## Gamma Ray Imaging with a Rotating ModulatorAstronomy And Astrophysics 120, 150-155 (1983)- P. Durouchoux
- H. Hudson
- G. Hurford
- K. Hurley
- J. Matteson
- E. Orsal
O
In practice, the source strength s may be extracted from the
observation vector
S
where <S Then, summing over the i components of the vector, the background contribution drops out:
Σ
= sTN The standard deviation associated with the number of counts in the ith component is. for Gaussian statistics,
(O Since the standard deviations add as the square root of the sum of the squares, the standard deviation associated with the above is
(Σ
= N
=(bTNc) for b >> s. Thus the statistical significance of the observation is
s(TNc/b) or just proportional to the square root of the variance of the sky vector. |

Notes transcribed from GH.

O_{i}=observed counts in time bin i

B=background (assumed constant)

P_{im}=probability of photon passage at pixel m, time i

S_{m}=true source strength at pixel m (presumed a point
source?)

A=effective area of collimator

T=time in time bin i (assumed equal for all time bins)

i=1,...,N

from which GH derived:

S_{m}= Σ_{i} O_{i}
( P_{im} - <P_{m} >_{})/ {AT ( <
P_{m}^{2} > - <P_{m} >^{2})}
(2)

where < P_{m} ^{2} > is the mean square of
P_{im}, averaged over time, and <P_{m} >^{2}
is the squared mean, averaged over time.

It appears from equation (1) that the point source S

The expressions for the point source strength in back projection and
clean.pro (also MEM?) must be replaced with the time-averaged values
of equation (2) for S_{m}.

Edward J. Schmahl Last modified: Mon Nov 26 11:04:20 EST 2001