry might be 
used to map out the dust distribution with A_V < 5 in nearby 
molecular complexes. An application could be to study the 
A_V - N(CO) relationship which is uncertain for A_V exceeding 
a few magnitudes.

The G2V stars. Assuming V=16 and A_V = 0 [Fe/H] may be determined from
the delta(m_1) index with an accuracy better than 0.18 dex for [Fe/H] 
ranging from solar to about -3 dex. The corresponding upper 
distance limit is 1800 pc, accurate to 2%. For high galactic 
latitudes this means very accurate stellar volume densities in a 
volume complete sense of a very frequent stellar type. Ages, [Fe/H] 
and log(g) may be estimated. Combining the data from the plane and 
poles the data comprises U,V,W, [Fe/H] for a volume complete sample 
for |Z| out to 2 kpc. This would be an excellent data set for studies
of the Galactic structure.
Adopting A_V=5 and V=15 and sigma_[Fe/H] <= 0.2 dex limits the 
G2V stars to the volume within 200 pc.

The A0V stars have approximately the same M_V as the K3III stars 
but have a much large flux in the blue photometric bands. 
Accuracies as quoted above for the K3III stars are thus obtained 
for fainter V magnitudes. A significant difference is of course 
that we sample a much younger population with the A stars and 
consequently may study other phenomenae. With A_V = 0 and V=17 
we may have data from distances beyond 10 kpc maintaining an 
accuracy of 0.02 in del_m1 implying that we can discern solar 
and metal rich A stars.  A stars may thus be studied at 
|Z| > 10 kpc, including BHB stars. At 10 kpc the relative distance 
accuracy is 10%. The existence of young mergers may be studied 
in great detail.

Finally the B1V stars with A_V = 5. The photometric classification 
is not a problem from e.g. the Q(u,P,v) - Q(P,v,b) diagram. 
Sigma_Q(u,P,v) = 0.075 and sigma_Q(p,v,b) = 0.013. Spectral 
classification is no problem but the luminosity classification 
might be for the earliest B type stars.  The luminosity class may 
anyway have very little to do with stellar evolution according to 
recent Hipparcos results. The early B stars span the same distance 
range as the K3III stars but with V=15 and A_V = 5. V and W may 
thus be studied outside the galactic windows and compared to the K3III
results. Due to the difference in stellar ages it is most 
interesting to do this comparison.  Another item concerning the B1V 
stars is the dynamics of very young clusters themselves.
Another important application of the early type stars is to use 
the measured distances and absorptions for determining the 
scale length of the interstellar dust and for answering the 
question whether the Galaxy's disk is optically thick. In the 
solar vicinity, which may not be typical, the disk is marginally 
optical thick. An optically thick disk with a substantial scale 
length may be part of an explanation of the Galaxy's flat 
rotation curve.


8. Data rates
-------------
Number of stars with V<17.0  2240 stars/sq.deg (LL_120) =92*10^6 on sky.
Scan speed 120 "/s -> 0.033 sq.deg/s -> 75 stars/s entering the APT.
MMS, p.4, of Payload Data Handling 1050 stars/s per band.


The reading of CCD pixels and samples:
0.5" pixel/120 "/s = 4.2 ms to read 7200 pixels across each CCD.
Reading in the SM at 2 MHz takes 3.6 ms. 
Corresponding readnoise = 8 e- according to MMS, p.16, Payload Design.

Reading the samples in the bands at 200 kHz gives readnoise = 2e-.
This takes 4*0.005 ms=0.02 ms per star requiring 4 samples (Figure 1d).
Flushing at 7.5 MHz (as MMS FPA p.11) takes 1 ms.
4.2-1.0 mas=3.2 ms allows 160 stars/10"/band -> 60.000 stars/sq.deg.
This is the upper limit of star density where all data could be read.


Our calculation of data rates:
We have assumed a square root coding of flux and background.
                    per band        per crossing
Total flux, coded      10      *7 = 70 bits
Background, coded      10      *7 = 70
x,y for SM only                     64
Datation                            32
                                   ---
Total                              236 bits/star per crossing

           236 bits/star *75 stars/s -> 17.7 kbits/s total on average.

This calculation disagrees with MMS's  420 kbits/s
which we do not understand. So here is a question <<<<<<<<<<<
Is the "datation" required in every band ? But even that could not
explain the factor 20 discrepancy.
What does datation contain ?

If the data rates would permit, we propose to transmit more than the
flux and background per band. This could allow some information on
stellar duplicity and on variing background to become available on the
ground.


9. Conclusion
-------------
(a) The photometric accuracy for star observations has been 
predicted when using very simple onboard algorithms for the 
estimation of background and background+star. The expected 
accuracy for each of six Stromvil bands (uPvbZS) is better 
than 0.01 mag for early stars (<=G2) brighter than V=16.0 
for the average from 100 observations obtained during a 5 year mission. 
This is a large fraction of the 40 million stars with I<15.0 
for which the highest astrometric accuracy of 10 microarcsec 
is expected.

(b) The estimated photometric accuracy is based on the use of the 
planned multicolour survey from the main GAIA telescopes in the 
final reduction where parasites are taken into account. This is
important in areas with high star density.

(c) The measured surface brightness (see Section 4) around every star 
is a by-product from the APT. We studied in Section 4, as an example,
whether the Stromvil S-band may be used to map the Halpha emission 
from the warm ionized component of the Galaxy interstellar medium.
The result was negative in this case. But the APT (and GAIA SM) surface
photometry is to a higher degree free from contaminating light from
stars than other observation methods owing to the median method applied
in determining the background. This fact and the full sky
coverage could make some unique surface brightness observations 
possible.

(d) The possible CCD imperfections have not been taken into
account for lack of precise information. Cosmic hits have been shown to
be negligible.
------------------------------------------------------------------====
 
                   ANNEX
                   =====

Table 8. Sensitivity to two basic parameters and the sky background.

Table 9. Four types G2V, B1V, A0V, K3III. A_V=0 and =5 for each.


------------------------------------------------------------------
Table 8. Sensitivity to two basic parameters and the sky background.
The two first tables show the precision with different assumptions on 
readnoise (r=3 e-) and number of samples (20) used for the background. 
The final choice was r=2 e- and 40 samples, used in Table 5 and all 
following tables. The effect is quite significant for the faintest
stars. Part #3 shows the effect of a very high sky background of V=15
mag/sq.arcsec. All precisions are then shifted to about 1 mag brighter.


Part #1:

The expected background of V=21.0 mag/arcsec^2:

G2V   A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 11.3      13    11    10     9     7     6     7
13.0 12.3      21    18    16    15    12    10    10
14.0 13.3      34    30    26    24    19    16    17
15.0 14.3      57    54    46    41    32    27    28
16.0 15.3     103   107    87    76    56    47    48
17.0 16.3     206   233   185   153   109    89    92
---------------------------------------------------------
V=15.0: S=    450   623   820   883  1394  1851  1769 [e-/n samples]
        t=    0.2   6.5   6.5   3.0   3.0   3.0   3.0 [s/star]
   ncoadd=      1     5     5     4     4     4     4 [pixels/sample] 
        n=      1     4     4     4     4     4     4 [samples/star]
Backgr: b=    3.3   3.1   4.1   3.5   5.6   7.4   7.0 [e-/sample]
    nback=     20    20    20    20    20    20    20 [pixels/backgr.]
     sg_b=    2.8   4.3   4.4   3.5   3.6   3.7   3.7 [e-/sample]
Rnoise: r=     10     3     3     3     3     3     3 [e-/sample]
---------------------------------------------------------
 
Part #2:

Lower readnoise: r=2 for non-SM. Significant effect:

G2V   A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 11.3      13    11    10     9     7     6     7
13.0 12.3      21    18    15    15    12    10    10
14.0 13.3      34    29    25    24    19    16    17
15.0 14.3      57    49    42    39    31    26    27
16.0 15.3     103    90    75    68    52    44    45
17.0 16.3     205   182   148   127    94    79    81
---------------------------------------------------------
V=15.0: S=    450   623   820   883  1394  1851  1769 [e-/n samples]
        t=    0.2   6.5   6.5   3.0   3.0   3.0   3.0 [s/star]
   ncoadd=      1     5     5     4     4     4     4 [pixels/sample] 
        n=      1     4     4     4     4     4     4 [samples/star]
Backgr: b=    1.7   3.1   4.1   3.5   5.6   7.4   7.0 [e-/sample]
    nback=     20    20    20    20    20    20    20 [pixels/backgr.]
     sg_b=    2.8   3.0   3.1   2.5   2.6   2.7   2.7 [e-/sample]
Rnoise: r=     10     2     2     2     2     2     2 [e-/sample]
---------------------------------------------------------
 
Lower but realistic background of V=22.0 mag/arcsec^2
has been tested but had only little effect.
 
 
Part #3:

Now about 100 times higher background

G2V   A_V=0.0  V_back/sq.arcsec=15.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 11.3      13    14    12    11     9     8     8
13.0 12.3      22    27    24    21    17    14    15
14.0 13.3      40    59    51    44    35    30    31
15.0 14.3      77   138   120   101    80    69    71
16.0 15.3     166   336   292   243   193   167   171
17.0 16.3     387   833   725   599   475   412   422
---------------------------------------------------------
V=15.0: S=    450   623   820   883  1394  1851  1769 [e-/n samples]
        t=    0.2   6.5   6.5   3.0   3.0   3.0   3.0 [s/star]
   ncoadd=      1     5     5     4     4     4     4 [pixels/sample] 
        n=      1     4     4     4     4     4     4 [samples/star]
Backgr: b=  433.1 778.51024.4 882.61394.31851.11769.4 [e-/sample]
    nback=     20    40    40    40    40    40    40 [pixels/backgr.]
     sg_b=    6.5  12.5  14.3  11.9  14.9  17.1  16.7 [e-/sample]
Rnoise: r=     10     2     2     2     2     2     2 [e-/sample]
---------------------------------------------------------
------------------------------------------------------------------
 

------------------------------------------------------------------
Table 9. Four types G2V, B1V, A0V, K3III. A_V=0 and =5 for each.
The basic observation parameters are the same at all stars and 
are given only for the first.
 

G2V   A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 11.3      13    11    10     9     7     6     6
13.0 12.3      21    18    15    15    12    10    10
14.0 13.3      34    28    25    23    19    16    16
15.0 14.3      57    47    40    38    30    26    27
16.0 15.3     103    82    69    64    50    43    44
17.0 16.3     205   155   129   115    87    74    76
---------------------------------------------------------
V=15.0: S=    450   623   820   883  1394  1851  1769 [e-/n samples]
        t=    0.2   6.5   6.5   3.0   3.0   3.0   3.0 [s/star]
   ncoadd=      1     5     5     4     4     4     4 [pixels/sample] 
        n=      1     4     4     4     4     4     4 [samples/star]
Backgr: b=    1.7   3.1   4.1   3.5   5.6   7.4   7.0 [e-/sample]
    nback=     20    40    40    40    40    40    40 [pixels/backgr.]
     sg_b=    2.8   2.1   2.2   1.8   1.8   1.9   1.9 [e-/sample]
Rnoise: r=     10     2     2     2     2     2     2 [e-/sample]
---------------------------------------------------------

G2V   A_V=5.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0  9.4      11    44    31    23    12     8     4
13.0 10.4      17    77    52    37    20    12     6
14.0 11.4      28   144    93    62    32    19    10
15.0 12.4      47   301   181   110    54    31    16
16.0 13.4      82   683   392   215    95    52    26
17.0 14.4     158  1639   912   464   183    92    42
---------------------------------------------------------
V=15.0: S=    630    43    83   150   487  1310  4724 [e-/n samples]
---------------------------------------------------------

B1V   A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 12.3      13     4     4     6     6     6     9
13.0 13.3      20     7     7     9     9     9    14
14.0 14.3      33    11    11    14    15    15    22
15.0 15.3      55    18    18    23    24    24    36
16.0 16.3      98    29    29    37    39    40    60
17.0 17.3     194    48    48    63    67    68   109
---------------------------------------------------------
V=15.0: S=    483  3810  3798  2294  2116  2131  1017 [e-/n samples]
---------------------------------------------------------

B1V   A_V=5.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 10.3      12    16    13    13    10     7     5
13.0 11.3      20    26    22    21    15    11     8
14.0 12.3      32    43    35    35    25    17    13
15.0 13.3      54    75    60    58    41    28    20
16.0 14.3      96   140   108   102    69    46    33
17.0 15.3     188   291   217   196   127    80    55
---------------------------------------------------------
V=15.0: S=    500   285   416   421   801  1635  2947 [e-/n samples]
---------------------------------------------------------

A0V   A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 12.0      13     9     7     6     6     6     8
13.0 13.0      21    14    11    10    10    10    13
14.0 14.0      34    23    18    16    16    15    21
15.0 15.0      57    38    28    26    25    25    34
16.0 16.0     102    64    47    43    42    40    57
17.0 17.0     202   117    82    73    71    69   103
---------------------------------------------------------
V=15.0: S=    457   916  1574  1802  1905  2042  1105 [e-/n samples]
---------------------------------------------------------

A0V   A_V=5.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 10.1      12    35    21    15    10     7     5
13.0 11.1      20    59    34    25    16    11     8
14.0 12.1      32   106    58    40    27    18    12
15.0 13.1      54   210   105    68    44    29    20
16.0 14.1      96   460   209   122    75    48    32
17.0 15.1     189  1081   458   243   139    84    54
---------------------------------------------------------
V=15.0: S=    499    67   174   322   702  1525  3117 [e-/n samples]
---------------------------------------------------------

K3III A_V=0.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0 10.7      13    29    24    16     9     7     5
13.0 11.7      20    48    39    26    14    11     8
14.0 12.7      33    85    66    43    22    18    13
15.0 13.7      55   162   123    73    35    28    22
16.0 14.7      99   342   250   133    60    47    35
17.0 15.7     197   787   561   269   107    82    60
---------------------------------------------------------
V=15.0: S=    474    94   139   283  1022  1563  2617 [e-/n samples]
---------------------------------------------------------

K3III A_V=5.0  V_back/sq.arcsec=21.0  /Detection by SM :    400-700 nm           
   V     I     SM     u     P     v     b     Z     S
 mag   mag   mmag  mmag  mmag  mmag  mmag  mmag  mmag

12.0  8.8      10   156    94    43    15     8     3
13.0  9.8      16   329   183    73    24    14     5
14.0 10.8      25   753   396   133    39    22     8
15.0 11.8      41  1814   922   269    67    35    14
16.0 12.8      71  4476  2239   596   122    60    22
17.0 13.8     133 11163  5547  1412   247   108    35
---------------------------------------------------------
V=15.0: S=    786     6    13    45   335  1040  6554 [e-/n samples]
---------------------------------------------------------
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