Spectroscopic Data Reduction in Observational Astronomy: A Practical Guide

1. Observational Astronomy SPECTROSCOPIC data reduction Piskunov & Valenti 2002, A&A 385, 1095 29 August 2024 1

2. Worse-case scenario… 2

3. In addition we have calibration data:  Bias  Flat field  Dark current  Order tracing  Wavelength map (comparison spectrum)  Blaze calibration 3

4. Spectroscopic reduction in a nutshell The intensity is given by: s b d t I f b         ThAr  ; ( , , ) g F x x x x ThAr 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 4

5. The problem is the errors:       2 f 2 b 2 rd        2 s 2 b 2 rd 2 d  I    s b d t    I f b         2 rd 2 rd s b s b d t    d t f b     ; f b )     (  ) ( ( s b d t     S N s b d t d t    f b  .   s b      2 rd 2 rd ( ) ) f b f b If f is close to b, the S/N is determined by the S/N of the flat field!!! 5

6. 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 6

7. Example using flats: 7

8. Example using flats: 6 times larger vertical scale 8

9. Flat field Fragment of a master flat field 9

10. Order tracing 10

11. Order tracing (2) 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    ( , ) f x y ( ) ( ) P x L y y c L(y) P (x) sin? + ? ∙ ?−? 2 ? looks like a real spectral order 29-Aug-24 12

13. Now the Real Thing… y x  CCD pixel with coordinates by: ( , ) f x y  and is given      ( ) ( ' y ) ( ') L y dy ' P x y c y  In practice we reconstruct the slit function on some discrete grid with resolution ≥ than CCD pixels. Thus we can write: ( , ) ( ) f x y P x  L   j L , x y j j 29-Aug-24 13

14. Slit function decomposition Ideal model: Image on CCD is a sequence of monochromatic images of the entrance slit sampled with CCD pixels Sp Sf    S xy x  y Sp Sf S i i  , , i x y xy x y i y  14

15. Normalizing flat field Original FF “Spectrum” Model FF Normalized FF 15

16. Extracting science spectrum 16

17. Wavelength calibration   i j a m x , , x m i j Pixel number , i j Order number 17

18. Continuum fit Blaze function is a good start: 18

19. … but it is not perfect 19

20. Fringing Accurate fringing removal requires identical slit illumination by the FF as it is illuminated by the science target 20

21. Comparison with other algorithms UVES POP Library, Bagnulo et al. 2003, Messenger 114, 10 29-Aug-24 21

22. 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 22