Introduction Flashcards
very weak signals and incorrect assumptions leads to
systematic errors
a new probe of the universe - gravitational waves
will give us a different, non EM view of the universe, and open a new spectrum for observation
complementary information
from near-infrared through to UV wavelengths, astronomical data arrives as
photons, which trigger a CCD response
a CCD is a
semiconductor array of light-sensitive pixels - typically about 10 micrometers across
CCDs - electrons released when
photon strikes semiconductor
CCDs - bias voltage draws…
electron into potential well, stored there during exposure
a great deal of astronomical data consists of counts of photons, these obey
poisson statistics
the number of photons arriving at a detector from a given source will
fluctuate
we can treat the arrival rate of photons statistically which means
we can calculate the average number of photons which we expect to arrive in a given time interval
axioms for a poisson distribution
- photons arrive independently in time
- average photon arrival rate is constant
expectation value of number of photons
E=<N>=Rt</N>
R is arrival rate
t is exposure time
If we made a series of observations, each of time seconds, we
wouldn’t expect to receive <N> photons every time, but the
average number of counts should equal</N>
<N>=Rt
</N>
probability of receiving N photons in time t
(Rt)^Ne^-Rt / N!
probability of N events given an expectation value of μ
p(N)=μ^Ne^-μ / N!
as Rt increases…
the shape of the poisson distribution becomes more symmetrical
(it tends to a normal or gaussian distribution)
variance of N
a measure of the spread in the poisson distribution
var(N)=σ=E{[N-E(n)]^”}
for a poisson distribution, var(N)=
Rt
for a poisson distribution, the standard deviation of N is
σ=sqrt(Rt)
in practice, we usually only observe for one period of t seconds during which
we receive a count of Nobs photons
estimated arrival rate
R hat = Nobs/t
we take Nobs as our
best estimate for <N> with error sqrt(Nobs)</N>
we quote our experimental result for the number count of photons in time interval t as
Nobs +/- sqrt(Nobs)
raw image includes
hot pixels, readout noise, fixed pattern noise (combination of random and systematic uncertainties)
careful calibration needed to extract data
corrected image -
bias, dark and flat frames
accurate photometry can now begin
