From erik Wed Aug 5 11:21:33 1998 Subject: CUO_42.txt Simulations BBP: 1 To: gaia-sag@astro.estec.esa.nl (GAIA SAG), Frederic.Arenou@obspm.fr (Arenou) Date: Wed, 5 Aug 1998 11:21:33 +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: 12163 Status: RO Simulation of BBP observations for single and double stars ---------------------------------------------------------- E. Hoeg, V.V. Makarov 30 July 1998 SAG_CUO_42 ABSTRACT: Simulations of observations with the broad-band photometer have been carried out. 100 observations in random scan directions in the Sloan i' band were superposed and analyzed with a maximum cross correlation method giving a position and slit photometry. The standard error for a star of I=20.0 was sg_m=0.027 mag, in good agreement with the 0.030 mag for the aperture photometry described in CUO_37. A fainter component (B) at a distance of 180 mas from this star was hardly affected and obtained sg_m=0.07, 0.14, 0.32 mag in i' for respectively I_B=21.0, 22.0, 23.0 mag. Smaller separations and the precision of the resulting astrometry were also studied. Introduction ------------ Monte-Carlo simulations of observations with the broad-band photometer have been carried out. Observations or patches in random scan directions in the Sloan i' band were superposed and analyzed with a maximum cross correlation (MCC) method giving a position and slit photometry for single and double stars. The MCC method is used for a very similar analysis in the second Tycho reduction. Illustrations are given in the Annex (separate .ps-file): "Progress on the Tycho2 Catalogue from the Hipparcos Mission". See especially the Fig. 2. This method is the only one used in the present report. It is the first of the following two methods for which we will investigate the photometric precision. The second method will be studied in CUO_43. (1) The positions of both components of double stars are estimated by MCC from the set of patches, and the magnitude is then estimated by a cross correlation of the PSF and the observation data at the given position. (2) The positions of both components are known from other sources, i.e. from the estimation in white light and all broad bands. The magnitude is then estimated as in (1). In both methods a star position is assumed predicted from astrometric parameters and attitude, not containing the uncertainty as if it were predicted from an astrometric sky mapper estimation for every BBP observation. Only the proper motion and parallax (and possibly an orbit) must be known with high accuracy in Method 1. We assumed a binning of 1*8 pixels/sample and 16 samples/patch. This allows solution of double stars with separations of, e.g., 100- 200 mas if the patch is centred on one of the components. But larger separations than 200 mas would require a larger patch. The standard errors were estimated from the internal agreement of the 150 trials (stars) each one with 100 observations. With 150 degrees of freedom the relative error of the standard errors should be 0.058 (=sqrt(1/300)). For a single star of I=20.0 mag the precision of i' is given in Table 1. The agreement with CUO_37 is seen. The error from the simulation of slit photometry is 10 per cent smaller than that estimated for aperture photometry. The background was assumed to be V=21.0 mag/arcsec^2, and to be determined from N_b=12 undisturbed samples. Table 2 shows that the precision at Ic=20.0 mag is rather unaffected by this assumption, even when the background is 10 times higher. ------------------------------------------------------------------ Table 1. Single star. From 100 superposed observations. Precision at Ic=20.0 mag of BBP photometry for Sloan i' for a G2V star. The first line corresponds to the aperture photometry assumed for the Fig. 1 in CUO_37, but here sg_i' does not contain the margin factor 1.2 applied in CUO_37. Sample RON sg_i' Note pixels e- mag 1*8 4.5 30 CUO_37, Fig.1, aperture photometry 1*8 4.5 27 simulation, slit photometry ------------------------------------------------------------------ ------------------------------------------------------------------ Table 2. Effect of background. From 100 superposed observations. Precision at Ic=20.0 mag of BBP photometry and astrometry from Sloan i' for a G2V star. i'_b e-/sample 1.43 1.43 1.43 14.3 N_b 6 12 24 12 sg_m mag 0.029 0.027 0.026 0.030 sg_xy mas 1.7 1.8 2.0 2.2 ------------------------------------------------------------------ Double stars ------------ Astrometry and photometry simulations for various separations of double stars are shown in Table 3. At 180 mas neither component is significantly affected by the other one. The systematic errors are much smaller than the corresponding standard errors. The standard errors are hardly larger than those for a single star, except for B when it is 23 mag. For the 100 mas separation the photometric standard error of A is hardly increased, but the systematic error is about equal to the standard error if B=22.0 mag. The photometric standard errors of the B component are, of course, increasing more rapidly towards fainter stars than in the case of 200 mas separation. The systematic astrometric errors are much smaller than the standard errors. The astrometric standard errors do not differ much from those for 180 mas separation, except when B is 23 mag. At the separation 70 mas meaningful results are still obtained in the sense that systematic errors in photometry and astrometry are usually smaller than the standard errors. But this is not the case when B=21.0. Separation 50 mas. Meaningful photometric results are still obtained except in photometry for B=21 and 22 mag. But the values for B=23 mag are reasonable. ------------------------------------------------------------------ Table 3. Double star. Precision of BBP photometry and astrometry from Sloan i'. Standard errors (sg_ ) of values obtained from 100 superposed observations using a maximum cross-correlation method. Photometry Astrometry---------- Note Comp i'_true i'_obs sg_m x y sg_x sg_y mag mag mag mas mas mas mas Separation=180 mas: A 20.0 19.991 .028 0.3 0.2 2.0 1.9 Comp B=21.0 mag B 21.0 21.006 .063 181.3 -0.2 4.0 4.4 B 22.0 21.975 .127 182.5 -0.2 9.5 9.7 B 23.0 22.869 .294 184.9 1.8 40.2 30.7 sep 180 mas, PA=90: A 20.0 19.997 0.027 0.2 0.2 1.9 2.1 B 21.0 21.006 0.065 181.5 -0.2 3.8 3.7 A 20.0 19.998 0.024 -0.1 -0.3 2.3 2.1 B 22.0 21.995 0.146 181.8 -0.5 9.9 12.0 A 20.0 20.006 0.033 -0.0 0.1 2.1 2.1 B 23.0 22.879 0.339 150.7 2.5 69.6 83.3 Outlier in x Separation=100 mas: A 20.0 19.977 .027 1.0 -0.1 2.4 2.4 B 21.0 21.023 .075 102.4 0.2 4.3 4.9 A 20.0 19.996 .030 0.4 0.2 2.1 2.0 B 22.0 21.981 .175 102.1 0.9 10.0 11.8 A 20.0 19.995 .032 0.5 0.1 2.4 1.9 B 23.0 22.920 .480 102.7 0.2 38.0 40.7 sep 100 mas, PA=90: A 20.0 19.998 0.037 0.5 0.2 2.6 2.2 B 21.0 20.994 0.086 100.5 -0.2 5.7 4.4 A 20.0 19.997 0.031 0.2 -0.2 2.3 1.8 B 22.0 21.986 0.187 101.1 0.4 12.2 11.4 A 20.0 20.003 0.033 0.1 -0.1 2.2 2.0 B 23.0 22.835 0.389 100.7 -0.7 42.7 41.5 sep 70 mas, PA=90: A 20.0 19.924 0.047 4.0 -0.2 3.6 2.5 B 21.0 21.197 0.177 79.3 -0.1 6.2 6.0 A 20.0 19.979 0.044 1.8 0.1 3.2 2.5 B 22.0 22.185 0.356 78.4 0.3 18.9 18.0 A 20.0 20.003 0.045 0.7 -0.2 2.8 2.3 B 23.0 22.818 0.449 76.7 4.4 55.0 67.5 sep 70 mas, PA=45: A 20.0 19.920 0.047 3.1 2.9 3.6 3.1 B 21.0 21.239 0.230 57.3 58.1 14.7 20.6 A 20.0 19.972 0.045 1.5 1.5 2.9 2.8 B 22.0 22.171 0.329 60.2 54.6 33.0 31.0 A 20.0 20.007 0.044 0.5 1.0 2.5 2.4 B 23.0 22.887 0.546 55.4 38.8 75.4 68.8 sep 50 mas, PA=90: A 20.0 19.808 0.052 7.4 -0.2 3.4 2.1 B 21.0 21.798 0.373 72.7 1.0 16.5 22.7 A 20.0 19.929 0.042 3.2 0.2 3.3 2.5 B 22.0 22.579 0.518 66.7 -6.8 52.6 46.9 A 20.0 19.995 0.041 1.4 0.2 2.4 2.6 B 23.0 22.956 0.507 53.9 -2.2 64.3 63.8 ------------------------------------------------------------------ Annex ----- In separate .ps-file: "Progress on the Tycho2 Catalogue from the Hipparcos Mission". See especially the Fig. 2. ===================================================================== APPENDIX: Technical details ============================= Simulations for BBP1 -------------------- Sloan i'; 1 sample = 1 pixel along scan for the star, and infinite across scan; 16 samples/patch; background is assumed determined from N_b undisturbed samples; 1 sample=1*8 pixel is assumed for the background, as in CUO_37; 100 patches/star; a star position is estimated from the set of patches, i.e. Method 1 in the Introduction; a star of Ic=20.0 mag (cf. Table 1 in CUO_37); Interesting further studies --------------------------- Assume that positions are known, i.e. Method 2 described in the Introduction. 1 sample = 2*8 pixels for BBP1. This may be an interesting alternative to the presently assumed 1*8 pixels because of lower RON, a larger area (and double star separations) covered by 16 samples, and only slightly reduced spatial resolution. 1 sample= 6*8 pixels for BBP2. Narrow-band photometry. Discussion of crowded fields based on the double star results. PSF --- Optical PSF from Fabio as in mail of 15 May 1998. K4V star, A_V=0 mag, Strehl ratio=1.0. Fabio has introduced along scan smearing due to mismatch of scan velocity with the star velocity over the 0.9 s integration. This is equivalent to 1.0 pixel thus contained in the psfs.fits file. Smearing of the PSF due to the width of the sample ws and to the motion of the star during the sampling, also ws, has been taken into account by us. It seems from Fabio's description that he has not taken the smearing due to star motion during the sampling into account. Fabio, please check this.<<<<<<<<<<<<<<<<<<< For future: We should make plot of the resulting sampled PSFs as measured with infinitely high sample. Assume along scan width of the sample: ws=1, 2, 3, 4, 5, 6 pixels, where ws=1, 3 and 6 pixels corresponds to the samples in CUO_40, Fig.1. Total observed charge: 100 000 e-. Standard assumptions -------------------- Nearly as in CUO_37, see below. Integration time = 0.9 s per CCD. Counts rates from LL_021, e.g. for Ic=15.0 mag, G2V, A_V=0 the rate is for i' = 5411 e-/0.9s. This is 0.942 times our assumption in CUO_37. RON = 4.5 e-/sample. The background is i'_b = 1.43 e-/sample; The parallel shift of charges along scan is instantaneous by 1 pixel, or e.g. 3 pixels in case of 3*8 pixels/sample. Technical details from CUO_37 : ============================= Astrometric telescopes, BBP and ASM2. ------------------------------ Figures in CUO_37: Figs 1&2 Figs 3&4 Fig.5 BBP1 BBP2 as Fig.3 CCD#3 but only Aperture 1.19 m^2 g'r'i'z' 1 pixel = 37*111 mas 1 sample: 1*8 pixels 3*8 pixels read out noise, r: 4.5 e- 4.5 e- samples/star, Ns: 6 3 samples for background, Nb: 12 6 For G (ASM2), the sample is 2*2 pixels, Ns=9, Nb=18 in all figures. The background has a G2V spectrum and an intensity of V=21 mag/sq_arcsec. This gives for one sample of 8 or 24 pixels (4 pixels for G): GAIA BBP: Photometric bands: g' r' i' z' z" G Rc Ic B V Background 8 pix: 1.08 1.75 1.43 0.75 0.57 2.69 1.33 1.25 0.55 1.06 [e-] Background 24 pix: 3.23 5.24 4.29 2.25 1.71 2.69 3.99 3.76 1.66 3.19 [e-] -----------------------------------***************