Lecture 1 and 2

Question 1

CCD imaging

Answer 1

From near infra-red through to UV wavelengths, astronomical data arrives as photons, which trigger a CCD response

Question 2

What is a CCD

Answer 2

A CCD is a semiconductor array of light sensitive pixels typically about 10μm across

Question 3

Image

Answer 3

direct ‘map’ of where photons arrive

Question 4

How does a CCD work

Answer 4

Electron released when photon strikes semiconductor

Bias voltage draws electron into potential well ; stored there during exposure

Question 5

counts of photons obey

Answer 5

Poisson statistics

Question 6

The number of photons arriving at our detector from a given source will

Answer 6

fluctuate

Question 7

We make certain assumptions (axioms)

Answer 7

1. Photons arrive independently in time
2. Average photon arrival rate is constant

Question 8

If observed photons satisfy the axioms the they are said to follow a

Answer 8

Poisson distribution

Question 9

Expectation value

Answer 9

E(N) = {N} = Rτ

Question 10

probability of receiving N photons in time τ

Answer 10

p(N) = (Rτ)^N e^-(Rτ) / N!

Question 11

We can define the variance of N, which is a measure of the spread in the Poisson distribution

Answer 11

var(N) = σ^2 = E{[N-E(N)]^2}

Question 11

We can define the variance of N, which is a measure of the spread in the Poisson distribution

Answer 11

var(N) = σ^2 = E{[N-E(N)]^2}

Question 12

the variance of N is

Answer 12

var(N) = Rτ

Question 13

the standard deviation of N is

Answer 13

σ = √Rτ

Question 14

We estimate the arrival rate as

Answer 14

Ř = Nobs / τ

Question 15

We quote our experimental result for the number count of photons in time interval τ as

Answer 15

Nobs ± √Nobs

Question 16

mean =

Answer 16

total number / area