1 Filter parameters using stars alone? M.Lampton Space Sciences Lab U.C.Berkeley 8 Sept 2003 Updated 31 Oct 2003 using Bower filter functions, starting at chart 12

2 Filter Model successive ratios=1.15 raised halfwave cosines SW HWHM=0.1 * peakmicrons LW HWHM=0.2 * peakmicrons FWHM = 0.3 * peakmicrons three parameters: area, peakmicrons, FWHM

3 Assumptions Three parameters per filter: –Zeroth moment: integral Aeff dLambda, or “grasp” –First moment: Lambda peak –Second moment: FWHM Asymmetry is fixed at HWLW:HWSW=2:1 –No higher moments are of interest: red leak etc How well can we determine these three? –Photometric errors, ten stars, wide range color

4 Realm of interest “easy” calibration stars –S/N = few hundred “common” calibrators –Viewed repeatedly during scans –Internal checks for constancy Data values = few hundred Sigma values = Strongly overdetermined fit –Ten messurements –Three adjustables –Seven D.o.F. in post-fit chi square –Therefore data quality has built-in validation

5 Filter Fitting Experiments compare parms; histograms etc

6 Ten Planck calibration ”stars”

7 Results for 10 Planck “stars” {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000} LambdaPeak = 0.6 microns true parmvec = (0.18, 0.6, 0.18) Star True Noisy Post-Fit Jacobian matrix at true parms Covariance matrix at true parms: RMS parameter errors are sqrt(cov[i,i]) Repeat to get distributions of parms....and chisq

8 Results for 10 Planck “stars” {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000} LambdaPeak = 1.0 microns true parmvec = (0.3, 1.0, 0.3) Star True Noisy Post-Fit Jacobian matrix at true parms Covariance matrix at true parms: RMS parameter errors are sqrt(cov[i,i]) Repeat to get distributions of parms....and chisq

9 Results for 10 Planck “stars” {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000} LambdaPeak = 1.4 microns true parmvec = (0.42, 1.4, 0.42) Star True Noisy Post-Fit Jacobian matrix at true parms Covariance matrix at true parms: RMS parameter errors are sqrt(cov[i,i]) Repeat to get distributions of parms....and chisq

10 Yet to come… More realistic errors: perhaps based on an actual set of cal stars and observation plan with Exposure Time Calculator SNR More realistic stars: put in Pickles + WDs Do all nine filters What about systematics.

11

12 Bower Filters Chuck’s “B” filter + translate and stretch

13 Filter function detail Java code “Chuckb()” is original code; “tunable()” makes it tunable static double chuckb(double microns) // Lampton's take on Chuck Bower's B filter function // only here I want a single point per call // peak = is at 0.42 microns // integral chuckb dlam = um = * peakLambda // HM at and um; FWHM = um. { double nm = *microns; if (nm < 360.0) return 0.0; if (nm > 560.0) return 0.0; if (nm < 420.0) return 1./(1. + Math.exp(-0.17*(nm-390.0))) *(nm-390.0)/30.0; double cosfun = Math.cos( *(nm-420.0)/140.0); return Math.pow(cosfun, 2.4); } static double tunable(double microns, double p[]) // chuckb filter form, with stretches: // Example: // p[0] = *peakmicrons; // p[1] = peakmicrons; // p[2] = *peakmicrons; { double arg = *(microns - p[1])/p[2]; double coef = p[0] / p[2]; return coef * chuckb(arg); }

14 Test Plan Choose ten Planck “stars” with wide range of Teff Test one filter using these ten stars But adjust the exposure times to get SNR=100 for every star in that filter This is “one percent photometry” on every star Determine three parms, getting Fisher matrix and separate RMS errors –Integrated throughput –Peak wavelength –FWHM width of filter band Determine just first two parms, FWHM being given Determine only first parm, others being given Sanity check: 10 independent 1% measurements =>0.316% first parm alone REPEAT for several filters: blue, red, NIR. double T[] = {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000};

15 Results for 0.42 micron filter 3, 2, 1 parameter set RMS errors relative to each Ptrue RMS errors relative to each Ptrue RMS errors relative to each Ptrue

16 Results for 0.6 micron filter 3, 2, 1 parameter set RMS errors relative to each Ptrue RMS errors relative to each Ptrue RMS errors relative to each Ptrue

17 Results for 0.8 micron filter 3, 2, 1 parameter set RMS errors relative to each Ptrue RMS errors relative to each Ptrue RMS errors relative to each Ptrue

18 Results for 1.0 micron filter 3, 2, 1 parameter set RMS errors relative to each Ptrue RMS errors relative to each Ptrue RMS errors relative to each Ptrue

19 Results for 1.2 micron filter 3, 2, 1 parameter set RMS errors relative to each Ptrue RMS errors relative to each Ptrue RMS errors relative to each Ptrue

20 Results for 1.4 micron filter 3, 2, 1 parameter set RMS errors relative to each Ptrue RMS errors relative to each Ptrue RMS errors relative to each Ptrue

21 Conclusions Filter FWHM is rather poorly determined and is hopeless in the NIR Center wavelengths are well determined, even in the NIR: better than 1% Throughputs are well determined, mostly below 1% except out in the NIR where FWHM uncertainty contributes end losses