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Instrument Science Report NICMOS 98-008

Statistics of Accumulating Signal
W.B. Sparks, STScI May 1998

ABSTRACT NICMOS detectors accumulate charge which can be read non-destructively. The charge accumulation is a Poisson process, and readout noise is present. Here, formulae are presented for the variance (i.e., "error") of two estimators of the underlying rate of accumulation of charge, or "countrate," subject to these two processes only. The formulae are tested using Monte-Carlo simulations and are applied to the standard NICMOS MULTIACCUM sequences using the known NICMOS dark properties. These algorithms are essentially the current one employed by calnica, least-squares fit of a straight line, and the previous version, weighted mean of first differences. The usual formula for the error on the slope of the least-squares straight line is inapplicable because data points are not independent of previous data points. Also, the usual formula for the error on the weighted mean is inappropriate because of the presence of readout noise (which cancels out to a degree depending on the timing intervals). The results can be used to infer: (i) the least-squares fit algorithm gives a significantly better estimate of the countrate than the weighted mean of first differences, in the readnoise dominated regime (ii) the uncertainty goes down approximately linearly with exposure time in the readnoise dominated regime which suggests longer integrations should be used where possible (iii) Multiple Initial and Final reads (MIFs) improve the uncertainty by about 20% in regions of the detector where ampglow is small (cf. other sequences) (iv) there is little difference otherwise between any of the standard MULTIACCUM sequences. Tables are provided to allow optimal choice of sequence, and to show the characteristics of the uncertainties of MULTIACCUM data in various circumstances.These variances represent fundamental theoretical limits on the utility of the algorithms. Additional noise sources include cosmic rays and inaccuracies in the shading correction. A fairly high sensitivity to cosmic rays suggest using as many readouts as possible, but the consequent accumulation of ampglow can add significant noise.

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1. Model of a MULTIACCUM sequence
In NICMOS detectors charge accumulates in each pixel as incident photons are detected, and this charge can be read non-destructively. The accumulating charge between each readout is expected to obey Poisson statistics, and, in addition, associated with each readout there is electronic "readout noise" that imposes a random error on the measurement of the charge within an individual pixel. Hence if readouts are at times xi, and the actual accumulated charge is yi, then between x
i­1

and xi the actual additional accumulated charge is yi ­ y
i­1

i­1

= pi, where pi is drawn from

a Poisson distribution with expected value b.(x

­ xi) and b is the underlying countrate

sought. For example, if the underlying source countrate is 0.1 electrons/sec, and xi­1 = 256 sec and xi = 384 sec, then the expected value (mean) of the accumulating charge in that interval is 12.8 electrons. For any particular integration, there will be an actual value of charge accumulated in that period which is randomly drawn from a Poisson distribution of mean=12.8. Hence, yi = pi + yi­1 = pi + pi­1 + pi­2 ... or in other words yi is a type of random walk. It should be stressed that once the interval of time has elapsed and pi is measured, the actual value pi propagates throughout the subsequent series; it is fixed thereafter and no longer contributes a random element. In addition to the statistical fluctuations associated with the Poisson component of the accumulating signal in which the actual accumulated charge is the sum of the preceding Poisson trials, there is an uncertainty associated with the measurement of that charge, namely the "readout noise." That uncertainty is assumed to be independent from one measurement to the next. Figure 1 illustrates. Figure 1: Charge y accumulates during the sequence, and is read at times xi. Actual charge increments are pi and there is superimposed readout noise.
y
Underlying countrate

y3
Readout noise

Charge

y2

}

p3

y1
0

}
0

}
p1 x2 Time

p2

x1

x3

x

2


Here, calculations are presented of the variance of estimators in use, or that have been used. The work does not attempt to calculate new estimators, nor reveal whether those used represent minimum variance estimates. Least squares fitting gives better answers than averaging first differences.

2. Model of a NICMOS MULTIACCUM observation
This simple two component model is sufficiently flexible to capture the important elements of a NICMOS dark, see NICMOS ISR-026 by Skinner and Bergeron. The dark comprises (i) a time variable shading term, assumed here to be noiseless and known, (ii) a "linear dark" term which is conventional accumulating dark current, so that the amount of charge accumulated is proportional to the time since the last reset/read, i.e. the elapsed exposure time, and (iii) ampglow, in which every individual readout deposits a certain amount of charge into a pixel. The ampglow is strongly field dependent and varies from approximately 10­20 electrons/read in the detector centers to ten times that in the corners of the field of view. The linear dark term is low, and is approx 0.05 electrons/sec. We assume the values are known and the external countrate corrected accordingly. In addition to internal dark current, there is external background emission from zodiacal light and thermal emission from the HST optics, depending on wavelength and filter. For example, in the F160W "minimum background" wide band filter, where NICMOS is maximally sensitive, the estimated background countrate is approx 0.09 electron/sec. Finally, there is emission from the source itself. Conversion from countrate to flux obviously depends on the filter used, whereas the statistics depend on the detection process itself, i.e., the countrate, and can therefore be scaled. For example, a countrate of 0.1 electron/sec using the F160W filter corresponds to 3.17 x 10
­7

Jy or H = 23.66.

3. Variance calculations
Least squares fit of straight line If y i = a + b x i + i , the "least squares fit" which minimizes the weighted sum of the squares of the residuals =
2



( w i ( y i ­ a ­ bx i ) ) is

2

xy ­ x y 1 -b = ------------------------------------ -- ( xy ­ x y ) 2 2 x ­ (x) where denotes the sum of the weights, typically fit, and xy etc. are implicitly
i

1 w i = ----2 i
2

, or wi = 1 for an unweighted
2

wi xi y

i

above, and

= x ­ (x)

.

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If the data points {xi,yi} are independent, then the uncertainty of the estimator b is
b = /

. This "textbook" formula is the one used in calnica at the time of writing. Now,

suppose b is the estimator used, given the model above we can calculate the actual variance of b once the equation for it is recast in a form that isolates terms which are independent of one another. As in Figure 1, ignoring readout noise for now, let yi = y
i­1

+ p i where p i P ( b x i + d x i + A )

where d is the linear dark, A the ampglow and xi the time interval between two readouts. P(a) represents the Poisson distribution of mean a from which pi is drawn. The sums involved in calculating the slope may be recast in a form which groups together statistically independent terms.


i=1

n

y i = y1 + y2 + y3 + . . . + yn = p1 + (p1+p2) + (p1+p2+p3) + ... =np1 + (n ­ 1) p2 + (n ­ 2) p3 + . . . + p
n

More generally, with weighting, wi yi = p
1


1

n

wi + p

2


2

n

wi + p

3


3

n

wi + ...

Similarly, xi yi = x1 y1 + x2 y2 + x3 y3 . . . xn yn = x1 p1 + x2 (p1 + p2) + x3 (p1 + p2 + p3) + . . . + xn
i=1 n n n

P

i

= p1 (x1 + x2 + . . . xn) + p2
2

x

i

+ p3
3

x

i

+ . . . + xn p

n

and wi xi yi =


r=1

n

p

r


i=r

n

wi x

i

Substituting for y and xy above and using 1 b = -


=
i=r i=1

n

n

r­1

­



, we find

i=1


r=1

n

pr s s

r­1

{x ­ x

r­1

}

4


Where

S=


i=1

n

r­1

w

i

,

S

r­1

=



w

i

,

x=


i=1

n

wi xi /


i=1

n

r­1

w

i

, and

x

r­1

=



r­1

wi xi /

wi .

i=1

i=1

i=1

Hence, since pr are independent with variance (b + d) xi + A, the variance of b is 2 1 = ----2 b


r=1

n

ss

22 r­1

(x ­ x

r­1

) [ b xi + d xi + A ]

2

Similarly, if we work with estimates yi' of the yi which are inaccurate due to the presence of readout noise r, we assume that the additional contribution to

2 b

is

nr ------

2

, as given by

the "textbook" variance for independent data, which adds in quadrature to give a final formula for the variance of the countrate estimator b 2 1 = ----2 b


r=1

n

s (s

2

r­1

) (x ­ x

2

r­1

2 nr ) [ b x i + d x i + A ] + ------

2

For completeness, the variance of the intercept is, by a similar route and neglecting readout noise, given by: 2 = a where
sx =


r=1 wi x
i

n

sr ­ 1 1 + ---------- ( sx x and
sxx =

r­1

­ sxx )

2


i=1

n


i=1

n

wi x

2 i

.

Weighted mean of first differences By "first differences" we mean the series yi ´­ y
i­1

´ using the same notation as above.
i­1

Each "difference" provides an estimate of the countrate, bi =(yi ´­ yi­1´) / (ti ­ t

). Then

the estimator of the countrate is the weighted mean of the bi. By taking first differences, the Poisson component is now independent of the history of charge accumulation, and it is correct to adopt a simple weighting scheme depending on the individual uncertainties of each difference. During mid-1997, calnica version 2.2 attempted to take advantage of this fact and utilized a "first differences" approach. However, in regimes where readout noise is important, this is not the case. To illustrate, suppose the only thing present is readnoise. The source countrate is zero, the dark is zero, and there is no ampglow. Then the underlying charge accumulated is always zero, however the measurement of that zero charge follows a Gaussian with standard deviation r (if r is the readnoise). Hence the set yi ´ is a set of random numbers r x N(0,1) and N(0,1) is

5


the zero mean, unit variance normal distribution. Let the first differences be di = yi ´­ yi­1´, and the countrate estimates bi = di / dti with dti = ti ­ ti­1. On taking the first differences, if terms are independent the formal ence is 2 r , and so the uncertainty on the mean would be ( 2 r ) / ( N uncertainty on the measurement as noted above, and N the number of note that when taking the mean of the differences, cancellation occurs b1´ = (y1´ ­ y0´) / dt b2´ = (y2´ ­ y1´) / dt b3´ = (y3´ ­ y2´) / dt ... bN´ = (yN´ ­ y
(n ­ 1)´) 1 2 3

error on each differ) with r the measurements. But in the readout term:

/ dt

N

For example, if the dti are all the same equal to unity, the average is = (bi ´) / N =(yN´­ y0´) / N, which has an uncertainty only 2 â r / N compared to 2 â r / N . That is

the expected uncertainty on the mean in the case of independence of

the uncertainty is less by a factor of 1 / N than in the case of independent data. The amount of cancellation depends on the spacing of the readout times, as shown below. Generally, we can calculate the variance, and incorporate the cancellation into an effective readnoise as follows: Let an individual count rate estimate from the first differences be di yi ­ yi ­ 1 b i = ------ = --------------------- . ti ti Then form a weighted mean b =



di w i ----- / t



wi =



wi ------ ( y i ­ y ti

i­1

) / w i , then

w1 wn b = ------- y n ­ ------- y 0 + tn t1

n­1



i=1

wi wi + 1 ------ ­ ------------- r / w t i t i + 1 i

i

Consider the case where only readnoise is present, and the uncertainty on each yi´ is the same, r. Then wn w1 ( b ) = r ------- + ------- + t2 t2 n 1
2 2 2 2 n­1



i=1

wi wi + 1 2 ------ ­ ------------- / ( w ) i t i t i + 1

2

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For readout noise only, and weighting each bi is
2r ------2 ti
2

1 w i = ----2 i

, we have

ti w i = ------2 2r

2

since the uncertainty on

if r is the readout noise per read. Then substituting for wi, we obtain
n­1

2 2 2 t1 + tn + (ti ­ ti + 1) 2 2r 2 i=1 ( b ) = ----------- ------------------------------------------------------------------------2 2 2 ti t i
2



which can be made equivalent to the representation which would be valid if the data were independent,
2 2r = ----------2 t i

, if we define an effective readout noise
n­1

r

eff

2 2 2 t1 + tn + (ti ­ ti + 1) i=1 = r ------------------------------------------------------------------------2 2 ti



1/2

For example, if the data are equally spaced as in the example above, t i = t and r
eff

i+1

= t

= r / n.

Finally, therefore, in this scheme, we adopt a total variance that includes the Poisson 1 component ( b ) = ----------- where w i = wi
2

2 t ------------------ . di 2 --- + r eff g

4. Validation of the formulae
Monte Carlo simulations of the MULTIACCUM process were run for the standard NICMOS MULTIACCUM sequences and for each individual readout within the sequences. The formulae presented in the previous section give excellent agreement with the empirically derived distributions from Monte-Carlo simulations, as may be seen in the tables and figures that follow. The countrate estimators have expected values equal to the mean countrate so they are unbiased, and this too is born out in the testing.

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5. Results
Caveats: The exact numerical details in the tables may differ from real NICMOS observations because (1) readout noise is assumed per read, not per pair of reads, (2) only unweighted least squares regression line and a simple weighting were used (3) a zeroth read is included in the fit. Nevertheless, the qualitative conclusions will remain valid, and quantitative comparison is likely to reveal only minor differences. The variance associated with the least-squares substantially lower than for the weighted mean of standard deviation is about 50% lower for the line dominated regime. In a high countrate regime, the least squares fitting is better than first differences. straight line estimator of count rate is first differences. The corresponding fit in the low background readout noise two methods are comparable. That is,

In the low countrate regime, the uncertainty on the countrate estimate declines linearly with time, as expected if the S/N has S t and N ~ constant. The cluster of final reads in the MIF1024 sequence reduces the uncertainty by about 20% compared to the same sequence just prior to the final cluster of readouts, in the low ampglow case. In other words, judicious choice of readout timing can make a significant difference to the performance. In the high ampglow case, the extra reads make little difference, and the overall uncertainty is higher by about a factor two. The countrate uncertainty in the low countrate (faint object) limit depends primarily on exposure time and not on the specific sequence chosen. Example: in Table 1, for a MIF1024 sequence and exposure 1024 sec, the uncertainty is 0.0275 using a least-squares fit prior to the final readout cluster, and 0.022 after. Hence a three sigma detection requires a countrate 0.0825 e/sec and 0.066 e/sec respectively, or 2.61x10­7 Jy and 2.09x10­7 Jy for the F160W filter, or H=24.1 and 24.35 respectively. The NICMOS exposure time calculator gives very similar answers, with S/N=3 for 0.1 e/s in slightly less than 1000sec.

6. Appendix:
Tables of uncertainties for all the standard NICMOS MULTIACCUM sequences as a function of readout number follow for various circumstances. Table 1 gives the minimum background faint object limit near the detector center, i.e. low ampglow, and Table 2 gives the same table for near the detector corners. Table 3 gives an example run at high source countrate. External thermal emission is not distinguished from source emission in this case. The columns are (1) sequence name (2) readout number (3) old (incorrect) estimate of uncertainty from least squares fit of straight line (4) empirical estimate of the same quantity from Monte-Carlo simulation (5) revised formula for uncertainty of weighted mean of

8


first differences (6) empirical estimate of the same from Monte-Carlo simulation (7) revised analytical formula for uncertainty on least squares fit. THE FINAL COLUMN represents the current best estimate of the uncertainty associated with a particular observation. For Table 1:
Output is sequence, read, texp, els_an,els_emp,ewt_an,ewt_emp Empirical estimate uses n = 100 Parameters of run: Source countrate: Readout noise: Amp glow: Linear dark: 0.0880000 30.0000 15.0000 0.0500000 electron/sec electron/sec electron/read electron/sec

For Table 2:
Output is sequence, read, texp, els_an,els_emp,ewt_an,ewt_emp Empirical estimate uses n = 100 Parameters of run: Source countrate: Readout noise: Amp glow: Linear dark: 0.0880000 30.0000 150.000 0.0500000 electron/sec electron/sec electron/read electron/sec

For Table 3:
Source has H=19.4, or 16 micro Jy. Empirical estimate uses n = Parameters of run: Source countrate: Readout noise: Amp glow: Linear dark: 5.00000 30.0000 15.0000 0.0500000 electron/sec electron/sec electron/read electron/sec 100

Table 1. Minimum background uncertainty; no source
Seqname MCAMRR MCAMRR MCAMRR MCAMRR read 5 6 7 8 Texp (sec) 1.5116 1.8140 2.1163 2.4186 lsline (anal) 23.8643 19.2578 15.5997 13.2298 lsline (empir) 25.0058 22.9796 17.8739 13.4719 wtdiff (anal) 28.5067 23.8821 20.5224 17.9593 wtdiff (empir) 27.9717 28.1567 26.5162 18.3746 Poisson (anal) 25.2199 20.1916 16.6865 14.1204

9


Table 1. Minimum background uncertainty; no source (Continued)
Seqname MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 read 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Texp (sec) 2.7210 3.0233 3.3256 3.6279 3.9303 4.2326 4.5349 4.8372 5.1396 5.4419 5.7442 6.0466 6.3489 6.6512 6.9535 7.2559 7.5582 1.5116 1.8140 2.1163 2.4186 63.9930 127.9902 255.9833 383.9764 511.9694 639.9625 767.9556 895.9487 1023.9418 1024.2441 lsline (anal) 11.1009 9.6471 8.4961 7.5020 6.7196 6.0552 5.4956 5.0215 4.5636 4.1877 3.8947 3.5846 3.3224 3.1137 2.9346 2.7676 2.6088 23.8643 19.2578 15.5997 13.2298 0.5077 0.2219 0.1137 0.0692 0.0513 0.0385 0.0292 0.0241 0.0200 0.0181 lsline (empir) 13.2438 10.4646 9.1184 7.8468 7.2114 6.2886 6.3504 5.5613 5.4069 4.7314 4.6927 4.4911 4.1564 3.8241 3.7486 3.7513 3.8736 25.0058 22.9796 17.8739 13.4719 0.5592 0.2415 0.1037 0.0870 0.0491 0.0416 0.0314 0.0298 0.0252 0.0262 wtdiff (anal) 16.0267 14.4435 13.1587 12.1024 11.1944 10.4166 9.7330 9.1409 8.5968 8.1406 7.7290 7.3669 7.0110 6.7117 6.4049 6.1717 5.9203 28.5067 23.8821 20.5224 17.9593 0.6911 0.3417 0.1957 0.1180 0.0848 0.0667 0.0550 0.0469 0.0410 0.0409 wtdiff (empir) 17.9880 15.1183 12.2512 12.6695 11.5251 11.2036 10.9296 9.7090 8.5946 8.0359 7.9309 7.9788 7.2300 7.5770 6.4684 6.5212 5.9912 27.9717 28.1567 26.5162 18.3746 0.7814 0.3124 0.2050 0.1133 0.0895 0.0589 0.0511 0.0525 0.0422 0.0398 Poisson (anal) 12.2362 10.7539 9.5952 8.6612 7.8790 7.2412 6.6914 6.2272 5.8301 5.4853 5.1731 4.9087 4.6718 4.4568 4.2659 4.0956 3.9478 25.2199 20.1916 16.6865 14.1204 0.5205 0.2451 0.1237 0.0789 0.0570 0.0449 0.0369 0.0315 0.0275 0.0254

10


Table 1. Minimum background uncertainty; no source (Continued)
Seqname MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF3072 MIF3072 MIF3072 read 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 Texp (sec) 1024.5464 1024.8487 1025.1511 1025.4534 1025.7557 1026.0580 1026.3604 1.5116 1.8140 2.1163 2.4186 127.9889 255.9820 511.9812 767.9804 1023.9797 1279.9789 1535.9781 1791.9773 2047.9766 2048.2789 2048.5812 2048.8836 2049.1859 2049.4882 2049.7905 2050.0929 2050.3952 1.5116 1.8140 2.1163 lsline (anal) 0.0168 0.0159 0.0149 0.0141 0.0139 0.0136 0.0130 23.8643 19.2578 15.5997 13.2298 0.2575 0.1176 0.0567 0.0377 0.0246 0.0188 0.0149 0.0123 0.0105 0.0092 0.0084 0.0078 0.0074 0.0073 0.0071 0.0069 0.0067 23.8643 19.2578 15.5997 lsline (empir) 0.0230 0.0216 0.0233 0.0245 0.0210 0.0204 0.0225 25.0058 22.9796 17.8739 13.4719 0.2814 0.1322 0.0622 0.0427 0.0284 0.0257 0.0204 0.0170 0.0130 0.0147 0.0146 0.0127 0.0125 0.0126 0.0123 0.0118 0.0127 25.0058 22.9796 17.8739 wtdiff (anal) 0.0410 0.0408 0.0409 0.0409 0.0409 0.0409 0.0409 28.5067 23.8821 20.5224 17.9593 0.3402 0.1703 0.0982 0.0598 0.0433 0.0341 0.0283 0.0243 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 28.5067 23.8821 20.5224 wtdiff (empir) 0.0454 0.0407 0.0510 0.0430 0.0400 0.0446 0.0439 27.9717 28.1567 26.5162 18.3746 0.3525 0.1695 0.1033 0.0681 0.0461 0.0377 0.0299 0.0246 0.0217 0.0206 0.0214 0.0226 0.0216 0.0194 0.0245 0.0225 0.0225 27.9717 28.1567 26.5162 Poisson (anal) 0.0243 0.0234 0.0229 0.0225 0.0223 0.0221 0.0220 25.2199 20.1916 16.6865 14.1204 0.2581 0.1228 0.0627 0.0407 0.0298 0.0236 0.0197 0.0170 0.0150 0.0141 0.0135 0.0131 0.0129 0.0127 0.0126 0.0125 0.0125 25.2199 20.1916 16.6865

11


Table 1. Minimum background uncertainty; no source (Continued)
Seqname MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 read 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 Texp (sec) 2.4186 127.9889 255.9820 639.9802 1023.9784 1407.9766 1791.9748 2175.9730 2559.9712 3071.9684 3072.2707 3072.5730 3072.8754 3073.1777 3073.4800 3073.7823 3074.0847 3074.3870 1.5116 1.8140 2.1163 2.4186 31.9879 63.9871 127.9843 191.9815 255.9786 319.9758 383.9730 447.9702 511.9674 lsline (anal) 13.2298 0.2575 0.1176 0.0451 0.0278 0.0183 0.0140 0.0106 0.0087 0.0070 0.0062 0.0059 0.0053 0.0051 0.0050 0.0047 0.0046 0.0045 23.8643 19.2578 15.5997 13.2298 0.9933 0.4685 0.2255 0.1427 0.0995 0.0758 0.0607 0.0497 0.0407 lsline (empir) 13.4719 0.2814 0.1322 0.0517 0.0304 0.0234 0.0182 0.0138 0.0132 0.0109 0.0093 0.0100 0.0090 0.0100 0.0088 0.0093 0.0092 0.0093 25.0058 22.9796 17.8739 13.4719 1.1105 0.5302 0.2553 0.1713 0.1102 0.0838 0.0732 0.0606 0.0542 wtdiff (anal) 17.9593 0.3402 0.1703 0.0820 0.0460 0.0323 0.0251 0.0207 0.0177 0.0170 0.0170 0.0170 0.0170 0.0170 0.0170 0.0170 0.0170 0.0170 28.5067 23.8821 20.5224 17.9593 1.4352 0.6929 0.3914 0.2344 0.1679 0.1314 0.1078 0.0918 0.0799 wtdiff (empir) 18.3746 0.3525 0.1695 0.0858 0.0448 0.0298 0.0228 0.0186 0.0175 0.0142 0.0156 0.0163 0.0173 0.0168 0.0185 0.0168 0.0165 0.0176 27.9717 28.1567 26.5162 18.3746 1.3700 0.7207 0.3819 0.2459 0.1718 0.1168 0.1004 0.0858 0.0794 Poisson (anal) 14.1204 0.2581 0.1228 0.0519 0.0315 0.0225 0.0176 0.0147 0.0127 0.0110 0.0103 0.0099 0.0096 0.0094 0.0093 0.0093 0.0092 0.0092 25.2199 20.1916 16.6865 14.1204 1.0611 0.4953 0.2476 0.1562 0.1124 0.0872 0.0710 0.0602 0.0523

12


Table 1. Minimum background uncertainty; no source (Continued)
Seqname MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SPARS256 SPARS256 read 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 Texp (sec) 512.2697 512.5720 512.8743 513.1767 513.4790 513.7813 514.0836 514.3860 1.0150 1.2180 1.4210 1.6240 1.8270 2.0300 2.2330 2.4360 2.6390 2.8420 3.0450 3.2480 3.4510 3.6540 3.8570 4.0600 4.2630 4.4660 4.6690 4.8720 5.0750 767.9930 1023.9923 lsline (anal) 0.0372 0.0346 0.0316 0.0307 0.0285 0.0281 0.0270 0.0261 35.5299 28.8540 23.2513 19.6624 16.5426 14.3859 12.6793 11.1566 10.0072 9.0000 8.1792 7.4726 6.8074 6.2411 5.8076 5.3509 4.9616 4.6420 4.3619 4.1140 3.8768 0.0394 0.0297 lsline (empir) 0.0445 0.0413 0.0438 0.0413 0.0430 0.0427 0.0392 0.0399 37.5637 33.2283 26.7798 20.3513 19.5679 15.6040 13.5172 11.6316 10.6676 9.3749 9.3620 8.3253 8.0471 6.9931 6.9105 6.6837 6.1870 5.7727 5.6821 5.5402 5.9579 0.0449 0.0317 wtdiff (anal) 0.0798 0.0796 0.0796 0.0796 0.0798 0.0797 0.0795 0.0796 42.4649 35.5759 30.5769 26.7506 23.8631 21.5127 19.5992 18.0262 16.6715 15.5174 14.4979 13.6139 12.8063 12.1249 11.5129 10.9756 10.4402 9.9932 9.5458 9.1971 8.8100 0.0574 0.0436 wtdiff (empir) 0.0766 0.0795 0.0782 0.0892 0.0790 0.0808 0.0800 0.0866 41.1513 41.5112 39.4040 27.1607 25.5942 22.4239 18.1764 18.6913 17.3404 16.3860 16.2808 14.2272 12.7877 11.9827 11.7062 11.7763 10.6698 11.6008 10.3087 9.5263 9.1325 0.0551 0.0445 Poisson (anal) 0.0480 0.0454 0.0439 0.0428 0.0420 0.0416 0.0411 0.0408 37.5688 30.0638 24.8619 21.0262 18.2232 16.0164 14.2872 12.8978 11.7334 10.7837 9.9636 9.2757 8.6807 8.1684 7.7045 7.3116 6.9575 6.6377 6.3542 6.0997 5.8764 0.0448 0.0331

13


Table 1. Minimum background uncertainty; no source (Continued)
Seqname SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 read 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 Texp (sec) 1279.9915 1535.9907 1791.9899 2047.9892 2303.9884 2559.9876 2815.9868 3071.9861 3327.9853 3583.9845 3839.9837 4095.9830 4351.9822 4607.9814 4863.9806 5119.9799 5375.9791 5631.9783 5887.9775 191.9869 255.9841 319.9813 383.9784 447.9756 511.9728 575.9700 639.9671 703.9643 767.9615 831.9587 895.9558 lsline (anal) 0.0227 0.0178 0.0145 0.0128 0.0105 0.0094 0.0083 0.0078 0.0067 0.0060 0.0058 0.0052 0.0048 0.0044 0.0042 0.0039 0.0037 0.0035 0.0033 0.1585 0.1181 0.0867 0.0696 0.0581 0.0506 0.0446 0.0370 0.0337 0.0293 0.0272 0.0247 lsline (empir) 0.0241 0.0183 0.0165 0.0178 0.0172 0.0133 0.0124 0.0115 0.0111 0.0098 0.0092 0.0081 0.0089 0.0087 0.0075 0.0078 0.0076 0.0070 0.0067 0.2018 0.1407 0.0890 0.0729 0.0619 0.0522 0.0487 0.0432 0.0361 0.0405 0.0360 0.0301 wtdiff (anal) 0.0352 0.0297 0.0257 0.0227 0.0204 0.0185 0.0170 0.0157 0.0147 0.0137 0.0129 0.0122 0.0116 0.0110 0.0105 0.0101 0.0097 0.0093 0.0089 0.2254 0.1690 0.1360 0.1139 0.0979 0.0860 0.0770 0.0698 0.0635 0.0584 0.0541 0.0504 wtdiff (empir) 0.0346 0.0307 0.0234 0.0262 0.0205 0.0200 0.0170 0.0146 0.0141 0.0133 0.0139 0.0126 0.0109 0.0127 0.0114 0.0103 0.0094 0.0095 0.0090 0.2617 0.1661 0.1235 0.1175 0.0975 0.0870 0.0835 0.0713 0.0696 0.0557 0.0598 0.0498 Poisson (anal) 0.0262 0.0218 0.0187 0.0164 0.0147 0.0134 0.0124 0.0115 0.0108 0.0101 0.0096 0.0091 0.0087 0.0084 0.0080 0.0077 0.0075 0.0073 0.0070 0.1732 0.1253 0.0975 0.0797 0.0672 0.0581 0.0514 0.0462 0.0419 0.0383 0.0355 0.0330

14


Table 1. Minimum background uncertainty; no source (Continued)
Seqname SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP128 read 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 Texp (sec) 959.9530 1023.9502 1087.9474 1151.9445 1215.9417 1279.9389 1343.9361 1407.9332 1471.9304 2.9882 3.9859 4.9835 5.9811 6.9787 7.9764 8.9740 9.9716 10.9692 11.9669 12.9645 13.9621 14.9597 15.9574 16.9550 17.9526 18.9502 19.9479 20.9455 21.9431 22.9407 3.9846 lsline (anal) 0.0227 0.0209 0.0187 0.0177 0.0164 0.0152 0.0144 0.0132 0.0125 11.4805 8.5111 6.2441 5.0205 4.0450 3.2884 2.8166 2.5087 2.1946 1.9454 1.7605 1.5704 1.4618 1.3154 1.2240 1.1141 1.0280 0.9833 0.9005 0.8439 0.8042 8.7978 lsline (empir) 0.0284 0.0254 0.0283 0.0282 0.0259 0.0232 0.0239 0.0214 0.0189 14.0624 8.7712 6.4884 5.1499 4.2769 3.6860 3.1325 2.8503 2.4273 2.0679 2.1704 1.8134 1.7954 1.6624 1.6038 1.5359 1.3911 1.2881 1.2174 1.1875 1.0309 10.8038 wtdiff (anal) 0.0472 0.0444 0.0419 0.0398 0.0378 0.0360 0.0344 0.0330 0.0317 15.7885 11.1308 8.5717 6.9764 5.9057 5.1179 4.5207 4.0475 3.6644 3.3470 3.0804 2.8664 2.6628 2.5036 2.3469 2.2205 2.1013 1.9964 1.8999 1.8116 1.7315 13.2688 wtdiff (empir) 0.0526 0.0464 0.0449 0.0413 0.0363 0.0373 0.0356 0.0336 0.0278 17.0324 11.1848 9.0398 7.1908 6.4867 5.7295 4.5100 3.9113 3.7140 3.4024 3.1670 2.9961 3.0317 2.4317 2.3941 2.2244 2.2897 2.1929 1.8650 1.9239 1.5935 14.0003 Poisson (anal) 0.0310 0.0292 0.0276 0.0263 0.0251 0.0240 0.0231 0.0222 0.0214 12.2786 8.6353 6.5581 5.2507 4.3656 3.7288 3.2520 2.8806 2.5877 2.3498 2.1512 1.9853 1.8484 1.7276 1.6243 1.5371 1.4557 1.3865 1.3238 1.2672 1.2157 9.3700

15


Table 1. Minimum background uncertainty; no source (Continued)
Seqname STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 read 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 Texp (sec) 7.9784 15.9720 31.9651 63.9643 127.9615 255.9546 383.9477 511.9408 639.9338 767.9269 895.9200 1023.9131 1151.9062 1279.8992 1407.8923 1535.8854 1663.8785 1791.8716 1919.8646 2047.8577 3.9846 7.9784 15.9720 31.9651 47.9582 63.9513 79.9444 95.9374 111.9305 127.9236 143.9167 lsline (anal) 4.1272 1.9204 0.9941 0.4879 0.2389 0.1169 0.0718 0.0495 0.0366 0.0300 0.0248 0.0211 0.0177 0.0157 0.0136 0.0118 0.0111 0.0100 0.0094 0.0085 8.7978 4.1272 1.9204 0.9941 0.6099 0.4278 0.3197 0.2476 0.2076 0.1762 0.1514 lsline (empir) 4.5065 2.2554 0.9860 0.4782 0.2738 0.1217 0.0885 0.0521 0.0458 0.0359 0.0282 0.0277 0.0235 0.0205 0.0190 0.0168 0.0181 0.0167 0.0147 0.0149 10.8038 4.5065 2.2554 0.9860 0.7038 0.4505 0.3432 0.2562 0.2415 0.2192 0.1874 wtdiff (anal) 6.5949 3.2808 1.6360 0.8197 0.4104 0.2066 0.1190 0.0842 0.0655 0.0540 0.0458 0.0399 0.0354 0.0318 0.0290 0.0267 0.0247 0.0229 0.0215 0.0202 13.2688 6.5949 3.2808 1.6360 0.9425 0.6628 0.5133 0.4180 0.3538 0.3075 0.2710 wtdiff (empir) 6.0530 2.9552 1.7167 0.8467 0.4322 0.1906 0.1304 0.0792 0.0617 0.0565 0.0441 0.0435 0.0345 0.0281 0.0304 0.0267 0.0248 0.0206 0.0223 0.0232 14.0003 6.0530 2.9552 1.7167 0.9628 0.6544 0.5005 0.3914 0.3453 0.3460 0.3069 Poisson (anal) 4.4541 2.1444 1.0443 0.5142 0.2549 0.1273 0.0803 0.0578 0.0452 0.0372 0.0317 0.0277 0.0247 0.0223 0.0204 0.0189 0.0177 0.0165 0.0157 0.0149 9.3700 4.4541 2.1444 1.0443 0.6524 0.4630 0.3557 0.2872 0.2409 0.2076 0.1821

16


Table 1. Minimum background uncertainty; no source (Continued)
Seqname STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 read 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Texp (sec) 159.9098 175.9028 191.8959 207.8890 223.8821 239.8752 255.8682 271.8613 287.8544 303.8475 3.9846 5.9786 7.9726 9.9665 11.9605 13.9545 15.9485 17.9424 19.9364 21.9304 23.9244 25.9183 27.9123 29.9063 31.9003 33.8942 35.8882 37.8822 39.8762 41.8701 43.8641 lsline (anal) 0.1306 0.1158 0.1037 0.0937 0.0863 0.0784 0.0714 0.0679 0.0627 0.0583 8.7978 5.6690 3.8650 2.9335 2.2671 1.7993 1.5547 1.3402 1.1811 1.0568 0.9161 0.8364 0.7523 0.6805 0.6240 0.5800 0.5288 0.4984 0.4650 0.4424 0.4092 lsline (empir) 0.1714 0.1652 0.1328 0.1273 0.1227 0.1077 0.0929 0.0872 0.0825 0.0750 10.8038 6.2578 4.2015 3.3699 2.1786 2.0394 1.8364 1.7416 1.3247 1.2120 1.2456 0.9857 1.0642 0.8819 0.8875 0.7704 0.7741 0.6793 0.6681 0.6716 0.5673 wtdiff (anal) 0.2426 0.2203 0.2011 0.1854 0.1725 0.1603 0.1508 0.1412 0.1337 0.1264 13.2688 7.6380 5.3642 4.1455 3.3821 2.8601 2.4748 2.1865 1.9568 1.7697 1.6235 1.4928 1.3859 1.2934 1.2089 1.1388 1.0742 1.0173 0.9640 0.9170 0.8761 wtdiff (empir) 0.2751 0.2707 0.2134 0.1983 0.1700 0.1538 0.1591 0.1518 0.1456 0.1165 14.0003 7.7076 5.8153 4.5818 3.0137 2.9205 2.6510 2.1592 1.9332 1.7893 1.5072 1.4912 1.4756 1.3870 1.2872 1.1210 1.1998 0.9873 0.9536 0.9554 0.9065 Poisson (anal) 0.1626 0.1477 0.1346 0.1243 0.1154 0.1079 0.1015 0.0961 0.0911 0.0869 9.3700 5.7639 4.0555 3.1026 2.4914 2.0787 1.7799 1.5580 1.3818 1.2412 1.1337 1.0391 0.9617 0.8967 0.8402 0.7905 0.7477 0.7100 0.6776 0.6473 0.6201

17


Table 1. Minimum background uncertainty; no source (Continued)
Seqname STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 read 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 Texp (sec) 3.9846 7.9784 15.9720 31.9651 63.9643 127.9615 255.9546 511.9538 767.9530 1023.9523 1279.9515 1535.9507 1791.9499 2047.9492 2303.9484 2559.9476 2815.9468 3071.9461 3327.9453 3583.9445 3839.9437 3.9846 7.9784 15.9720 31.9651 63.9643 95.9636 127.9628 159.9620 191.9612 223.9605 lsline (anal) 8.7978 4.1272 1.9204 0.9941 0.4879 0.2389 0.1169 0.0575 0.0358 0.0251 0.0188 0.0148 0.0122 0.0103 0.0086 0.0077 0.0070 0.0061 0.0056 0.0050 0.0046 8.7978 4.1272 1.9204 0.9941 0.4879 0.2933 0.2027 0.1535 0.1251 0.0981 lsline (empir) 10.8038 4.5065 2.2554 0.9860 0.4782 0.2738 0.1217 0.0670 0.0472 0.0329 0.0255 0.0188 0.0167 0.0162 0.0149 0.0127 0.0111 0.0104 0.0101 0.0090 0.0087 10.8038 4.5065 2.2554 0.9860 0.4782 0.3156 0.2000 0.1482 0.1427 0.1315 wtdiff (anal) 13.2688 6.5949 3.2808 1.6360 0.8197 0.4104 0.2066 0.1040 0.0605 0.0430 0.0336 0.0277 0.0237 0.0208 0.0186 0.0167 0.0153 0.0141 0.0131 0.0123 0.0116 13.2688 6.5949 3.2808 1.6360 0.8197 0.4722 0.3325 0.2573 0.2105 0.1778 wtdiff (empir) 14.0003 6.0530 2.9552 1.7167 0.8467 0.4322 0.1906 0.0994 0.0603 0.0475 0.0363 0.0282 0.0225 0.0208 0.0187 0.0178 0.0154 0.0154 0.0132 0.0117 0.0121 14.0003 6.0530 2.9552 1.7167 0.8467 0.4692 0.3390 0.2453 0.2055 0.2044 Poisson (anal) 9.3700 4.4541 2.1444 1.0443 0.5142 0.2549 0.1273 0.0642 0.0412 0.0301 0.0238 0.0198 0.0171 0.0151 0.0136 0.0124 0.0115 0.0107 0.0101 0.0095 0.0090 9.3700 4.4541 2.1444 1.0443 0.5142 0.3219 0.2288 0.1761 0.1430 0.1199

18


Table 1. Minimum background uncertainty; no source (Continued)
Seqname STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 read 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Texp (sec) 255.9597 287.9589 319.9581 351.9574 383.9566 415.9558 447.9550 479.9543 511.9535 543.9527 575.9519 3.9846 7.9784 15.9720 31.9651 63.9643 127.9615 191.9587 255.9559 319.9530 383.9502 447.9474 511.9446 575.9418 639.9389 703.9361 767.9333 831.9305 895.9276 959.9248 1023.9220 lsline (anal) 0.0882 0.0736 0.0654 0.0579 0.0509 0.0469 0.0415 0.0382 0.0361 0.0333 0.0303 8.7978 4.1272 1.9204 0.9941 0.4879 0.2389 0.1469 0.1022 0.0748 0.0608 0.0491 0.0417 0.0380 0.0306 0.0280 0.0246 0.0228 0.0206 0.0188 0.0173 lsline (empir) 0.1022 0.0927 0.0845 0.0663 0.0638 0.0590 0.0609 0.0590 0.0518 0.0515 0.0461 10.8038 4.5065 2.2554 0.9860 0.4782 0.2738 0.1764 0.1021 0.0899 0.0706 0.0604 0.0461 0.0447 0.0384 0.0322 0.0339 0.0341 0.0277 0.0302 0.0269 wtdiff (anal) 0.1538 0.1363 0.1220 0.1108 0.1014 0.0935 0.0866 0.0809 0.0761 0.0715 0.0679 13.2688 6.5949 3.2808 1.6360 0.8197 0.4104 0.2364 0.1670 0.1296 0.1062 0.0898 0.0780 0.0689 0.0622 0.0563 0.0517 0.0477 0.0443 0.0414 0.0388 wtdiff (empir) 0.1728 0.1459 0.1281 0.1073 0.1027 0.1015 0.0977 0.0973 0.0804 0.0794 0.0664 14.0003 6.0530 2.9552 1.7167 0.8467 0.4322 0.2416 0.1729 0.1290 0.1018 0.0819 0.0744 0.0647 0.0677 0.0526 0.0497 0.0530 0.0433 0.0443 0.0416 Poisson (anal) 0.1035 0.0914 0.0816 0.0741 0.0680 0.0629 0.0583 0.0547 0.0519 0.0491 0.0466 9.3700 4.4541 2.1444 1.0443 0.5142 0.2549 0.1599 0.1142 0.0886 0.0723 0.0609 0.0528 0.0468 0.0421 0.0383 0.0353 0.0327 0.0306 0.0288 0.0272

19


Table 1. Minimum background uncertainty; no source (Continued)
Seqname STEP64 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 read 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Texp (sec) 1087.9192 3.9846 7.9784 15.9720 23.9656 31.9592 39.9528 47.9464 55.9400 63.9336 71.9272 79.9208 87.9144 95.9080 103.9016 111.8951 119.8887 127.8823 135.8759 143.8695 151.8631 159.8567 lsline (anal) 0.0158 8.7978 4.1272 1.9204 1.2530 0.8597 0.6722 0.5289 0.4496 0.3610 0.3262 0.2730 0.2435 0.2110 0.1952 0.1711 0.1603 0.1510 0.1367 0.1289 0.1178 0.1116 lsline (empir) 0.0250 10.8038 4.5065 2.2554 1.3447 0.9450 0.7888 0.6004 0.5814 0.4225 0.3208 0.3448 0.2897 0.2824 0.2712 0.2149 0.2257 0.2015 0.2088 0.1985 0.1726 0.1592 wtdiff (anal) 0.0367 13.2688 6.5949 3.2808 1.8845 1.3244 1.0258 0.8358 0.7056 0.6126 0.5393 0.4856 0.4388 0.4020 0.3690 0.3434 0.3194 0.2987 0.2817 0.2658 0.2516 0.2380 wtdiff (empir) 0.0367 14.0003 6.0530 2.9552 1.8617 1.4206 1.3105 0.8594 0.8290 0.6604 0.5691 0.4987 0.4451 0.4288 0.4312 0.3760 0.3118 0.3096 0.2995 0.3123 0.2650 0.2495 Poisson (anal) 0.0259 9.3700 4.4541 2.1444 1.3302 0.9429 0.7237 0.5846 0.4895 0.4200 0.3679 0.3287 0.2967 0.2715 0.2491 0.2311 0.2164 0.2029 0.1922 0.1820 0.1730 0.1649

Table 2. Minimum background uncertainty; no source; high ampglow
Seqname MCAMRR MCAMRR MCAMRR MCAMRR read 5 6 7 8 Texp (sec) 1.5116 1.8140 2.1163 2.4186 lsline (anal) 24.6152 19.0963 15.8637 13.1977 lsline (empir) 30.0277 25.5626 25.1893 21.4848 wtdiff (anal) 33.3051 28.5872 25.1189 22.5884 wtdiff (empir) 36.5845 28.9847 28.6854 26.0344 Poisson (anal) 34.4904 28.8891 24.9865 22.1745

20


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 read 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Texp (sec) 2.7210 3.0233 3.3256 3.6279 3.9303 4.2326 4.5349 4.8372 5.1396 5.4419 5.7442 6.0466 6.3489 6.6512 6.9535 7.2559 7.5582 1.5116 1.8140 2.1163 2.4186 63.9930 127.9902 255.9833 383.9764 511.9694 639.9625 767.9556 895.9487 1023.9418 1024.2441 lsline (anal) 11.4132 10.0151 8.7911 7.9397 7.1112 6.3576 5.8363 5.4002 4.9669 4.6916 4.3284 3.9750 3.7650 3.5397 3.3294 3.1822 2.9638 24.6152 19.0963 15.8637 13.1977 0.5550 0.2619 0.1295 0.0791 0.0558 0.0423 0.0335 0.0278 0.0232 0.0209 lsline (empir) 18.7213 19.0039 17.9016 14.4452 13.3009 14.8211 13.9544 12.7533 13.1723 11.3646 11.7776 11.0319 11.9776 9.7668 10.7332 10.3154 9.7875 30.0277 25.5626 25.1893 21.4848 0.6827 0.3633 0.1996 0.1199 0.0868 0.0807 0.0699 0.0580 0.0589 0.0505 wtdiff (anal) 20.5613 18.9287 17.5690 16.4563 15.4856 14.6868 13.9547 13.3160 12.7569 12.2449 11.7916 11.3797 11.0067 10.6635 10.3406 10.0528 9.7787 33.3051 28.5872 25.1189 22.5884 0.7169 0.3654 0.2088 0.1313 0.0979 0.0794 0.0672 0.0590 0.0529 0.0528 wtdiff (empir) 20.5231 20.4210 19.1804 15.2038 14.7303 14.9831 14.3954 14.8241 14.2612 13.1608 13.0971 11.5782 12.2565 10.7227 11.3649 10.2840 10.6816 36.5845 28.9847 28.6854 26.0344 0.7765 0.3875 0.2146 0.1239 0.0948 0.0815 0.0675 0.0662 0.0604 0.0649 Poisson (anal) 20.0097 18.3407 16.9856 15.8652 14.9256 14.1476 13.4675 12.8704 12.3549 11.8768 11.4584 11.0853 10.7442 10.4310 10.1463 9.8831 9.6445 34.4904 28.8891 24.9865 22.1745 0.6254 0.3232 0.1723 0.1164 0.0887 0.0726 0.0619 0.0546 0.0491 0.0467

21


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF3072 MIF3072 MIF3072 read 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 Texp (sec) 1024.5464 1024.8487 1025.1511 1025.4534 1025.7557 1026.0580 1026.3604 1.5116 1.8140 2.1163 2.4186 127.9889 255.9820 511.9812 767.9804 1023.9797 1279.9789 1535.9781 1791.9773 2047.9766 2048.2789 2048.5812 2048.8836 2049.1859 2049.4882 2049.7905 2050.0929 2050.3952 1.5116 1.8140 2.1163 lsline (anal) 0.0192 0.0178 0.0170 0.0164 0.0159 0.0155 0.0150 24.6152 19.0963 15.8637 13.1977 0.2753 0.1304 0.0646 0.0395 0.0279 0.0212 0.0168 0.0139 0.0116 0.0105 0.0096 0.0089 0.0085 0.0082 0.0080 0.0078 0.0075 24.6152 19.0963 15.8637 lsline (empir) 0.0523 0.0485 0.0542 0.0452 0.0505 0.0510 0.0487 30.0277 25.5626 25.1893 21.4848 0.3372 0.1808 0.1000 0.0607 0.0439 0.0411 0.0357 0.0298 0.0303 0.0261 0.0269 0.0250 0.0279 0.0234 0.0261 0.0262 0.0250 30.0277 25.5626 25.1893 wtdiff (anal) 0.0528 0.0527 0.0527 0.0528 0.0528 0.0527 0.0528 33.3051 28.5872 25.1189 22.5884 0.3528 0.1819 0.1048 0.0663 0.0497 0.0404 0.0343 0.0302 0.0271 0.0271 0.0271 0.0270 0.0270 0.0271 0.0271 0.0270 0.0271 33.3051 28.5872 25.1189 wtdiff (empir) 0.0632 0.0486 0.0587 0.0552 0.0548 0.0591 0.0556 36.5845 28.9847 28.6854 26.0344 0.3824 0.1931 0.1075 0.0622 0.0479 0.0415 0.0344 0.0340 0.0309 0.0333 0.0323 0.0250 0.0300 0.0284 0.0280 0.0302 0.0284 36.5845 28.9847 28.6854 Poisson (anal) 0.0455 0.0451 0.0449 0.0451 0.0453 0.0456 0.0461 34.4904 28.8891 24.9865 22.1745 0.3081 0.1608 0.0865 0.0588 0.0451 0.0370 0.0317 0.0280 0.0253 0.0241 0.0235 0.0233 0.0232 0.0233 0.0234 0.0235 0.0238 34.4904 28.8891 24.9865

22


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 read 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 Texp (sec) 2.4186 127.9889 255.9820 639.9802 1023.9784 1407.9766 1791.9748 2175.9730 2559.9712 3071.9684 3072.2707 3072.5730 3072.8754 3073.1777 3073.4800 3073.7823 3074.0847 3074.3870 1.5116 1.8140 2.1163 2.4186 31.9879 63.9871 127.9843 191.9815 255.9786 319.9758 383.9730 447.9702 511.9674 lsline (anal) 13.1977 0.2753 0.1304 0.0537 0.0306 0.0207 0.0154 0.0120 0.0099 0.0081 0.0072 0.0065 0.0060 0.0058 0.0055 0.0053 0.0052 0.0050 24.6152 19.0963 15.8637 13.1977 1.1269 0.5287 0.2602 0.1588 0.1118 0.0847 0.0671 0.0557 0.0464 lsline (empir) 21.4848 0.3372 0.1808 0.0809 0.0458 0.0323 0.0297 0.0254 0.0213 0.0212 0.0181 0.0186 0.0171 0.0191 0.0160 0.0179 0.0179 0.0170 30.0277 25.5626 25.1893 21.4848 1.4053 0.7390 0.4017 0.2391 0.1729 0.1602 0.1385 0.1144 0.1160 wtdiff (anal) 22.5884 0.3528 0.1819 0.0862 0.0503 0.0365 0.0292 0.0246 0.0215 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 33.3051 28.5872 25.1189 22.5884 1.4867 0.7423 0.4185 0.2616 0.1943 0.1571 0.1329 0.1166 0.1043 wtdiff (empir) 26.0344 0.3824 0.1931 0.0893 0.0490 0.0348 0.0295 0.0245 0.0235 0.0231 0.0233 0.0238 0.0176 0.0216 0.0208 0.0211 0.0222 0.0208 36.5845 28.9847 28.6854 26.0344 1.6097 0.7851 0.4313 0.2482 0.1887 0.1615 0.1335 0.1300 0.1194 Poisson (anal) 22.1745 0.3081 0.1608 0.0702 0.0446 0.0332 0.0268 0.0228 0.0200 0.0176 0.0167 0.0162 0.0160 0.0159 0.0160 0.0160 0.0161 0.0163 34.4904 28.8891 24.9865 22.1745 1.2917 0.6567 0.3465 0.2327 0.1766 0.1441 0.1227 0.1079 0.0969

23


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SPARS256 SPARS256 read 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 Texp (sec) 512.2697 512.5720 512.8743 513.1767 513.4790 513.7813 514.0836 514.3860 1.0150 1.2180 1.4210 1.6240 1.8270 2.0300 2.2330 2.4360 2.6390 2.8420 3.0450 3.2480 3.4510 3.6540 3.8570 4.0600 4.2630 4.4660 4.6690 4.8720 5.0750 767.9930 1023.9923 lsline (anal) 0.0419 0.0383 0.0355 0.0340 0.0327 0.0318 0.0310 0.0300 36.6593 28.4401 23.6258 19.6552 16.9976 14.9155 13.0925 11.8245 10.5907 9.4683 8.6919 8.0424 7.3971 6.9871 6.4463 5.9200 5.6072 5.2717 4.9585 4.7392 4.4140 0.0441 0.0306 lsline (empir) 0.0993 0.1030 0.0955 0.1067 0.0889 0.0995 0.1003 0.0961 44.7196 38.0696 37.5136 31.9965 27.8808 28.3017 26.6599 21.5125 19.8083 22.0723 20.7816 18.9928 19.6168 16.9246 17.5397 16.4291 17.8375 14.5451 15.9843 15.3621 14.5759 0.0509 0.0408 wtdiff (anal) 0.1040 0.1040 0.1039 0.1039 0.1040 0.1040 0.1038 0.1041 49.6006 42.5742 37.4089 33.6403 30.6214 28.1899 26.1650 24.5078 23.0622 21.8725 20.7822 19.8310 18.9983 18.2359 17.5607 16.9473 16.3919 15.8807 15.3999 14.9712 14.5630 0.0630 0.0491 wtdiff (empir) 0.1273 0.1250 0.0956 0.1158 0.1089 0.1080 0.1170 0.1100 54.4847 43.1662 42.7203 38.7723 30.5643 30.4124 28.5647 22.6424 21.9373 22.3137 21.4384 22.0769 21.2387 19.6000 19.5049 17.2430 18.2530 15.9688 16.9253 15.3156 15.9076 0.0597 0.0461 Poisson (anal) 0.0920 0.0897 0.0887 0.0884 0.0887 0.0891 0.0898 0.0907 51.3660 43.0240 37.2119 33.0240 29.8000 27.3143 25.2963 23.6277 22.2283 21.0696 20.0568 19.1675 18.3997 17.6878 17.0646 16.5089 16.0010 15.5345 15.1106 14.7186 14.3632 0.0530 0.0412

24


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 read 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 Texp (sec) 1279.9915 1535.9907 1791.9899 2047.9892 2303.9884 2559.9876 2815.9868 3071.9861 3327.9853 3583.9845 3839.9837 4095.9830 4351.9822 4607.9814 4863.9806 5119.9799 5375.9791 5631.9783 5887.9775 191.9869 255.9841 319.9813 383.9784 447.9756 511.9728 575.9700 639.9671 703.9643 767.9615 831.9587 895.9558 lsline (anal) 0.0237 0.0189 0.0159 0.0135 0.0116 0.0103 0.0092 0.0082 0.0074 0.0069 0.0063 0.0059 0.0054 0.0050 0.0047 0.0044 0.0041 0.0040 0.0037 0.1759 0.1218 0.0945 0.0750 0.0630 0.0536 0.0460 0.0410 0.0364 0.0323 0.0293 0.0271 lsline (empir) 0.0379 0.0317 0.0269 0.0273 0.0256 0.0204 0.0186 0.0203 0.0192 0.0172 0.0180 0.0155 0.0159 0.0148 0.0161 0.0132 0.0144 0.0137 0.0130 0.1995 0.1591 0.1469 0.1214 0.1026 0.1037 0.0969 0.0771 0.0697 0.0765 0.0721 0.0646 wtdiff (anal) 0.0406 0.0350 0.0309 0.0278 0.0254 0.0235 0.0219 0.0205 0.0193 0.0184 0.0175 0.0167 0.0160 0.0154 0.0149 0.0144 0.0139 0.0135 0.0131 0.2477 0.1920 0.1583 0.1361 0.1198 0.1076 0.0980 0.0904 0.0840 0.0787 0.0741 0.0703 wtdiff (empir) 0.0427 0.0375 0.0305 0.0309 0.0292 0.0236 0.0221 0.0216 0.0212 0.0196 0.0213 0.0172 0.0184 0.0150 0.0176 0.0145 0.0156 0.0134 0.0143 0.2348 0.1806 0.1667 0.1454 0.1171 0.1191 0.1119 0.0908 0.0845 0.0828 0.0811 0.0751 Poisson (anal) 0.0341 0.0296 0.0264 0.0240 0.0221 0.0206 0.0193 0.0183 0.0174 0.0166 0.0160 0.0154 0.0148 0.0143 0.0139 0.0135 0.0132 0.0128 0.0125 0.2072 0.1598 0.1315 0.1135 0.1005 0.0909 0.0835 0.0776 0.0727 0.0687 0.0653 0.0624

25


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP128 read 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 Texp (sec) 959.9530 1023.9502 1087.9474 1151.9445 1215.9417 1279.9389 1343.9361 1407.9332 1471.9304 2.9882 3.9859 4.9835 5.9811 6.9787 7.9764 8.9740 9.9716 10.9692 11.9669 12.9645 13.9621 14.9597 15.9574 16.9550 17.9526 18.9502 19.9479 20.9455 21.9431 22.9407 3.9846 lsline (anal) 0.0247 0.0232 0.0214 0.0196 0.0185 0.0173 0.0162 0.0155 0.0144 12.3917 8.3795 6.4296 5.0383 4.1927 3.5522 3.0288 2.6864 2.3789 2.1018 1.9055 1.7566 1.5972 1.5013 1.3788 1.2608 1.1888 1.1155 1.0437 0.9968 0.9265 9.5579 lsline (empir) 0.0674 0.0578 0.0595 0.0555 0.0602 0.0488 0.0537 0.0513 0.0486 14.4633 11.1236 9.9028 8.0596 6.7417 6.7262 6.2756 4.9728 4.4616 4.9031 4.5960 4.1185 4.2786 3.6616 3.7679 3.5117 3.7982 3.0752 3.3867 3.2353 3.0570 10.8797 wtdiff (anal) 0.0669 0.0638 0.0611 0.0587 0.0566 0.0546 0.0528 0.0512 0.0497 17.5389 12.8245 10.2374 8.6390 7.5223 6.7036 6.0724 5.5780 5.1695 4.8402 4.5492 4.3091 4.0961 3.9086 3.7419 3.5963 3.4624 3.3446 3.2335 3.1352 3.0432 14.1957 wtdiff (empir) 0.0811 0.0655 0.0698 0.0569 0.0665 0.0550 0.0590 0.0506 0.0542 18.9155 13.6307 10.9701 10.5632 7.5269 7.1640 7.2364 5.4160 5.1722 5.1811 5.0119 4.6785 4.8226 4.0006 3.9379 3.7735 3.8951 3.3358 3.7535 3.2076 3.2589 14.7818 Poisson (anal) 0.0598 0.0574 0.0554 0.0536 0.0519 0.0504 0.0490 0.0478 0.0466 15.2802 11.3288 9.0972 7.6979 6.7246 6.0270 5.4907 5.0666 4.7222 4.4446 4.2073 4.0033 3.8294 3.6703 3.5324 3.4106 3.3001 3.1994 3.1083 3.0246 2.9489 11.3184

26


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 read 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 Texp (sec) 7.9784 15.9720 31.9651 63.9643 127.9615 255.9546 383.9477 511.9408 639.9338 767.9269 895.9200 1023.9131 1151.9062 1279.8992 1407.8923 1535.8854 1663.8785 1791.8716 1919.8646 2047.8577 3.9846 7.9784 15.9720 31.9651 47.9582 63.9513 79.9444 95.9374 111.9305 127.9236 143.9167 lsline (anal) 4.4302 2.1822 1.0453 0.5262 0.2649 0.1312 0.0802 0.0564 0.0427 0.0338 0.0280 0.0233 0.0204 0.0178 0.0156 0.0141 0.0128 0.0116 0.0108 0.0099 9.5579 4.4302 2.1822 1.0453 0.6599 0.4652 0.3478 0.2764 0.2300 0.1929 0.1660 lsline (empir) 5.6174 3.0561 1.5316 0.7298 0.4051 0.2138 0.1240 0.0887 0.0822 0.0708 0.0585 0.0593 0.0485 0.0477 0.0414 0.0439 0.0342 0.0377 0.0343 0.0310 10.8797 5.6174 3.0561 1.5316 0.9358 0.7856 0.6633 0.4915 0.4000 0.4176 0.3840 wtdiff (anal) 7.0388 3.5065 1.7576 0.8785 0.4398 0.2203 0.1333 0.0979 0.0789 0.0666 0.0584 0.0523 0.0475 0.0437 0.0407 0.0381 0.0360 0.0341 0.0324 0.0310 14.1957 7.0388 3.5065 1.7576 1.0559 0.7743 0.6200 0.5240 0.4571 0.4085 0.3705 wtdiff (empir) 7.3325 3.8183 1.9715 0.9856 0.4500 0.2303 0.1359 0.0953 0.0828 0.0675 0.0606 0.0622 0.0447 0.0490 0.0360 0.0413 0.0345 0.0388 0.0341 0.0306 14.7818 7.3325 3.8183 1.9715 1.1489 0.7844 0.6191 0.5562 0.4187 0.4165 0.4090 Poisson (anal) 5.5198 2.7395 1.3795 0.6979 0.3556 0.1813 0.1201 0.0906 0.0738 0.0627 0.0552 0.0495 0.0451 0.0416 0.0388 0.0364 0.0345 0.0328 0.0313 0.0300 11.3184 5.5198 2.7395 1.3795 0.9063 0.6828 0.5534 0.4702 0.4122 0.3702 0.3376

27


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 read 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Texp (sec) 159.9098 175.9028 191.8959 207.8890 223.8821 239.8752 255.8682 271.8613 287.8544 303.8475 3.9846 5.9786 7.9726 9.9665 11.9605 13.9545 15.9485 17.9424 19.9364 21.9304 23.9244 25.9183 27.9123 29.9063 31.9003 33.8942 35.8882 37.8822 39.8762 41.8701 43.8641 lsline (anal) 0.1481 0.1294 0.1182 0.1064 0.0957 0.0887 0.0820 0.0757 0.0717 0.0662 9.5579 5.6537 4.0279 3.0119 2.4194 2.0000 1.6696 1.4585 1.2808 1.1214 1.0082 0.9259 0.8355 0.7819 0.7154 0.6526 0.6133 0.5744 0.5358 0.5111 0.4744 lsline (empir) 0.3276 0.3424 0.2873 0.2897 0.2620 0.2799 0.2232 0.2450 0.2299 0.2132 10.8797 7.3956 6.0300 4.6579 3.8142 3.7317 3.4569 2.7069 2.3852 2.6020 2.4279 2.1512 2.2407 1.9100 1.9586 1.8152 1.9598 1.5805 1.7407 1.6582 1.5613 wtdiff (anal) 0.3411 0.3171 0.2966 0.2791 0.2645 0.2519 0.2407 0.2305 0.2217 0.2137 14.1957 8.5415 6.2327 5.0069 4.2221 3.6861 3.2848 2.9847 2.7398 2.5476 2.3793 2.2440 2.1250 2.0213 1.9286 1.8496 1.7770 1.7131 1.6534 1.6007 1.5525 wtdiff (empir) 0.3568 0.3633 0.2896 0.3090 0.2611 0.2683 0.2447 0.2510 0.2398 0.2263 14.7818 8.9325 6.5431 5.4536 4.5505 3.7816 3.8342 3.0249 2.6882 2.8642 2.6631 2.3630 2.4827 2.0606 2.1099 1.8613 2.0491 1.6310 1.9080 1.7121 1.6373 Poisson (anal) 0.3121 0.2914 0.2736 0.2588 0.2463 0.2353 0.2258 0.2173 0.2097 0.2029 11.3184 7.3199 5.4556 4.4117 3.7404 3.2837 2.9462 2.6880 2.4832 2.3212 2.1851 2.0699 1.9727 1.8848 1.8092 1.7429 1.6832 1.6291 1.5805 1.5359 1.4958

28


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 read 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 Texp (sec) 3.9846 7.9784 15.9720 31.9651 63.9643 127.9615 255.9546 511.9538 767.9530 1023.9523 1279.9515 1535.9507 1791.9499 2047.9492 2303.9484 2559.9476 2815.9468 3071.9461 3327.9453 3583.9445 3839.9437 3.9846 7.9784 15.9720 31.9651 63.9643 95.9636 127.9628 159.9620 191.9612 223.9605 lsline (anal) 9.5579 4.4302 2.1822 1.0453 0.5262 0.2649 0.1312 0.0648 0.0402 0.0283 0.0213 0.0170 0.0138 0.0118 0.0101 0.0088 0.0078 0.0070 0.0063 0.0059 0.0054 9.5579 4.4302 2.1822 1.0453 0.5262 0.3288 0.2282 0.1715 0.1376 0.1127 lsline (empir) 10.8797 5.6174 3.0561 1.5316 0.7298 0.4051 0.2138 0.0951 0.0606 0.0521 0.0428 0.0349 0.0345 0.0279 0.0271 0.0232 0.0245 0.0190 0.0209 0.0188 0.0168 10.8797 5.6174 3.0561 1.5316 0.7298 0.5281 0.4126 0.2937 0.2318 0.2355 wtdiff (anal) 14.1957 7.0388 3.5065 1.7576 0.8785 0.4398 0.2203 0.1112 0.0674 0.0498 0.0401 0.0341 0.0299 0.0268 0.0244 0.0225 0.0210 0.0197 0.0185 0.0176 0.0168 14.1957 7.0388 3.5065 1.7576 0.8785 0.5284 0.3867 0.3108 0.2624 0.2294 wtdiff (empir) 14.7818 7.3325 3.8183 1.9715 0.9856 0.4500 0.2303 0.1131 0.0598 0.0551 0.0381 0.0383 0.0344 0.0238 0.0278 0.0214 0.0222 0.0199 0.0206 0.0186 0.0163 14.7818 7.3325 3.8183 1.9715 0.9856 0.5502 0.3877 0.2954 0.2494 0.2394 Poisson (anal) 11.3184 5.5198 2.7395 1.3795 0.6979 0.3556 0.1813 0.0931 0.0619 0.0470 0.0383 0.0327 0.0288 0.0259 0.0236 0.0218 0.0203 0.0191 0.0181 0.0172 0.0164 11.3184 5.5198 2.7395 1.3795 0.6979 0.4606 0.3465 0.2810 0.2386 0.2095

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Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 read 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Texp (sec) 255.9597 287.9589 319.9581 351.9574 383.9566 415.9558 447.9550 479.9543 511.9535 543.9527 575.9519 3.9846 7.9784 15.9720 31.9651 63.9643 127.9615 191.9587 255.9559 319.9530 383.9502 447.9474 511.9446 575.9418 639.9389 703.9361 767.9333 831.9305 895.9276 959.9248 1023.9220 lsline (anal) 0.0949 0.0831 0.0717 0.0647 0.0577 0.0516 0.0475 0.0437 0.0401 0.0379 0.0349 9.5579 4.4302 2.1822 1.0453 0.5262 0.2649 0.1624 0.1126 0.0857 0.0680 0.0557 0.0477 0.0405 0.0360 0.0318 0.0282 0.0257 0.0235 0.0214 0.0202 lsline (empir) 0.2137 0.1806 0.1876 0.1565 0.1564 0.1400 0.1489 0.1180 0.1296 0.1206 0.1110 10.8797 5.6174 3.0561 1.5316 0.7298 0.4051 0.2775 0.1839 0.1397 0.1365 0.1214 0.1015 0.1045 0.0864 0.0857 0.0756 0.0803 0.0631 0.0693 0.0639 wtdiff (anal) 0.2045 0.1861 0.1713 0.1590 0.1487 0.1402 0.1329 0.1266 0.1208 0.1158 0.1114 14.1957 7.0388 3.5065 1.7576 0.8785 0.4398 0.2645 0.1945 0.1559 0.1320 0.1151 0.1031 0.0938 0.0862 0.0800 0.0750 0.0707 0.0671 0.0638 0.0610 wtdiff (empir) 0.2143 0.2104 0.1934 0.1621 0.1635 0.1341 0.1362 0.1257 0.1300 0.1203 0.1090 14.7818 7.3325 3.8183 1.9715 0.9856 0.4500 0.2688 0.1995 0.1534 0.1447 0.1199 0.1098 0.1109 0.0874 0.0927 0.0756 0.0774 0.0679 0.0731 0.0634 Poisson (anal) 0.1878 0.1714 0.1584 0.1475 0.1385 0.1310 0.1246 0.1190 0.1141 0.1098 0.1060 11.3184 5.5198 2.7395 1.3795 0.6979 0.3556 0.2345 0.1768 0.1433 0.1220 0.1069 0.0960 0.0876 0.0808 0.0752 0.0707 0.0668 0.0635 0.0607 0.0581

30


Table 2. Minimum background uncertainty; no source; high ampglow (Continued)
Seqname STEP64 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 read 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Texp (sec) 1087.9192 3.9846 7.9784 15.9720 23.9656 31.9592 39.9528 47.9464 55.9400 63.9336 71.9272 79.9208 87.9144 95.9080 103.9016 111.8951 119.8887 127.8823 135.8759 143.8695 151.8631 159.8567 lsline (anal) 0.0185 9.5579 4.4302 2.1822 1.3209 0.9430 0.7154 0.5609 0.4655 0.3969 0.3390 0.2968 0.2685 0.2373 0.2190 0.1984 0.1796 0.1673 0.1555 0.1441 0.1369 0.1266 lsline (empir) 0.0583 10.8797 5.6174 3.0561 1.9526 1.3861 1.2635 1.1206 0.8468 0.7117 0.7567 0.7009 0.6041 0.6330 0.5341 0.5426 0.4951 0.5311 0.4256 0.4674 0.4414 0.4119 wtdiff (anal) 0.0585 14.1957 7.0388 3.5065 2.1134 1.5459 1.2422 1.0459 0.9142 0.8152 0.7412 0.6802 0.6331 0.5928 0.5579 0.5276 0.5027 0.4804 0.4607 0.4422 0.4265 0.4122 wtdiff (empir) 0.0558 14.7818 7.3325 3.8183 2.3684 1.6615 1.2372 1.1946 0.9042 0.8072 0.7828 0.7394 0.6362 0.6790 0.5443 0.5897 0.4894 0.5242 0.4688 0.5032 0.4558 0.4324 Poisson (anal) 0.0559 11.3184 5.5198 2.7395 1.7979 1.3492 1.0955 0.9308 0.8166 0.7324 0.6691 0.6185 0.5775 0.5438 0.5143 0.4894 0.4680 0.4491 0.4324 0.4175 0.4040 0.3920

Table 3. Example of moderate to high countrate
Seqname MCAMRR MCAMRR MCAMRR MCAMRR read 5 6 7 8 Texp (sec) 1.5116 1.8140 2.1163 2.4186 lsline (anal) 22.4389 18.0473 14.5509 12.1456 lsline (empir) 24.7412 18.4376 15.6656 14.9297 wtdiff (anal) 28.5510 23.9134 20.5343 18.0501 wtdiff (empir) 26.9684 22.5610 19.0454 19.1770 Poisson (anal) 25.2285 20.1832 16.6998 14.1940

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Table 3. Example of moderate to high countrate (Continued)
Seqname MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MCAMRR MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 read 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Texp (sec) 2.7210 3.0233 3.3256 3.6279 3.9303 4.2326 4.5349 4.8372 5.1396 5.4419 5.7442 6.0466 6.3489 6.6512 6.9535 7.2559 7.5582 1.5116 1.8140 2.1163 2.4186 63.9930 127.9902 255.9833 383.9764 511.9694 639.9625 767.9556 895.9487 1023.9418 1024.2441 lsline (anal) 10.2801 8.9679 7.8120 6.9521 6.4178 5.7879 5.3159 4.7870 4.4680 4.0856 3.7979 3.5978 3.3138 3.1284 2.9013 2.7374 2.5789 22.4389 18.0473 14.5509 12.1456 0.5036 0.2280 0.1167 0.0720 0.0511 0.0397 0.0321 0.0269 0.0238 0.0204 lsline (empir) 14.2764 10.9055 9.6434 7.9097 8.6022 8.0244 6.1198 6.0171 5.3166 4.9802 5.0918 4.6639 4.5323 4.1809 4.1817 3.7890 3.5666 24.7412 18.4376 15.6656 14.9297 0.6588 0.3158 0.1808 0.1562 0.1019 0.0946 0.0822 0.0882 0.0774 0.0695 wtdiff (anal) 16.0843 14.5138 13.2201 12.1806 11.2415 10.4875 9.7662 9.2022 8.6574 8.2181 7.8000 7.4037 7.0828 6.7426 6.4734 6.2101 5.9728 28.5510 23.9134 20.5343 18.0501 0.7470 0.3944 0.2434 0.1657 0.1310 0.1110 0.0978 0.0882 0.0809 0.0808 wtdiff (empir) 18.0290 15.4772 13.2426 12.0661 12.1448 10.9711 9.6988 8.7168 8.0386 8.2264 7.5390 7.4028 7.1945 7.0638 6.8851 6.8063 5.6146 26.9684 22.5610 19.0454 19.1770 0.7391 0.3736 0.2391 0.1719 0.1133 0.1068 0.0887 0.0965 0.0854 0.0715 Poisson (anal) 12.3142 10.8096 9.6684 8.7217 7.9654 7.3304 6.7628 6.3004 5.8887 5.5700 5.2560 4.9821 4.7474 4.5348 4.3413 4.1765 4.0152 25.2285 20.1832 16.6998 14.1940 0.5891 0.3158 0.1883 0.1410 0.1167 0.1019 0.0915 0.0839 0.0779 0.0756

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Table 3. Example of moderate to high countrate (Continued)
Seqname MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF1024 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF2048 MIF3072 MIF3072 MIF3072 read 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 Texp (sec) 1024.5464 1024.8487 1025.1511 1025.4534 1025.7557 1026.0580 1026.3604 1.5116 1.8140 2.1163 2.4186 127.9889 255.9820 511.9812 767.9804 1023.9797 1279.9789 1535.9781 1791.9773 2047.9766 2048.2789 2048.5812 2048.8836 2049.1859 2049.4882 2049.7905 2050.0929 2050.3952 1.5116 1.8140 2.1163 lsline (anal) 0.0191 0.0177 0.0173 0.0159 0.0154 0.0150 0.0147 22.4389 18.0473 14.5509 12.1456 0.2497 0.1141 0.0595 0.0370 0.0267 0.0212 0.0174 0.0147 0.0133 0.0113 0.0106 0.0098 0.0096 0.0088 0.0085 0.0082 0.0081 22.4389 18.0473 14.5509 lsline (empir) 0.0796 0.0698 0.0721 0.0795 0.0687 0.0696 0.0728 24.7412 18.4376 15.6656 14.9297 0.3630 0.1824 0.1135 0.1024 0.0684 0.0643 0.0565 0.0613 0.0546 0.0480 0.0548 0.0486 0.0501 0.0552 0.0479 0.0485 0.0507 24.7412 18.4376 15.6656 wtdiff (anal) 0.0809 0.0808 0.0809 0.0809 0.0809 0.0809 0.0809 28.5510 23.9134 20.5343 18.0501 0.3938 0.2197 0.1410 0.1011 0.0824 0.0712 0.0636 0.0580 0.0536 0.0536 0.0536 0.0536 0.0536 0.0536 0.0536 0.0536 0.0536 28.5510 23.9134 20.5343 wtdiff (empir) 0.0880 0.0805 0.0764 0.0870 0.0700 0.0798 0.0806 26.9684 22.5610 19.0454 19.1770 0.3973 0.2047 0.1353 0.1069 0.0715 0.0687 0.0575 0.0630 0.0576 0.0480 0.0576 0.0534 0.0511 0.0580 0.0471 0.0529 0.0536 26.9684 22.5610 19.0454 Poisson (anal) 0.0747 0.0740 0.0738 0.0736 0.0735 0.0734 0.0734 25.2285 20.1832 16.6998 14.1940 0.3244 0.1870 0.1183 0.0919 0.0778 0.0688 0.0624 0.0575 0.0537 0.0523 0.0517 0.0514 0.0512 0.0512 0.0511 0.0510 0.0511 25.2285 20.1832 16.6998

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Table 3. Example of moderate to high countrate (Continued)
Seqname MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF3072 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 read 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 Texp (sec) 2.4186 127.9889 255.9820 639.9802 1023.9784 1407.9766 1791.9748 2175.9730 2559.9712 3071.9684 3072.2707 3072.5730 3072.8754 3073.1777 3073.4800 3073.7823 3074.0847 3074.3870 1.5116 1.8140 2.1163 2.4186 31.9879 63.9871 127.9843 191.9815 255.9786 319.9758 383.9730 447.9702 511.9674 lsline (anal) 12.1456 0.2497 0.1141 0.0496 0.0290 0.0202 0.0160 0.0130 0.0110 0.0098 0.0083 0.0077 0.0072 0.0069 0.0064 0.0061 0.0059 0.0058 22.4389 18.0473 14.5509 12.1456 1.0233 0.4593 0.2319 0.1424 0.1002 0.0765 0.0616 0.0513 0.0447 lsline (empir) 14.9297 0.3630 0.1824 0.1012 0.0853 0.0577 0.0530 0.0469 0.0503 0.0450 0.0392 0.0442 0.0397 0.0403 0.0452 0.0392 0.0395 0.0421 24.7412 18.4376 15.6656 14.9297 1.2599 0.5814 0.3078 0.2489 0.1580 0.1443 0.1236 0.1296 0.1114 wtdiff (anal) 18.0501 0.3938 0.2197 0.1237 0.0848 0.0682 0.0586 0.0522 0.0475 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 28.5510 23.9134 20.5343 18.0501 1.4902 0.7481 0.4437 0.2875 0.2199 0.1820 0.1576 0.1402 0.1272 wtdiff (empir) 19.1770 0.3973 0.2047 0.1206 0.0878 0.0597 0.0558 0.0469 0.0508 0.0466 0.0384 0.0457 0.0429 0.0410 0.0466 0.0380 0.0418 0.0440 26.9684 22.5610 19.0454 19.1770 1.4490 0.7178 0.4476 0.2943 0.1920 0.1761 0.1439 0.1554 0.1315 Poisson (anal) 14.1940 0.3244 0.1870 0.1030 0.0778 0.0652 0.0574 0.0518 0.0477 0.0437 0.0424 0.0419 0.0416 0.0416 0.0415 0.0414 0.0414 0.0414 25.2285 20.1832 16.6998 14.1940 1.1281 0.5684 0.3186 0.2276 0.1826 0.1561 0.1383 0.1254 0.1156

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Table 3. Example of moderate to high countrate (Continued)
Seqname MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 MIF512 SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SCAMRR SPARS256 SPARS256 read 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 Texp (sec) 512.2697 512.5720 512.8743 513.1767 513.4790 513.7813 514.0836 514.3860 1.0150 1.2180 1.4210 1.6240 1.8270 2.0300 2.2330 2.4360 2.6390 2.8420 3.0450 3.2480 3.4510 3.6540 3.8570 4.0600 4.2630 4.4660 4.6690 4.8720 5.0750 767.9930 1023.9923 lsline (anal) 0.0386 0.0360 0.0333 0.0325 0.0300 0.0292 0.0284 0.0278 34.3952 27.1920 22.6139 19.1377 16.0288 14.2549 12.3986 10.8942 9.9095 8.8685 7.9960 7.3132 6.6955 6.1823 5.7772 5.3643 4.9715 4.6735 4.3496 4.1018 3.9004 0.0472 0.0336 lsline (empir) 0.1028 0.1178 0.1019 0.1056 0.1158 0.1000 0.1012 0.1061 30.1576 28.9286 25.7494 21.8398 19.6068 15.9632 14.6843 13.2389 10.1925 10.6757 9.6203 8.5425 7.7278 8.2787 6.5348 7.6303 6.7760 6.0527 5.8505 5.6344 5.7287 0.1024 0.0810 wtdiff (anal) 0.1268 0.1270 0.1269 0.1271 0.1271 0.1270 0.1271 0.1271 42.5646 35.5854 30.6182 26.8760 23.9328 21.5650 19.6865 18.0715 16.7035 15.5766 14.5478 13.6655 12.8807 12.1943 11.5750 11.0126 10.4803 10.0485 9.6151 9.2347 8.8557 0.0985 0.0817 wtdiff (empir) 0.1101 0.1402 0.1256 0.1198 0.1351 0.1088 0.1249 0.1256 36.2418 36.0088 33.1889 27.6065 24.3322 21.6256 20.4763 19.1036 17.1461 15.0082 14.2207 12.2808 11.3852 13.8909 11.3221 10.5833 10.0878 9.9086 10.5413 9.3262 9.1583 0.1073 0.0824 Poisson (anal) 0.1116 0.1098 0.1085 0.1081 0.1077 0.1074 0.1072 0.1072 37.5264 30.0531 24.9093 21.1277 18.2771 16.0918 14.3430 12.9756 11.8075 10.8526 10.0455 9.3465 8.7442 8.2287 7.7638 7.3972 7.0351 6.7202 6.4139 6.1755 5.9472 0.0946 0.0800

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Table 3. Example of moderate to high countrate (Continued)
Seqname SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS256 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 read 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 Texp (sec) 1279.9915 1535.9907 1791.9899 2047.9892 2303.9884 2559.9876 2815.9868 3071.9861 3327.9853 3583.9845 3839.9837 4095.9830 4351.9822 4607.9814 4863.9806 5119.9799 5375.9791 5631.9783 5887.9775 191.9869 255.9841 319.9813 383.9784 447.9756 511.9728 575.9700 639.9671 703.9643 767.9615 831.9587 895.9558 lsline (anal) 0.0277 0.0222 0.0193 0.0172 0.0155 0.0141 0.0124 0.0116 0.0103 0.0100 0.0092 0.0086 0.0081 0.0076 0.0070 0.0067 0.0064 0.0063 0.0056 0.1674 0.1153 0.0952 0.0755 0.0617 0.0561 0.0478 0.0434 0.0378 0.0356 0.0306 0.0296 lsline (empir) 0.0686 0.0660 0.0547 0.0518 0.0589 0.0460 0.0489 0.0433 0.0433 0.0450 0.0373 0.0396 0.0407 0.0354 0.0379 0.0339 0.0374 0.0362 0.0315 0.2564 0.2014 0.1709 0.1460 0.1250 0.1133 0.1249 0.1006 0.1050 0.0893 0.0906 0.0951 wtdiff (anal) 0.0712 0.0639 0.0583 0.0540 0.0505 0.0476 0.0451 0.0430 0.0412 0.0395 0.0381 0.0368 0.0356 0.0345 0.0335 0.0326 0.0318 0.0310 0.0303 0.2760 0.2185 0.1837 0.1604 0.1434 0.1304 0.1201 0.1118 0.1049 0.0991 0.0941 0.0897 wtdiff (empir) 0.0692 0.0646 0.0565 0.0518 0.0591 0.0456 0.0490 0.0426 0.0423 0.0442 0.0364 0.0402 0.0391 0.0367 0.0353 0.0333 0.0353 0.0336 0.0310 0.2902 0.2271 0.1886 0.1568 0.1420 0.1238 0.1365 0.1098 0.1121 0.0991 0.0928 0.1005 Poisson (anal) 0.0707 0.0642 0.0591 0.0552 0.0519 0.0492 0.0468 0.0448 0.0430 0.0415 0.0400 0.0387 0.0376 0.0365 0.0355 0.0346 0.0338 0.0330 0.0323 0.2401 0.1921 0.1635 0.1447 0.1309 0.1204 0.1120 0.1053 0.0995 0.0948 0.0906 0.0870

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Table 3. Example of moderate to high countrate (Continued)
Seqname SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 SPARS64 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP1 STEP128 read 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 Texp (sec) 959.9530 1023.9502 1087.9474 1151.9445 1215.9417 1279.9389 1343.9361 1407.9332 1471.9304 2.9882 3.9859 4.9835 5.9811 6.9787 7.9764 8.9740 9.9716 10.9692 11.9669 12.9645 13.9621 14.9597 15.9574 16.9550 17.9526 18.9502 19.9479 20.9455 21.9431 22.9407 3.9846 lsline (anal) 0.0271 0.0248 0.0233 0.0219 0.0202 0.0190 0.0180 0.0176 0.0155 11.6337 7.6156 5.7215 4.7334 3.8785 3.3421 2.7771 2.4115 2.1479 1.9427 1.6946 1.5385 1.4327 1.2955 1.2168 1.1393 1.0658 0.9787 0.9138 0.8596 0.7978 9.0534 lsline (empir) 0.0778 0.0806 0.0843 0.0724 0.0775 0.0694 0.0783 0.0751 0.0649 11.5830 8.1820 6.5680 5.4639 4.5376 4.1450 3.3903 3.0769 2.4329 2.2255 2.0270 2.0416 1.7027 1.6862 1.7072 1.4833 1.4787 1.5382 1.2975 1.2624 1.2304 7.9651 wtdiff (anal) 0.0857 0.0823 0.0793 0.0766 0.0740 0.0718 0.0697 0.0677 0.0660 15.8580 11.1811 8.6551 7.0531 5.9755 5.1852 4.5961 4.1138 3.7229 3.4118 3.1528 2.9214 2.7267 2.5554 2.4097 2.2796 2.1558 2.0503 1.9564 1.8741 1.7899 13.3626 wtdiff (empir) 0.0804 0.0906 0.0856 0.0813 0.0750 0.0742 0.0763 0.0706 0.0669 14.0215 10.9380 8.2038 7.4729 6.6957 5.0280 4.8902 3.8861 3.7422 3.3451 2.7133 2.9281 2.7483 2.3601 2.5451 2.2141 2.0140 2.3673 2.0464 1.9397 1.8915 12.8810 Poisson (anal) 0.0837 0.0808 0.0782 0.0758 0.0737 0.0717 0.0698 0.0681 0.0666 12.3437 8.6856 6.6480 5.3177 4.4457 3.8140 3.3467 2.9651 2.6634 2.4373 2.2436 2.0768 1.9378 1.8156 1.7190 1.6296 1.5484 1.4797 1.4168 1.3617 1.3118 9.4304

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Table 3. Example of moderate to high countrate (Continued)
Seqname STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP128 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 read 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 Texp (sec) 7.9784 15.9720 31.9651 63.9643 127.9615 255.9546 383.9477 511.9408 639.9338 767.9269 895.9200 1023.9131 1151.9062 1279.8992 1407.8923 1535.8854 1663.8785 1791.8716 1919.8646 2047.8577 3.9846 7.9784 15.9720 31.9651 47.9582 63.9513 79.9444 95.9374 111.9305 127.9236 143.9167 lsline (anal) 4.2207 2.0227 0.9959 0.4815 0.2421 0.1211 0.0749 0.0530 0.0407 0.0334 0.0270 0.0234 0.0207 0.0187 0.0168 0.0153 0.0139 0.0128 0.0119 0.0109 9.0534 4.2207 2.0227 0.9959 0.6025 0.4277 0.3287 0.2542 0.2095 0.1786 0.1566 lsline (empir) 4.5648 2.2642 1.2666 0.5933 0.3380 0.1924 0.1391 0.1019 0.1068 0.0966 0.0792 0.0788 0.0789 0.0726 0.0607 0.0571 0.0543 0.0481 0.0470 0.0564 7.9651 4.5648 2.2642 1.2666 0.7489 0.5974 0.4274 0.3630 0.2887 0.2769 0.2668 wtdiff (anal) 6.6385 3.3397 1.7000 0.8780 0.4657 0.2574 0.1694 0.1327 0.1117 0.0981 0.0883 0.0810 0.0753 0.0706 0.0664 0.0631 0.0602 0.0577 0.0554 0.0535 13.3626 6.6385 3.3397 1.7000 1.0029 0.7238 0.5727 0.4779 0.4127 0.3643 0.3280 wtdiff (empir) 7.0299 3.3652 1.7666 0.7634 0.4077 0.2529 0.1665 0.1256 0.1141 0.1013 0.0826 0.0796 0.0783 0.0748 0.0578 0.0572 0.0559 0.0496 0.0487 0.0529 12.8810 7.0299 3.3652 1.7666 0.9063 0.6988 0.6329 0.4976 0.3969 0.3350 0.3306 Poisson (anal) 4.5097 2.2108 1.1193 0.5862 0.3237 0.1904 0.1418 0.1173 0.1021 0.0918 0.0840 0.0781 0.0733 0.0693 0.0657 0.0628 0.0602 0.0579 0.0558 0.0541 9.4304 4.5097 2.2108 1.1193 0.7284 0.5438 0.4388 0.3726 0.3266 0.2923 0.2671

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Table 3. Example of moderate to high countrate (Continued)
Seqname STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP16 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 STEP2 read 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Texp (sec) 159.9098 175.9028 191.8959 207.8890 223.8821 239.8752 255.8682 271.8613 287.8544 303.8475 3.9846 5.9786 7.9726 9.9665 11.9605 13.9545 15.9485 17.9424 19.9364 21.9304 23.9244 25.9183 27.9123 29.9063 31.9003 33.8942 35.8882 37.8822 39.8762 41.8701 43.8641 lsline (anal) 0.1326 0.1195 0.1086 0.0996 0.0910 0.0831 0.0765 0.0700 0.0645 0.0606 9.0534 5.1921 3.7565 2.9212 2.2282 1.7985 1.5917 1.3507 1.1978 1.0619 0.9091 0.8218 0.7625 0.6946 0.6559 0.5965 0.5622 0.5000 0.4795 0.4477 0.4241 lsline (empir) 0.2344 0.2353 0.2273 0.2207 0.1868 0.1807 0.1622 0.1464 0.1354 0.1611 7.9651 6.0651 4.3451 3.1987 2.6022 2.1371 1.5909 1.5572 1.1336 1.3229 1.2109 0.9860 1.0854 0.8919 0.8753 0.8800 0.8019 0.8166 0.6880 0.7645 0.7062 wtdiff (anal) 0.2991 0.2756 0.2566 0.2406 0.2251 0.2133 0.2022 0.1936 0.1849 0.1782 13.3626 7.7041 5.4274 4.2131 3.4425 2.9217 2.5352 2.2485 2.0167 1.8302 1.6801 1.5504 1.4424 1.3461 1.2589 1.1909 1.1237 1.0731 1.0182 0.9731 0.9303 wtdiff (empir) 0.2959 0.2945 0.2700 0.2664 0.2037 0.2141 0.2073 0.1821 0.1741 0.1617 12.8810 8.2727 6.3994 4.4805 3.4450 2.9064 2.3018 2.4903 1.7430 1.8049 1.6687 1.4832 1.2105 1.4157 1.2833 1.1059 1.2853 1.0940 1.0893 1.0898 0.9762 Poisson (anal) 0.2463 0.2304 0.2171 0.2058 0.1951 0.1866 0.1788 0.1724 0.1660 0.1613 9.4304 5.8156 4.1147 3.1779 2.5684 2.1623 1.8654 1.6466 1.4721 1.3353 1.2241 1.1322 1.0568 0.9912 0.9345 0.8870 0.8435 0.8067 0.7720 0.7440 0.7154

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Table 3. Example of moderate to high countrate (Continued)
Seqname STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP256 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 read 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 Texp (sec) 3.9846 7.9784 15.9720 31.9651 63.9643 127.9615 255.9546 511.9538 767.9530 1023.9523 1279.9515 1535.9507 1791.9499 2047.9492 2303.9484 2559.9476 2815.9468 3071.9461 3327.9453 3583.9445 3839.9437 3.9846 7.9784 15.9720 31.9651 63.9643 95.9636 127.9628 159.9620 191.9612 223.9605 lsline (anal) 9.0534 4.2207 2.0227 0.9959 0.4815 0.2421 0.1211 0.0608 0.0383 0.0274 0.0218 0.0172 0.0146 0.0127 0.0115 0.0102 0.0094 0.0085 0.0079 0.0074 0.0067 9.0534 4.2207 2.0227 0.9959 0.4815 0.3013 0.2137 0.1581 0.1262 0.1051 lsline (empir) 7.9651 4.5648 2.2642 1.2666 0.5933 0.3380 0.1924 0.1206 0.0820 0.0822 0.0706 0.0588 0.0592 0.0600 0.0534 0.0449 0.0415 0.0395 0.0340 0.0344 0.0407 7.9651 4.5648 2.2642 1.2666 0.5933 0.4211 0.3037 0.2465 0.1880 0.1896 wtdiff (anal) 13.3626 6.6385 3.3397 1.7000 0.8780 0.4657 0.2574 0.1493 0.1038 0.0837 0.0719 0.0640 0.0583 0.0539 0.0503 0.0473 0.0449 0.0427 0.0409 0.0393 0.0379 13.3626 6.6385 3.3397 1.7000 0.8780 0.5304 0.3911 0.3148 0.2670 0.2332 wtdiff (empir) 12.8810 7.0299 3.3652 1.7666 0.7634 0.4077 0.2529 0.1511 0.1006 0.0855 0.0706 0.0597 0.0577 0.0580 0.0539 0.0421 0.0412 0.0395 0.0344 0.0344 0.0376 12.8810 7.0299 3.3652 1.7666 0.7634 0.4760 0.4139 0.3229 0.2378 0.2223 Poisson (anal) 9.4304 4.5097 2.2108 1.1193 0.5862 0.3237 0.1904 0.1190 0.0923 0.0780 0.0689 0.0625 0.0577 0.0538 0.0506 0.0479 0.0456 0.0436 0.0419 0.0403 0.0390 9.4304 4.5097 2.2108 1.1193 0.5862 0.3965 0.3060 0.2542 0.2206 0.1965

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Table 3. Example of moderate to high countrate (Continued)
Seqname STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP32 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 STEP64 read 15 16 17 18 19 20 21 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Texp (sec) 255.9597 287.9589 319.9581 351.9574 383.9566 415.9558 447.9550 479.9543 511.9535 543.9527 575.9519 3.9846 7.9784 15.9720 31.9651 63.9643 127.9615 191.9587 255.9559 319.9530 383.9502 447.9474 511.9446 575.9418 639.9389 703.9361 767.9333 831.9305 895.9276 959.9248 1023.9220 lsline (anal) 0.0905 0.0755 0.0673 0.0607 0.0554 0.0503 0.0458 0.0419 0.0384 0.0354 0.0331 9.0534 4.2207 2.0227 0.9959 0.4815 0.2421 0.1507 0.1044 0.0796 0.0639 0.0539 0.0443 0.0390 0.0348 0.0317 0.0286 0.0260 0.0237 0.0217 0.0201 lsline (empir) 0.1811 0.1562 0.1575 0.1533 0.1458 0.1235 0.1199 0.1095 0.0996 0.0910 0.1101 7.9651 4.5648 2.2642 1.2666 0.5933 0.3380 0.2332 0.1790 0.1347 0.1385 0.1305 0.1088 0.1092 0.1077 0.1015 0.0845 0.0817 0.0764 0.0687 0.0641 wtdiff (anal) 0.2089 0.1900 0.1751 0.1631 0.1531 0.1438 0.1365 0.1298 0.1244 0.1192 0.1151 13.3626 6.6385 3.3397 1.7000 0.8780 0.4657 0.2925 0.2214 0.1825 0.1573 0.1398 0.1267 0.1166 0.1086 0.1020 0.0960 0.0912 0.0869 0.0834 0.0800 wtdiff (empir) 0.2109 0.1757 0.1763 0.1659 0.1620 0.1269 0.1329 0.1268 0.1145 0.1086 0.1084 12.8810 7.0299 3.3652 1.7666 0.7634 0.4077 0.2973 0.2221 0.1649 0.1562 0.1450 0.1176 0.1168 0.1103 0.1084 0.0823 0.0859 0.0826 0.0739 0.0705 Poisson (anal) 0.1792 0.1652 0.1546 0.1457 0.1383 0.1313 0.1256 0.1206 0.1163 0.1121 0.1089 9.4304 4.5097 2.2108 1.1193 0.5862 0.3237 0.2297 0.1840 0.1570 0.1387 0.1259 0.1158 0.1082 0.1019 0.0966 0.0917 0.0877 0.0842 0.0812 0.0783

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Table 3. Example of moderate to high countrate (Continued)
Seqname STEP64 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 STEP8 read 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Texp (sec) 1087.9192 3.9846 7.9784 15.9720 23.9656 31.9592 39.9528 47.9464 55.9400 63.9336 71.9272 79.9208 87.9144 95.9080 103.9016 111.8951 119.8887 127.8823 135.8759 143.8695 151.8631 159.8567 lsline (anal) 0.0186 9.0534 4.2207 2.0227 1.2845 0.8581 0.6743 0.5117 0.4352 0.3584 0.3002 0.2596 0.2490 0.2174 0.1994 0.1801 0.1619 0.1530 0.1419 0.1281 0.1188 0.1120 lsline (empir) 0.0784 7.9651 4.5648 2.2642 1.2689 0.9014 0.7641 0.7488 0.5472 0.4804 0.4370 0.4253 0.3952 0.3839 0.3194 0.3271 0.3220 0.2411 0.2723 0.2497 0.2550 0.2308 wtdiff (anal) 0.0773 13.3626 6.6385 3.3397 1.9507 1.3866 1.0869 0.8991 0.7670 0.6723 0.5997 0.5423 0.4949 0.4581 0.4252 0.3979 0.3750 0.3534 0.3354 0.3192 0.3053 0.2918 wtdiff (empir) 0.0752 12.8810 7.0299 3.3652 1.7967 1.3247 1.1984 0.9345 0.8068 0.6403 0.5807 0.5546 0.5449 0.4840 0.4125 0.3962 0.4097 0.3638 0.3301 0.2701 0.3113 0.2829 Poisson (anal) 0.0760 9.4304 4.5097 2.2108 1.4068 1.0250 0.8109 0.6736 0.5783 0.5116 0.4601 0.4196 0.3878 0.3611 0.3400 0.3210 0.3052 0.2912 0.2785 0.2678 0.2583 0.2493

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7. Figures
Figure 2: Example simulation; 200 trials showing empirical and analytical error estimates in good agreement.

Figure 3: Comparison of errors from two algorithms.

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Figure 4: Uncertainty in derived countrate as a function of exposure time for all sequences (data from Table 1) using least-squares fit of straight line.

Figure 5: Uncertainty in derived count rate for example MIF sequence and different amp glow contributions, Tables 1 and 2.

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Figure 6: Uncertainty in derived count rate for all sequences for the high amp glow case showing the degradation of S/N in the detector corners due to a large number of reads, data of Table 2.

45