# Description¶

## Assumptions¶

It is assumed that the input science exposure data for near-IR instruments have had the superbias subtraction step applied, therefore the correction coefficients stored in the linearity reference files for those instruments must have been derived from data that has also been bias subtracted. MIRI data, on the other hand, do not receive bias subtraction (see calwebb_detector1) and hence the linearity correction is derived from data that has not been bias subtracted.

It is also assumed that the saturation step has already been applied to the input data, so that saturation flags are set in the GROUPDQ array of the input science data.

## Algorithm¶

The linearity step applies the “classic” linearity correction adapted from the HST WFC3/IR linearity correction routine, correcting science data values for detector non-linearity. The correction is applied pixel-by-pixel, group-by-group, integration-by-integration within a science exposure.

The correction is represented by an nth-order polynomial for each pixel in the detector, with n+1 arrays of coefficients read from the linearity reference file.

The algorithm for correcting the observed pixel value in each group of an integration is currently of the form:

$F_\text{c} = c_{0} + c_{1}F + c_{2}F^2 + c_{3}F^3 + ... + c_{n}F^n$

where $$F$$ is the observed counts (in DN), $$c_n$$ are the polynomial coefficients, and $$F_\text{c}$$ is the corrected counts. There is no limit to the order of the polynomial correction; all coefficients contained in the reference file will be applied.

Upon successful completion of the linearity correction the S_LINEAR keyword is set to “COMPLETE”.

### Special Handling¶

• Pixels having at least one correction coefficient equal to NaN will not have the linearity correction applied and the DQ flag “NO_LIN_CORR” is added to the science exposure PIXELDQ array.

• Pixels that have the “NO_LIN_CORR” flag set in the DQ array of the linearity reference file will not have the correction applied and the “NO_LIN_CORR” flag is added to the science exposure PIXELDQ array.

• Pixel values that have the “SATURATED” flag set in a particular group of the science exposure GROUPDQ array will not have the linearity correction applied to that group. Any groups for that pixel that are not flagged as saturated will be corrected.

The ERR array of the input science exposure is not modified.

The flags from the linearity reference file DQ array are propagated into the PIXELDQ array of the science exposure using a bitwise OR operation.

## Subarrays¶

This step handles input science exposures that were taken in subarray modes in a flexible way. If the reference data arrays are the same size as the science data, they will be applied directly. If there is a mismatch, the routine will extract a matching subarray from the reference file data arrays and apply them to the science data. Hence full-frame reference files can be used for both full-frame and subarray science exposures, or subarray-dependent reference files can be provided if desired.