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17 November 2011 1
Observational Astronomy
SPECTROSCOPIC data reduction
Piskunov & Valenti 2002, A&A 385, 1095
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Worse-case scenario…
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In addition we have calibration data:
Bias Flat field Dark current Order tracing Wavelength map (comparison spectrum) Blaze calibration
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Spectroscopic reduction in a nutshell
The intensity is given by:
s – signal in science exposure
b – bias level
f – flat field signal
g – gain (e-/ADU)
d – dark current signal per unit time
t – exposure time
; ( , , )x x ThAr ThAr
s b d tI g F x x
f b
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The problem is the errors:
2 2 22 2 2 2
2 2
;
f b rds b rd d
rd rd
I
I s b d t f b
s b d t f b
s b d t f b
2 2
( ) ( ).
( ) ( )rd rd
S s b d t f b
N f b s b d t s b d t f b
If f is close to b, the S/N is determined by the S/N of the flat field!!!
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One step at a time: making master bias and master flat/dark The goal is to replace the actual calibration data with a model which
is free of random noise but carries all the necessary calibration signatures.
Master S/N must be much larger than the S/N in science frames!!! Add together signal in many frames
Main issue: getting rid of random errors, e.g. cosmic ray hits
Method: filtering within a frame or across a stack of frames Cross-check between groups of calibration frames
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Example using flats:
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Example using flats: 6 tim
es la
rger v
ertica
l scale
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Flat field
Fragment of a master flat field
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Order tracing
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Order tracing (2)
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17-Nov-11 12
Conceptual Algorithm
Any point in the focal plane can (in principle) be
represented by a product of the sPectrum and the sLit illumination function ( , ) ( ) ( )cf x y P x L y y
looks like a real spectral
order
L(y) P (x)
sin 𝑥 + 𝑎 ∙ 𝑒−
𝑦𝑏
2
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17-Nov-11 13
Now the Real Thing…
CCD pixel with coordinates and is given
by:
In practice we reconstruct the slit function on some discrete grid with resolution ≥ than CCD pixels. Thus we can write:
x y
,( , ) ( ) j
x y j
j
f x y P x L
( , ) ( ) ( ' ) ( ') 'c
y
f x y P x y y L y dy
L
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Slit function decomposition
Ideal model: Image on CCD is a sequence of monochromatic images of the entrance slit sampled with CCD pixels
, , y
xy x y
xy i x y x i i
i y
S Sp Sf
S Sp Sf
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Normalizing flat field
“Spectrum”
Model FF
Original FF
Normalized FF
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Extracting science spectrum
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Wavelength calibration
, ,
,
i j
x m i j
i j
a m x Pixel number
Order number
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Continuum fit
Blaze function is a good start:
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… but it is not perfect
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Fringing
Accurate fringing
removal requires identical slit illumination by the FF as it is illuminated by the science target
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17-Nov-11 21
Comparison with other algorithms
UVES POP Library, Bagnulo et al. 2003, Messenger 114, 10
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FIES data reduction
Attend a tutorial on using REDUCE
Setup your own reduction script to create: - Master bias - Master flat - Normalized flat and to extract: - ThAr - your science spectra + pulsating star spectra
Create a wavelength solution using wavecal and ThAr spectrum
Fit the continuum using make_cont
Compare spectra in selected wavelength regions