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Re: Noise Problem
Dear Tom,
You may want to add one or possibly both of the following statistical
tests. We have use them now for 25 yeard on photon counting photometry.
They are described in :
Title: Three statistical tests for digital photometry
Authors: Bartholdi, P.; Burnet, M.; Rufener, F.
Affiliation: AA(Geneve, Observatoire, Sauverny, Switzerland)
Journal: Astronomy and Astrophysics (ISSN 0004-6361),
vol., 134, no. 2, May 1984, p. 290-295.
Let us say Di are your data, D their mean, S their sigma, n their number.
We assume at first that the data are independant, uncorrelated, comming from
a single (probably normal) distribution.
The first is to look at the third order momentum of the data.
Then G = Sum( ( Di - D ) ^ 3 ) / ( n S ^ 3 )
G should be near zero, Any large positive value is the signature for spikes,
any large negative for drops.
The second test, first suggested almost 150 yeards ago by Abbe (the optician),
compares successve differences squared to the variance. If Di-1 and Di are
two succesive values, then R = Sum( ( Di - Di-1 ) ^ 2 ) / ( 2 S ^ 2 ) .
R should be around one. Small value of R indicates slow changes, while R near
2 indicates oscillations.
In our article you will find how to decide that a value is acceptable or not,
depending on n. Your experience will certainly be unvaluable to make the final
decision. Eventually, it is not necessary to keep all data in memory. Running
sums can be used and only the last two are necessarly available. In that way,
alarms can be sound during the acquisition.
You may find other use of these tests, as on the signal from the ccd etc.
Once you have gained some acquintance with them, you will feel much more
secure than just with mean and sigma.
If you have any question, do not hesitate to contact me.
Good luck ! Paul
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+ Paul Bartholdi Paul.Bartholdi@obs.unige.ch +
+ Observatoire de Geneve tel +41 22 755 2611 +
+ CH-1290 Sauverny fax +41 22 755 3983 +
+ Switzerland www http://obswww.unige.ch/ +
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