# calwf3

`calwf3` is the name of the main executable which processes data from the WFC3 instrument onboard Hubble taken with either the UVIS or IR detectors. The code automatically calls the appropriate tasks, but users may also run the tasks independently if they desire special processing for their datasets. wf3cte, wf3ccd and wf32d are used for processing UVIS images, while IR image processing is done with wf3ir. The wf3rej program is used for both UVIS and IR images to combine multiple exposures contained in a CR-SPLIT or REPEAT-OBS set. Figure 3 is the flow diagram for the UVIS pipeline as a whole, while Figure 4 contains the flow for the IR pipeline.

During automatic pipeline processing by the STScI archive, `Astrodrizzle` follows `calwf3`. All calibrated images are corrected for geometric distortion correction and associated sets of dithered images are combined into a single product. See the WFC3 Data Handbook for more information, or Astrodrizzle .

## Where to Find calwf3

`calwf3` is part of HSTCAL package, which can be downloaded from http://www.stsci.edu/institute/software_hardware/stsdas/download-stsdas and is installed along with the STScI distributed package Ureka.

A detailed description of the improved `calwf3`, Version 3.3, which is more generally referred to as the UVIS2.0 update, will be available in a future publication of WFC3 Data Handbook and several ISRs which will accompany the update.

The current WFC3 Data Handbook can be found at http://www.stsci.edu/hst/wfc3/documents/handbooks/currentDHB/ . In the meantime, if you have questions not answered in this documentation, please contact STScI Help Desk (help[at]stsci.edu).

## Running calwf3

`calwf3` can be run on a single input raw file or an asn table listing the members of an associtaion. When processing an association, it retrieves calibration switch and reference file keyword settings from the first image listed in the asn table. `calwf3` does not accept a user-defined list of input images on the command line (e.g. `*raw.fits` to process all raw files in the current directory).

The wf3ccd, wf32d, wf3cte and wf3ir tasks on the other hand, will accept such user-defined input file lists, but they will not accept an association table( asn ) as input.

> In Python without TEAL:

>     >>> from wfc3tools import calwf3
>     >>> calwf3(filename)

> In Python with TEAL:

>     >>> from stsci.tools import teal
>     >>> from wfc3tools import calwf3
>     >>> teal.teal('calwf3')

> In Pyraf:

>     >>> import wfc3tools
>     >>> epar calwf3

### Running many files at the same time

The recommended method for running `calwf3` in batch mode is to use Python and the `wfc3tools` package in the STSDAS distribution .

For example:

    from wfc3tools import calwf3
    from glob import glob

    for fits in glob('j*_raw.fits'):
        calwf3(fits)

### Command Line Options

calwf3 can also be called directly from the OS command line:

    >>> calwf3.e iaa001kaq_raw.fits [command line options]

The command line executable only accepts one file at a time, but you can use os tools like awk to process everything in a directory:

    >>> ls *raw.fits | awk '{print "calwf3.e",$1}' | csh

The following options are available

- t: Print verbose time stamps.
- s: Save temporary files.
- v: Turn on verbose output.
- d: Turn on debug output.
- q: Turn on quiet output.
- r: Print the current software version number (with full revision information)
- –version: Print the current software version number only

### Types of files used as input to calwf3

- _asn file: name of an association table
- _raw file: name of an individual, uncalibrated exposure
- _crj file: name of any sub-product from an association table

While both CR-SPLIT and REPEAT-OBS exposures from an association get combined using calwf3, dithered observations from an association do not.

Figure 1: UVIS data raw file format

Figure 2: IR data raw file format

- The science image contains the data from the focal plane array detectors.
- The error array contains an estimate of the statistical uncertainty associated with each correcsponding science image pixel
- The data quality array contains independent flags indicating various status and problem conditions associated with each correspoinding pixel in the science image
- The sample array (IR ONLY) contains the number of samples used to derive the corresponding pixel values in the science image.
- The time array (IR ONLY) contains the effective integration time associated with each corresponding science image pixel value.

### Types of output file from calwf3

The suffixes used for WFC3 raw and calibrated data products closely mimic those used by ACS and NICMOS:

SUFFIX | DESCRIPTION | UNITS
--- | --- | ---
_raw | raw data | DN
_rac | UVIS CTE corrected raw data, no other calibration | DN
_asn | association file for observation set |
_spt | telescope and wfc3 telemetry and engineering data |
_blv_tmp | overscan-trimmed UVIS exposure | DN
_blc_tmp | overscan0trimmed UVIS, CTE corrected exposure | DN
_crj_tmp | uncalibrated, cosmic-ray rejected combined | DN
_crc_tmp | uncalibrated, cosmic-rat rejected, cte cleaned | DN
_ima | calibrated intermediate IR multiaccum image | \(e^{-}/s\)
_flt | UVIS calibrated exposure | \(e^{-}\)
_flc | UVIS calibrated exposure including CTE correction | \(e^{-}\)
_flt | IR calibrated exposure | \(e^{-}/s\)
_crj | UVIS calibrated, cosmic ray rejected image | \(e^{-}\)
_crj | IR calibrated, cosmic ray rejected image | \(e^{-}/s\)
_crc | UVIS calibrated, cr rejected, cte cleaned image | \(e^{-}\)
.tra | trailer file, contains processing messages |

** DRZ and DRC products are produced with Astrodrizzle, see Astrodrizzle **

### Keyword Usage

calwf3 processing is controlled by the values of keywords in the input image headers. Certain keywords, referred to as calibration switches, are used to control which calibration steps are performed. Reference file keywords indicate which reference files to use in the various calibration steps. Users who which to perform custom reprocessing of their data may change the values of these keywords in the _raw FITS file headers and then rerun the modified file through calwf3. See the WFC3 Data Handbook for a more complete description of these keywords and their values.

## UVIS Pipleline

Figure 3: Flow diagram for `calwf3` data. wf3cte occurs as the very first step, before wf3ccd.

As of version 3.3, the calwf3 pipeline processes all UVIS data twice, once with the CTE correction applied as the first step, and a second time without the CTE correction. A short description of the calibration steps, in the order they are performed:

- Calculate and remove and CTE found in the image (PCTECORR)
- Calculate a noise model for each pixel and record in the error array (ERR) of the image (NOISCORR)
- Initialize the data quality(DQ) array of the image (DQICORR)
- Correct fo A-toD conversion errors where necessary, currently skipped (ATODCORR)
- Subtract bias level determined from overscan regions (BLEVCORR)
- Subtract the bias image (BIASCORR)
- Detect and record SINK pixels in the DQ mask (performed if DQICORR is set to PERFORM)
- Perform unit conversion
- Subtract the post-flash image if applicable (FLSHCORR)
- Scale and subtract the dark image (DARKCORR)
- Perform flatfielding (FLATCORR)
- Perform shutter-shading correction where necessary, currently skipped (SHADCORR)
- Populate photometric header keywords (PHOTCORR)
- Correct chips to be on the same zeropoint (FLUXCORR)
- Calculate image statistics for the header

### Correction For Charge Transfer Efficiency (PCTECORR)

The charge transfer (CTE) of the UVIS detector has been declining over time as on-orbit radiation damage creates charge traps in the CCDs. Faint sources in particular can suffer large flux losses or even be lost entirely if observtions are not planned and analyzed carefully. The CTE depends on the morphology of the source, the distribution of electrons in the field of view, and the population of charge traps in the detector column between the source and the transfer register. Further details of the current understanding of the state of the WFC3/UVIS charge transfer efficieny (CTE) are presented in Section 5 of the data handbook as well as on the WFC3 CTE webpage . The PCTECORR step aims to mitigate the flux loss incurred from CTE.

More information on this part of the pipeline can be found in the wf3cte documentation.

### Error Array Initialization

The image error array is initialized. The function examines the RR extension of the input data to determine the state of the array. The input _raw image contains an empty ERR array. If the ERR array has already been expanded and contains values other than zero, then this function does nothing. Otherwise it will intialize the ERR array by assigning pixel values based on a simple noise model. The noise model uses the science (SCI) array and for each pixel calculates the error value \(\sigma\) in units of DN:

\[\sigma_{CCD} = \sqrt{(SCI-bias)/(gain) + (readnoise/gain)^{2}}\]

The CCDTAB reference file contains the bias, gain and readnoise values used for each CCD aplifier quadrant used in this calculation. The table contains one row for each configuration that can be used during readouse, which is uniquely identified by the list of amplifiers (replicated in the CCDAMP header keyword), the particular chip being read out (CCDCHIP), the commanded gain (CCDGAIN), the commanded bias offset level (CCDOFST) and the pixel bin size (BINAXIS). These commanded values are used to find the table row that matches the characteristics of the image that is being processed and reads each amplifiers characteristics, including readnoise (READNSE), A-to-D gain (ATODGN) and the mean bias level (CCDBIAS).

### Data Quality Array Initialization (DQICORR)

This step initializas the data quality array by reading a table of known bad pixels for the detector, as stored in the Bad Pixel reference table BPIXTAB. The types of bad pixels that can be flagged are:

NAME | VALUE | DESCRIPTION
--- | --- | ---
GOODPIXEL | 0 | OK
SOFTERR | 1 | Reed-Solomon decoding error
DATALOST | 2 | data replaced by fill value
DETECTORPROB | 4 | bad detector pixel or beyond aperture
DATAMASKED | 8 | masked by occulting bar
HOTPIX | 16 | hot pixel
CTETAIL | 32 | UVIS CTE tail
WARMPIX | 64 | warm pixel
BADBIAS | 128 | bad bias value
SATPIXEL | 256 | full-well or a-to-d saturated pixel
BADFLAT | 512 | bad flatfield value
TRAP | 1024 | UVIS charge trap, SINK pixel
ATODSAT | 2048 | a-to-d saturated pixel
ne TBD | 4096 | reserved for Multidrizzle CR rej
DATAREJECT | 8192 | rejected during image combination UVIS, IR CR rejection
CROSSTALK | 16384 | ghost or crosstalk
RESERVED2 | 32768 | can’t use

### Sink Pixel Detection and Marking

Sink pixels are a type of image defect. These pixels contain a number of charge traps and under-report the number of electrons that were generated in them during an exposure. These pixels can have an impact on nearby upstread or downstream pixels, though they often only impact one or two pixels when the background is high, they can impact up to 10 pixels if the background is low.

Flagging of SINK pixels in the DQ extension of calibrated images is controlled with the DQICORR header keyword, happens after the bias correction has been performed, and is done in the amp-rotated CDAB full image format used and described in the CTE correction. When set to perform, the sink pixels are located and flagged with help from the SNKCFILE reference image. Given the reference image, the procedure for flagging the sink pixel in science data involves:

- Extract the MJD of the science exposure
- Go through the reference image pixel by pixel looking for those pixels with values greater than 999, which indicates that the current pixel is a sink pixel. The value of this pixel in the reference file corresponds to the date at which this pixel exibited the sink behavior.
- If the turn on date of the sink pixel is after the exposure date of the science image, then we ignore the sink pixel in this exposure and move on to the next pixel
- If the turn on date of the sink pixel is before the exposure date of the science image, then this science pixel was compromised at the time of the exposure.The corresponding DQ extension pixel for this science pixel is flagged with the “charge trap” flag of 1024.
- If the pixel “below” the sink pixel in the long format image has a value of -1 in the reference image, then it is also flagged with the “charge trap” value in the DQ extension. We then proceed vertically “up” from the sink pixel and compare each pixel in the reference file to the value of the sink pixel in the science exposure at hand. If the value of the sink pixel in the exposure is below the value of the upstream pixel in the reference image, we flag that pixel with the “charge trap” value in the DQ extension. We continue to flag pixels until the value of the pixel in the reference image is zero or until the value of the sink pixel in the exposure is greater than the value of the upstream pixel in the reference image.

WFC3 ISR 2014-19 has a detailed analysis on detection of the sink pixels, while the strategy for flagging them is discussed in WFC3 ISR 2014-22 .

Sink pixels are currently only flagged in full frame science images, a future release of calwf3 will also perform flagging in subarray images. The pipeline currently does no further analysis or correction on pixels which have been flagged as affected by sink pixels

### Unit Conversion to Electrons

The UVIS image is multiplied by gain right after BIASCORR, converting it to ELECTRONS. This step is no longer embedded within FLATCORR.

### Bias Correction (BIASCORR)

This step subtracts the two dimensional bias struction from the image using the superbias reference image listed in the header keyword BIASFILE. The dimensions of the image are used to distinguish between full and sub-array images. Because the bias image is already overscan-subtracted, it will have a mean pixel value of less than one. The BIASFILE has the same dimensions as a full-size science image, complete with overscan regions. Only after completion of wf3ccd are the science images trimmed to their final calibrated size. The same reference image is used for full-frame and subarray images, calwf3 will extract the matching region from the full-size bias file and apply it to the subarray image.

### Overscan Bias Correction (BLEVCORR)

The location of the overscan regions in a raw image varies, depending upon the type of readout that is performed. The overscan regions are used to monitor the instrument as well as provide a measure of the bias level at the time the detector was exposed. The bias level which is calculated for subtraction is done on a line-by-line basis in the image. If the image has no overscan region the BIAS level to be subtracted is obtained from the CCDTAB reference file. Otherwise, the columns to use for the calculation are referenced in the OSCNTAB reference file. A bias drift calculation is made if there are virtual overscan pixels which exist, if neither of the virtual overscan regions are specfied then the physical overscan region is used.

If there are two sections available to use for the line because only 1 amp was used then they are averaged. The parallel overscan region is split into two if there is more than one amp. If the virtual overscan is used, a straight line is fit as a function of the column number. The fit is evaluated for each line and then subtracted from the data. Iterative sigma clipping is used to reject outliers from the array of bias values.

The mean value of all the bias levels which were subtracted is recorded in the SCI extension output header in MEANBLEV.

### Dark Current Subtraction (DARKCORR)

The reference file listed under the DARKFILE header keyword is used as the reference dark image.

In the UVIS, the dark image is scaled by EXPTIME and FLASHDUR.

The reference file pointed to with DARKFILE is used for the non-CTE corrected data.

The reference file pointed to with DRKCFILE is used for the CTE corrected data

### Shutter Shading Correction (SHADCORR)

This step corrects the science image for differential exposure time across the detector cased by the amount of time it takes for the shutter to completely open and close, which is a potentially signiciant effect only for images with very short exposure times (less than ~5 seconds). Pixels are corrected based on the exposure time using the relation:

\[corrected = uncorrected \times EXPTIME \div (EXPTIME + SHADFILE)\]

WFC3 tests have shown that the shutter shading effect is insignificant (< 1%), even for the shortest allowed UVIS exposure time of 0.5 seconds (see WFC3 ISR 2007-17). Therefore this step is ALWAYS set to OMIT in calwf3.

### Post-Flash Correction (UVIS ONLY) (FLSHCORR)

WFC3 has post-flash capability to provide a means of mitigating the effects of Charge Transfer Efficiency (CTE) degredation. When FLSHCORR=PERFORM, this routine subtracts the post-flash reference image, FLSHFILE, from the science image after DARKCORR in the WF32D step. The success of the post-flash operation during the exposure is first verified by checking the keyword FLASHSTA. The FLSHFILE is renormalized to the appropriate post-flash current level (LOW, MED, HIGH) recorded in the FLASHCUR keyword, and the flash duration (FLASHDUR) and is then subtracted from the science image. The mean value of the scaled post-flash image is written to MEANFLSH in the output SCI extension header. Different members of an association can have different values of SHUTRPOS because it varies by exposure, and this is fine for calibration because the references files are populated separately for each exposure.

KEYWORD | DESCRIPTION
--- | ---
FLSHDUR | is the length of time of the flash exposure
FLSHCUR | is the current that was used to the lamp as calculated by TRANS, which also calculates FLASHEXP, (ZERO, LOW, MED,HIGH)
FLSHFILE | is the flash reference file, which has an illumination pattern for each shutter
SHUTRPOS | says which shutter was used
FLASHSTA | indicates an interrupted exposure (ABORTED, SUCCESSFUL, NOT PERFORMED)
FLASHLVL | post flash level in electrons
MEANFLSH | the mean level which calwf3 calculated and then subtracted

Futher reading:
  - WFC3 Post-Flash Calibration ISR
  - CTE-Loss Mitigation Before Data Acquisition

### FLATCORR

Correct the image for pixel quantum efficiency using the reference image specified by the FLATFILE keyword in the header. Conversion from DN to ELECTRONS no longer depends on FLATCORR=PERFORM, all images are converted appropriately.

This actually consists of correction using up to 3 reference flat images:

- PFLTCORR: apply a pixel-to-pixel flat (ground flats)
- DFLTCORR: apply a delta flat, applies any needed changes to the small-scale PFLTFILE
- LFLTCORR: apply a low order flat, correcting for large scale sensativity variations (on-orbit)

The pipeline is currently only using the P-flats. If two or more reference files are specified, they are read in line-by-line and multiplied together to form a combined flatfield correction image.

Subarray science images use the same reference file as the full-frame images; calwf3 will extract the appropriate region from the reference file and apply it to the subarray input image.

### Photometry Keywords (PHOTCORR)

The PHOTCORR step is performed using tables of precomputed values instead of calls to SYNPHOT, it uses the reference table specified in the IMPHTTAB header keyword. Each DETECTOR uses a different table.

If you do not wish to use this feature, set the header keyword PHOTCORR to OMIT. However, if you intend to use the FLUXCORR step, then PHOTCORR must be set to PERFORM as well.

- PHOTFNU: the inverse sensitivity in units of :math: Jansky sec electron^{-1}`
- PHOTFLAM: the inverse sensistiy in units of \(ergs\ cm^{-2} A^{-1} electron^{-1}\)
- PHOTPLAM: the bandpass pivot wavelength
- PHOTBW: the bandpass RMS width
- PHTFLAM1: the inverse sensistiy in units of \(ergs cm^{-2} A^{-1} electron^{-1}\)
- PHTFLAM2: the inverse sensistiy in units of \(ergs cm^{-2} A^{-1} electron^{-1}\)

For versions 3.3 and beyond, the value PHOTFNU is calculated specific for each UVIS chip, see the section on FLUXCORR for more information.

The SCI headers for each chip contain the PHOTFNU keyword, which is valid for its respective chip, where PHOTFNU is calculated as:

For UVIS 1: \(photfnu = 3.33564e^{4} * PHTFLAM1 * PHOTPLAM^{2}\)

For UVIS 2: \(photfnu = 3.33564e^{4} * PHTFLAM2 * PHOTPLAM^{2}\)

The IMPHTTAB file format for WFC3 UVIS is as follows:

    EXT#  FITSNAME      FILENAME              EXTVE DIMENS       BITPI OBJECT

    0     z7n21066i_imp z7n21066i_imp.fits                       16
    1       BINTABLE    PHOTFLAM              1     5Fx256R
    2       BINTABLE    PHOTPLAM              1     5Fx256R
    3       BINTABLE    PHOTBW                1     5Fx256R
    4       BINTABLE    PHTFLAM1              1     5Fx256R
    5       BINTABLE    PHTFLAM2              1     5Fx256R

where each extension contains the photometry keyword information for that specific header keyword. The rows inside the tables are split on observation mode.

### Flux normalization for UVIS1 and UVIS2 (FLUXCORR)

The FLUXCORR step was added in calwf3 v3.1.2 as a way to scale the UVIS chips so that the flux correction over both chips is uniform. This requires new keywords which specify new PHOTFLAM values to use for each chip as well as a keyword to specify the scaling factor for the chips. New flatfields must be used and will replace the old flatfields in CDBS but the change will not be noticable to users. Users should be aware that flatfield images used in conjunction with v3.2.1 of the software should not be used with older versions as the data, and vice versa will be scaled incorrectly.

The new keywords include:

- PHTFLAM1: The FLAM for UVIS 1
- PHTFLAM2: The FLAM for UVIS 2
- PHTRATIO: The ratio: PHTFLAM2 / PHTFLAM1, which is calculated by calwf3 and is multiplied with UVIS2 (SCI,1 in the data file)

In order for FLUXCORR to work properly the value of PHOTCORR must also be set to perform since this populates the header of the data with the keywords FLUXCORR requires to compute the PHTRATIO.

This step is performed by default in the pipeline and the PHOTFLAM keyword will be valid for both chips after the correction has been applied.

## IR Pipeline

IR pipeline output files using the RAW file as input:

> - flt.fits: output calibrated, ramp-fitted exposure produced after CRCORR has been run
> - ima.fits: output ramp calibrated exposure. Remember that the signal rate recorded in each SCI extension of the ima file represents the average flux between that particular readout and the zero read.
> - _crj.fits: a cosmic-ray rejected sub-product produced from images in an association table
> - .tra: output text information about the processing

Figure 4: Flow diagram for IR data using wf3ir in calwf3

### Data Quality Initialization (DQICORR)

Initialize the data quality array for the image using the reference file specified in its header with BPIXTAB. The DQ array is no longer updated to reflect any TDF transition during the sample. If you want to update DQ pixel values yourself before running further processing, do it after this first step has been completed, remembering that the data in this extension is always in units of UNSIGNED INTEGER. The following table lists the DQ flag values and their meanings:

NAME | VALUE | DESCRIPTION
--- | --- | ---
GOODPIXEL | 0 | OK
SOFTERR | 1 | Reed-Solomon decoding error
DATALOST | 2 | data replaced by fill value
DETECTORPROB | 4 | bad detector pixel or beyond aperture
DATAMASKED | 8 | masked by occulting bar
BADZERO | 8 | deviant IR zero-read pixel
HOTPIX | 16 | hot pixel
UNSTABLE | 32 | IR unstable pixel
WARMPIX | 64 | warm pixel
BADBIAS | 128 | bad bias value
SATPIXEL | 256 | full-well or a-to-d saturated pixel
BADFLAT | 512 | bad flatfield value
SPIKE | 1024 | CR spike detected during cridcalc IR
ZEROSIG | 2048 | IR zero-read signal correction
ne TBD | 4096 | reserved for Multidrizzle CR rej
DATAREJECT | 8192 | rejected during image combination UVIS, IR CR rejection
HIGH_CURVATURE | 16384 | pixel has more than max CR’s
RESERVED2 | 32768 | can’t use

### Estimate the signal in the zero read (ZSIGCORR)

This step measures the signal between the super zero read in the linearity reference file (NLINFILE) and the science zero read exposure, the steps are roughly as follows:

- copy the zero sig image from the linearity reference file
- compute any subarray offsets
- subtract the super zero read reference image from the zero read science image
- compute the noise in the zero image
- pixels which contain more than ZTHRESH*noise of detected signal are flagged and that signal is passed to the NLINCORR step to help judge saturation and linearity, avoiding reference pixels.
- low signal pixels are masked out by setting them to zero
- the NLINCOR file has an extension with saturation values for each pixel which is referenced here. Pixels which are saturated in the zeroth or first reads are flagged in the DQ and the number of found saturated pixels are reported.
- This step works poorly for bright targets which are already begining to saturate in the zeroth and first reads
- This step acutally subtractes the super zero read from the science zero read instead of calculating an estimated signal based on the first read and zero read + estimated exposure time between them so that the difference in readout time for subarrays is not an issue.

### Bias Correction (BLEVCORR)

This step subtracts the bias level using the reference pixels around the perimeter of the detector, the boundries fo the reference pixels are defined in the OSCNTAB reference file. There are 5 reference pixels on each end of each row, but 1 is ignored on each side, for a total of 8 being used per row. The resistent mean of the standard deviation of all the reference pixels in the image is subtracted from the entire image and the value is stored in the MEANBLEV keyword in the output image header. The reference pixels are left in place in the IMA output image through processeing, but the final FLT image has been trimmed to just the science pixels.

### Zero read subtraction (ZOFFCORR)

The original zero read is subtracted from all groups in the science image, including the zeroth read itself, combining the DQ arrays with a logical OR. The ERR and SAMP arrays are unchanged and the TIME arrays are subtracted from each other. The exposure time for the group being corrected is reduced by an amount equal to the exposure time of the zero-read. At this point we’ve subtracted the mean bias using the reference pixels (BLEVCORR) and added back in the signal from the super zero read (done at the end of ZSIGCORR). What’s left in the zero read of the science image is the superbias subtracted signal. The TIME and SAMP arrays are saved to the FLT image only AFTER the CRCORR step has been completed.

### Error array initialization

The errors associated with the raw data are estimated according to the noise model for the detector which currently includes a simple combination of detector readnoise and poisson noise from the pixel. Readnoise and gain are read from the CCDTAB reference file. The ERR array continues to be summed in quadrature as the SCI array is processed. Inside the final FLT image, the ERR array is calculated by CRCORR as the calculated uncertainty of the count-rate fit to the multiaccum samples.

\[\sigma_{IR} = \frac{\sqrt{(readnoise^{2}) + (counts * gain)}}{gain}\]

### Detector Non-linearity Correction (NLINCORR)

The integrated counts in the science images are corrected for the non-linear response of the detectors, flagging pixels which extend into saturation (as defined in the saturation extension of the NLINFILE reference image. The observed response of the detector can be represented by two regimes:

- At low and intermediate signal levels the detector response deviates from the incident flux in a way that is correctable using the following expression

\[F_{c} = (1 + c_{1} + c_{2} \times F + c_{3}\times F^{2} + c_{4} \times F^{3}) \times F\]

where c1, c2, c3, and c4 are the correction coefficients, F is the uncorrected flux in DN and \(F_{c}\) is the corrected flux. The current form of the correction uses a third-order polynomial, but the algoritm can handle an arbitrary number of coefficients. The number of coefficients and error terms are given by the values of the NCOEFF and NERR keywords in the header of the NLINFILE.

- At high signal levels, as saturation sets in, the response becomes highly non-linear and is not correctable to a scientifically useful degree.

The signal in the zero read is temporarily added back to the zeroth read image of the science data before the linearity correction is applied and before the saturation is judged. Once the correction has been applied the signal is once again removed. This only occurs if the ZSIGCORR step is set to PERFORM. Saturation values for each pixel are stored in the NODE extension of the NLINFILE. After each group is corrected, the routine also sets saturation flags in the next group for those pixels that are flagged as saturated in the current group. This is necessary because the SCI image value of saturated pixels will sometimes start to go back down in the subsequent reads after saturation occurs, which means they could go unflagged by normal checking techniques. The SAMP and TIME arrays are not modified during this step.

The format of the linearity reference file:

    EXT#  FITSNAME      FILENAME              EXTVE DIMENS       BITPI OBJECT

    0     u1k1727mi_lin u1k1727mi_lin.fits                       -32
    1       IMAGE       COEF                  1     1024x1024    -32
    2       IMAGE       COEF                  2     1024x1024    -32
    3       IMAGE       COEF                  3     1024x1024    -32
    4       IMAGE       COEF                  4     1024x1024    -32
    5       IMAGE       ERR                   1     1024x1024    -32
    6       IMAGE       ERR                   2     1024x1024    -32
    7       IMAGE       ERR                   3     1024x1024    -32
    8       IMAGE       ERR                   4     1024x1024    -32
    9       IMAGE       ERR                   5     1024x1024    -32
    10      IMAGE       ERR                   6     1024x1024    -32
    11      IMAGE       ERR                   7     1024x1024    -32
    12      IMAGE       ERR                   8     1024x1024    -32
    13      IMAGE       ERR                   9     1024x1024    -32
    14      IMAGE       ERR                   10    1024x1024    -32
    15      IMAGE       DQ                    1     1024x1024    -32
    16      IMAGE       NODE                  1     1024x1024    -64
    17      IMAGE       ZSCI                  1     1024x1024    -32
    18      IMAGE       ZERR                  1     1024x1024    -32

### Dark Current Subtraction (DARKCORR)

The reference file listed under the DARKFILE header keyword is used to subtract the dark current from each sample. Due to potential non-linearities in some of the signal components, such as reet-related effecets in the first one or two reads of an exposure, the dark current subtraction is not aplied by simply scaling a generic reference dark image to the exposure time and then subtracting it. Instead, a library of dark current images is maintained that includes darks taken in each of the available predefined multiaccum sample sequences, as well as the available sub-array readout modes. The multiaccum dark reference file is subtracted read-by-read from the stack of science image readouts so that there is an exact match in the timings and other characteristics of the dark image and the science image. The subtraction does not include the reference pixel. The ERR and DQ arrays from the reference dark file are combined with the SCI and DQ arrays from the science image, but the SAMP and TIME arrays are unchanged. The mean of the dark image is saved to the MEANDARK keyword in the output science image header.

### Photometry Keywords (PHOTCORR)

The PHOTCORR step is performed using tables of precomputed values instead of calls to SYNPHOT. The correct table for a given image must be specified in the IMPHTTAB header keyword in order for calwf3 to perform the PHOTCORR step. The format of the file for the IR detectors is:

    EXT#  FITSNAME      FILENAME              EXTVE DIMENS       BITPI OBJECT

    0     wbj1825ri_imp wbj1825ri_imp.fits                       16
    1       BINTABLE    PHOTFLAM              1     5Fx38R
    2       BINTABLE    PHOTPLAM              1     5Fx38R
    3       BINTABLE    PHOTBW                1     5Fx38R

where each extension contains the photometry keyword information for that specific header keyword. The rows in the tables are split on observation mode.

- PHOTFLAM: the inverse sensistiy in units of \(ergs\ cm^{-2} A^{-1} electron^{-1}\)
- PHOTPLAM: the bandpass pivot wavelength
- PHOTBW: the bandpass RMS width

### Conversion to Signal Rate (UNITCORR)

This step converts the science data from a time-integrated signal to a signal rate by dividing the SCI and ERR arrays for reach readout by the TIME array. No reference file is needed. The BUNIT keyword in the output data header reflects the appropriate data units. The FLATCORR keyword is checked to decide on proper units for BUNIT and skip this step if “countrate” is found. If FLATCORR is set to “complete”, then the units should be electrons, otherwise they are counts(the digitized signal from the FPA).

### Fit accumulating signal and identify cosmic ray hits (CRCORR)

This step fits the accumulating signal up the image ramp and identifies cosmic-ray hits for each sample using the Fixsen et al (2000) methods.

The process is described below:

- An iterative fit to the accumulating sample time is calculated for each pixel
    - Finding a cosmic ray ends one interval and beins the next; the cosmic ray must be included in the next interval
        - intervals are first defined based on existing cosmic rays
            - CRSIGMAS from the CRREJTAB reference file is used to set the rejection threshold

        - then each interval is fitted separately

        - then each interval is inspected for SPIKES

        - then each interval is inspected for more cosmic rays

    - If any SPIKES or cosmic rays are found then the entire procedure repeats, new intervals are defined, etc ...

    - After the iteration ends because no new SPIKES or cosmic rays are found, each interval is fitted separately once again, with optimum weighting, and then the results for each interval are combined to obtain the final solution for the pixel.

    - The linearity fit includes readnoise in the sample weights and Poisson noise from the source in the final fit uncertainty

    - negative cosmic ray hits are detected and detected SPIKES have their 1024 bit flipped in the DQ extension

    - If the first read is saturated the output pixels are never zeroed out
        - The output pixel values in this case are the value in the input zeroth read image, regardless of whether the zero-read image was saturated. If it is saturated in the zero-read, the DQ flag will get carried over to the outpu DQ array to indicate that it’s bad.

    - The DATAREJECT DQ flag is set for all samples following a hit. This is done so that anyone looking at the IMA file will know that the absolute value of the pixel is wrong after the firs t hit, but it smears the location of any hits which occurred in addition to the first one.

    - Pixels in the DQ image of the output IMA file are flagged with a value of 8192, the SCI and ERR image arrays are left unchanged

    - DQ values from any sample are carried through to the output pixel if a pixel has no good samples

- The UNSTABLE DQ flag is used to record pixels with higher than max allowed cosmic ray hits recorded.

The result of this step is stored as a single imset in the output FLT file. In the FLT file, the SCI array contains the final slope computed for each pixel, the ERR array contains the estimated uncertainty in the slope, the SAMP array contains the number of non-flagged samples used to compute the slope, and the TIME array contains the total exposure time of those smaples. Pixels for which no unflagged sample exisists (dead pixels for example) still get a slope computed which is recorded in the SCI array of the output FLT image, but the DQ flags in the FLT will reflect their bad status.

### Flatfield Correction (FLATCORR)

This step corrects for sensativity variations across the detector by dividing the images by one or more reference flatfields (taken from the PFLTFILE, DFLTFILE or LFLTFILE header keywords). The mean gain from all the amps is used to convert to the image to units of electrons. Errors and DQ flags from the flatfields are combined with the science data errors and flag, the TIME and SAMP arrays are unchanged.

### Calculation of image statistics

The min, mean, maxmin and max SNR (for the SCI and ERR) for data values flagged as “good” in the DQ array (i.e. zero) are calculated and stored in the output SCI image header, the reference pixels are not used. This is performed for all samples in the IMA file as well as the FLT image but the input data is not modified in any way. Updated keywords in the science header include:

- NGOODPIX
- GOODMEAN
- GOODMIN
- GOODMAX
- SNRMEAN
- SNRMIN
- SNRMAX

### Reject cosmic rays from multiple images (RPTCORR)

Reject cosmic rays from multiple images. CR-SPLIT and REPEAT-OBS exposures get combined, other members of the association file must be combined with Astrodrizzle (see Astrodrizzle ), which will also correct for geometric distortion. This step is also referred to as wf3rej. The task uses the same statistical detection algorithm developed for ACS (acsrej), STIC (ocrrj) and WFPC2(crrej), providing a well-tested and robust procedure.