From erik Mon Jun 14 14:02:52 1999 Subject: CUO_67.txt NBP design: II To: gaia-sag@astro.estec.esa.nl (GAIA SAG), straizys@itpa.lt (Vytas Straizys), ffavata@astro.estec.esa.nl (Fabio Favata), brown@bufadora.astrosen.unam.mx (A. Brown), Frederic.Arenou@obspm.fr (F. Arenou), michel.grenon@obs.unige.ch (M. Grenon), indus (Jens Knude), helge (Helge J. Sorensen), cf (Claus Fabricius), makarov (Valeri Makarov), smid (Mattia Vaccari), carme@am.ub.es (Carme Jordi) Date: Mon, 14 Jun 1999 14:02:52 +0200 (MET DST) X-Mailer: ELM [version 2.4 PL23] MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Content-Length: 47187 Status: RO Design of narrow-band photometry: II ==================================== E. Hoeg, C. Fabricius, V.V. Makarov 10 June 1999 SAG_CUO_67 ABSTRACT: An improved design is presented based on that in CUO_55. The main new idea is a clear separation between the astrometric and photometric tasks in the Spectro instrument, similar to that in Astro. A patch of samples from the Spectro sky mapper (SSM) is transmitted to ground and used for the detection, astrometry and G band photometry of neighbouring stars with V<23 mag out to a distance of 3.0 arcsec from the main star. The advantage of the new design is that fainter neighbours are detected, a better performance at high star density, a lower telemetry rate, and a simplification of the data analysis. It is noted that neighbouring stars with V<23 mag at distances up to 1.0 arcsec are known already from the Astro instruments. The possible need for ground-based photometric observations with high resolution in a few per cent of the sky is again pointed out and should probably be mentioned in the red report. === 1. Introduction A clear separation is proposed between the astrometric and the multi-colour photometric tasks in the Spectro instrument, similar to that already existing in the Astro. The sampling in the Spectro sky mapper (SSM) is by 1 pixel/sample, with 0.5*0.5 arcsec^2/pixel, and all pixels are read. This dataset is used to detect point sources onboard, called stars henceforth. A patch of samples centred on each detected star is subsequently collected from the SSM, from all bands in the narrow-band photometer (NBP) and from the radial-velocity spectrometer (RVS). These data are transmitted to ground where the final astrometric and photometric analyses are performed. In contrast to the previous design we now propose to extract a patch also of the SSM samples after the detection has been made. This patch is used on the ground for detection, astrometry and G band photometry of point sources. The Appendix contains the following Sections Bxx, figures and tables: B1. Quick epoch photometry B2.1. Astrometric analysis of SSM data B2.2. Photometric analysis of SSM and NBP data B3. Background estimation B4. Double stars and high star density B5. Ground-based observations B6. Diffuse Galactic sky background B7. Details B8. Arrangement of filters, fast moving asteroids A9. Dichroic filter (implemented, see Table 2) B10. Data rates B11. Angular resolution B12. Simulations Figures 1,2,3,4 Tables 1,2,3,4,5 === 2. The CUO_55 design The new design supersedes that in CUO_55 but some parts of that report are still valid and are included below with small adaptations. The CUO_55 design assumed that the disturbing stars in the neighbourhood of the main stars are detected by means of the data in the patches for all colour bands. That should give all stars with V<21.0 up to 3 arcsec from the main star. The new design goes to V=23.0 up to 3.0 arcsec. The Section A2 (Astrometric analysis) in CUO_55 is obsolete. Section A3 (Background estimation) and A4 (Double stars...) are obsolete because we can now assume all disturbing stars to V=23.0 to be known. The subjects are discussed below in B2, B3, B4. The Sections A1 (Quick epoch photometry), A5 (Ground-based observations), A6 (Diffuse Galactic sky), A7 (Details) are included with small adaptations as B1, B5, B6, B7. === 3. Main conclusions for the new design A quick epoch photometry (Section B1) can be obtained from analysis of the patches of a star belonging to a single field crossing, without depending critically on any other observational data. This epoch photometry can be used for verification and for scientific studies, e.g. of supernovae and other sudden events. The following discussion is, however, only concerned with NBP photometry in its final form where all information from analysis of the Astro instruments is available, especially the ASM, AF and PSM astrometry, the satellite attitude and the geometric calibration. --------------------------------------------------------------------- Table 1. Approximate limits in V for good NBP photometry (Col. 2). The size of areas as function of N_19, the density of stars having V<19.0 mag, is derived from http://www.astro.ku.dk/~cf/b/gaia/ Fig.3. N_19 Limit Total area stars/deg^2 mag deg^2 percent < 10 000 20.0 31100 76 > 10 000 9900 24 = 30 000 20.0 > 30 000 1500 3.7 > 45 000 600 1.4 < 90 000 41000 > 99.6 > 90 000 < 160 < 0.4 = 100 000 20.0 = 300 000 19.0 --------------------------------------------------------------------- The analysis of ASM and AF data from the Astro instrument will give the positions of all stars on the sky with G<20.0 mag with an angular resolution about 50 mas. The analysis of PSM data for each of the detected stars will give the positions of all other stars with G<23 mag within 1.0 arcsec of the detected star and with a resolution of 70 mas. This should be used as input to the final analysis of NBP data, but 1.0 arcsec is not enough, therefore the patches from SSM and NBP must be utilized. An astrometric and photometric analysis of all patches from the Spectro sky mapper (SSM) of a star (Section B2.1) is required before the final photometric estimation of the patches from the NBP. Stars as faint as V=23.0 can thus be detected. A resolution of double stars with separation of 0.5 arcsec is expected for equally bright components. A length of 8 samples/patch from the NBP, instead of previously 16, has now been chosen as sufficient to estimate the background and magnitude of the main star and the disturbing stars (Section B2.2). These 8 samples have unequal size as shown in Fig.4 because this is adequate for photometry and it saves telemetry compared with the 14 samples of equal size shown in Fig.3. The present MMS design will allow to acquire NBP samples for all stars in areas with a density up to 270 000 stars/deg^2 with a total readnoise of 3 e- (Sections 4 and B7). But photometry with 0.01 mag precision in each band is hampered in such areas by fainter disturbing stars, i.e. double stars. This precision can only be obtained for stars with V<19.0 mag in such areas (see Table 1). At a density of N_19=100 000 only a small disturbance is expected from optical doubles at V=20.0. With PSF photometry most of the patches can be used, especially since disturbing stars will be known from the preceding astrometric analysis of SSM data (Sections B2.1 and B2.2). It is known that less than 0.4 per cent of the entire sky contains more than N_19=90 000 stars/deg^2. It is thus concluded that the NBP with the proposed sampling will be nearly unaffected by crowding at V=20.0 in about 99 per cent of the sky. It is feasible to obtain narrow-band photometry for all stars brighter than V=20.0 mag since, e.g., a standard error in the y-band about 0.06 mag would be achieved as mission average in most of the sky. The use of single pixel resolution is discussed in Section B11. We mention here that its use in the small areas with very high star density has been considered, but the profit could be only marginal. (see e.g. EHs email of 26 May 1999 to SAG 12). These areas may have high scientific interest, but they cover only a few per cent of the sky. They should probably be observed from the ground (Section B5), also because the angular resolution of the NBP is exceeded by the best on-ground telescopes with good seeing, e.g. the NOT and VLT. The fairly small areas, totaling less than 0.5 per cent of the sky, having a surface brightness uR<19.9 mag/arcsec^2 due to Galactic diffuse light should probably also be observed from the ground (Section B6). Fast-moving asteroids, up to 0.5 arcsec/s, may be better detected with the Spectro instrument than with the Astro (Section B8). === 4. Design The description is adapted to the photometric F system, recently adopted as baseline by the SAG. Table 2 gives the arrangement of the F filters. The sampling of the October'98 baseline given in CUO_53 is modified as shown in Figs.2 and 4. For very bright stars however where CCD saturation could occur the sampling of the NBP should collect single pixels in order to allow using the spikes (see Section B11). Single pixel data for bright stars are also needed for the astrometric calibration of the CCDs in the SSM and NBP. In the following text the word readnoise (=r=RON) always means the total noise for one sample, including digitization error etc. (see Section B7: Details.) A sky mapper for bright stars (SSM0) with 0.003 s integration time is provided. Its data are read and transmitted as for the following sky mapper (SSM1) with 3 s integration time. Only SSM1 is discussed in the following and is called SSM. Table 3 gives photometric standard errors for the sky mapper (SSM) and the y- band as representative for the NBP. The SSM gives an error of 0.16 mag at V=20.0 for 2 s integration time and for the realistic readnoise of 5.3 e- (Column 1). This corresponds to SNR=6 so that a detection limit of V=20.0 should be feasible. An integration time of 3 s is recommended in order to have some margin. For the NBP it appears from Table 3, Columns 4 and 5 that the errors would improve by only 10 per cent in the y band for stars of V=20 mag if the number of background samples n_b is increased from 3 to 6, which is almost negligible. It has been shown (Section B7: Details) that a maximum star density of 270 000 stars/deg^2 can be sampled with 16 samples per patch and a readnoise of 3 e- can be achieved with the MMS final design. A very slight increase could be obtained when only 14 samples are now required to be read. According to the Galaxy model in LL_012 the average number of stars/deg^2 of V<19.0 mag is N_19=7900 for the whole sky and 30 000 at b=0, averaged over all longitudes (cf. Table 4). There are 325 million stars with V<19.0 on the whole sky. A study was presented by C. Fabricius at the Lorentz workshop in 1998 of the USNO-A1.0 catalogue of 488 million stars. Scaling to the 325 million stars with V<19.0, the study showed that < 0.4 per cent of the entire sky contains more than N_19=90 000 stars/deg^2 (see Table 1). The reason for the '< 0.4' instead of 'approx.' is that the areas in the A1.0 catalogue with density zero were counted as a high density area ( N_19> 90 000) although that is not always true. We conclude that the sampling rate of 300 samples per TDI period corresponding to a maximum star density of N_19=270 000 stars per deg^2 is sufficient to measure all stars with V<20.0 mag in about 98 per cent of the real sky. Most of the remaining 600 deg^2 will also obtain an acceptable number of observations per star of V<19.0. But photometry with 0.01 mag precision cannot be obtained for so faint stars in these dense areas as we shall see in Sections B3 and B4. ---------------------------------------------------------------- APPENDIX === B1. Quick epoch photometry A first epoch photometry can be obtained from analysis of the patches of a star belonging to a single field crossing. The sky mapper observation and preliminary geometric and photometric calibration of the CCDs are required, but not any other observations or data, e.g. an accurate absolute satellite attitude. A PSF photometry is carried out on each of the patches at the position defined by the SSM observation (cf. CUO_53 Section 7.3.3). The standard errors will be 10 times that given e.g. in Table 3 Column 4 for the y band, i.e. 0.08 mag at V=17.0. This standard error only takes photon noise and readnoise into account, but not errors due to disturbing stars in high density regions. Such quick epoch photometry can be used for verification purposes and for scientific studies, e.g. of supernovae and other sudden events. === B2.1. Astrometric analysis of SSM data Analysis of patches as shown in Fig.1 would give detection with position and magnitude of stars up to 3.0 arcsec from the main star. This would require transmission of 14*9 = 126 samples per star crossing which is a large number for this purpose compared with the data from the colour bands. Standard error for the detection of V=20 mag in the single crossing is obtained from Col.1 in Table 3 as 10*0.016 = 0.16 mag, or SNR>5. Analysis of the data shown in Fig.2 can give nearly the same sensitivity but requires only transmission of 42 samples per star crossing. Table 3, columns 1 and 2, show the standard errors from the average of 100 observations, i.e. crossings, of t=2 s integration time corresponding to Fig.1 and 2, respectively. The are nearly identical. Column 3 gives the values for 3 s integration. The standard error is 0.179 corresponding to SNR>5 for V=23 mag. The 3 s integration time is recommended. It is noted that the samples of 3 pixels in Fig.2 are obtained by addition of the single pixel values. The total readnoise for 1 pixel in the SSM is 5.3 e- according to Section B7, and recently confirmed by Michael. The equivalent total noise for the sample of 3 added pixels is the sqrt(3)*5.3 =9.2 e-. This total noise could be decreased if the patch in Fig.2 were obtained by direct reading of a second SSM (SSM2), corresponding to ASM3 in the Astro telescopes. But this does not seem to be required for our purpose. At the high star density N_19=100 000 stars/deg^2 the detection of all stars with V<23 should still be possible with the patch in Fig.2. The number of stars with V<22.0 per sample area of 0.75 arcsec^2 would be 0.64*0.75/12=0.04 (see Table 4 Part 3) and it would be 0.08 for V<23.0 which would probably allow a detection of nearly all stars with distances from its neighbours larger than about 0.5 arcsec. The mean distance is 1.4 arcsec. === B2.2. Photometric analysis of SSM and NBP data The positions of all stars (point sources) brighter than G=23.0 out to a distance of 3.0 arcsec from the main star will be available from the SSM data analysis. The photometric analysis shall provide the photometric parameters of the stars and background in the SSM and for each band. Let there be n_star stars in the area and n_obs observations per filter. The stars may at first be assumed to be of constant magnitude so that one amplitude value per star shall be determined. The background may at first be assumed to be constant over the area, but it will be different for each patch, e.g. due to Zodiacal light. The simplest observation model thus contains n_star amplitudes and n_obs background values which shall be determined from the 8*nobs samples in each band. We assume for the final photometry that all geometric calibration values, satellite attitudes, CCD sensitivities, and PSF values are available. The derivation of star amplitudes and background values in each band can then be formulated as a linear least-squares problem. A simple consideration shows that the problem is usually well determined. At a density of N_19=100 000 there are on average 0.74 stars/12 arcsec^2 of V<23.0 according to Table 4, Part 3. This means 0.046 star/sample in the smallest NBP samples, and 0.14 stars in the largest samples (#2 and 7 in Fig.4). The density is even smaller in the SSM samples for the G band. In the 28 arcsec^2 area within 3 arcsec of the main star there are on average 1.8 additional (called disturbing) star brighter than V=23. Thus, n_star=1+1.8~=3 amplitudes and n_obs=100 background values are the unknowns. The number of equations for a band is n_eq=8*n_obs=800. The system is overdetermined with 697 degrees-of-freedom. After a lsq solution the residuals may be analysed in order to find variable stars and variation of the background over the field, e.g. due to a galaxy. This should first be carried out in the SSM data because the count rate is much higher than in any of the narrower NBP bands. Other numerical methods for the photometric analysis than least-squares should be studied on simulated observations before a final choice is made, e.g. the (non-linear) maximum cross correlation and the maximum likelihood methods. The following Sections B3 and B4 illustrate the photometry mainly by simple numerical examples. They are not meant to represent alternative numerical methods or to provide any better arguments than given in the present section. === B3. Background estimation A background value as average of n_b=3 or 6 elementary samples of 1*4 pixels/sample, only affected by Poisson noise and readnoise is assumed in the precision estimates in Table 3, columns 4 and 5, respectively. It appears that the improvement by n_b=6 is modest, e.g. only 10 per cent at V=20 mag. Therefore the four large samples #2,3,7,8 in Fig.3 derived from 10 elementary samples should ensure a good background even if some of them are disturbed by other stars. The disturbance by one or more stars will be corrected in the numerical solution discribed in Section B2. It is however interesting for illustration to derive the bias in the magnitude of the main star if a disturbing star were not taken into account. We might for simplicity assume that the background value per elementary sample is obtained as an average from the large samples #2 and 7 in Fig.4. The effect of a disturbing star of V=21.0 on a main star of V=18.0 of the same spectral type is independent of the colour band. If the disturbing star is centred on the sample #7 in the area A it would contribute to the mean background value per sample from A and B by a flux corresponding to 6 times fainter, i.e. V=21.0+2.0=23.0 mag. The effective background in PSF photometry corresponds to about 2 samples in aperture photometry, i.e. to V=22.25 mag. A main star of V=18.0 would be measured too faint by about 0.02 mag. This is not negligible compared to the standard error of 0.013 mag for the mission average in a y band, but the disturbance will be corrected by the proposed numerical solution and, furthermore, such a bright disturbance is very seldom and even if there is one within 3 arcsec it will not always affect a background sample. If a disturbing star has V=23.0 it will perhaps not be known from the SSM analysis. The bias on a main star of V=20.0 will be 0.02 mag if the background is calculated in the simple way. This would be acceptable, but an even smaller bias is expected because such a disturbing star will be seldom even at N_19=100 000, and it will not always affect a background sample. === B4. Double stars and high star density Table 4 gives a limit in V for good NBP photometry. The limit is e.g. V=20.0 for N_19=100 000 stars/deg^2. This means that the presence of another star will seldom disturb the measurement of a star with V<20.0 significantly, as we shall now illustrate. The probability of having another star with V<22.0 in the 8 arcsec^2 area C of Fig.3 is 1-exp(-0.43)=0.35 since the star density is 0.64*8/12=0.43. The mean distance to the closest neighbour with V<22.0 is 2.2 arcsec. The disturbance from a star of V=22.0 on the measurement of the one with V=18.0 is at most 0.025 mag, corresponding to the 4 mag difference. And this only happens if the disturbing star is very near the centre of area C. This is a maximum bias and may be compared with the expected standard error of 0.013 mag for y (Table 3, Column 4) for the average of 100 observations. Such a bias would only be introduced if the disturbing star were not known from the analysis of Astro or SSM data. Physical or optical double stars with a separation of 0.5 arcsec may be resolved by PSF analysis of the SSM observations, as judged from our experience with the Tycho-2 reduction and the GAIA BBP simulations in CUO_42 and 43. This resolution is expected for double stars of V<20.0 even in areas of the density N_19=100 000. If the separation is larger than 0.5 arcsec a bias will be avoided by way of the numerical analysis. If the separation is between 0.07 and 1.0 arcsec it is known from the Astro and this information should be utilized in some TBD way, e.g. in the epoch photometry (see below). For main stars of V=19 and 20 the resulting bias on average photometry, without correction, would be about 2.5 and 6 times 0.025 mag. This should be compared with the larger intrinsic standard errors at these magnitudes. Since a bias is avoided through the numerical analysis we may assume a limit of V=20 for good NBP photometry at this star density. In the densest area, considered in Part 4, having N_19=300 000 stars/deg^2 we have set a tentative limit of V<19.0 mag. The disturbance of epoch photometry values may be eliminated by a similar analysis or the disturbed values may be completely rejected since the presence of a disturbing star will most often be known, e.g. from the Astro data. These conclusions may speak for the use of a higher limit of SNR in very dense areas in order to prevent transmission of inaccurate data. Also the use of single pixel resolution may be considered (see Section B5.) === B5. Ground-based observations Photometry from the ground might be obtained with a reasonable effort only for a small part of the sky. This seems to be a good option in the less than one per cent of the sky with a star density in excess of N_19=100 000 stars/deg^2 and in areas of the Milky Way with high surface brightness. The angular resolution of ground-based observations is critical and shall be discussed here. The angular resolution of, e.g., the Danish 1.5 m in Chile is characterized by a seeing of typically 1.2 arcsec (FWHM of the stellar image) and 0.7 arcsec at best. The CCD has 0.39 arcsec/pixel. This resolution is not as good as the NBP resolution along scan, but better than in the cross scan direction. So the 1.5 m instrument has an overall resolution comparable to the NBP with the proposed sampling. The Nordic Optical Telescope (NOT) of 2.5 m uses a pixel of 0.19 arcsec in the ALFOSC and has typically 0.5 arcsec seeing which makes it better than the NBP, even along scan. Even if single pixel resolution were introduced in the NBP in dense areas the ground-based resolution would be better, with an instrument like the NOT. So the single-pixel sampling is no good option if the areas to be measured from the ground are not too large. Less than two hundred square degrees on the sky has a higher star density than 100 000 stars/deg^2 and such an area is small enough to cover from ground with multicolour photometry with a reasonable effort, e.g. with the Danish 1.5 m, the ESO VST and the 2.2 m wide field telescopes. The Danish telescope has a rather small field of 0.22x0.22 deg^2. The VLT Survey Telescope (VST) will probably have a field of 1.0x1.0 deg^2, and the 2.2 m has 0.5x0.5 deg^2. They can both be expected to show a seeing about 0.5 arcsec. An area at l,b=253,2 deg was e.g. measured with the 1.5 m telescope. It has a density of measured stars of 102 000 stars/deg^2, the faintest were V=21.5, and the measurements were complete to V=20.5. There was no problem with resolution and the precision was about 0.03 mag at 20 mag. Other examples are given in CUO_05 of much higher star densities measured with the Danish telescope. Fig.1 of CUO_05 shows a field in Omega Cen with 3.5 million stars/deg^2 between V=13.0 and 21.0, 17 second exposure in Johnson V. It was one of many images used to find variables. For this application a high star density is not such a problem because only repeatability from image to image is required, but no accuracy of the photometry. From the CUO experiences we conclude that 100 000 stars/deg^2 can be measured with the 1.5 m with little confusion of the faintest stars. We also conclude that a density about 400 000 stars/deg^2 can be measured with a telescope having 0.5 arcsec seeing like the NOT. Sky background corrections will be a problem for some stars, but "gradient techniques" can possibly be applied. === B6. Diffuse Galactic sky background The approximate size of areas with certain levels of brightness can be obtained from Fig.66 and 67 of Leinert et al. (1998, A&AS 127, 1). Table 5 gives such values. It appears that about 200 deg^2 have a surface brightness exceeding uR=19.9 mag/arcsec^2, and only 30 deg^2 exceed 19.5 mag/arcsec^2. These areas contain, e.g., the star forming regions where the background variation is particularly high. Such variations would disturb photometry with the NBP more than with a ground-based telescope because the latter has a higher angular resolution. It seems that such areas should be observed from the ground because of the moderate total size of the areas. === B7. Details 1 pixel = 10 * 10 um = 0.50 * 0.50 arcsec = 4.1 ms TDI period 7300 pixels = 1.00 deg across scan = 73 mm. Two video chains per band are foreseen by MMS (Final report, Sect.5.5). I quote from messages from Martin of 14 and 17 Dec. 1998: A flush frequency of 15 MHz is assumed. ---NBP noise budget: Pixel read-out frequency 58.9 75.0 20 KHz RON 1.94 2.0 1.8 e- Max. star density 200000 255000 68600 stars/deg^2 and other noise contributions: Video chain analog noise 0.12 0.15 0.04 e- Analog-digital qtzn noise 2.20 2.20 2.20 e- Total noise 3.07 3.1 2.9 e- ---SSM noise budget: Pixel read-out frequency 885 kHz RON 4.1 e- Video chain analog noise 1.8 e- Analog-digital quantization noise 2.20 e- Total noise for detection chain 5.3 e- This assumes that the same type of CCD is used in SSM and NBP, which still has to be confirmed. Summary of Martin's messages: r=5.3 e- for the SSM, r=3.0 e- for the NBP will be assumed as total noise figures. ---SSM: 890 kHz is required to read all pixels in the SSM (=7300/2/4.1 ms) which gives total noise per pixel of r=5.3 e- ---Narrow bands: 1*5 pixels/sample in the bands with long integration, u and P. 1*4 pixels/sample in the other bands with short integration. 16 samples/patch in all bands, length of a patch is 8 arcsec. see illustration of patch and Airy disk in Fig.6 of CUO_50. r=3.0 e- is assumed as total readnoise per sample for all bands. This may be obtained at 75 ksamples/s with 4 non-destructive read-out per sample. This is also valid for samples of 4 or 5 pixels across scan. The pixel outside each end of a sample probably contributes some of its charge to the sample due to the sudden change of reading frequency from flushing at 15 MHz to slow reading at 75 kHz, and viceversa. This transition cannot be improved according to Martin. Whether a constant fraction is contributed we do not know. Please ask MMS<<<<<<<<<<<<< Please also ask MMS whether I have to assume a charge handling capacity of only 100 000 e- for the 10x10 um^2 pixels ? I took that from the 400 000 for the 20x20 um^2 mentioned in section 5 page 8 in the final report. In previous plots we assumed a maximum charge handling capacity of 500 000 e- has been assumed for the serial register, so this will give 1.7 mag fainter saturation limit ! Reading 75 ksamples/s gives 300 samples in 4 ms. We thus assume a maximum star density of 300 stars per TDI period per video chain which will always be read in order to produce a constant power consumption. These samples cover 300*5=1500 pixels or 41 per cent of the area in case of the u and P bands, and 33 per cent for the other bands. This is close to the maximum star density that can be measured without too much being lost by overlap of patches. There are then not more than 3650-300*4=2450 pixels to be flushed which takes not more than 2450/15000=0.163 ms which is just about available. With 16 samples per patch it is possible to sample 300 stars on an area of 0.5*8/3600 =1/900 deg^2 corresponding to a maximum star density of 270 000 stars/deg^2. A lower maximum star density of e.g. 200 000 or even 100 000 may also be acceptable in view of the degradation of photometry at the highest densities and because these areas are fairly scarce and could be measured from the ground if required. === B8. Arrangement of filters, fast moving asteroids The arrangement in Table 2 does not simply follow the sequence of wavelengths. Immediately after the SSM come the rather wide bands bands at 570 and 674 nm, not the UV band. This arrangement greatly improves the capability to measure fast moving asteroids. An asteroid with a velocity up to 0.5 arcsec/s along scan and 0.2 across scan detected in the SSM would still be inside the patch of the F57 band which comes 4.0 s after the SSM. A position measurement along scan is possible although with low accuracy due to the outer wide samples shown in Fig.4. The limiting magnitude for one observation in the F57 band is about V=19.0 where the error is roughly 0.3 mag, extrapolating from Table 3, Column 4. An ordinary asteroid has a velocity about 0.01 arcsec/s. With this velocity an asteroid detected in the ASM1 of the Astro instrument would remain inside the ASM3 and the first AF patches and always within the PSM patch. But much faster moving asteroids could not be detected since they would be rejected in the comparison of the positions measured in ASM1 and 3. The F82 band has also been moved forward to come before the RVS, as explained in the notes to Table 2. The filters will all have the same optical thickness in order to keep the correct focus. In present photometers such filters are interference filters, about 10 mm thick, e.g. for Stromvil bands. We supply a specification in Table 6 of CUO_55 as an example. === B10. Data rates The MMS final report Figure 6.7/2 assumes: 75 stars/s entering the SSM, field height 1.0 deg, Vlim=17. We assumed in CUO_55, Section A10: Vlim=19.5 --> 500 mio stars on the sky --> 12 000 star/deg^2 --> 400 stars/s. 64 bits for SSM and 16*16 bits per band for the patch, compression ratio 3.0 --> 85 bits/band, SSM + 7 bands/star --> 659 bits/star, 400 stars/s or 500 million stars in total --> 264 kbits/s We assume now: Vlim=20.0 --> 1000 mio stars on the sky --> 24 000 star/deg^2 --> 800 stars/s. NBP: 14 patches: 11 colours, but 3* F33 and 2* F51 8 samples/patch = 112 samples for the bands SSM: 14*3 = 42 samples 14 patches: 112 samples --- Total 154 samples = 154*16 = 2464 bits compression ratio 3.0* --> 821 bits/star 800 stars/s or 1000 million stars in total --> 657 kbits/s for SSM + 14 NBP patches/star =============== Thus, the data rate is 2.5 times higher than in CUO_55. The number of stars is 2.0 times higher, the number of colour bands is 11 instead of 7, the disturbance from faint stars is under better control. Further data compression will of course decrease the rate, but the compression is already high. Probably too high. This point must be investigated. All error estimates are based on loss-free compression. A method for representation of observed signals with low SNRs has recently been described by Lupton et al. (4 Mar 1999, astro-ph/9903081). The method is called "asinh magnitudes" and will be used for the publication of the Sloan results. It could perhaps be used for the publication (not for encoding) of GAIA photometry, but we stress that we do not *recommend* its use for GAIA or anything, only that a critical study is first required. The length of patches for NBP has been decreased from 16 to 10 samples. This is acceptable because the SSM patch is now used to find the disturbing stars within 3 arcsec of the main star. The NBP photometry is obtained for disturbing stars up to a separation of 3 arcsec. Savings on telemetry may be envisaged by transmitting data for only some of the bands for the faint stars. The full size patch may not be required for all repeated observations of the same band (F33, F51), or these patches may be added before transmission. Saving could also be achieved if the colour index is estimated onboard e.g. from the broad bands F33, F41, F57 and F67. This colour could then be used to decide if the F33 is at all so significant for a given faint star that its transmission is justified. It may even be considered to transmit only 6 samples for most of the sky with not too high star density. The 6 samples would be 1+2,3,4,5,6, and 7+8 in Fig.4. This may be sufficient for the 96 per cent of the sky with N_19<30 000 (see Table 1). At such densities there is mostly not more than one disturbing star in any of the samples with V<23.0 mag (see Table 4). This is true even for N_19=100 000 (see Section B2.2). The actual density of stars should be obtained onboard by analysis of the number of stars detected in the SSM. We conclude tentatively that it is perhaps possible to observe with the SSM and NBP for a billion stars, i.e. to a limit of V=20, within a telemetry rate of 600 kbits/s. === B11. Angular resolution A high angular resulotion is desirable from a scientific point of view and can be obtained by reading single pixels and transmitting all values to the ground for numerical analysis. This should be done for bright stars, but the penalty if this were done for faint stars would be a lower precision because of the higher readnoise and a too high telemetry rate. The sampling shown in Fig.4 has full resolution along scan in the central four samples, but the outer two samples on each side are wider. This gives a low readnoise and a lowest possible telemetry rate. The low resolution across scan means that epoch photometry is deteriorated if the main star is a double star and its two components happen to lie along the long samples. At other orientations of the scan the components may be resolved. The resolution in the mission average is therefore nearly as good as if single pixels were available. Another star in the field may also be a double star. Let us consider the one marked by + + in Fig.4. It is detected and resolved in the on-ground analysis of the SSM data so that the positions and the G amplitudes of the components are known and can be used in the analysis of the NBP patches. The epoch photometry in a NBP band cannot separate the components at the scan orientation shown in Fig.4. But we are not directly interested in the epoch photometry of the two disturbing stars. The indeterminacy does not affect the epoch photometry of the main star which must be considered the only important issue. The mission average of both components will be obtained with sufficient accuracy since their light acts on different samples, or partly on no sample at all, at some other orientations. It happens in this case e.g. when the components point at about 45 deg towards lower right. We conclude that the full angular resolution is obtained with the patch in Fig.4 for all point sources out to 3 arcsec and for the central point source. The resolution for non-point sources is reduced compared to a single pixel resolution. A second penalty is that the resolution is sometimes reduced for epoch photometry. For very bright stars single pixel resolution should be preserved, especially where CCD saturation could occur. The sampling of the SSM and NBP should collect single pixels in order to allow the use of the spikes for photometry. The trailing spike will be affected by the saturated central part of the image, but the three other spikes could be used. A patch of 14*8=120 pixels for stars with G<12 mag should be sufficient to cover also the vertical spikes. The telemetry will not be much increased because only a few million stars will be thus sampled. The single pixel data for bright stars are also needed for the astrometric calibration of the CCDs in the SSM and NBP. === B12. Simulations The computations involved in the proposed NBP photometry are similar to those carried out at CUO for the second Tycho reduction. We intend to estimate the required computational effort for the NBP photometry by scaling of our IDL programmes. This might give a better indication than the present guesses. Simulations with an adapted programme would be a natural next step (not intended at CUO in the near future.) The algorithms described in Section B2.2 could be tested on the following data. Example #1: Assume a density of N_19=100 000 stars/deg^2. Generate a field of random stars with realistic magnitude distribution down to G=25 mag in a field of 36*360 arcsec^2=0.001 deg^2, giving e.g. 100 stars with G<19.0. Assume G2V stars, zero parallaxes, proper motions, and orbital motions, leaving more realistic assumptions to later simulations. Assume realistic PSF. Observe the field in the SSM and NBP. Observe in various scan directions. Analyse by lsq method. ---------------------------------------------------------------- _ _ _ _ _ _ _ _ _ _ _ _ _ _ |_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_*_|_|_|_|_|_|_| <-- Main star at asterisk |_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_| 0.5*0.5 arcsec^2/pixel |_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_| Fig.1. Patch from SSM, 14*9 sample/patch, 1 pixel/sample. Could be used to detect other stars up to 3.0 arcsec from the main star at the asterisk, but the high cross-scan resolution is not required for this purpose. The suggested design is given in Fig.2. ---------------------------------------------------------------- ---------------------------------------------------------------- _ _ _ _ _ _ _ _ _ _ _ _ _ _ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |_|_|_|_|_|_|_|_|_|_|_|_|_|_| | | | | | | | | | | | | | | | | | | | | | | * | | | | | | | <-- Main star at asterisk |_|_|_|_|_|_|_|_|_|_|_|_|_|_| | | | | | | | | | | | | | | | Area = 7.0*4.5 = 31.5 arcsec^2 | | | | | | | | | | | | | | | |_|_|_|_|_|_|_|_|_|_|_|_|_|_| Fig.2. Patch read from the SSM, 14*3 samples/patch, 1*3 pixels/sample. Recommended for detection of other stars up to 3.0 arcsec from the main star at the asterisk. ---------------------------------------------------------------- ---------------------------------------------------------------- _ _ _ _ | C | <-- Upper part of area C of 2*4 = 8 arcsec^2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ see Sections B3 and B4 | | | | | | | | | | | | | | | | | | | | | | * | | | | | | | <-- Main star at asterisk | | | | | | | | | | | | | | | |_|_|_|_|_|_|_|_|_|_|_|_|_|_| Fig.3. Patch read from the NBP, 14*1 samples/patch, 1*4 pixels/sample. Could be used, but is not transmitted, for narrow-band photometry of main star and disturbing stars up to 3.0 arcsec from the main star at the asterisk. ---------------------------------------------------------------- ---------------------------------------------------------------- _ _ _ _ _ _ _ _ _ _ | A | | B | <-- Areas A and B of 2.5*4 = 10 arcsec^2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ see Sections B3 and B4 | | | | | | | | | | | | | * | | + + | | <-- Main star at asterisk | 1 | 2 |3|4|5|6| 7 | 8 | Double star at + +, |_ _|_ _ _|_|_|_|_|_ _ _|_ _| see Section B11 |_ _ _ _ _| |_ _ _ _ _| Fig.4. Transmitted patch from NBP, 8*1 samples/patch. The two outer large-area samples in each side are obtained by numerical addition of the two or three outer samples in the preceding figure. This provides an adequate resolution in most of the sky, thus saving on telemetry. The two dashed rectangles A,B are used in the discussion of disturbing stars. ---------------------------------------------------------------- ---------------------------------------------------------------- Table 2. Spectro focal plane, allocation of space for SSM, 11-colour photometry (F system), and RVS. CCDs: CCD#1B / CCD#2 Name Centre FWHM t Notes nm nm s SSM0 (No Filter) 0.004 G band, bright stars SSM1 (No Filter) 3 G band F57 570 90 3 (1) F67 674 116 3 F82 816 48 3 (2) F33 326 96 3*3 F41 405 60 3 <-- Centre of field F47 465 45 3 F51 508 27 2*3 F65N 656 4 3 F75 747 28 3 F78 778 31 3 F89 894 48 3 Spaces 12*1 (3) ---- 57...57 RVS 60 Placed at centre of field ---- Total 117 Available 4 deg 120 (4) ---- Spare 3s Notes: (1) The filters F57 and F67 with fairly wide bands are placed right after the SSM in order to detect as faint as possible fast-moving asteroids (cf. Section B8). (2) The F82 band is close to the centre of the band at 850 nm used for radial-velocity measurement. A photometric value in this band should therefore probably be obtained in onboard and be used to decide whether an RVS will be accurate enough to warrant a transmission to the ground. (3) The space between CCDs is usually 2.4 mm = 1 s, but much less space (e.g. <0.1 mm) is required between the CCDs for repeated measurement of a colour, i.e. F33 and F51. Therefore only 12 spaces of 1s are counted. (4) A total field of 4.0*1.0 deg^2 can be assumed for filter photometry + RVS, either as one field in the direct focus, or as a field of 2*1 deg^2 viewed in two foci by way of a dichroic mirror. In the case of dichroic mirror it is not quite simple to arrange detection in the G band, so perhaps a SSM must be included in both foci. ------------------------------------------------------------- Table 3. Photometric standard errors for the average of n_obs=100 observations in the Spectro telescope. Spectral type G2V, V-Ic=0.72, V-G=0.26 mag. Sky background uV=21.0 mag/arcsec^2 and Sp.T.=G2V. Count rates from LL 6 Feb 1999, CCD#1B, dichroic mirror. G is with no filter, y has 20 nm FWHM. The Stroemgren y band serves as an example of an intermediate band although it is not included in the F system of photometry. Only photon noise and total RON for star and background are included in the standard errors. About the n_s-term see Sec.7.2.1 in CUO_53. The 1*3 sample is obtained by numerical binning, not electronic as for the 1*4 sample, giving sqrt(3) time higher RON than for one pixel where it is 5.3 e-. The suggested design is given in Columns 3 and 4. The other columns are included for comparison. (1) (2) (3) (4) (5) SSM SSM SSM NBP NBP Band G G G y y V I mag mag mmag mmag mmag mmag mmag 17.0 16.3 2 2 1 8 7 18.0 17.3 3 3 3 13 13 19.0 18.3 7 7 5 27 25 20.0 19.3 16 16 12 59 53 21.0 20.3 38 39 29 139 122 22.0 21.3 93 96 72 - 295 23.0 22.3 232 238 179 - - ------------------------------------------------------------- Sample = 1*1 1*3 1*3 1*4 1*4 [pixel] Sample area = .25 0.75 0.75 1.00 1.00 [arcsec^2] V=15.0: S1= 17196 17196 17196 564 564 [e-/s] Integr. t= 2.0 2.0 3.0 3.0 3.0 [s] V=15.0: S= 34392 34392 51588 1692 1692 [e-] n_s= 9 6 6 3 3 Backgr: uV= 21.0 21.0 21.0 21.0 21.0 [mag/as^2] Backgr: b= 34.1 102.3 153.4 2.2 2.2 [e-] Total RON: r= 5.3 9.2 9.2 3.0 3.0 [e-] sg_b1= 7.9 13.7 15.4 3.3 3.3 [e-] n_b= 9 6 6 3 6 sg_b.mean= 2.6 5.6 6.3 1.9 1.3 [e-] n_s-term= 1119 2243 2856 67 50 [e-] V_b= 18.7 18.0 18.1 18.5 18.8 [mag] n_obs= 100 100 100 100 100 ------------------------------------------------------------- --------------------------------------------------------------------- Table 4. A modification of Table 4 in CUO_55. The approximate limit in V for good photometry is given (Section B4). Star density is given as function of magnitude for various values of N_19, the densities of stars with V<19.0. The mean distance to the closest neighbour is derived for a random distribution of stars. This distance is 0.50 times the distance if the stars were placed in a regular mesh of squares. Part 2 corresponds to the density at b=0 deg averaged over all longitudes, and the other parts are simply scaled. Part 3 corresponds to a density of 100 000, close to the one in Lennart's model at l,b=0,0, which has 85000 stars according to Table 3 of CUO_25. Part 4 assumes the maximum density that can be sampled for all stars with V<19.0 with readnoise r=3e-. V<18.0 V<19.0 V<20.0 V<21.0 V<22.0 mag Part 1. N_19=10 000 stars/deg^2, limit V=20.0 : Density 5 000 10 000 20 000 40 000 70 000 stars/deg^2 Density 0.005 0.003 0.018 0.037 0.064 st/12 as^2 Mean distance 25.5 18.0 12.7 9.0 6.8 arcsec Part 2. N_19=30 000 stars/deg^2, limit V=20.0 : Density 15 000 30 000 60 000 120 000 220 000 stars/deg^2 Density 0.014 0.027 0.056 0.111 0.20 st/12 as^2 Mean distance 14.7 10.4 7.3 5.2 3.8 arcsec Part 3. N_19=100 000 stars/deg^2, limit V=20.0 : Density 50 000 100 000 200 000 400 000 700 000 stars/deg^2 Density 0.05 0.09 0.18 0.37 0.64 st/12 as^2 Mean distance 8.0 5.7 4.0 2.8 2.2 arcsec Part 4. N_19=300 000 stars/deg^2, limit V=19.0 : Density 150 000 300 000 600 000 1200 000 2200 000 stars/deg^2 Density 0.14 0.28 0.56 1.11 2.04 st/12 as^2 Mean distance 4.6 3.3 2.3 1.6 1.2 arcsec --------------------------------------------------------------------- --------------------------------------------------------------------- Table 5. Diffuse Galactic sky background. Approximate size of the area in [deg^2] in the zone -15 < b < +15 deg exceeding a given surface brightness in the R band in [mag/arcsec^2]. The areas have an uncertainty about 30 % which could be improved using the tabular values available at CDS. Column 1 is an estimate from visual inspection of Fig.67 R of Leinert et al. (see Section B6) Column 2 from a comparison of Figs.66 and 67. The figures are based on data with resolutions of 0.25x0.25 deg^2. (1) (2) Longitude 278 < l < 314 0 < l < 360 uR < 19.5 10 30 uR < 19.9 70 200 uR < 20.3 450 1400 uR > 20.3 630 9400 Total area 1080 10800 ---------------------------------------------------------------------