observational astrophysics ii (l3)

Observational Astrophysics II: May-June, 2004 [email protected]

Observational Astrophysics II (L3)

What do want to do?1. Nightly planning overwiew2. Reduce spectroscopic observations3. Reduce photometric imaging observations4. Perhaps, `massage´ our images

http://www.astro.su.se/utbildning/kurser/astro_obs2/




Obs. Group

Filter (type / #)

Grism #

Slit(arcsec)

Object(Name)

RA 2000

(h m s)Dec 2000

(o ´ ´´)Proposal

.and.Finder chart (Y/N)

2Jeanette

(Christoffer)

78, 50 8 0.5, 0.75, 1.0, 1.3,

2.5

NGC 5984 15 42 53.18 +14 13 53.4 YN

3Andrej Milan

76, 49, 51 8 0.5, 0.75, 1.0, 1.3,

2.5

NGC 6389 17 32 39.8 +16 24 06 YY

1Anna

Thomas

78, 50 8 0.5, 1.0, 1.3, 2.5

NGC 5112 13 21 56.43 +38 44 05 NN

4Sven

Morten

12, 15, 17, 18, 19, 20,

44error

14 1.0, 1.2, 1.3

SAO104782NGC 7023B 335

19 11 01.2521 01 35.6219 37 15.8

+14 42 46.5+68 10 10.4+07 34 00

NN

http://www.not.iac.es/observing/cookbook



Grupp 1 + Alla

->23:30Grupp 2->01:15

Grupp 3->03:00 Grupp 4

+ Alla?

23:30 01:15 03:00

19:00 07:00

7 h a-natt=>

1h45m/ grpn-tid


Data Reductions

neither from theoretical nor from reduction

point of viewany fundamental difference between

Spectroscopic image frames

Photometric image frames


IRAF

• Bias imarith • Dark current• Hot/cold columns• Sky background• Cosmic Rays imcombine• Flat Field• Photometric calibration apphot• Spectrometric calibration identify rectify spectrum in spatial domain longslit – fitcoords, transform extract spectrum noao.twodspec.apextract – apall measure lines (Gaussian fitting) splot slit losses sbands

Correct for / obtain from multiple image frames:


Image restauration techniques

How to recover the information in an `image´

or, actually,

How to optimise the information extraction



function caseupper theof TransformFourier thedesignates caselower re whe)()()(

functions over the integraln convolutio thedesignates where)()()(

toi

TOI

I is the observed image, which is a function of the angle vector , and I equals the convolution of the object O with the filter function T.

An equivalent expression is the product of the Fourier Transforms o and t.

To derive the object O, one would simply divide i by t and transform back.

)]([)(

)()()(

oFTO

tio

cumbersome simple



In practice, this involves division by zero (or very small numbers) and therefore is impractical numerically. One way out are suggestions like:

Inversion techniques use conditions like:

Source has positivity

Source has bounded support

CLEANMaximum Entropy Method (MEM)Maximum Likelihood Method

)max(

0)(

O

Jan Högbom, em. Stockhom Observatory



Image `entropy´ is a function which is maximal when image contains minimal (extra) information:

Maximum Entropy Method (MEM) / Maximum Likelihood Method

Most probable object O is that which

1. Is most consistent with observed image I2. Uses least extra information

)( and errors with valuesmeasured factor weightingpositive

0)( and 2

ln)

function of maximum find

d )(ln)(

)ln :entropy of definitionBoltzmann (c.f.

2

2

1

image

k kkk

ik k

kk

i

N

ii

IFTiσIw

IwΦIiwIIΦ(w

Φ

IIS

PkS

max Entropy

for

Equilibrium

min Information


Example: Maximum Likelihood Algorithm (modified Richardson-Lucy)

input

sourcepositions

RestoredImage + Noise

undersampled

observations

?


Larsson et al. 2000, Astron. A

strophys. 363, 253

Iteration Number 0 = start value

1

2

3 done!

4

5

testcase



Before we go to the mountain... don´t forget

k O



... och nu en liten övning:

Slut ögonen och tänk dig att du närmar dig teleskopdomen...

Beskriv (i telegramstil) vad du gör härnäst – steg för stegnär du nu ska observera med NOT

- numrera gärna stegen

- lämna gärna mellanrum mellan stegen

- vi kommer att jämföra i realtid och fylla i vid behov

glöm inte att

glöm inte attskriva ditt namn

skriva ditt namn

observational astrophysics ii (l3)

Documents