From erik Wed Jan 20 12:58:22 1999 Subject: CUO_55.txt NBP photometry To: erik (Erik Hoeg) Date: Wed, 20 Jan 1999 12:58:22 +0100 (MET) 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: 41077 Status: RO Design of narrow-band photometry ================================= E. Hoeg, C. Fabricius, J. Knude, V.V. Makarov 19 Jan. 1999 SAG_CUO_55 ABSTRACT: Design of a narrow-band photometer (NBP) for the GAIA Spectro instrument for the Stromvil photometric system is described. The photometric data analysis is discussed, especially the questions related to high star densities and readnoise. It appears that good quality photometry of all stars brighter than V=18.0 can be obtained also in areas with the highest star density given by Lennart's model (LL_012), i.e. at l,b=0,0 deg. At 50 per cent higher density the limit is about V=17.5 mag. Some 600 square degrees on the sky have an even higher star density for which multicolour photometry may be obtained from the ground with a reasonable effort, e.g. with the ESO VST and 2.2 m wide field telescopes. 1. Introduction ---------------- The narrow-band photometry as presently proposed is the result of considerations since December 1997 on how to obtain the best science when photon noise, readnoise, data transmission etc are taken into account. The preceding design in CUO_26 of 12 Feb. 1998 is described in Section 2. The new design is discussed in Sections 3 (Conclusions) and 4 (Design). It is in accordance with the baseline in CUO_53. The introduction of a dichroic filter is not assumed in this report, only briefly mentioned. The dichroic option will be discussed in a separate report (CUO_56). The Appendix contains the sections: A1. Quick epoch photometry A2. Astrometric analysis A3. Background estimation A4. Double stars and high star density A5. Ground-based observations A6. Diffuse Galactic sky background A7. Details A8. Arrangement of filters, fast moving asteroids A9. Dichroic filter A10. Data rates A11. Computational effort Figures 1, 2 Tables 2 - 5 2. The CUO_26 design --------------------- The new design superceeds the one in CUO_26. The CUO_26 design assumed that on-board photometric reduction would be carried out and only the position, flux and background values would be transmitted to ground. This would result in a data rate of 18 kbits/s for the 92 million stars brighter than V=17.0 mag. The present design assumes that the raw data of 16 samples (a patch) per colour band per field crossing are transmitted, resulting in 264 kbits/s for the 500 million stars with V<19.5 mag. Thus, many more stars are measured, but the data rate is feasible. The many advantages of on-ground analysis of the raw data compared with on-board reduction have been discussed in CUO_52. In CUO_26 the samples for the star were assumed to be 4 or 5 pixels across scan, the same as in the present design. But the sampling for the background was subject to discussion. The present design was only reached a few months later during which time the concept of stacking the patches took form. The Sections 4 and 7 of CUO_26 (Multicolour surface photometry, and Astrophysical comments) are still of interest and not repeated here. 3. Main conclusions ------------------- A quick epoch photometry (Section A1) 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. The analysis of ASM and AF data 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. An astrometric analysis of all patches of a star (Section A2) is required before the final photometric estimation. The length of 16 samples/patch was chosen in order to locate the disturbing stars to a distance of 3 arcsec by stacking of the about 700 patches obtained for each star in the NBP. Stars as faint as V=21.0 can thus be detected. A resolution of double stars with separation of 0.5 arcsec is expected. --------------------------------------------------------------------- Table 1. Approximate limits in V for good NBP photometry. The size of areas as function of the density of stars having V<19.0 mag is derived from http://www.astro.ku.dk/~cf/b/gaia/ Fig.3. Density Limit Total area stars/deg^2 mag deg^2 percent = 300 000 16.0 = 100 000 17.0 > 90 000 < 160 < 0.4 < 90 000 41000 > 99.6 > 45 000 600 1.4 > 30 000 1500 3.7 = 30 000 18.0 > 10 000 9900 24 < 10 000 19.0 31100 76 --------------------------------------------------------------------- The present MMS design will allow to acquire 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 A7). 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 be obtained for stars with V<16.0 mag in such areas (see Table 1). At a density of 100 000 only a small disturbance is expected from optical doubles at V=17.0. With PSF photometry most of the patches can be used, especially since disturbing stars will be known from the preceding astrometric analysis. It is known that less than 0.4 per cent of the entire sky contains more than 90 000 stars/deg^2 of V<19.0. It is thus concluded that the NBP with the proposed sampling will be nearly unaffected by crowding at V=17.0 in about 99 per cent of the sky. At b=0 deg the density is on average 30 000 and these stars can be measured with only small disturbance at V=18.0. It is proposed to obtain narrow-band photometry for all stars brighter than V=19.0 mag since a standard error in the y-band about 0.03 mag and better would be achieved as mission average in most of the sky. The use of single pixel resolution in the small areas with very high star density has been considered, but the profit could be only marginal. These areas may have high scientific interest, but they cover only a few per cent of the sky. They should therefore be observed from the ground (Section A5), 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 also be observed from the ground (Section A6). Asteroids of much higher speed, up to 0.5 arcsec/s, may be better detected with the Spectro instrument than with the Astro (Section A8). 4. Design --------- The description is focussed on the Stromvil system according to the October'98 baseline given in CUO_53. This can easily be changed in case of modifications, for instance in order to include more bands in the photometric system. Table 2 gives the arrangement of the Stromvil filters, discussed in Section A8. In the following text the word readnoise (=r=RON) always means the total noise for one sample, including digitization error etc. (see Section A7: Details.) Table 3 gives photometric standard errors for the sky mapper (SSM) and the y- and u-bands as representative for the NBP, in some cases for two values of the readnoise. The SSM gives an error of 0.090 mag at V=19.0 with the realistic readnoise of 5.3 e- (Column 2). This corresponds to SNR=11 so that a detection limit of V=19.5 (SNR=8.5) should be feasible. For the NBP it appears that the errors would improve by only 10 per cent in the y band for stars of V=19 mag if the RON could be improved from 3 e- to 2 e-, which is however not realistic. For r=3 e- (Column 3) the error is about 0.03 mag as average of 100 observations which is an astrophysically valuable precision. It is therefore proposed that the detection limit is set about V=19.5 which should ensure that all stars as faint as V=19.0 will obtain a large number of observations from which the average may be derived. It is shown below (Section A7: 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. According to the Galaxy model in LL_012 the average number of stars/deg^2 of V<19.0 mag is 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 of the USNO-A1.0 catalogue of 488 million stars. Scaling to 325 million stars, the number of stars in the sky with V<19.0, the study showed that < 0.4 per cent of the entire sky contains more than 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 ( > 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 270 000 stars per deg^2 is sufficient to measure all stars with V<18.0 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 A3 and A4. ---------------------------------------------------------------------- APPENDIX ======== A1. 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 3, i.e. 0.07 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. A2. Astrometric analysis ------------------------ An astrometric analysis of all patches shall preceed the photometric analysis as explained in Section 7.3 of CUO_53. The length of 16 samples/patch (Fig.1) was chosen in order to locate disturbing stars to a distance of 3 arcsec by stacking the about 700 patches obtained for each star in the NBP. Stars lying far from the detected star are covered less frequently by patches with the proposed samples of 1x4 pixels. We may count the coverage as satisfactory if the second star is less than 0.5 arcsec from the horizontal midline of the patch shown in Fig.1. For a distance D>0.5 arcsec the fraction of good coverages is then approximately F= 1/90 arcsin 0.5/D This means F=0.33, 0.16, 0.11 for D= 1, 2, 3 arcsec, respectively. It may be a good idea for the purpose of astrometric analysis to combine the 5 Stromvil bands of longest wavelength in one stacking which would then contain about 500 patches per star. A star at a distance D=1 arcsec would be effectively covered by about 0.33x500=165 patches. It follows from Table 3, Column 3 that a star of V=22.0 obtains a precision of 0.349 mag from 100 patches in the y band. Accordingly, the star at D=1 arcsec would obtain 0.349/sqrt(1.65)=0.27 mag. This corresponds to a SNR=4.0. We thus conclude that stars of V=22.0 can be detected at D=1 arcsec. A star of V=21.0 at D=3 arcsec would obtain 0.143/sqrt(5x0.11)=0.19 mag precision and SNR=5.7 which indicates a safe detection. We thus assume that a star of V=21.0 will be detected up to 3 or 3.5 arcsec from the main star. It is noted that stars with separations <1.0 arcsec is known already from the Astro instrument. A3. Background estimation ------------------------- A first background estimate for a patch may be obtained from the 3+3 samples with label b in Fig.2. A background as average of n_b=6 samples only affected by Poisson noise and readnoise is assumed in the precision estimates in Table 3. The samples may however be disturbed by one or more stars which if uncorrected will introduce a bias in the magnitude and a lower precision. If a star is inside the areas A or B in Fig.2 the samples from the disturbed area should be rejected or corrected before the background value is calculated. A star outside the areas will disturb so much less that we shall neglect it in the present preliminary discussion. This discussion is intended as a first step towards simulations of the photometry in order to gain some simple, fundamental and quantitative insight into the problems. The process described is not considered to be the optimal algorithm. If the disturbing star has V<20.0 it would always be known through its detection in the Astro instrument. If the area A contains the star we may chose to reject A when the background is calculated. A subtraction in a narrow band should use the narrow-band magnitude calculated from the observed Sloan magnitudes. The probability of rejection is about 0.06 at a star density of 30 000 (see Table 4, Part 2) which will have only marginal effect on the precision of the epoch photometry for the star. If the disturbing star has 20.0From 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. A6. 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. A7. 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). Could we ask Martin to write all these things into one message for documentation, inluding formulae ? He should please use a text editor producing a text which is not corrupted by email transmission as the last ones were. 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. A8. Arrangement of filters, fast moving asteroids ------------------------------------------------- The arrangement in Table 2 differs with respect to the sequence of filters from previous tables in CUO reports. Immediately after the SSM come the bands between 467 and 656 nm, not the UV band. There are two reasons for this change. The detection is done in a wide visual band (Vw) approximately centred among the Stromvil bands since we want to minimize the number of stars which are too faint in some bands to give a useful observation. But this band is far from the 850 nm band of the radial velocity spectrometer (RVS) so that a colour index should perhaps be derived onboard and be used in a decision whether the star should be recorded in the RVS. The second reason is that the new arrangement greatly improves the capability to measure fast moving asteroids. An asteroid with a velocity up to 0.5 arcsec/s along scan and 0.3 across scan detected in the SSM would still be inside the patch of the y band which comes 2.5 s after the SSM. An ordinary asteroid has a velocity about 0.01 arcsec/s. With this velocity an asteroid detected in the ASM1 of an 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 limiting magnitude for one observation in the y band is about V=18.0 where the error is 0.14 mag according to Table 3, Column 3. 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, for all Stromvil bands, except that it is coloured glass for the P band. The P filter could most probably also be manufactured as an interference filter. We supply a specification in Table 5 as an example. It is important to minimise the space between the filters because the time goes from the integration time. Could MMS inform us if the foreseen spacing (Table 2) of 1s = 2.4 mm between the filters is sufficient to avoid vignetting of the beams at the edges of the glas filters where the converging beam enters the glass, taking the required geometric alignment of filters and CCDs into account. The problem of vignetting is relaxed if the dichroic filter is introduced since a large spacing can then better be accepted. Another problem is the reflex in the glass edges where the filters join. This light will be disturbing even when the direct star image is outside the CCD. The problem can be avoided if all filters in front of each of the four CCD chips are evaporated onto a single glass surface. This has e.g. been done for application at the ESO 3.6 m and NTT telescopes. A9. Dichroic filter ------------------- This option will be described in more detail in CUO_56. The performance of the NBP could be greatly improved by increasing the available area for filters from the present 1*1 deg^2 up to 3*1 deg^2. This is possible by means of a dichroic filter placed in front of the present focal plane. The separation wavelength might be 700 nm. The field with the longer wavelengths is used for the RVS and some TBD red bands. The field with shorter wavelength has an area of 2*1 deg and could be used for the Stromvil bands and TBD other bands. We prefer to increase the integration time on all bands compared with those given in Table 2 so that the data rate would not be 3 times as high as given below. Columns 5 and 6 show the resulting precision for y and u. A10. Data rates --------------- The MMS final report Figure 6.7/2 assumes: 75 stars/s entering the SSM, field height 1.0 deg, Vlim=17. 64 bits per band, incl. SSM --> 7 bands *64=448 bits/star --> 33.6 kbits/s We assume: 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 =============== Further 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. The rate could perhaps be decreased by use of shorter patches. The length of 16 samples/patch was chosen for the reason mentionend above, of finding all disturbing stars within 3 arcsec. But this requirement may be relaxed in most of the sky where the star density is low. The patches could therefore be shorter, perhaps 10 samples. But a few bands, e.g. u, y and S should always obtain 16 samples/patch. A11. Computational effort ------------------------- 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 next step, but much more demanding. ------------------------------------------------------------------ Fig. 1. A patch from the NBP. The patch is centred on a star at the asterisk (*) detected in the spectro sky mapper (SSM). Another star, not too bright, will not or only slightly disturb the central star if it is separated by 1.0 arcsec in the scan direction or 3 arcsec in the cross scan direction, taking into account the Airy disk which is sometimes elongated by cross-scan motion (cf. Fig.10c in CUO_50). This conservative assumption corresponds to the indicated area of 2*6=12 arcsec^2. A separation of double stars by PSF analysis is feasible at a separation of 0.5 arcsec along scan. <------- 8 arcsec ------------> _ _ _ _ | | <-- area C of 2x6 = 12 arcsec^2 | C | in which stars may disturb the main star at the asterisk _ _ _ _ _ _|_ _ _ _|_ _ _ _ _ _ | | | | | | | | | | | | | | | patch = 16 samples = 16 arcsec^2 | | | | | | | | * | | | | | | | | sample = 4 pixels | | | | | | | | | | | | | | | pixel = 0.5*0.5 arcsec^2 |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| | | |_ _ _ _|<-- the C area ------------------------------------------------------------------ ------------------------------------------------------------------ Fig. 2. A patch from the NBP. The samples labeled b are used for a first estimate of the background. The two dashed rectangles A and B are used in the discussion of disturbing stars. <------- 8 arcsec ------------> _ _ _ _ _ _ _ _ _ _ | A | | B | <-- areas A and B of 2.5x4 = 10 arcsec^2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | | | | | | | | | | | | | | | | | | |b|b|b| | * | |b|b|b| | | | | | | | | | | | | | | | | | | |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_ _ _ _ _| |_ _ _ _ _| ------------------------------------------------------------------ ------------------------------------------------------------------ Table 2 The assumed CCD arrangement in the Stromvil narrow-band photometer. NBP photometry, preceding and followings fields: PFOV: Vw 1.0s detection in SSM, flux in 400-700 nm = Vw 1s =2.4mm spacing between CCDs y 2.2s flux, at 547 nm, FWHM=23 nm, Tmax=0.80 1s b 2.2s flux, at 467 nm, FWHM=18 nm, Tmax=0.70 1s Z 2.2s flux, at 516 nm, FWHM=21 nm, Tmax=0.80 1s S 2.2s flux, at 656 nm, FWHM=20 nm, Tmax=0.80 13.8s =total FFOV: v 2.2s flux, at 411 nm, FWHM=19 nm, Tmax=0.60 1s u 6.0s flux, at 350 nm, FWHM=30 nm, Tmax=0.40 1s =2.4mm P 6.0s flux, at 374 nm, FWHM=26 nm, Tmax=0.42 16.2s =total 30.0s =total of PFOV + FFOV Notes: (1) in the PFOV the integration time of 1.0s is now assumed for the Spectro Sky Mapper (SSM), compared with 0.2 s in CUO_26. This is required in order to achieve a limiting magnitude of V=19 or 20. The SSM measures in a wide band Vw for which the count rates are taken as g'+r' from LL_021. The integration times for u and P are accordingly reduced from 6.5 to 6.0s in order to fit into the total available space in the field, with a negligible effect on the photometric precision. (2) The final distribution of integration times on the bands must result from further astrophysical discussions. We should probably optimize the Stromvil bands for the F and G stars because these stars represent the complete range of metallicities and ages. ------------------------------------------------------------------ --------------------------------------------------------------------- Table 3. Photometric standard errors for one observation in the SSM and for the average of n_obs=100 observations in the NBP. Spectral type G2V, A_V=0, V-Ic=0.72, V-G=0.24 mag. Sky background uV=21.0 mag/arcsec^2 and Sp.T.=G2V. Count rates from SAG_LL_021. Only photon noise and total RON for star and background is included. Columns 1-4: present design with 1*1 deg^2 for Stromvil NBP. Columns 5-6: future design with 2*1 deg^2 for Stromvil NBP. Columns 1 and 4 are not proposed, but given for the discussion in the Section: Design. (1) (2) (3) (4) (5) (6) Proposed - Yes Yes - Yes Yes SSM SSM NBP NBP NBP NBP Band Vw Vw y y y u V I mag mag mmag mmag mmag mmag mmag mmag 17.0 16.3 30 28 7 7 5 10 18.0 17.3 56 48 14 13 9 19 19.0 18.3 115 90 27 24 17 40 20.0 19.3 259 186 60 52 36 94 21.0 20.3 - - 143 120 85 228 22.0 21.3 - - 349 290 206 564 --------------------------------------------------------------------- Sample = 1*1 1*1 1*4 1*4 1*5 1*5 [pixels] Sample area = 0.25 0.25 1.00 1.00 1.25 1.25 [arcsec^2] V=15.0: S1= 10764 10764 765 765 765 104 [e-/s] Integration t= 1.00 1.00 2.2 2.2 5.0 6.0 [s] V=15.0: S= 10764 10764 1683 1683 3825 624 [e-] n_s= 4 4 3 3 3 3 Backgr: uV= 21.0 21.0 21.0 21.0 21.0 21.0 [mag/arcsec^2] Backgr: b= 10.7 10.7 6.7 6.7 19.0 2.5 [e-] Total RON: r= 9.0 5.3 3.0 2.0 3.0 3.0 [e-] sg_b1= 9.6 6.8 4.0 3.3 5.3 3.4 [e-] n_b= 8 8 6 6 6 6 sg_b.mean= 3.4 2.4 1.6 1.3 2.2 1.4 [e-] n_s-term= 550 280 72 48 126 52 [e-] V_b= 18.2 19.0 18.4 18.9 18.7 17.7 [mag] n_obs= 1 1 100 100 100 200 --------------------------------------------------------------------- --------------------------------------------------------------------- Table 4. Star density as function of magnitude for various densities of stars with V<19.0. The mean distance to the closest neighbour is derived for a random distribution of stars. Part 2 corresponds to the density at b=0 deg averaged over all longitudes, and the other parts are simply scaled. Part 4 assumes the maximum density that can be sampled for all stars with V<19.0 with readnoise r=3e-. The approximate limit in V for good photometry is given (Section A4). V<18.0 V<19.0 V<20.0 V<21.0 V<22.0 mag Part 1. 10 000 stars/deg^2, limit V=19.0 : 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. 30 000 stars/deg^2, limit V=18.0 : 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. 100 000 stars/deg^2, limit V=17.0 : 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. 300 000 stars/deg^2, limit V=16.0 : 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. 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 --------------------------------------------------------------------- ------------------------------------------------------------------ Table 5. Specification of Stroemgren filters, a recent example from CUO. (d. and e. are not applicable for GAIA.) 1. Stromgren u 350/35 (Central Wavelength CWL/FWHM) 2. Stromgren v 411/18 3. Stromgren b 468/18 4. Stromgren y 548/20 Common Specifications a. CWL: In beam f/9 or greater at 5 degrees C. Tolerance is +/-15% of FWHM. b. FWHM Tolerance: +/- 15%. c. Blocking: No leaks worse than 0.01% (10e-4) 0.3-1.2 microns. d. Size: 90.0 +0 -0.3 mm diameter. e. Minimum Clear Aperture: 86 mm diameter. f. Thickness: 10.0 mm maximum. g. Flatness: lambda/4 per inch. h. Parallelism: 1 arc minute. i. Scratch-Dig: 60-40. j. A/R Coating: Both surfaces, reflectivity < 1% per surface. The filters should not produce any detectable ghost images. ------------------------------------------------------------------ ---end