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Application of Digital Filtering Techniques for Analysis of X-ray Signals Using Interactive Data Language

A. Kiseleva1,3, A. Bleile2,3, P. Egelhof2,3, O. Kisselev2, D. McCammon4, J. Meier2,3
1 2 3 4 St.-Petersburg State University, St.-Petersburg, Russia GSI, Darmstadt, Germany Mainz University, Mainz, Germany Wisconsin State University, Madison, USA


Motivation
n=2 j = 3/2 2p3/2 2s1/2 j = 1/2
}

2p1/2

classical Lamb shift
Lyman-

n=1

j = 1/2

1s1/2

}1s-Lamb shift
Dirac QED

Bohr

H - at om bi n d i n g e n e r g y 1 s
1/ 2

U 13 , 6 e V 10 e V Ly m a n - cl a s si ca l L a m b s h i f t 1s - L a m b s h i f t 4, 4 10 3, 4 10
-6 -5

91+

13 2 k e V 10 0 k e V eV eV 75 e V 45 8 eV

The precise determination of the Lyman-transitions in hydrogen-like heavy ions, such as 238U91+, provides a sensitive test of quantum electrodynamics in very strong Coulomb fields (Z1), especially of contributions to the self energy of higher order in Z, which are not accessible by alternative methods. Such Lamb shift measurements became possible recently by X-ray spectroscopy using highly charged ions, stored and cooled in the heavy ion storage ring ESR at GSI Darmstadt. In order to improve the experimental precision, presently limited by the poor energy resolution of conventional Ge-detectors, a high resolving calorimetric low-temperature detector for hard X-rays (E 100 keV) is presently developed.


Detector development
Status of the recent experiments: exp. error (13 eV) 13 в theor. uncertainty (1 eV)
(ref.: Th. StЖhlker et al. Phys. Rev. Lett. 85, 3109 (2000))

particle detector 91+ (U ) U92+ (300 MeV/ from SIS

To achieve the experimental accuracy of 1 eV: use detectors with higher energy resolution: crystal spectrometers u) calorimetric low-temperature detectors

x-ray detectors electron cooler

ESR

gas jet target

Germ anium detector Energy resolution Efficiency 800 eV 10-3 ­ 10
-4

Crystal spectrom etr < 50 eV 10
-7

Calorim etr 100 eV 10-5 ­ 10-6


Low temperature calorimeter

x-ray absorber

implanted leads

Thermistor array: Originally designed for the astrophysical application Monolithic silicon 36 pixel array Each pixel: 2 mm в 0,5 mm Temperature of operation ­ 10 ­ 70 mK
load resistor

silicon pixel

implanted thermistor absorber attachment point

support beam
0.5 mm

cold FET

detector

amplifier

High absorption efficiency ( high Z) Small specific heat Rapid and complete thermalization Simple detection principal ­ measurement of the temperature rise


Signal shape
Typical signal from 60 keV photon
1 0 -1 -2 -3 -4 -5 -6 0 10 20 time [ms] 30

Signal shape is constant and depends only on the detector parameters ­ A = H * S(t)

Limiting factors ­ noise and variation of the baseline

Possible solution ­ pulse shape analysis

signal amplitude [V]

Thermal time constant: = 5.9 ms, count rate ­ up to 30 Hz per pixel


Creation of GUI and data analysis using IDL

Start menu:
number of digitization points energy of basic line duration of signal correction line(-s) Interactive Data Language (IDL) from Research Systems, Inc.


Analysis step

Window for plots or histograms Information windows:
comments and help for user


Plots and histograms ­ active selection of data

Window for histograms:

variable bins size Gaussian fit save histogram into file

Window for plots:

zoom plot select of area repeat the action


Selection of signals
Rise-time
0,2 MIN

0,8 MIN MIN

Signal after low-pass filter

Qi

Qj

Original signal

Small number of digitization points ­ poor rise time and amplitude determination For best selection of signals apply low-pass filter


Selection 'signal - noise' for all spectra

Selection of trigger (threshold) for 'signal - noise' determination using plot for MAX and MIN amplitude of signals
Trigger

Noise Trigger

Signal

Creation of noise- and signal-arrays for further analysis


Selection of good data
Rejection of signals with big noise

Selection of signal and noise

Selection of signals with offset

Rejection of signals with big deflection of peak


Determination of bad or multi-peaks signals
Good signal Good signal

Bad signal

Residual of derivative of signal and derivative of averaged basic signal

Bad signal

0,007 Residual of differentials 0,007

Residual of differentials


Algorithm of filtering

Model of the single pulse ­ A = H в S(t) H ­ amplitude, S(t) ­ constant pulse shape For the given pulse D(t): 2= (D(f) ­ H в S(f))2/N2(f), N2(f) ­ power spectrum of noise Minimization gives: H = (D(f) в S(f))/N2(f)


Fourier transformation


Total spectrum after filtering
Before filtering peaks are almost invisible

Photopeak 60 keV

K ­ escape 35 keV


Final histograms with K-escape and Photopeak
FWHM = 39,9 eV position of MAX = 35,0 keV K ­ escape

Photopeak

FWHM = 62,5 eV position of MAX = 59,9 keV


Summary of Results
-3

Energy resolution at E = 60 keV: EFWHM = 63 eV, or 10 accumulated statistics of 4000 events gives required accuracy of 1 eV

For comparison: theoretical limit for a conventional Si-semiconductor detector (at 60 keV) is EFWHM = 380 eV

Program, developed for the low temperature detectors and X-ray analysis can be used for any signals with the constant shape in presence of stationary noise


Interactive Data Language

object-oriented language very powerful language, advanced I/O a lot of integrated mathematical libraries development environment (editor, compiler, debugger, application generation internal visualization capabilities cross-platform application development (Windows, MacOS, UNIX, Linux

Price