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

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Filter parameters using stars alone?

M.Lampton

Space Sciences Lab

U.C.Berkeley

8 Sept 2003Updated 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}



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


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


0.000001439 0.000005090 0.000029571

0.000005090 0.000020542 0.000125380

0.000029571 0.000125380 0.000801431


0.001199419 0.004532371 0.028309564


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}



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


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


0.000037703 0.000120813 0.000650225

0.000120813 0.000391856 0.002122868

0.000650225 0.002122868 0.011643783


0.006140244 0.019795355 0.107906364


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


0.003162278


0.003186849 0.001145970

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0.003735971 0.005622357 0.138134858


0.003406938 0.001654710


0.003162278

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0.004927049 0.008133857 0.277057954


0.004507213 0.002277703


0.003162278

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0.011316285 0.011070937 0.486450297


0.006159324 0.002950693


0.003162278

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0.023448627 0.014501154 0.780280986


0.008114606 0.003665971


0.003162278

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0.041705337 0.018418729 1.168308881


0.010254744 0.004415638


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

Documents

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