4. Technical specifications

In this page we summarize the assumptions that are made in galario and the specifications for the input quantities.

Full details are presented in Section 3 of Tazzari, Beaujean and Testi (2018) MNRAS 476 4527 [MNRAS] [arXiv] [ADS].

4.1. Image specifications

Following the Figure below, there are two fundamental coordinate systems that define the input image for the sampleImage() and chi2Image() functions:

• the matrix axes \([i, j]\) mapping the pixel coordinates, running from 0 to Nxy-1 (Nxy is the number of pixels on each axis).

• the physical axes \((R.A., Dec.)\) mapping Right Ascension and Declination coordinates.

The origin [i, j] = [0, 0] of the matrix axes can be put either in the upper left or in the lower left corner of the matrix. By default galario assumes the origin is in the upper left corner of the matrix, but it can be changed to the lower corner by specifying the optional parameter origin='lower' in the sampleImage() and chi2Image() functions.

The origin \((R.A., Dec.)=(0,0)\) of the physical axes is always in the center of the [Nxy/2, Nxy/2] pixel (grey pixel in the Figure below) for any value of origin. The \(R.A.\) axis always increases leftwards, following the usual convention of having East to the left and West to the right: therefore, the \(R.A.\) axis always decreases with increasing j index. Note that, with origin='upper', both the \((R.A., Dec.)\) axes decrease with increasing i, j index (see Figure below).

Warning

galario assumes that the values of the input image are evaluated in the pixel centers (not in the pixel edges).

For instructions on how to compute the correct \((R.A., Dec.)\) coordinate meshgrid to create the image, see the Cookbook.

The left and right panels of the Figure below show the relative orientations of matrix and physical axes for the origin='upper' and origin='lower' cases, respectively (click on the images for a larger version).

Note

The origin parameter in galario follows the same definition as in the matshow and imshow commands of the matplotlib library. To get the desired orientation of the Declination axis in galario, use the same origin parameter that produces the desired image orientation with matshow or imshow.