Post on 22-Feb-2016
description
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Filter parameters using stars alone?M.Lampton
Space Sciences LabU.C.Berkeley8 Sept 2003
Updated 31 Oct 2003 using Bower filter functions, starting at chart 12
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Filter Modelsuccessive ratios=1.15
raised halfwave cosines SW HWHM=0.1 * peakmicronsLW HWHM=0.2 * peakmicrons
FWHM = 0.3 * peakmicronsthree parameters: area, peakmicrons, FWHM
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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
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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
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Filter Fitting Experiments
compare parms; histograms etc
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Ten Planck calibration ”stars”
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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)
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
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
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
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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)
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
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
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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)
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
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
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
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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.
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Bower FiltersChuck’s “B” filter + translate and stretch
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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);
}
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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};
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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....
0.003162278
RMS errors relative to each Ptrue....
0.003186849 0.001145970
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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
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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
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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
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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
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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
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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