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Filter parameters using stars alone?

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.

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Filter parameters using stars alone?

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  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 Modelsuccessive ratios=1.15raised halfwave cosines SW HWHM=0.1 * peakmicronsLW HWHM=0.2 * peakmicronsFWHM = 0.3 * peakmicronsthree 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 = 1.000 • 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 micronstrue parmvec = (0.18, 0.6, 0.18) Covariance matrix at true parms: 0.000000172 0.000000455 0.000002110 0.000000455 0.000001756 0.000010215 0.000002110 0.000010215 0.000067188 RMS parameter errors are sqrt(cov[i,i])... 0.000414781 0.001325099 0.008196850 Repeat to get distributions of parms....and chisq 1 0.17943 0.59798 0.16877 5.28 2 0.18050 0.60187 0.18862 8.73 3 0.18031 0.60190 0.19388 14.47 4 0.18096 0.60040 0.17013 4.24 5 0.18003 0.60027 0.18282 7.03 Jacobian matrix at true parms 0 390.9 392.5 5.9 1 741.9 375.9 -32.3 2 1094.6 213.1 -51.7 3 1414.6 -23.2 -50.9 4 1930.4 -537.6 -14.3 5 2305.4 -993.7 37.4 6 2875.6 -1791.3 151.6 7 3184.5 -2266.4 229.2 8 3665.1 -3053.4 368.4 9 3907.9 -3469.2 445.8 Star True Noisy Post-Fit 0 70.366 70.831 70.819 1 133.541 133.599 133.579 2 197.025 195.053 196.664 3 254.634 255.892 253.986 4 347.471 347.615 346.544 5 414.966 412.472 413.982 6 517.600 516.641 516.752 7 573.213 572.529 572.541 8 659.721 659.210 659.445 9 703.420 703.821 703.392

  8. Results for 10 Planck “stars” {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000}LambdaPeak = 1.0 micronstrue parmvec = (0.3, 1.0, 0.3) Covariance matrix at true parms: 0.000001439 0.000005090 0.000029571 0.000005090 0.000020542 0.000125380 0.000029571 0.000125380 0.000801431 RMS parameter errors are sqrt(cov[i,i])... 0.001199419 0.004532371 0.028309564 Repeat to get distributions of parms....and chisq 1 0.29796 0.99348 0.25728 10.49 2 0.30058 1.00064 0.29245 3.13 3 0.29899 0.99659 0.27986 4.86 4 0.29992 0.99985 0.30633 6.03 5 0.30157 1.00255 0.29649 3.63 Star True Noisy Post-Fit 0 305.015 305.942 305.694 1 289.530 288.558 289.848 2 282.639 283.998 282.888 3 278.947 279.827 279.200 4 275.246 274.808 275.550 5 273.462 275.119 273.815 6 271.522 270.168 271.956 7 270.718 270.449 271.195 8 269.689 271.312 270.234 9 269.244 270.023 269.823 Jacobian matrix at true parms 0 1016.7 197.9 -48.0 1 965.1 -117.6 -25.4 2 942.1 -291.5 -2.8 3 929.8 -400.8 15.1 4 917.5 -529.0 39.7 5 911.5 -600.8 55.1 6 905.1 -689.8 75.6 7 902.4 -731.0 85.7 8 899.0 -788.6 100.2 9 897.5 -815.3 107.1

  9. Results for 10 Planck “stars” {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000}LambdaPeak = 1.4 micronstrue parmvec = (0.42, 1.4, 0.42) Covariance matrix at true parms: 0.000037703 0.000120813 0.000650225 0.000120813 0.000391856 0.002122868 0.000650225 0.002122868 0.011643783 RMS parameter errors are sqrt(cov[i,i])... 0.006140244 0.019795355 0.107906364 Repeat to get distributions of parms....and chisq 1 0.42408 1.41356 0.48084 8.01 2 0.43244 1.43792 0.59623 9.05 3 0.42669 1.42395 0.52723 3.77 4 0.42404 1.41275 0.47274 5.74 5 0.40869 1.36509 0.13682 2.78 Jacobian matrix at true parms 0 1008.5 -168.3 -21.6 1 716.2 -277.9 6.5 2 591.7 -304.9 18.6 3 524.9 -313.2 24.8 4 456.7 -316.6 31.0 5 422.6 -316.1 33.9 6 384.1 -313.7 37.1 7 367.5 -312.1 38.4 8 345.5 -309.3 40.1 9 335.7 -307.8 40.8 Star True Noisy Post-Fit 0 423.586 423.073 422.922 1 300.790 297.972 298.763 2 248.493 246.979 246.633 3 220.474 219.265 218.898 4 191.803 191.390 190.659 5 177.503 177.782 176.629 6 161.334 158.979 160.806 7 154.352 151.813 153.988 8 145.101 146.181 144.965 9 140.978 141.775 140.948

  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. Bower FiltersChuck’s “B” filter + translate and stretch

  12. 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 = 1.000 is at 0.42 microns // integral chuckb dlam = 0.095139 um = 0.22652 * peakLambda // HM at 0.3900 and 0.4845 um; FWHM = 0.0945 um. { double nm = 1000.0*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))) + 0.006*(nm-390.0)/30.0; double cosfun = Math.cos(1.57079633*(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] = 0.2262*peakmicrons; // p[1] = peakmicrons; // p[2] = 0.2262*peakmicrons; { double arg = 0.42 + 0.0945*(microns - p[1])/p[2]; double coef = p[0] / p[2]; return coef * chuckb(arg); }

  13. Test Plan double T[] = {3000,4000,5000,6000,8000,10000,15000,20000,40000,80000}; • 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.

  14. Results for 0.42 micron filter3, 2, 1 parameter set RMS errors relative to each Ptrue.... 0.003709176 0.003749791 0.061517502 RMS errors relative to each Ptrue.... 0.003186849 0.001145970 RMS errors relative to each Ptrue.... 0.003162278

  15. Results for 0.6 micron filter3, 2, 1 parameter set RMS errors relative to each Ptrue.... 0.003735971 0.005622357 0.138134858 RMS errors relative to each Ptrue.... 0.003406938 0.001654710 RMS errors relative to each Ptrue.... 0.003162278

  16. Results for 0.8 micron filter3, 2, 1 parameter set RMS errors relative to each Ptrue.... 0.004927049 0.008133857 0.277057954 RMS errors relative to each Ptrue.... 0.004507213 0.002277703 RMS errors relative to each Ptrue.... 0.003162278

  17. Results for 1.0 micron filter3, 2, 1 parameter set RMS errors relative to each Ptrue.... 0.011316285 0.011070937 0.486450297 RMS errors relative to each Ptrue.... 0.006159324 0.002950693 RMS errors relative to each Ptrue.... 0.003162278

  18. Results for 1.2 micron filter3, 2, 1 parameter set RMS errors relative to each Ptrue.... 0.023448627 0.014501154 0.780280986 RMS errors relative to each Ptrue.... 0.008114606 0.003665971 RMS errors relative to each Ptrue.... 0.003162278

  19. Results for 1.4 micron filter3, 2, 1 parameter set RMS errors relative to each Ptrue.... 0.041705337 0.018418729 1.168308881 RMS errors relative to each Ptrue.... 0.010254744 0.004415638 RMS errors relative to each Ptrue.... 0.003162278

  20. 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

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