The calacs pipeline consists of five individual calibration tasks: acsccd, acscte, acsrej, acs2d, and acssum. These tasks are listed in Table 3.2 and diagrammed in Figure 3.1. calacs is responsible for controlling the processing rather than the actual calibration of the data. The individual tasks within calacs apply the appropriate calibration steps to the data and create the output products.

Raw ACS images are in units of Data Numbers (DN). Calibrated images are in units of electrons, and drizzled images are in units of electrons/second.

The following five sections provide a detailed description of the calibration steps, and their related reference files, within each calacs task.

3.4.1 acsccd

This task contains the initial processing functions for all ACS CCD data. These functions are listed, in operational order, in Table 3.3.

acsccd processes each image in the input list, one at a time, using the header keywords to determine which calibration steps to perform. Upon completion of acsccd, the prescan and overscan regions will be trimmed from the image, and an output image with the file suffix "blv_tmp.fits" is created.

Table 3.3: acsccd Processing Functions

doDQI - Bad Pixel Determination

• Header switch: DQICORR
• Header keywords updated: None
• Reference file keyword (file type, suffix): BPIXTAB (FITS table, bpx.fits), CCDTAB (FITS table, ccd.fits)

The function doDQI initializes the Data Quality (DQ) array by combining it with a table of known permanent bad pixels for the detector, stored in the bad pixel reference table (named by the image header keyword BPIXTAB). The type of bad pixel flags are listed in Table 3.4.

The DQ array may have already been partially populated to reflect pixels which were affected by telemetry problems or compression buffer overflow. Other DQ flags will be added in further processing steps (such as cosmic ray rejection and sink pixel flagging). For CCD data, the values in the SCI extension are also checked for A-to-D saturation. See ACS ISR 2020-03 for details. 

For each observation, the doDQI function combines the DQ flags from prior calibration processing (obtained from the BPIXTAB reference table) and from saturation tests, into a single DQ result.  These values are combined using a "bitwise OR operator" for each pixel. Thus, if a single pixel is affected by two DQ flags, the sum of those flag values is assigned to the corresponding pixel in the final DQ array. For example, a hot pixel (flag 16) that is also unstable throughout an anneal cycle (flag 32) would be given a flag value of 48 (16+32=48). This array then serves as a mask so that calacs will ignore bad pixels during processing.

Table 3.4: Flags for the DQ Array

doBias - Bias Image Subtraction

• Header switch: BIASCORR
• Header keywords updated: None
• Reference file keyword (file type, suffix): BIASFILE (image, bia.fits)

doBias removes the low order, quasi-static structure of the bias, including the bias gradient in post-SM4 images.

Subtraction of the bias image is performed prior to cosmic ray rejection using the function doBias. The default reference image, named in the header keyword BIASFILE, is assigned based on the DETECTOR, APERTURE, CCDAMP, and CCDGAIN image header keyword values. The dimensions of the science image, given by the NAXIS[1, 2] and RAW_LTV[1, 2] header keywords, are used to distinguish subarray observations from those that use the entire chip.

The bias reference file data is in units of DN. Therefore, it is applied to the image before the data is converted to units of electrons. Since the prescan and overscan values are already subtracted from the bias reference image, it may have a mean pixel value of less than 1.

Due to the way the bias reference image is created, part of the dark subtraction is also included in this step. Dark counts accumulate for an additional time beyond the exposure time, primarily the time required to read out the detector, and this portion of the dark current is subtracted along with the bias. This is described in the section on doDark – Dark Image Subtraction.

For full frame images, the BIASFILE has the same dimensions as a full-size science image, 1062 × 1044 for HRC and 4144 × 2068 for WFC, allowing for simple image arithmetic on arrays of equal size. For WFC subarray images in pre-SM4 cycles and post-SM4 cycles 17-23, aperture-specific BIASFILEs are used to account for different bias gradients, but the concept of simple image arithmetic remains. Only after the completion of acsccd are the images trimmed to 1024 x 1024 (HRC) and 4096 x 2048 (WFC). ACS CCD data arrays are not binned, so any image which is not the full size is assumed to be a subarray.

For WFC subarray images in HST Cycles 24 to present, calacs uses the LTV[1, 2] keywords to extract the appropriate region from the reference file and apply it to the subarray input image. For pre-SM4 Cycles and Cycles 17-23, the low order bias structure in WFC subarray images differs significantly from that in full frame WFC images. Therefore, bias calibration images are available for supported subarray configurations.

For users who make their own bias files, the BIASFILE keyword will need to be updated manually before recalibrating. This is described in detail in Section 3.5.2.

toElectrons – Unit Conversion From DN to Electrons

• Header switch: None
• Header keyword updated: BUNIT
• Reference file keyword (file type, suffix): CCDTAB (FITS table, ccd.fits)

Data is multiplied by gain for respective amplifiers. BUNIT is changed from DN to electrons in SCI and ERR extensions.

doBlev – Bias level Correction

• Header switch: BLEVCORR
• Header keywords updated: BIASLEV[A,B,C,D], MEANBLEV, CRPIX[1,2], LTV[1,2]
• Reference file keyword (file type, suffix): OSCNTAB (reference table, osc.fits)

There are two branches in the doBlev function, one for pre-SM4 data and another for post-SM4 data.

Pre-SM4 images

doBlev fits the bias level from the physical pre-scan¹ section (defined in the OSCNTAB reference table), and subtracts it from the image data.

A subset of the pixels along each row of the vertical pre-scan is used to obtain a linear fit of the bias level as a function of image row. If the measured pre-scan level for a given row is more than 3σ from the mean of all rows, that row will be excluded from the linear fit. The fitted value for each pre-scan row is then subtracted from the image pixels for that row. If the pre-scan level cannot be determined, or if the pre-scan region is not present in the input image, a default value gets derived from the CCD reference table (given by the keyword CCDTAB), with the value coming from the "CCDBIAS" column. That value will be subtracted and a warning message will be written to the image trailer file.

The positional image header keywords CRPIX1, CRPIX2, and LTV1, LTV2 are updated to reflect the offset due to removal of the overscan. In addition, the mean value of all overscan levels is computed and written to the SCI extension header keyword MEANBLEV. The individual bias level measured for each amplifier is written to the SCI header keywords BIASLEVA, BIASLEVB, BIASLEVC, and BIASLEVD.

The "Overscan Region Table" reference file, named in the header as OSCNTAB, describes the overscan regions to be used for measuring the bias level of the observation. Each row corresponds to a specific configuration, given by the CCD amplifier, chip, binning ratio, and dimensions. The TRIMX*² columns give the number of columns to trim off the beginning and end of each line (the physical prescan region), while the TRIMY* columns give the number of rows to trim off the top and bottom of each column (the virtual overscan region). The result of trimming (TRIMX1 + TRIMX2) columns and (TRIMY1 + TRIMY2) rows gives the final calibrated image sizes, 4096 × 2048 for a full WFC image and 1024 × 1024 for a full HRC image.

The OSCNTAB columns BIASSECTA*² and BIASSECTB* give the range of image columns to be used for determining the bias level in the leading and trailing regions, respectively, of the physical prescan region.

The VX* and VY* columns in the OSCNTAB define the virtual overscan region, but are not used in calibration.

To determine which overscan regions were actually used for determining the bias level, users are encouraged to check the OSCNTAB reference file. If desired for manual calibration, users may modify the bias section and virtual overscan region definitions in the reference table, but the TRIMX*, TRIMY* columns must not be changed.

Post-SM4 Full Frame WFC images

For all WFC data except subarrays, the following corrections are done by doBlev:

First, a bias shift correction is done to remove an artifact associated with the CCDs' external pre-amplifiers and the dual-slope integrators within the CCD Electronics Box Replacement. This effect is signal-dependent, causing the pixel-to-pixel bias level to be offset by 0.02–0.3%, with an offset that decays slowly in the serial (horizontal) clocking direction. Detailed information about the bias shift can be found in ACS ISR 2012-02.

The effects of cross-talk, negative ghost images that are mirror-symmetric to bright sources in adjacent quadrants, are also removed. To learn more about cross-talk, please refer to ACS ISR 2010-02.

Corrections are simultaneously made for two other artifacts: 1) amplifier offsets, slight bias level offsets in each amplifier; and 2) bias stripes, low amplitude, horizontal striping caused by electronic 1/f noise in the replacement electronics (see ACS ISR 2011-05).

Bias Striping Noise

For post-SM4 full frame WFC images, the bias level subtraction is more complicated, as this step also removes the 1/f bias striping noise. To overcome read noise fluctuations, all of the pre-scan pixels are used, not just those in columns 20–24 where the bias level has stabilized.

The procedure first computes a robust average bias using all of the pixels in columns 20–24 (inclusive) in each amplifier's prescan region. This constant is subtracted from each amplifier's pixels.

The next step is to remove the bias settling feature at the beginning of the prescan row, that occurs after the parallel shift. This trend is different for each amplifier, but is very stable and can be removed with high fidelity by subtracting, column by column, the robust average of the 2048 pixels in each prescan column.

With all the prescan pixels normalized in this way, the next step is estimation and removal of the bias striping noise. This noise is highly consistent along rows, and is also highly consistent among the four amplifiers. For each of the 2048 rows, the 24 pixels from each of the four amplifiers' prescans are combined for a total of 96 estimates of the systematic 1/f noise residual. The robust average of these 96 pixels is then subtracted from the corresponding row of all four amplifier quadrants. The striping correction has a read noise-driven uncertainty of 0.4 e¯, compared with the highly stable 0.9 e¯ standard deviation of the striping noise. A more accurate removal of the striping noise may be possible outside calacs by using the entire image region rather than only the prescan. Please refer to the ACS web page about de-striping for additional information, as well as the documentation for acstools, and see Example 5 in Section 3.5.2.

In summary, the net bias level correction for each science pixel in the post-SM4 WFC full frame images is the sum of the average bias from that amplifier plus an additional correction for the striping noise in the pixel's particular row. This prescan-based striping correction is only possible for full frame mode; subarray modes contain too few prescan pixels in each row to estimate the striping correction with sufficient precision.

doFullWellSat - Full-well saturated pixels flagging

• Header switch: None
• Header keywords updated: None
• Reference file keyword (file type, suffix): SATUFILE (FITS image, sat.fits).

 doFullWellSat flags full-well saturated pixels with the value 256 in the DQ array of WFC and HRC images. It does this by comparing the science image pixel values with the values in the full-well saturation level pixel map. See ACS ISR 2020-02 for more details.

doNoise - Error Array Initialization

• Header switch: None
• Header keywords updated: None
• Reference file keyword (file type, suffix): CCDTAB (FITS table, ccd.fits)

Input raw.fits images delivered by Generic Conversion will contain a null error (ERR) array, defined by the header keywords NPIX1³, NPIX2³ and PIXVALUE,³ where PIXVALUE = 0.

If this ERR array has already been expanded in prior processing and contains values other than zero, doNoise does nothing. Otherwise, calacs initializes the array and the doNoise function assigns a simple noise model to the ERR array.

The noise model reads the science array and calculates the error value σ (in units of electrons) for each pixel. For non-bias exposures:

For bias exposures:

The algorithms shown above are used for initializing the ERR array for the CCDs (Eqs. 1 and 2) and MAMA (Eq. 3) observations.

For CCD observations: prior to SM4, there was a negligible gradient in the bias, therefore a constant value was used for the bias variable in the noise equation. However, for post-SM4 processing, the bias variable now also incorporates the bias gradient as given in the corresponding bias calibration image.

The doNoise function is called later as part of acs2d to process the SBC data because MAMA data is not processed by acsccd.

The "CCD Characteristics Table" reference file, recorded in the image header keyword CCDTAB, is used to determine the bias (for certain subarrays only), gain, and read noise values for an observation, and for use in calculating error values (σ_CCD) for the ERR array. The table columns are

• CCDAMP: every possible configuration of the amplifiers used for readout.
• CCDCHIP: the chip being read out.
• CCDGAIN: the commanded gain.
• CCDBIASA, CCDBIASB, CCDBIASC, CCDBIASD: the commanded bias level of the amplifiers.
• BINAXIS1, BINAXIS2: the pixel bin sizes.

The CCDTAB reference table uses these commanded values to determine an observation's physical readout characteristics that are written to the flt.fits/flc.fits calibration file. For instance, read noise values for each amplifier are populated in header keywords READNSEA, READNSEB, READNSEC, and READNSED; A-to-D gain in ATODGNA, ATODGNB, ATODGNC, and ATODGND; bias voltage offset values in CCDOFSTA, CCDOFSTB, CCDOFSTC, and CCDOFSTD).

doSink - Sink pixels flagging

• Header switch: SINKCORR
• Header keywords updated: None
• Reference file keyword (file type, suffix): SNKCFILE (FITS image, snk.fits).

 doSink flags sink pixels, as well as adjacent affected pixels, with the value 1024 in the DQ array of WFC images. See Section 4.3.4 for a description of sink pixels. A sink pixel reference image is created for each anneal cycle after January 2015. This reference image encodes the locations of the sink pixels, trailing low pixels, and excessively high downstream pixels, as well as information relevant to flagging the correct number of trailing pixels based on the background level in a science image (see ACS ISR 2017-01 for more details). The reference image in the header keyword SNKCFILE is assigned based on the DETECTOR keyword and the observation date of the science image. All WFC images taken after January 2015 will have doSink performed.

Final Output From acsccd

Upon completion of acsccd, the prescan and overscan regions will be trimmed from the image when it is written out, but only if doBlev is performed successfully. Otherwise, the full image array will be written out.

3.4.2 acscte - Pixel-Based CTE Corrections 

• Header switch: PCTECORR
• Header keyword added or updated: CTE_VER, CTE_NAME, CTEDATE0, CTEDATE1, PCTENFOR, PCTENPAR, PCTETLEN, FIXROCR, PCTEFRAC, PCTERNOI, PCTETRSH, PCTENSM
• Reference file keyword (file type, suffix): PCTETAB (FITS table, cte.fits)

For all WFC exposures, except bias images, the pixel-based CTE correction is applied between the acsccd and acs2d steps, after BLEVCORR. Parameters characterizing the CTE correction are stored in a reference table, PCTETAB, and also in SCI image headers. As long as PCTECORR is set to PERFORM and the correct reference file or parameters are provided, CTE loss correction is also available for a WFC 2K subarray of the old format or any WFC subarray of the new format. However, due to uncorrected striping in all WFC subarrays, PCTECORR is set to OMIT by default in the pipeline for all subarrays. To perform CTE loss correction for an eligible WFC subarray, please set PCTECORR to PERFORM in the image header and use the acs_destripe_plus task in acstools to de-stripe the data. Then CTE correction will be performed. Upon completion, a CTE-corrected version of "blv_tmp.fits" (created in acsccd), named "blc_tmp.fits," is created. Both files are passed to acs2d for further processing. (Please see Example 5 in Section 3.5.2 for a worked example.)

The ACS CTE-correction algorithm has been updated to a "generation 2" version. Due to the time-consuming nature of this algorithm, the parallel processing option is available and enabled by default. Details regarding the earlier "generation 1" correction are available in ACS ISRs 2010-03 and 2012-03. See ACS ISR 2018-04 for a description of the most up-to-date pixel-based CTE correction model. For details on the pixel-based CTE correction software, see the documentation on the acstools task acscte, which runs the CALACS step PCTECORR. 

3.4.3 acsrej

• Header switch (in flt.fits/flc.fits, crj.fits/crc.fits images): CRCORR
• Header keywords updated (in crj.fits/crc.fits image): TEXPTIME, SKYSUM, EXPEND, REJ_RATE, EXPTIME, NCOMBINE, ROOTNAME
• Header keywords added or updated (in crj.fits/crc.fits image): INITGUES, SKYSUB, CRSIGMAS, MEANEXP, CRRADIUS, CRTHRESH, SCALENSE, CRMASK, NEXTEND
• Reference file keyword (file type, suffix): CRREJTAB (FITS table, crr.fits)

acsrej, the cosmic ray rejection task in calacs, combines "CR-SPLIT" exposures and repeated sub-exposures in an exposure, into a single image, free of cosmic rays. The task uses the same statistical detection algorithm developed for STIS data (ocrrej) and WFPC2 data (crrej), providing a well-tested and robust procedure. The parameters used by acsrej are obtained from the "Cosmic Ray Rejection Table" (named in header keyword CRREJTAB), and depend on the type of chip, number of "CR-SPLIT" or repeated sub-exposure images, and exposure time of each image.

To maintain backward compatibility (in order to use existing rejection parameter values), although input data are now in electrons and not DN, it is converted back to DN within this task prior to rejection, then back to electrons.

First, acsrej will compute the sky background using the mode of each image. Sky subtraction is performed before any statistical checks are made for cosmic rays. Next, acsrej constructs an initial comparison image from each input exposure. The comparison image can either be a median- or minimum-value sky-subtracted image constructed from all the input images, and represents the "first guess" of a cosmic ray-free image. This comparison image serves as the basis for determining the statistical deviation of each pixel from the input image.

A detection threshold is then calculated for each pixel based on the comparison image. This threshold is equal to a constant times sigma squared, given in the equation below:

where:

• σ is the sigma value used as the detection limit,
• scale is the scale factor for the noise model,
• Τ_n is the exposure time (in sections) for the input image, and
• pix(x,y) is the sky-subtracted pixel value (in electrons/sec) from the median, or minimum, combined comparison image.

The actual cosmic ray detection criteria at each pixel is determined as:

where:

• pix_n(x,y) is the pixel value (in DN) from input image n,
• sky_n is the sky background (in DN) of image n, and
• median_n(x,y) is the median or minimum pixel value (in DN/sec) from the comparison image.

If Δ > τ_n , the pixel is flagged as a cosmic ray in the input image's DQ array and is ignored when images are summed together. Surrounding pixels within a given expansion radius are marked as "spill" pixels and are given less stringent detection thresholds.

When all input images have been processed, the values of the acceptable pixels are summed over all input images. Each pixel in the summed output array is then scaled by the total exposure time:

where:

• Τ_n is the exposure time for image n,
• m_n(x,y) is the mask value (0 for CR-rejected pixels, 1 for good data) for image n at pixel (x, y),
• Τ is the total exposure time (regardless of whether all input images were used for that particular pixel). This corresponds to the header keyword values TEXPTIME and EXPTIME.

If the pixel is CR-rejected in all input images, pixout(x,y) is the sum of sky_n values computed for each input image. The DQ flag for this pixel is 8192 (Table 3.4).

The following crj.fits/crc.fits image keywords are derived from the variables in this computation:

• TEXPTIME = EXPTIME = T
• SKYSUM = $//<![CDATA[ \begin{array}{l}\Sigma_n \mathrm{sky}_n\end{array} //]]>$
• REJ_RATE = $//<![CDATA[ \begin{array}{l}\Sigma_n T_n m_n(x,y)/T\end{array} //]]>$ averaged over all pixels
• NCOMBINE = n

The remaining keywords EXPSTART and EXPEND are updated based on the input image headers.

In summary, the cosmic ray rejection task sums all accepted pixel values, computes the true exposure time for that pixel, and scales the sum to correspond to the total exposure time. The final scaled, cleaned pixel is written to the comparison image to be used for the next iteration. This process is then repeated with successively less stringent detection thresholds, as specified by the crj.fits/crc.fits image header keyword CRSIGMAS. Further processing by calacs will scale the pixout(x,y) array by the gain, resulting in the summed, cosmic ray eliminated, but not sky-subtracted product (crj.fits/crc.fits) in units of electrons.

Cosmic Ray Rejection Table

acsrej uses the "Cosmic Ray Rejection Parameter Table" (header keyword CRREJTAB) to determine the number of iterations for cosmic ray rejection, the sigma levels to use for each iteration, and the spill radius to use during detection. This allows the rejection process to be tuned to each detector, with suitable defaults being applied during pipeline processing. Observers may fine-tune the cosmic ray rejection parameters when manually reprocessing data with acsrej by editing the CRREJTAB reference table.

The CRREJTAB reference file contains the basic parameters necessary for performing cosmic ray rejection. The column names and default values for the CRREJTAB are given in Table 3.5. The appropriate row is selected based on the chip being processed (CCDCHIP), the number of images into which the exposure was split ("CR-SPLIT" Phase II optional parameter), and the exposure time of each "CR-SPLIT" image (MEANEXP). The sky fitting algorithm is controlled by the parameter SKYSUB which can have values of "mode" or "none". The "first guess" CR-combined image is then created using the median or minimum value of the input exposures, as specified by the table column INITGUES.

Table 3.5: Columns in Cosmic Ray Rejection Parameters Table

Cosmic ray detection requires the specification of a threshold above which a pixel value is considered a cosmic ray. This threshold, defined earlier as τ_n = σ² × constant, uses the sigma rejection thresholds σ that correspond to the column CRSIGMAS in the CRREJTAB reference file. The table column SCALENSE is a multiplicative term (in percent) for the noise model and is given as scale in the threshold equation. This term can be useful when the pointing of the telescope has changed by a small fraction of a pixel between images. Under such circumstances, the undersampling of the image by the CCD will cause stars to be rejected as cosmic rays if a scale noise term is not included. This is a crude but effective step taken to satisfy the maxim of "first do no harm." However, for cases in which there have been no frame-to-frame offsets, or if the image is locally well-sampled, this will unduly bias against rejecting cosmic rays.

Pixels within a given radius of a cosmic ray, specified in the table column CRRADIUS, will also be treated as cosmic rays. A less stringent rejection threshold, CRTHRESH, can be used for detecting pixels adjacent to a cosmic ray. As in CRSIGMAS, CRTHRESH is also given as a sigma value. If CRTHRESH is exceeded, pixels within a defined radius of the cosmic ray will also be flagged. All pixels determined to be affected by a cosmic ray will have their DQ values set to 8192, as described in Table 3.4.

The pipeline adopts a conservative value for SCALENSE to avoid doing harm. In recalibrating several frames for a new cosmic ray elimination, it would be advisable to determine the full range of relative x,y offsets. An appropriate value of SCALENSE is 100*(maximum offset in pixels), thus if the full offset range was 0.1 pixels an appropriate SCALENSE is 10.0. To alter this value, one may edit the CRREJTAB table (calibration file with the extension crr.fits). The number of exposures obtained in a repeated observation set can be larger than the maximum "CR-SPLIT=8" allowed in Phase II proposals.

For instance, in CAL/ACS program 9662, 14 individual HRC exposures of duration 1.0 sec. were obtained at the same pointing. A check of relative offsets showed that a shift of about 0.2 pixels occurred between the first and last exposures. To obtain a crj.fits combined image of all 14 inputs at 1.0s and with better sensitivity to cosmic ray elimination than provided by the conservative default of SCALENSE = 30.0, the following should be done:

1. Create a new asn.fits table with one EXP-CRJ entry for each of the 14 raw 1.0s images, and an appropriately named PROD-CRJ file line.
2. Edit the crr.fits table adding a line with a "CR-SPLIT" value of 14, and a SCALENSE value of 20.0.
3. Given such a large number of inputs it would also make sense here to change the INITGUES value to "median."
4. Then rerun calacs on the new association table with 14 entries to obtain a crj.fits extension image based on the full stack of 1.0s images.

For a detailed discussion on manually recalibrating ACS data, please see Section 3.5.

3.4.4 acs2d

Every observation, whether taken with the MAMA or CCD detectors, will be processed by acs2d. The primary functions of the task, listed in Table 3.6, include, but are not limited to dark current subtraction, flat-fielding, and photometric keyword calculations. acs2d contains the same data quality and error array initialization functions used in acsccd, but acs2d will check to ensure that the array initialization is not performed twice on CCD data. Calibration switches in the image header control the performance of the remaining calibration functions, with MAMA-specific functions being initiated only when the relevant calibration switches are set.

Table 3.6: The Functions Performed in acs2d (in Operational Order)

doDQI – Bad Pixel Determination

• Header switch: DQICORR
• Header keywords updated: None
• Reference file keyword (file type, suffix): BPIXTAB (FITS table, bpx.fits)

If the DQICORR header keyword switch is set to COMPLETE (e.g., for CCD data), this step is skipped. Otherwise, the same initialization is performed as described in "doDQI – Bad Pixel Determination" for acsccd.

doNonLin – Linearity Correction for MAMA Data

• Header switch: LFLGCORR, GLINCORR
• Header keyword updated: GLOBLIM
• Reference file keyword (file type, suffix): MLINTAB (FITS table, lin.fits)

This routine flags global and local nonlinearity in ACS MAMA observations; the term "global" refers to the entire ACS MAMA detector, while "local" refers to an individual detector pixel. The MAMA Linearity Table, MLINTAB, provides the basic parameters for determining linearity.

The global limit (header keyword GLOBAL_LIMIT) column in this table refers to the total count rate at which the data are affected by greater than 10% non-linearity across the detector.

calacs attempts to correct for non-linearity up to the global limit using the non-linearity time constant in the column TAU. The global linearity correction is computed for every pixel below the global linearity limit specified by iteratively solving the equation n = Ne^(-τN) to get the true count rate N.

The local limit (header keyword LOCAL_LIMIT) can actually be much higher than the global limit and is difficult to correct using a simple algorithm. Each pixel found to exceed this limit will simply be marked as non-linear in the DQ file. This DQ flag will be extended by a fixed radius from the original pixel, given in the EXPAND column and is currently set to 2 pixels.

If the LFLGCORR switch is set to PERFORM, acs2d will flag excessive global and local nonlinearity in the DQ array. If GLINCORR is set to PERFORM, it will correct excessive global nonlinearity in the SCI array, if it is not too large. If the global linearity limit is exceeded, the keyword GLOBLIM in the SCI extension header will be set to EXCEEDED. Otherwise, it will have the value NOT-EXCEEDED.

doNoise - Error Array Initialization

• Header switch: None
• Header keywords updated: None
• Reference file keyword (file type, suffix): None

acs2d checks the image error array (ERR) to determine if there are non-zero values that were created from previous processing steps. If all pixel values are zero, indicating no prior calibration steps were performed, acs2d runs the same initializations described in "doNoise – Error Array Initialization" for acsccd. However, if the input image's ERR array has non-zero values, indicating processing in earlier calibration steps, the doNoise function in acs2d does not change the ERR array.

doDark – Dark Image Subtraction

• Header switch: DARKCORR
• Header keyword updated: MEANDARK
• Reference file keyword (file type, suffix): DARKFILE (image in electrons/sec., drk.fits), DRKCFILE (image in electrons/sec, dkc.fits)

For the SBC, the header switch DARKCORR is set to OMIT because the SBC dark count rate is so negligible that corrections are not needed, even for long exposures.

For CCD data, the dark reference file image (in electrons/sec) is multiplied by the DARKTIME header keyword of the input image. DARKTIME is calculated from the timings in the unique data log (UDL) and corresponds to the sum of exposure time, post-flash duration (if applicable), and commanding overheads. Commanding overheads are typically 3-6 seconds. This scaled dark reference image is subtracted from the input image in memory. The mean dark value is then computed from the scaled dark image and used to update the MEANDARK keyword in the SCI image header. Any dark accumulation during readout time is automatically included in the bias image reference file (BIASFILE), and already removed during the doBias step in acsccd.

Dark and CTE-corrected dark reference files are regularly created⁴ after each anneal, and consist of the combination of 1000.5 second (long) and 0.5 second (short) dark frames taken every Monday, Wednesday, and Friday throughout the anneal period. These individual dark frames are bias-corrected and combined with cosmic ray rejection. Since 2015, dark frames have been flashed to better remove CTE loss effects on warm and hot pixels. Thus these darks are also flash corrected using a flash reference file (FLSHFILE).

Only hot pixels above a certain threshold (this number changes with time and is currently set at 0.14 e¯/sec) are identified with the flag 16 in the data quality (DQ) array of WFC and HRC reference darks; this flag value is propagated to the DQ array of the calibrated science data. Flag 32 marks pixels that are unstable. This includes pixels affected by random telegraph signal (RTS) noise, as described in ACS ISR 2017-05, and fading hot pixels, described in ACS ISR 2022-07. We only exclude pixels that are unstable in the subsequent processing steps because stable pixels can be properly calibrated.  The many "warm" pixels below this threshold are assumed to be adequately corrected by the dark calibration. This produces a high signal-to-noise reference file which accurately reflects (and corrects/flags) the hot pixels present for a given observation date. The "best" dark reference file is typically not available in the pipeline for several weeks after the date of observation, because it takes a few weeks to collect enough frames to make a superdark (see ACS ISR 2004-07 for more information).

The default reference files for dark subtraction, given in the header keywords DARKFILE and DRKCFILE, are assigned based on the values of the keywords DETECTOR, CCDAMP, CCDGAIN, and EXPSTART in the image header. The dark correction is applied after the overscan regions are trimmed from the input science image. As in the bias image correction (BIASFILE), calacs assumes that the images have not been binned, so any input image smaller than the full detector size will be interpreted as a subarray image. The reference file named by the DRKCFILE header keyword is the CTE-corrected version of the dark reference file named by the DARKFILE keyword, and it's only used in WFC image calibrations when pixel-based CTE correction is performed.

doFlash – Post-Flash Subtraction

• Header switch: FLSHCORR
• Header keyword updated: MEANFLSH
• Reference file keyword (file type, suffix): FLSHFILE (image in counts, fls.fits)

ACS has a post-flash capability to provide the means of mitigating the effects of charge transfer efficiency degradation. The proposer controls the use of this capability via the "FLASHEXP" optional parameter in the Phase II proposal. This is available for HRC and WFC full frame images using shutter positions A or B.

The reference file, named in the header keyword FLSHFILE, has the same dimensions as a full-size science image, 1062 × 1044 for HRC and 4096 × 2048 for WFC, allowing for simple image arithmetic on arrays of equal size. The appropriate FLSHFILE reference image is selected using the following keywords from the image header: DETECTOR, CCDAMP, CCDGAIN, FLASHCUR, and SHUTRPOS.

The function doFlash will subtract the post-flash in the following way:

1. The success of the post-flash exposure is verified by checking the header keyword FLASHSTA, which should be set to SUCCESSFUL. If any problems were encountered, a comment will be added to the HISTORY keywords in the SCI extension image header.
2. The FLSHFILE reference image, which is normalized to one second for the appropriate post-flash current level (LOW, MED, HIGH, given by the FLASHCUR keyword), is multiplied by the flash duration in seconds (given in the header keyword FLASHDUR) and subtracted from the science image.
3. Finally, the mean value of the scaled post-flash image is written to the output SCI extension image header as the keyword MEANFLSH.

doFlat – Flat-Field Image(s) Correction

• Header switch: FLATCORR
• Header keywords updated: None
• Reference files keywords (file type, suffix): PFLTFILE (image in fractional units, pfl.fits), LFLTFILE (lfl.fits), DFLTFILE (dfl.fits), CFLTFILE (cfl.fits)

The ACS doFlat routine corrects for pixel-to-pixel and large-scale sensitivity gradients across the detector by dividing the data with the flat-field image. (Conversion to electrons no longer depends on doFlat, as it did in the past.)

Because of geometric distortion effects, the area of the sky seen by a given pixel is not constant, and therefore, observations of a constant surface brightness object will have count rates per pixel that vary over the detector, even if every pixel has the same sensitivity. In order to produce images that appear uniform for uniform illumination, the flat fields make an implicit correction for the geometric distortion across the field that is equivalent to dividing each pixel by the optical distortion which is normalized to unity at the center of the field. A consequence of this procedure is that two stars of equal brightness do not have the same total counts after the flat-fielding step. Thus, point source photometry extracted from a flat-fielded image must be multiplied by the effective pixel area map, as shown in Figure 5.1.

Geometric distortion corrections are also implemented in the pipeline by AstroDrizzle which uses the geometric distortion solution to correct all pixels to equal areas. Thus, in drizzled images, photometry is correct for both point and extended sources.

The flat-field image used to correct the data is created using up to four flat-field reference files: the pixel-to-pixel file (PFLTFILE), the low-order flat (LFLTFILE), the delta flat (DFLTFILE), and for HRC, the coronagraphic spot flat (CFLTFILE).

• The PFLTFILE is a pixel-to-pixel flat-field correction file containing the small scale flat-field variations.
• The LFLTFILE is a low-order flat which will correct for any large-scale flat-field variations across each detector. This file is stored as a binned image which is expanded when it's applied by calacs.
• The DFLTFILE is a delta-flat containing any needed changes to the small-scale PFLTFILE.
• The CFLTFILE is a spot mask which contains the vignetting patterns of the HRC occulting spots and is applied to coronagraphic observations only.

If the LFLTFILE, DFLTFILE, or CFLTFILE reference images are not specified in the SCI image header, only the PFLTFILE is used for the flat-field correction. If all four reference files are specified, they are multiplied together to form a complete flat-field correction image which is then applied to the science data.

Currently, the LFLTFILE and DFLTFILE flats are not used for ACS data. The PFLTFILE reference flat in the pipeline is actually a combination of the pixel-to-pixel flats taken during the ground calibration and the low-order flat correction derived in-flight. The CFLTFILE is applied only when the OBSTYPE image header keyword is equal to CORONAGRAPHIC.

All flat-field reference images will be chosen based on DETECTOR, CCDAMP, FILTER1, FILTER2, and OBSTYPE keywords of a given observation. Any subarray science image will use the same reference file as a full-size image. calacs will extract the appropriate region from the reference file and apply it to the subarray input image.

doShad – Shutter Shading File Correction (skipped)

• Header switch: SHADCORR
• Header keywords updated: None
• Reference file keyword (file type, suffix): SHADFILE (image, shd.fits)

The doShad routine would apply the shutter shading correction image (named in image header keyword SHADFILE) to the science data if the SHADCORR header keyword switch were set to PERFORM. However, the SHADCORR calibration switch is currently set to OMIT and is unlikely to be used in future versions of calacs. Calibration data show that a shading correction is not needed for ACS data. For more information, refer to ACS ISR 2003-03.

doPhot – Photometry Keyword Calculation

• Header switch: PHOTCORR
• Header keywords updated: PHOTMODE, PHOTFLAM, PHOTZPT, PHOTPLAM, PHOTBW
• Reference files keywords (file types, suffixes): IMPHTTAB (FITS table, imp.fits)

Before photometry can be performed on ACS observations, a transformation from electrons to absolute flux units must be performed. For a given instrument configuration, as described in the PHOTMODE header keyword, calacs uses the IMPHTTAB⁵ reference look-up table to determine the total throughput of an observing mode (linear interpolation is done using pre-computed values when necessary).

Users who wish to convert calibrated images (in units of electrons) to flux units may simply divide the image by the exposure time and then multiply by the PHOTFLAM keyword value. Drizzled images are already in units of electrons per second and may simply be multiplied by the PHOTFLAM value in the drizzled image header to create an image in flux units.

doStat – Image Statistics Determination

• Header switch: None
• Header keywords updated: NGOODPIX, GOODMIN, GOODMAX, GOODMEAN, SNRMIN, SNRMAX, SNRMEAN
• Reference files keywords (file types, suffixes): None

This routine computes the number of pixels which are flagged as "good" in the data quality array. The minimum, mean, and maximum pixel values are then calculated for data flagged as "good" in both the science and error arrays. Similarly, the minimum, mean, and maximum signal-to-noise of "good" pixels is derived for the science array. These quantities are updated in the image header.

3.4.5 acssum

• Header switch: RPTCORR
• Header keywords updated: NCOMBINE, EXPTIME, EXPEND, ROOTNAME
• Reference files keywords (file types, suffixes): None

Multiple exposures of SBC MAMA data obtained using the Phase II repeated sub-exposures specification are flagged in the association table for summing by acssum. A straight pixel-to-pixel addition of the science values is applied, and the error calculated as the square root of the sum of the squares of the errors in the individual exposures. The calibration switch RPTCORR is set to COMPLETE upon successful completion of the summation. In addition, the keywords NCOMBINE, EXPTIME, and EXPEND are adjusted to reflect the total of the summed images.

¹ In full-frame mode, each WFC CCD is read out from adjacent corners by two amplifiers, as two 2072 column × 2068 row arrays. Each row has 24 columns of physical prescan followed by 2048 columns of pixel data. Each column has 2048 rows of pixel data followed by 20 rows of virtual overscan. The HRC full read out is a 1062 × 1044 array: 19 columns of physical overscan followed by 1024 columns of pixel data, then another 19 columns of physical overscan. Each column consists of 1024 rows of pixel data followed by 20 rows of virtual overscan.

² Here, the asterisk is used as a wildcard, following the UNIX convention.

³ These keywords only appear in Data Quality (DQ) and Error (ERR) extensions of raw images.

⁴ The cadence of dark reference file creation has changed over time. For current information about the frequency at which darks are delivered to CRDS, as well as more in depth information about their creation, visit the ACS Anneal Dates webpage.

⁵ The IMPHTTAB reference tables, one each for HRC, SBC, and WFC, contain pre-computed values of the photometry keywords for all observations.