(b) Assume that a source is detected against a strong background (an example would be the case of mid-infrared observations made from the ground). Assume that the number of counts detected on-source in time, 4t, is (S+ B), and the number of counts detected from the background in the same interval (measured from an adjacent patch of sky) is B.
(b) Assume that a source is detected against a strong background (an example would be the case of mid-infrared observations made from the ground). Assume that the number of counts detected on-source in time, 4t, is (S+ B), and the number of counts detected from the background in the same interval (measured from an adjacent patch of sky) is B.
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Transcribed Image Text:(b) Assume that a source is detected against a strong background (an example
would be the case of mid-infrared observations made from the ground). Assume
that the number of counts detected on-source in time, At, is (S + B), and the
number of counts detected from the background in the same interval (measured
from an adjacent patch of sky) is B.
What is the variance on the difference between the two measurements? Hence
calculate the significance for a source detection (i.e., signal / standard
deviation) and show that in the case of high background relative to the source
this can be represented in terms of the source and background count rates (rs
and r3, respectively) by:
Ts VAt
/2 TB
S
OB
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