Re: Radiation Detection Question
- From: glhansen@xxxxxxxxxxxxxxxxxxxxx (Gregory L. Hansen)
- Date: Thu, 15 Dec 2005 00:42:44 +0000 (UTC)
In article <1134596648.473471.35150@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Puppet_Sock <puppet_sock@xxxxxxxxxxx> wrote:
>Gregory L. Hansen wrote:
>> In article <ZvBnf.37650$Y7.35469@trnddc02>, Matt <zeusmta@xxxxxxxxxxx> wrote:
>> >Regarding radiation a radiation detection system for gamma rays, following
>> >is a quote from a paper I read:
>> >
>> >"Halving the distance between source and detector would increase the
>> >sensitivity by a factor of four; quadrupling the counting time would
>> >increase the sensitivity by a factor of two."
>> >
>> >I understand the first part -- i.e. source strength goes as the inverse
>> >square of the distance, therefore half distance implies four times
>> >sensitivity. I also understand the geometrical reasons for this.
>> >
>> >I don't understand why quadrupling counting time only increases the
>> >sensitivity by 2. In my ignorance, I cannot imagine why quadrupling the
>> >counting time would not result in four times the sensitivity or detection
>> >capability. Can someone please enlighten me on this? Perhaps someone could
>> >point me to an Internet source that explains this phenomenon.
>>
>> I don't understand the first part.
>>
>> Radioactive decay is statistically distributed-- Poisson, or something
>> like that. If "sensitivity" means precision in a measurement of average
>> number of counts per unit time, the uncertainty associated with N counts
>> is sqrt(N), and the relative uncertainty is then sqrt(N)/N=1/sqrt(N). If
>> you quadruple the number of counts, you halve the uncertainty. It doesn't
>> matter whether that quadrupling is done by moving the source closer or by
>> counting for a longer time.
>
>Not quite. If you are trying to distinguish a signal from a background,
>then moving the source closer will mean you have a larger signal.
>So, if sensitivity is defined as "the smallest size radioactive source
>that could be distinguished from background" then this clearly
>depends on how close to the source the detector is, and not just
>by the number of counts.
I wasn't really thinking of background at that point. But yes, if the
signal is lost in the background, then averaging for more time would
average over more background, too, and it's not clear that you'd gain
much.
>
>So, if you are 1 meter away, you can see 1E6 Bq, for example, but
>at 2 meters away you can only see 4E6 Bq. Assuming that moving
>your detector does not change the background. In each case, this
>assumes the same counting time.
>
>> Socks mentioned distinguishing a signal from background. That's really
>> best done by changing the signal periodically, e.g. by moving the source
>> back and forth, back and forth. Or by opening and closing a shutter.
>> Even a very small periodic signal can be distinguished from the background
>> if you average over enough periods. A complication is that radiation can
>> bounce around every which way inside the apparatus, and the amount of
>> backscattered radiation entering the detector will change when you change
>> the location of the source, so that must be simulated or measured so a
>> correction can be made.
>
>The problem with doing the periodic thing you mention is that it does
>not
>produce a periodic signal. What it produces is periodicity in the
>probability
>of getting a count. The number of counts will then be some statistical
>thing that follows whatever distribution is happening.
>
It produces a probability distribution that periodically increases and
decreases. The analysis is the same-- average separately over the
periods when the source is close and far. I've averaged cycles to get a
"typical" cycle and found signal that was completely invisible in the raw
data.
>So, even doing this, you get some kind of statistical thing happening.
>It's more complicated than for a source sitting still, and I have not
>tried to work out the details. But I'd expect (without having made the
>slightest effort to justify it) that there would still be some kind of
>1/root(N) involved.
>
>But basically, it's just a variation on the usual method. You put the
>source very far away, such as in a shieled container, and do your
>background count. Then you bring the source closer, and do your
>count again. The difference is the signal, plus or minus the
>statistical
>fluctuation estimates.
I guess it doesn't matter, as long as you expect the background to stay
sufficiently constant during the measurement. In the work I was doing, I
was taking measurements over many hours, and the background would change
significantly in that time. A twenty minute cycle overcame that.
--
"When the fool walks through the street, in his lack of understanding he
calls everything foolish." -- Ecclesiastes 10:3, New American Bible
.
- References:
- Radiation Detection Question
- From: Matt
- Re: Radiation Detection Question
- From: Gregory L. Hansen
- Re: Radiation Detection Question
- From: Puppet_Sock
- Radiation Detection Question
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