From erik Tue Sep 8 09:13:32 1998 Subject: CUO_45.txt Spectra or filters ? To: Vytas.Straizys@ITPA.FI.lt (Vytas Straizys), indus (Jens Knude), munari@astras.pd.astro.it (Ulysses Munari), gaia-sag@astro.estec.esa.nl (GAIA SAG) Date: Tue, 8 Sep 1998 09:13:32 +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: 16055 Status: RO Spectrophotometry or filter photometry with GAIA ? ================================================== E. Hoeg 8 Sep. 1998 SAG_CUO_45 With comments 15 Dec. 1998 ABSTRACT: The precision of spectrophotometry is estimated and compared with that given in PWG_006 by Fabio Favata. We find much larger errors with apparently the same assumptions. The errors are larger than those expected for Stromvil photometry. The reason(s) for this discrepancy should be found, we therefore give full details of our estimation. A meaningfull discussion of the scientific usefulness of low-resolution spectra versus filter photometry requires reliable accuracy estimates. PWG_006 makes the optimistic assumption that the disturbance from other stars is negligible, but it appears that faint stars with galactic latitude b<30 deg cannot be measured. We propose to introduce two dichroic filters and use the increased integration time to place some colour filter in the red part of the spectrum. Formulae for photometric precision ---------------------------------- Comment on 15 Dec: The following formulae are given in CUO_53 in more readable Latex form. A trivial error in Eq.(1) was corrected, in accordance with Eq.(11) of CUO_53. The following gives general formulae for the standard errors related to CCD aperture photometry, based on the derivations in CUO_26. The notation is slightly changed to conform with that introduced later by Lennart. Definitions and assumptions for aperture photometry: Ns = number of samples used to determine the signal+background t = integration time [s] S = star signal, unit is [e-] Nb = number of samples used to determine the background b = sky background [e- per sample] sg_b = standard error of sky background [e- per sample] r = readnoise [e- per sample] Nobs = number of observations, i.e., superposed sky patches The standard error of an estimated magnitude m is sg_m = 1.086 * sqrt[S+Ns*b+Ns*r^2 + (Ns*sg_b)^2] / (S*sqrt(Nobs)) [mag] (1) The standard error of an estimated median background is, according to ESA SP-1200, Volume 1, Equation 1.3.15 sg_b.med = sqrt(pi/2)*sg_b1/sqrt(Nb) (2) where Nb is the number of samples and sg_b1 is the standard error of the single sample value. This is valid in case of pure Gaussian noise, as when the photon noise plus readnoise dominates. The background may alternatively be estimated by a mean value which is, however, an optimistic assumption only valid for a very low density of stars sg_b.mean = sg_b1/sqrt(Nb) (3) where sg_b1 = sqrt(b+r^2) (4) Equations (1) and (4) are based on the assumption that the counts from star and sky background have a Poisson distribution and that the readnoise has a Gaussian distribution. Introducing (3) and (4) in (1) gives a formula valid only at star densities where disturbing stars can be neglected. sg_m = 1.086 * sqrt[S+Ns*(b+r^2)(1 + Ns/Nb)] / (S*Nobs) [mag] (5) This formula has been used in estimates from CUO, e.g. in CUO_37, 38 where a margin factor 1.2 was applied to all errors. The influence from disturbing stars is generally small for GAIA photometry with direct imaging and should be taken into account by means of the knowledge of the presence of these stars, especially obtained by the photometric sky mapper (PSM). The influence of other stars becomes even less by use of slit photometry (PSF fitting) as studied in CUO_42, 43. The condition of low star density for (5) is not generally fulfilled for spectrophotometry of faint stars as we shall discuss in a following section. Sampling -------- In PWG_006 the scale is 1 arcsec^2/pixel and 1 pixel/sample. A blue field spectrograph covers 300-630 nm and a red field covers 630-880 nm, each with 15 s integration time. A dispersion of 2 nm/pixel was proposed. The sampling for spectrophotometry was proposed to be 4*100 samples to cover the stellar spectrum and the sky to allow sky subtraction. The Z band (near V) has 20 nm width and should accordingly be sampled by a length of 10 pixels on the spectrum. We shall in the following consider the sampling which is not further specified in PWG_006. Figure 1 shows a possible sampling for the Z band. A minimum width of 3 pixels is required to cover the stellar spectrum at a position determined by a sky mapper. PWG_006 does not mention where this sky mapper is placed; a few figures should be added to PWG_006 in order to clarify the ideas about the focal planes. The sampling in Fig.1, 30 samples for the background and 30 samples for the spectral band+background, has been assumed in columns 1 and 2 of Table 1. In column 3 the number of background samples is 100, i.e., along the whole length of the spectrum and common for all bands. _ |_| |_| |_| |_| |_| |_| |_| |_| |_| |_|_ _ _ |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| Fig. 1. A possible sampling for the Z band. 30 samples in the left column are used to determine the sky background. The adjacent 3*10 samples are used to measure the Z band. Sky background -------------- Values for the sky background is given in GG_5. The zodiacal light is fainter than uV=22.0 mag/arcsec^2 nearly all over the sky. The brightness has been measured on HST images at (l,b)=(322,-13) with 0.1 arcsec resolution and uV=22.06 was found. But the heliocentric ecliptic coordinates of the observation, i.e., the direction of the HST image relative to the sun is not known (by G. Gilmore), so the contribution from zodiacal light is unknown. CUO_25 gives the sky background from diffused star light calculated from the galactic model in LL_12. It appears, e.g., that the contribution from stars between V=18.0 to 23.0 mag is uV=22.95 and 20.38 at l,b=90,0 and 0,0 deg, respectively. This indicates that an assumption of uV=22.0 is generally realistic, but we shall also consider uV=21.0 (in columns 2 and 3 of Table 1). But the real sky can be much brighter in crowded regions as clusters and galaxies. Disturbing stars ---------------- If the spectrum of another star contributes light to any of the pixels shown in Fig. 1 it would disturb the measurement of the first star, either the background or the star+background measurement. We aim at a precision of 0.01 mag or 1 per cent so the disturbance is critical. The following approximate estimate is proposed. We could require a disturbance less than 0.1 mag in each individual accepted measurement and then expect that the superposition of 100 observations would reduce the disturbance to less than 0.01 mag, as required for a star of V=18.0 since it obtains a standard error of 0.019 mag, according to Table 1, column 1. But a disturbing star is allways adding light so the disturbance is systematic. It adds not equally much light to background and star+background. A disturbance of 0.1 mag is expected from a star 2.5 mag fainter than the first. A star spectrum contributes to about 3*100 pixels. This implies that a star in an area of 7*100 pixels centred on the first star could disturb the measurement of a given band, e.g., the Z band illustrated in Fig. 1, or of the background pixels belonging to the band. Actually a somewhat larger area should be reckoned if the height and not only the width of the areas in Fig. 1 are taken into account. A star brighter than V=20.5 in an area of 700 arcsec^2 would therefore be unacceptable and should lead to a rejection of that particular observation. This check for disturbing stars would be just about feasible since all stars in the sky with V<20.0 will be catalogued by GAIA. The number of such stars in such an area is 2.5 and 16 at l,b=90,0 and 0,0, respectively, according to CUO_25. The conclusion is that low-resolution spectra would be so seriously disturbed by other stars at b=0 that they must be rejected. At b=10, 20, and 30 deg the number of such stars is respectively 2.1, 0.76, 0.36, according to LL_012. Most observations at b<30 deg must be rejected. In PWG_006 it is suggested to solve that problem by using smaller pixels, but the read-out rate and the RON would of course be seriously affected. The problem for the measurement of stars brighter than V=18.0 is equally serious. The precision would be equally much affected by a given faint star in relation to the lower photon noise. So the relative increase of standard error due to a disturbing star is rather independent of the magnitude of the first star. The conclusion is that the spectrophotometry of faint stars, say V>16.0 mag, at galactic latitudes of b< 30 deg would be seriously affected. Spectrophotometry ----------------- The precision of spectrophotometry has been estimated in SAG_PWG_006. I have tried to verify the precision table, but unsuccessfully, as appears from Table 1, especially columns 1 and 4. I agree with the values for the brightest stars so we seem to agree on the count rates for stars: 468 e-/s in the Z-band for V=15.0, G2V, is my assumption, based on Lennarts tables etc. But for a star of V=18 mag I get sg_m=19 mmag where PWG_006 has 7.2 mmag for 100 observations of 15 s. I assume in column 1 a sky brightness of uV=22.0 mag/arcsec^2 and RON=2 e-, the same as PWG_006, according to Fabio (but not stated in PWG_006). This gives b=89 e-/sample with 1 pixel/sample for a band of 300 nm, i.e. the blue part of the spectrum only as proposed in PWG_006. Columns 2 and 3 give estimates for a brighter, more conservative, sky background of uV=21.0 mag/arcsec^2. This results in considerably larger errors for faint stars. Two different assumptions on Nb have been made and it appears that the larger number of Nb=100 does not improve much on the errors obtained with Nb=30. This is also evident from a consideration of the equation 5. The insignificance of the RON compared with the sky background also appears from that equation. --------------------------------------------------------- Table 1. Photometric standard errors for the Z band by spectrophotometry and by the present NBP in the Spectro telescope. Only photon noise and RON for star and background is included. Valid for any spectral type since the Z band is close to V. Estimates by EH and by FF (Fabio in PWG_006) are compared. Estimates for NBP are taken from the curve in CUO_38 and dividing by the margin factor of 1.2. Spectrophotometry | NBP (1) (2) (3) (4) (5) V EH EH EH FF mag mmag mmag mmag mmag mmag 12.0 0.33 0.31 13.0 0.55 0.49 14.0 0.94 0.78 15.0 1.7 2.2 2.0 1.3 16.0 3.6 5.0 4.4 2.1 5 17.0 8.0 11.9 10.1 3.7 8 18.0 19.0 29.1 24.7 7.2 16 --------------------------------------------------------- pixel=sample: A= 1.0 1.0 1.0 1.0 [arcsec^2] V=15.0, NF: S1= 3752 3752 3752 ? [e-/s/arcsec^2] V=15.0, Z: S1= 468 468 468 ? [e-/s/arcsec^2] t= 15.0 15.0 15.0 15.0 [s/sample] Z: S= 7020 7020 7020 ? [e-] Ns= 30 30 30 ? [samples/band] Backgr: uV= 22.0 21.0 21.0 22.0 [mag/arcsec^2] Backgr: b= 89 224 224 ? [e-/sample] Nb= 30 30 100 ? [samples/backgr] sg_b= 1.8 2.8 1.6 ? [e-/sample] RON: r= 2.0 2.0 5.0 2.0 [e-/sample] --------------------------------------------------------- Observation in the ultraviolet ------------------------------ So far only measurement in the Z band was considered. The precision in the Sloan u' band and the Stromvil u band is given in Table 2 for an F5V star. The bands have a width of respectively 60 and 30 nm so that Ns becomes 3 and 1.5 times larger than in the Z band, with evident consequences for the precision at faint stars because of the larger contribution of light from sky background. We have increased the number Nb to remain equal to Ns. The precisions in the u' and the u bands for spectrophotometry are larger than for filter photometry for V>16.0. --------------------------------------------------------- Table 2. Photometric standard errors for the Sloan u' band and the Stromvil u by spectrophotometry and for u by the present NBP in the Spectro telescope for an F6V star. Only photon noise and RON for star and background is included. Estimates for NBP are taken from the curve in CUO_38 and dividing by the margin factor of 1.2. Sp. Sp. | NBP (1) (2) (3) Band: u' u u FWHM: 60 30 30 [nm] V mag mmag mmag mmag 15.0 2.9 4.1 4 16.0 6.8 9.6 7 17.0 16 23 12 18.0 41 57 24 --------------------------------------------------------- pixel=sample: A= 1.0 1 [arcsec^2] V=15.0, NF: S1= 3752 3752 [e-/s/arcsec^2] V=15.0,Band:S1= 369 185 [e-/s/arcsec^2] t= 15.0 15.0 [s/sample] Band: S= 5535 2775 [e-] Ns= 90 45 [samples/band] Backgr: uV= 22.0 22.0 [mag/arcsec^2] Backgr: b= 89 89 [e-/sample] Nb= 90 45 [samples/backgr] sg_b= 1.0 1.4 [e-/sample] RON: r= 2.0 2.0 [e-/sample] --------------------------------------------------------- Conclusions ----------- My estimate of standard error in the Z band is, e.g., 19 mmag at V=18.0 mag where PWG_006 has only 7.2 mmag with the same assumptions on count rates, sky background and RON. My estimates show larger standard errors for spectrophotometry than for narrow-band photometry (column 5 of Table 1) of the Z band for V>17.0. The reasons for this is the higher sky background and the lower precision in the measurement of the background. For the u band the NBP photometry is much more accurate for V>16.0. Furthermore, the performance of spectrophotometry relies much on the assumption made on the sky background. The value of RON is of little importance, even with r=5 e- the sky background dominates. Spectrophotometry is much more disturbed by other stars than filter photometry. Measurement of faint stars at galactic latitudes b<30 can rarely be obtained. At higher latitudes faint stars suffer a relative disturbance which is rather independent of their magnitude. A more thorough analysis, including realistic simulations, will probably not improve the situation for spectrophotometry with respect to precision. The only remaining advantage would be that the whole spectrum is available, an advantage that remains to be quantified. It should also be mentioned that the required data rate with 400 pixels per star is 2 Mbits/s according to PWG_006. A large degree of compression is required in order to arrive at something acceptable. The compressed data for narrow-band photometry requires only 128 kbits/s. It is proposed to introduced the two dichroic filters (see CUO_27) which would double the total photometric integration time in the Spectro telescope. The best choice of colour filters would probably be to increase the integration time for some of the Stromvil filters and to supplement them with other filters in the red part of the spectrum. The available integration time should also be increased by the use of a larger field than 2.0*1.0 deg. This is possible because the optical requirement for filter photometry is quite modest, less than for astrometry. The photometric disturbance could be estimated by the use of real PSFs from extreme parts of the field in simulations as described in CUO_43. Such a system for filter photometry gives better science and is much simpler than two low-dispersion spectrographs, each requiring a field rotation mechanism as in the RV spectrograph. ---------------------*****************--------------------------