Transcript A bit CCD imaging

A bit about CCD imaging
Paul McGale
Signal-to-noise ratio
SNR = CstarT / √(CstarT + CskyT+ CdarkT + R2)
where:
T
Cstar
Csky
Cdark
R
is the total integration time for the image (secs)
is the count rate of a star in the image (ADU/sec/pixel)
is the count rate from the sky (ADU/sec/pixel)
is the dark count rate from the CCD (ADU/sec/pixel)
is the readout noise from the CCD (ADU/pixel)
Sub-exposure stacking efficiency (1)
e.g. 1 long exposure vs. average of 10 short ones
E = √[(x + y) / (x + 10y)]
where
x is CstarT+ CskyT+ CdarkT
y is R2
Sub-exposure stacking efficiency (2)
** Dark sky **
0
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Sky: 0.1 ADU/s, Drk: 0.1 ADU/s, RN: 17 ADU^2
0
2
4
6
8
10
12
14
Total exposure time (min)
Star 0.1 ADU/s
Star 1.0 ADU/s
16
Star 0.5 ADU/s
Star 2.0 ADU/s
18
20
Sub-exposure stacking efficiency (3)
** Light-polluted sky **
0
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Sky: 2.0 ADU/s, Drk: 0.1 ADU/s, RN: 17 ADU^2
0
2
4
6
8
10
12
14
Total exposure time (min)
Star 0.1 ADU/s
Star 1.0 ADU/s
16
Star 0.5 ADU/s
Star 2.0 ADU/s
18
20
Number of sub-exposures (1)
For a bright object SNR ≈ √(CstarT)
≡ √(N, the number of sub exposures)
How does SNR change with increasing N?
Rate of change in SNR with N is 1/√(4N)
 stack 4, rate = 1/4, SNR decreasing quickly
 stack 25, rate = 1/10, SNR decreasing slowly
Number of sub-exposures (2)
Faintest part of object visible has SNR=3
i.e. CstarT/ √(CstarT+ CskyT) = 3
Solve for Cstar(snr=3):
Cstar(snr=3) = 9 + √(81 + 36CskyT)/(2T)
or for N sub-exposures, length t
Cstar(snr=3) = 9 + √(81 + 36CskyNt)/(2Nt)
Number of sub-exposures (3)
Limiting object brightness detected: SNR=3
0
.05
.1
.15
.2
.25
** Light-polluted sky [2.0 ADU/s] **
0
5
10
15
20
25
Number of sub-exposures
Sub-exposure = 300s
30
35
Sub-exposure = 1200s
40