Transcript CCD Detectors - University of St Andrews

CCD Detectors
• CCD=“charge coupled device”
– Silicon semiconductor chip
– array of up to crossed electrodes -> potential wells
– current models: up to 2048x2048 wells trap photoelectrons
• Readout method:
– Electronics adjust electrode potentials cyclically to shift
charge from one electrode to the next: “bucket brigade”.
Bottom row
read out, then
all others
shifted down
simultaneously.
Cooled by LN2
Amplifier:
Amplifier:
• takes charge from corner pixel
• thermal noise with fast readout
ADC
Analogue-to-digital converter:
• Converts voltage to digital
units (ADU)
• a.k.a. data numbers (DN)
Memory
Memory:
• Stores image
The pros and cons of CCDs
• Advantages:
– Quantum efficiency (QE) ~ 80 % (400 nm - 1 m)
– Linearity to (better than) << 0.1 %
– Dynamic range: Pixel well depth ~ 106 e–, RMS readout
noise ~ 4 to 10 e–
– Fixed format pixel grid
– Can extend blue response (thinned back-illuminated chip or
coronene coating)
• Disadvantages:
–
–
–
–
–
–
–
Readout noise 4 to 10 e– RMS
Slow readout ≥ 10 to 100 s
Cosmic-ray hits limit exposure times
Saturation via wells filling up and limited ADC range
Charge “bleeding” down columns, then across rows
Blemishes (charge traps, hot pixels)
Gaps between pixels
CCD calibration
Raw image
• Two main steps:
– bias subtraction
– flat-field division
Dxy  (Cxy  Bxy ) / Fxy
“Bias frame” = zero-exposure image
• Measures constant signal added by
readout electronics
“Flat-field frame”:
• Measures pixel-to-pixel
sensitivity variations under
uniform illumination.
Measuring bias and readout noise
• Calibrate by taking mean or median of many
zero-exposure images and/or
• “Overscan” the CCD by reading out additional
rows of data for which no physical pixels exist.
• Cosmic ray hits must be removed, e.g. by
taking median of many frames.
• “Readout noise” =  (Bxy): B 
Bxy / N x N y

x,y
Var(B)   (Bxy  B )2 /(N x N y 1)
x,y
• Voltage drift may cause <Bxy> to vary in time:
B(x, y;t)  B(x, y)  T(t)
• Need to scale bias frame to match overscan.
Flat-field division
• Direct imaging:
– twilight sky or inside of telescope dome
– OR median of many dark sky frames of different fields
(median eliminates stars)
• Spectroscopy:
– spectrum of internal comtinuum source (tungsten lamp)
• Pixel-to-pixel sensitivity variations => Fxy is
never uniform, even with uniform illumination.
• Take 10 to 30 flats with high exposure levels
–
–
–
–
subtract bias form each
scale to common mean value (if lamp/sky brightness drifts)
take average or median (to reject cosmic-ray hits)
fit a polynomial to flat field and divide so that <Fxy> ~ 1.
This preserves data numbers/photons while correcting
pixel-to-pixel variations.
Measuring the gain of a CCD -- 1
• The gain of a CCD is the number of photoelectrons per ADU (DN).
• Let X be a random variable representing
number of ADU recorded in a pixel.
• There are 3 types of noise that contribute to
variance 2(X)
– Readout noise 2
– Poisson noise :number of photons detected = X / G
– “Scale noise” with variance f2X2 -- usually dealt with by flatfielding
• At low count-rates, readout noise (=constant)
dominates.
• At high count-rates, Poisson noise ~X1/2
dominates.
Measuring the gain of a CCD -- 2
 (X)   02  X / G
1000
G=1
G=3.2
G=10
(X)
100
Noise
• Take several flats with
different levels of
illumination.
• Divide into sub-areas and
measure <X>,2(X) locally
• Make log-log scatterplot of
 (X) vs. <X>:
• Determine values of (0,G)
that give best-fitting curve
of form:
10
4.2
1
0.1
1
10
100
1000
Signal <X>
In this illustrative case we find
readout noise = 4.2 DN and
gain G = 3.2 electrons per DN
10000