Introduction

Question 1

very weak signals and incorrect assumptions leads to

Answer 1

systematic errors

Question 2

a new probe of the universe - gravitational waves

Answer 2

will give us a different, non EM view of the universe, and open a new spectrum for observation

complementary information

Question 3

from near-infrared through to UV wavelengths, astronomical data arrives as

Answer 3

photons, which trigger a CCD response

Question 4

a CCD is a

Answer 4

semiconductor array of light-sensitive pixels - typically about 10 micrometers across

Question 5

CCDs - electrons released when

Answer 5

photon strikes semiconductor

Question 6

CCDs - bias voltage draws…

Answer 6

electron into potential well, stored there during exposure

Question 7

a great deal of astronomical data consists of counts of photons, these obey

Answer 7

poisson statistics

Question 8

the number of photons arriving at a detector from a given source will

Answer 8

fluctuate

Question 9

we can treat the arrival rate of photons statistically which means

Answer 9

we can calculate the average number of photons which we expect to arrive in a given time interval

Question 10

axioms for a poisson distribution

Answer 10

1. photons arrive independently in time
2. average photon arrival rate is constant

Question 11

expectation value of number of photons

Answer 11

E=<N>=Rt</N>

R is arrival rate
t is exposure time

Question 12

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>

Answer 12

<N>=Rt
</N>

Question 13

probability of receiving N photons in time t

Answer 13

(Rt)^Ne^-Rt / N!

Question 14

probability of N events given an expectation value of μ

Answer 14

p(N)=μ^Ne^-μ / N!

Question 15

as Rt increases…

Answer 15

the shape of the poisson distribution becomes more symmetrical

(it tends to a normal or gaussian distribution)

Question 16

variance of N

Answer 16

a measure of the spread in the poisson distribution

var(N)=σ=E{[N-E(n)]^”}

Question 17

for a poisson distribution, var(N)=

Answer 17

Rt

Question 18

for a poisson distribution, the standard deviation of N is

Answer 18

σ=sqrt(Rt)

Question 19

in practice, we usually only observe for one period of t seconds during which

Answer 19

we receive a count of Nobs photons

Question 20

estimated arrival rate

Answer 20

R hat = Nobs/t

Question 21

we take Nobs as our

Answer 21

best estimate for <N> with error sqrt(Nobs)</N>

Question 22

we quote our experimental result for the number count of photons in time interval t as

Answer 22

Nobs +/- sqrt(Nobs)

Question 23

raw image includes

Answer 23

hot pixels, readout noise, fixed pattern noise (combination of random and systematic uncertainties)

careful calibration needed to extract data

Question 24

corrected image -

Answer 24

bias, dark and flat frames
accurate photometry can now begin