783620H / 1013
centroid is calculated as:
6. ANALYSIS METHODS
(50)
where:
l, h = the peak low and high channels
i
= the channel number
C i
= net contents of channel i
For the directed fit method, the centroid can be refined from the fitting process.
From the Table 5 values and the calculated background, the net spectrum is shown in Table 6, continuing the example calculation on this peak.
The FW.04M is 2.2 times the FWHM for a Gaussian peak. The peak integration channels are then 2284 to 2300. The channel numbers are rounded to the nearest integers. The centroid for this example is 4.0366×10
7
/ 1.761×10
4
= 2292.16.
6.3.6. Energy Recalibration
The spectrum energy calibration can be redone “on the fly” for the spectrum being analyzed.
This improves the analysis results and adjusts for small changes in the hardware gain. Energy recalibration is first performed using singlet peaks only. Then, after deconvolution, the spectrum is recalibrated using all the peaks. If the energy calibration changes, the spectrum is reanalyzed.
For all peaks in the library, the peak centroid energy in the spectrum is compared with the library energy. If the difference between the library energy and the centroid energy is less than 0.5 keV, or the current Match Width (the FWHM multiplier entered on the System tab
251
GammaVision
®
v7 (A66-BW)
under Analyze/Settings/Sample Type...), or one channel — whichever is greater — that centroid is associated with that library energy.
The FWHM multiplier can be changed. If it is within this limit and has counting error less than 10% or the input sensitivity value (whichever is less), it is a qualified recalibration peak.
The energy range is split into two parts and the number of qualified library peaks in each region is counted. It there are more than the user-set number of qualified recalibration peaks in both regions of the spectrum, these spectrum centroids and library energies are used to recalculate the energy calibration for the spectrum.
The default energy is 0 keV and the number of peaks is 1000 below and 1000 above. Only this analysis is affected and the calibration in the spectrum file is not changed. If the energy recalibration is performed, a notice is written on the report, even if the recalibration had little or no effect. The new coefficients are printed on the output report.
Since this energy recalibration is dependent on the library and the spectrum, changes in the library can affect the calibration, and hence the peak energies reported. Only the energy factors are changed. The shape coefficient and efficiency coefficients are not altered. While the automatic energy recalibration will correct for small changes in the calibration, it is not intended as a substitute for accurate calibrations or as a correction for systems suffering from stability problems.
For an accurately calibrated spectrum, this recalibration will have little effect. Its effect will be most pronounced on deconvolutions of multiplets; this is discussed in Section 6.5.
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783620H / 1013
Table 6. Example Net Spectrum.
2311
2312
2313
2314
2315
2316
2317
2318
2319
2305
2306
2307
2308
2309
2310
2297
2298
2299
2300
2301
2302
2303
2304
2291
2292
2293
2294
2295
2296
2283
2284
2285
2286
2287
2288
2289
2290
Channel
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
12.0230
12.0344
12.0458
12.0572
12.0686
12.0800
12.0914
12.1028
12.1142
12.1256
12.1370
12.1484
12.1598
12.1712
12.1826
12.1940
12.2054
12.2168
12.2282
12.2396
12.2510
12.2624
12.2738
Background
11.7152
11.7266
11.7380
11.7494
11.7608
11.7722
11.7836
11.7950
11.8064
11.8178
11.8292
11.8406
11.8520
11.8634
11.8748
11.8862
11.8976
11.9090
11.9204
11.9318
11.9432
11.9546
11.9660
11.9774
11.9888
12.0002
12.0116
622.977
295.965
175.954
56.942
28.931
11.920
-2.091
-1.102
1.885
1.874
1.863
4.851
3.840
-4.171
1.817
1.806
-3.205
9.783
-4.228
-1.239
-2.251
1.737
-0.273
Net Spectrum
5.284
2.273
2.262
2.250
-4.760
0.227
3.216
4.205
-2.806
4.182
-1.829
9.159
20.148
15.136
47.125
120.113
225.102
461.091
835.079
1369.068
1887.057
2321.046
2391.034
2393.023
1972.011
1503.000
933.988
783620H / 1013 6. ANALYSIS METHODS
Because of this recalibration feature, the analysis results of spectra can change when a library is changed, or if the peak sensitivity is changed to a value under 10% (see fixed cutoff above).
Such changes between analyses can result in the recalibration being enabled in one case and disabled in the other case. This can result in the analyses being different in several different ways. The peak areas and backgrounds can be different because the integration limits for each peak will change slightly. This change is usually very small, but in a spectrum with very few counts it can be a high percentage of the total peak. In a given spectrum, some peak areas might change and others might be constant. Some peaks might move from the identified list to the unknown list (or the reverse) because the uncorrected centroid is too far from the library energy for validation.
In addition, an energy difference for all good library peaks is calculated. This is the sum of the absolute value of the difference between the peak centroid energy (before recalibration) and the library energy, expressed as a fraction of the FWHM, divided by the number of peaks in the sum.
This yields a number between 0 and 1 for good 3-point (or more) calibrations, with 0 being the best calibration. For 2-point calibrations, this number can be much larger than 1.0 because the calculated FWHM (which is a linear function) does not fit the spectrum FWHM at the ends of the spectrum. If high values are reported, and the analysis results are unacceptable, a better calibration should be made. The calibration section can be used to produce a multi-point calibration which will reduce the energy difference.
(51)
where:
E pi
E
Li
FWHM
Li n
= the energy of the i th
peak in the spectrum
= the energy of the corresponding peak in the library
= the calculated FWHM of the peak at the library
= the number of peaks in a spectrum with matching library peaks
This “energy-normalized difference” is printed on the report. For a complex spectrum this number will range from 0.1 to 0.3. A large value indicates that a new calibration should be performed or that the library does not match the spectrum well. Smaller values are usually associated with fewer peaks or a better calibration.
If an energy recalibration has occurred, the library peak list is reanalyzed with the new energy calibration. This results in more accurate peak values for centroid and area.
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