FITS and WCS

Intro

FITS header < FITS format from IAU FITS Working Group!

Official reference documentation: http://fits.gsfc.nasa.gov/fits_standard.html

The FITS header

It's the astronomical standard metadata! Specifies all useful information associate with your data (obtaining conditions, reducing history, etc).

The header is a table with three possible fields:

Keyword; Value; Comment
- Keywords must start with a text character.
- Value can be of multiple types (interger, float, string).
- [Optional] Comment text.

FITS Header example

SIMPLE  =                    T / Standard FITS format
BITPIX  =                   16 / Number of bits for each pixel
NAXIS   =                    2 / Number of axes in frame
NAXIS1  =                 2148 / Number of pixels per row
NAXIS2  =                 4100 / Number of rows
BUNIT   = 'ADU     '           / Unit of original pixel value
CTYPE1  = 'pixel   '           / Pixel coordinate system
CTYPE2  = 'pixel   '           / Pixel coordinate system
CRPIX1  =                    1 / Reference pixel in axis1
CRVAL1  =                    1 / Physical value of the reference pixel
CDELT1  =                    1 / Size projected into a detector pixel in axis1
CRPIX2  =                    1 / Reference pixel in axis2
CRVAL2  =                    1 / Physical value of the reference pixel
CDELT2  =                    1 / Size projected into a detector pixel in axis2
...
OBJECT  = ' BD+28.4211 '       / Target Description
DATA-TYP= 'OBJECT  '           / Characteristics of this data
RA      = '21:51:12.055'       / RA of the tracked pos. on the slit guide pos.
DEC     = '+28:51:38.72'       / Dec of the tracked pos. on the slit guide pos.
...

Coordinates and projections

FITS conventions has been defined to specify the physical, or world, coordinates to be attached to each pixel of an N-dimensional image (http://fits.gsfc.nasa.gov/fits_wcs.html)

Paper I (units and world coordinates).

Paper II: celestianl coordinates and projection [!] schemes.

../figs/gai_fits-imgs_Lab3World_projections.jpg

../figs/gai_fits-imgs_map-projections.jpg

FITS Header and the WCS

World Coordinate System (WCS) keywords in the header of a FITS or IRAF image file define the relationship between pixel coordinates in the image and sky coordinates.

There are 25 projections of the proposed FITS WCS standard (http://tdc-www.harvard.edu/wcstools/wcstools.wcs.html):

AZP: Zenithal (Azimuthal) Perspective

SZP: Slant Zenithal Perspective

TAN: Gnomonic = Tangent Plane

SIN: Orthographic/synthesis

STG: Stereographic

ARC: Zenithal/azimuthal equidistant

ZPN: Zenithal/azimuthal PolyNomial

ZEA: Zenithal/azimuthal Equal Area

AIR: Airy

CYP: CYlindrical Perspective

CAR: Cartesian

MER: Mercator

CEA: Cylindrical Equal Area

COP: COnic Perspective

COD: COnic equiDistant

COE: COnic Equal area

COO: COnic Orthomorphic

BON: Bonne

PCO: Polyconic

SFL: Sanson-Flamsteed

PAR: Parabolic

AIT: Hammer-Aitoff equal area all-sky

MOL: Mollweide

CSC: COBE quadrilateralized Spherical Cube

QSC: Quadrilateralized Spherical Cube

TSC: Tangential Spherical Cube

NCP: North celestial pole (special case of SIN)

GLS: GLobal Sinusoidal (Similar to SFL)

WCS Keywords basics

CTYPE1 and CTYPE2 indicate the coordinate type and projection.

CTYEP1 = xxxxyyyy / 'Comment' CTYEP2 = xxxxyyyy / 'Comment'

The first four characters are RA-- and DEC-, GLON and GLAT, or ELON and ELAT, for equatorial, galactic, and ecliptic coordinates, respectively.

The second four characters contain a four-character code for the projection.

CRPIX1 and CRPIX2 are the pixel coordinates of the reference point to which the projection and the rotation refer.

CRVAL1 and CRVAL2 give the center coordinate as right ascension and declination or longitude and latitude in decimal degrees.

Many astronomical instruments provide image files in which the 'x' and 'y' coordinate axes are not orientated with equatorial north corresponding to 'up' (and east == 'left'). According to WCS, there are three options for the scale and rotation:

Historically, CDELT1 and CDELT2 have been used to indicate the plate scale in degrees per pixel and CROTA2 has been used to indicate the rotation of the horizontal and vertical axes in degrees. Usually the axes rotate together and CROTA2 is used to indicate that angle in degrees.

The FITS WCS standard uses a rotation matrix, CD1_1, CD1_2, CD2_1, and CD2_2 to indicate both rotation and scale, allowing a more intuitive computation if the axes are skewed. This model has been used by HST and IRAF for several years.

CD1_1 = CDELT1 * cos (CROTA2)
CD1_2 = -CDELT2 * sin (CROTA2)
CD2_1 = CDELT1 * sin (CROTA2)
CD2_2 = CDELT2 * cos (CROTA2)

The 1996 proposed FITS WCS standard used PC001001, PC001002, PC002001, and PC002002 to represent the rotation matrix but retained CDELT1 and CDELT2 for the scale. It is also read by this software, but should not be used for new WCS's.

ALMA OST requeriments

OST = Observation Support Tool, http://almaost.jb.man.ac.uk

[BUNIT:] The physical units of the FITS image array values.

CDELTn*: Coordinate increment along axis n.

[CROTAn]: Coordinate system rotation angle.

[CDn_n]: Usually a matrix of four values which describe the mapping of the Coordinate system within the FITS image, i.e both increment and rotation. CDn_n matrix values and CDELTn and CROTAn are degenerate.

CTYPEn: Name of the CDELTn coordinate axis.

NAXIS: Number of axes.

NAXISn: Size of the axis n.

CRVAL3: good to save wavelength info.

From an image to ALMA!

Attention! ALMA OST do not rotate images for now. Instead it assumes that an uploaded image does have equatorial north corresponding to 'up' (http://almaost.jb.man.ac.uk/help/#Rotation).

Suggestion - use of PyHdust (http://github.com/danmoser/pyhdust).

One example: ramp image with 2 AU in size at 10 parsecs, rotated at 45 degree (by definition, to east) at 21 cm.

import numpy as np
import pyhdust.phc as phc
import pyhdust.interftools as intt

img = np.arange(900).reshape((30,30))

intt.img2fits(img, 21., [2*phc.au.cgs/phc.Rsun.cgs], 10, orient=45., \
coordsinf=['21:51:12.055', '-28:51:38.72'], ulbd='cm', deg=True)

intt.img2fits(img, 21., [2*phc.au.cgs/phc.Rsun.cgs], 10, rot=45., \
coordsinf=['21:51:12.055', '-28:51:38.72'], ulbd='cm', deg=True, \
outname='model_rotated')

Output - Coordinate rotation:

Output - Image rotation:

FITS images header and coordinates

APLpy