# Description¶

## Overview¶

The mrs_imatch step “matches” image intensities of several input 2D MIRI MRS images by fitting polynomials to cube intensities (cubes built from the input 2D images), in such a way as to minimize - in the least squares sense - inter-image mismatches in intensity. The “background matching” polynomials are defined in the frame of world coordinates (e.g. RA, DEC, lambda).

If any of background polynomial coefficients are a nan then the step is skipped and S_MRSMAT is set to SKIPPED.

Any sources in the scene are identified via sigma clipping and removed from the matching region.

## Assumptions¶

Because the fitted polynomials are defined in terms of world coordinates, and because the algorithm needs to build 3D cubes for each input image, all input images need to have a valid WCS defined.

## Algorithm¶

This step builds a system of linear equations

$a \cdot c = b$

whose solution $$c$$ is a set of coefficients of (multivariate) polynomials that represent the “background” in each input image (these are polynomials that are “corrections” to the intensities in the input images) such that the following sum is minimized:

$L = \sum^N_{n,m=1,n \neq m} \sum_k \frac{\left[I_n(k) - I_m(k) - P_n(k) + P_m(k)\right]^2}{\sigma^2_n(k) + \sigma^2_m(k)}.$

In the above equation, index $$k=(k_1,k_2,...)$$ labels a position in an input image’s pixel grid [NOTE: all input images share a common pixel grid].

“Background” polynomials $$P_n(k)$$ are defined through the corresponding coefficients as:

$P_n(k_1,k_2,...) = \sum_{d_1=0,d_2=0,...}^{D_1,D_2,...} c_{d_1,d_2,...}^n \cdot k_1^{d_1} \cdot k_2^{d_2} \cdot \ldots .$

# Step Arguments¶

The mrs_imatch step has two optional arguments:

bkg_degree

The background polynomial degree (int; default=1)

subtract

Indicates whether the computed matching “backgrounds” should be subtracted from the image data (bool; default=False)

# Reference Files¶

This step does not require any reference files.

# Also See¶

See wiimatch package documentation for more details.