computeExposureSummaryStats.py

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# This file is part of pipe_tasks.
#
# Developed for the LSST Data Management System.
# This product includes software developed by the LSST Project
# (https://www.lsst.org).
# See the COPYRIGHT file at the top-level directory of this distribution
# for details of code ownership.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
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__all__ = ["ComputeExposureSummaryStatsTask", "ComputeExposureSummaryStatsConfig"]
 
import warnings
import numpy as np
from scipy.stats import median_abs_deviation as sigmaMad
import astropy.units as units
from astropy.time import Time
from astropy.coordinates import AltAz, SkyCoord, EarthLocation
from lsst.daf.base import DateTime
 
import lsst.pipe.base as pipeBase
import lsst.pex.config as pexConfig
import lsst.afw.math as afwMath
import lsst.afw.image as afwImage
import lsst.geom as geom
from lsst.meas.algorithms import ScienceSourceSelectorTask
from lsst.meas.algorithms.computeExPsf import ComputeExPsfTask
from lsst.utils.timer import timeMethod
import lsst.ip.isr as ipIsr
 
 
class ComputeExposureSummaryStatsConfig(pexConfig.Config):
    """Config for ComputeExposureSummaryTask"""
    sigmaClip = pexConfig.Field(
        dtype=float,
        doc="Sigma for outlier rejection for sky noise.",
        default=3.0,
    )
    clipIter = pexConfig.Field(
        dtype=int,
        doc="Number of iterations of outlier rejection for sky noise.",
        default=2,
    )
    badMaskPlanes = pexConfig.ListField(
        dtype=str,
        doc="Mask planes that, if set, the associated pixel should not be included sky noise calculation.",
        default=("NO_DATA", "SUSPECT"),
    )
    starSelection = pexConfig.Field(
        doc="Field to select full list of sources used for PSF modeling.",
        dtype=str,
        default="calib_psf_used",
    )
    starSelector = pexConfig.ConfigurableField(
        target=ScienceSourceSelectorTask,
        doc="Selection of sources to compute PSF star statistics.",
    )
    starShape = pexConfig.Field(
        doc="Base name of columns to use for the source shape in the PSF statistics computation.",
        dtype=str,
        default="slot_Shape"
    )
    psfShape = pexConfig.Field(
        doc="Base name of columns to use for the PSF shape in the PSF statistics computation.",
        dtype=str,
        default="slot_PsfShape"
    )
    starHigherOrderMomentBase = pexConfig.Field(
        doc="Base name of the columns from which to obtain the higher-order moments.",
        dtype=str,
        default="ext_shapeHSM_HigherOrderMomentsSource",
    )
    psfSampling = pexConfig.Field(
        dtype=int,
        doc="Sampling rate in pixels in each dimension for the maxDistToNearestPsf metric "
        "caclulation grid (the tradeoff is between adequate sampling versus speed).",
        default=8,
    )
    psfGridSampling = pexConfig.Field(
        dtype=int,
        doc="Sampling rate in pixels in each dimension for PSF model robustness metric "
        "caclulations grid (the tradeoff is between adequate sampling versus speed).",
        default=96,
    )
    minPsfApRadiusPix = pexConfig.Field(
        dtype=float,
        doc="Minimum radius in pixels of the aperture within which to measure the flux of "
        "the PSF model for the psfApFluxDelta metric calculation (the radius is computed as "
        "max(``minPsfApRadius``, 3*psfSigma)).",
        default=2.0,
    )
    psfApCorrFieldName = pexConfig.Field(
        doc="Name of the flux column associated with the aperture correction of the PSF model "
        "to use for the psfApCorrSigmaScaledDelta metric calculation.",
        dtype=str,
        default="base_PsfFlux_instFlux"
    )
    psfBadMaskPlanes = pexConfig.ListField(
        dtype=str,
        doc="Mask planes that, if set, the associated pixel should not be included in the PSF model "
        "robutsness metric calculations (namely, maxDistToNearestPsf and psfTraceRadiusDelta).",
        default=("BAD", "CR", "EDGE", "INTRP", "NO_DATA", "SAT", "SUSPECT"),
    )
    fiducialSkyBackground = pexConfig.DictField(
        keytype=str,
        itemtype=float,
        doc="Fiducial sky background level (ADU/s) assumed when calculating effective exposure time. "
        "Keyed by band.",
        default={"u": 1.0, "g": 1.0, "r": 1.0, "i": 1.0, "z": 1.0, "y": 1.0},
    )
    fiducialPsfSigma = pexConfig.DictField(
        keytype=str,
        itemtype=float,
        doc="Fiducial PSF sigma (pixels) assumed when calculating effective exposure time. "
        "Keyed by band.",
        default={"u": 1.0, "g": 1.0, "r": 1.0, "i": 1.0, "z": 1.0, "y": 1.0},
    )
    fiducialZeroPoint = pexConfig.DictField(
        keytype=str,
        itemtype=float,
        doc="Fiducial zero point assumed when calculating effective exposure time. "
        "Keyed by band.",
        default={"u": 25.0, "g": 25.0, "r": 25.0, "i": 25.0, "z": 25.0, "y": 25.0},
    )
    fiducialReadNoise = pexConfig.DictField(
        keytype=str,
        itemtype=float,
        doc="Fiducial readnoise (electrons) assumed when calculating effective exposure time. "
        "Keyed by band.",
        default={"u": 9.0, "g": 9.0, "r": 9.0, "i": 9.0, "z": 9.0, "y": 9.0},
    )
    fiducialExpTime = pexConfig.DictField(
        keytype=str,
        itemtype=float,
        doc="Fiducial exposure time (seconds). "
        "Keyed by band.",
        default={"u": 30.0, "g": 30.0, "r": 30.0, "i": 30.0, "z": 30.0, "y": 30.0},
    )
    fiducialMagLim = pexConfig.DictField(
        keytype=str,
        itemtype=float,
        doc="Fiducial magnitude limit depth at SNR=5. "
        "Keyed by band.",
        default={"u": 25.0, "g": 25.0, "r": 25.0, "i": 25.0, "z": 25.0, "y": 25.0},
    )
    maxEffectiveTransparency = pexConfig.Field(
        dtype=float,
        doc="Maximum value allowed for effective transparency scale factor (often inf or 1.0).",
        default=float("inf")
    )
    magLimSnr = pexConfig.Field(
        dtype=float,
        doc="Signal-to-noise ratio for computing the magnitude limit depth.",
        default=5.0
    )
    psfTE1 = pexConfig.ConfigurableField(
        target=ComputeExPsfTask,
        doc="Use treecorr for computing scalar value of TE1.",
    )
    psfTE2 = pexConfig.ConfigurableField(
        target=ComputeExPsfTask,
        doc="Use treecorr for computing scalar value of TE2.",
    )
    psfTE3 = pexConfig.ConfigurableField(
        target=ComputeExPsfTask,
        doc="Use treecorr for computing scalar value of TE3.",
    )
    psfTE4 = pexConfig.ConfigurableField(
        target=ComputeExPsfTask,
        doc="Use treecorr for computing scalar value of TE4.",
    )
 
    def setDefaults(self):
        super().setDefaults()
 
        self.starSelector.setDefaults()
        self.starSelector.doFlags = True
        self.starSelector.doSignalToNoise = True
        self.starSelector.doUnresolved = False
        self.starSelector.doIsolated = False
        self.starSelector.doRequireFiniteRaDec = False
        self.starSelector.doRequirePrimary = False
 
        self.starSelector.signalToNoise.minimum = 50.0
        self.starSelector.signalToNoise.maximum = 1000.0
 
        self.starSelector.flags.bad = ["slot_Shape_flag", "slot_PsfFlux_flag"]
        # Select stars used for PSF modeling.
        self.starSelector.flags.good = ["calib_psf_used"]
 
        self.starSelector.signalToNoise.fluxField = "slot_PsfFlux_instFlux"
        self.starSelector.signalToNoise.errField = "slot_PsfFlux_instFluxErr"
 
        min_theta = [1e-6, 5.0, 1e-6, 5.0]
        max_theta = [1.0, 100.0, 5.0, 20.0]
        psfTEx = [
            self.psfTE1,
            self.psfTE2,
            self.psfTE3,
            self.psfTE4,
        ]
 
        for tex, mint, maxt in zip(psfTEx, min_theta, max_theta):
            tex.setDefaults()
            tex.treecorr.min_sep = mint / 60.0
            tex.treecorr.max_sep = maxt / 60.0
            tex.treecorr.nbins = 1
            tex.treecorr.bin_type = "Linear"
            tex.treecorr.sep_units = "degree"
 
    def fiducialMagnitudeLimit(self, band, pixelScale, gain):
        """Compute the fiducial point-source magnitude limit based on config values.
        This follows the conventions laid out in SMTN-002, LSE-40, and DMTN-296.
 
        Parameters
        ----------
        band : `str`
            The band of interest
        pixelScale : `float`
            The pixel scale [arcsec/pix]
        gain : `float`
            The instrumental gain for the exposure [e-/ADU]. The gain should
            be 1.0 if the image units are [e-].
 
        Returns
        -------
        magnitude_limit : `float`
            The fiducial magnitude limit calculated from fiducial values.
        """
        nan = float("nan")
 
        # Fiducials from config
        fiducialPsfSigma = self.fiducialPsfSigma.get(band, nan)
        fiducialSkyBackground = self.fiducialSkyBackground.get(band, nan)
        fiducialZeroPoint = self.fiducialZeroPoint.get(band, nan)
        fiducialReadNoise = self.fiducialReadNoise.get(band, nan)
        fiducialExpTime = self.fiducialExpTime.get(band, nan)
        magLimSnr = self.magLimSnr
 
        # Derived fiducial quantities
        fiducialPsfArea = psf_sigma_to_psf_area(fiducialPsfSigma, pixelScale)
        fiducialZeroPoint += 2.5*np.log10(fiducialExpTime)
        fiducialSkyBg = fiducialSkyBackground * fiducialExpTime
        fiducialReadNoise /= gain
 
        # Calculate the fiducial magnitude limit
        fiducialMagLim = compute_magnitude_limit(fiducialPsfArea,
                                                 fiducialSkyBg,
                                                 fiducialZeroPoint,
                                                 fiducialReadNoise,
                                                 gain,
                                                 magLimSnr)
 
        return fiducialMagLim
 
 
class ComputeExposureSummaryStatsTask(pipeBase.Task):
    """Task to compute exposure summary statistics.
 
    This task computes various quantities suitable for DPDD and other
    downstream processing at the detector centers, including:
    - expTime
    - psfSigma
    - psfArea
    - psfIxx
    - psfIyy
    - psfIxy
    - ra
    - dec
    - pixelScale (arcsec/pixel)
    - zenithDistance
    - zeroPoint
    - skyBg
    - skyNoise
    - meanVar
    - raCorners
    - decCorners
    - astromOffsetMean
    - astromOffsetStd
 
    These additional quantities are computed from the stars in the detector:
    - psfStarDeltaE1Median
    - psfStarDeltaE2Median
    - psfStarDeltaE1Scatter
    - psfStarDeltaE2Scatter
    - psfStarDeltaSizeMedian
    - psfStarDeltaSizeScatter
    - psfStarScaledDeltaSizeScatter
 
    These quantities are computed based on the PSF model and image mask
    to assess the robustness of the PSF model across a given detector
    (against, e.g., extrapolation instability):
    - maxDistToNearestPsf
    - psfTraceRadiusDelta
    - psfApFluxDelta
 
    These quantities are computed as part of:
    https://rubinobs.atlassian.net/browse/DM-40780
 
    - psfTE1e1
    - psfTE1e2
    - psfTE1ex
    - psfTE2e1
    - psfTE2e2
    - psfTE2ex
    - psfTE3e1
    - psfTE3e2
    - psfTE3ex
    - psfTE4e1
    - psfTE4e2
    - psfTE4ex
 
    This quantity is computed based on the aperture correction map, the
    psfSigma, and the image mask to assess the robustness of the aperture
    corrections across a given detector:
    - psfApCorrSigmaScaledDelta
 
    These quantities are computed based on the shape measurements of the
    sources used in the PSF model to assess the image quality (i.e. as a
    measure of the deviation from a circular shape):
    - starEMedian
    - starUnNormalizedEMedian
 
    These quantities are computed to assess depth:
    - effTime
    - effTimePsfSigmaScale
    - effTimeSkyBgScale
    - effTimeZeroPointScale
    - magLim
    """
    ConfigClass = ComputeExposureSummaryStatsConfig
    _DefaultName = "computeExposureSummaryStats"
 
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
 
        self.makeSubtask("starSelector")
        self.makeSubtask("psfTE1")
        self.makeSubtask("psfTE2")
        self.makeSubtask("psfTE3")
        self.makeSubtask("psfTE4")
        self._isTEXComputationDone = False
 
    @timeMethod
    def run(self, exposure, sources, background, summary=None):
        """Measure exposure statistics from the exposure, sources, and
        background.
 
        Parameters
        ----------
        exposure : `lsst.afw.image.ExposureF`
        sources : `lsst.afw.table.SourceCatalog`
        background : `lsst.afw.math.BackgroundList`
        summary : `lsst.afw.image.ExposureSummary`, optional
            Summary object to be appended to if not `None`.  If `None` a new
            summary object will be created.
 
        Returns
        -------
        summary : `lsst.afw.image.ExposureSummary`
        """
        self.log.info("Measuring exposure statistics")
 
        if summary is None:
            summary = afwImage.ExposureSummaryStats()
 
        # Set exposure time.
        exposureTime = exposure.getInfo().getVisitInfo().getExposureTime()
        summary.expTime = exposureTime
 
        bbox = exposure.getBBox()
 
        psf = exposure.getPsf()
        self.update_psf_stats(
            summary, psf, bbox, sources, image_mask=exposure.mask, image_ap_corr_map=exposure.apCorrMap
        )
 
        wcs = exposure.getWcs()
        visitInfo = exposure.getInfo().getVisitInfo()
        self.update_wcs_stats(summary, wcs, bbox, visitInfo)
 
        photoCalib = exposure.getPhotoCalib()
        self.update_photo_calib_stats(summary, photoCalib)
 
        self.update_background_stats(summary, background)
 
        self.update_masked_image_stats(summary, exposure.getMaskedImage())
 
        self.update_magnitude_limit_stats(summary, exposure)
 
        self.update_effective_time_stats(summary, exposure)
 
        md = exposure.getMetadata()
        if "PSF_ADAPTIVE_THRESHOLD_VALUE" in md:
            summary.psfAdaptiveThresholdValue = md["PSF_ADAPTIVE_THRESHOLD_VALUE"]
        if "PSF_ADAPTIVE_INCLUDE_THRESHOLD_MULTIPLIER" in md:
            summary.psfAdaptiveIncludeThresholdMultiplier = md["PSF_ADAPTIVE_INCLUDE_THRESHOLD_MULTIPLIER"]
        if "REF_CAT_SOURCE_DENSITY" in md:
            summary.refCatSourceDensity = md["REF_CAT_SOURCE_DENSITY"]
        if "SFM_ASTROM_OFFSET_MEAN" in md:
            summary.astromOffsetMean = md["SFM_ASTROM_OFFSET_MEAN"]
            summary.astromOffsetStd = md["SFM_ASTROM_OFFSET_STD"]
 
        return summary
 
    def update_psf_stats(
            self,
            summary,
            psf,
            bbox,
            sources=None,
            image_mask=None,
            image_ap_corr_map=None,
            sources_is_astropy=False,
    ):
        """Compute all summary-statistic fields that depend on the PSF model.
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        psf : `lsst.afw.detection.Psf` or `None`
            Point spread function model.  If `None`, all fields that depend on
            the PSF will be reset (generally to NaN).
        bbox : `lsst.geom.Box2I`
            Bounding box of the image for which summary stats are being
            computed.
        sources : `lsst.afw.table.SourceCatalog` or `astropy.table.Table`
            Catalog for quantities that are computed from source table columns.
            If `None`, these quantities will be reset (generally to NaN).
            The type of this table must correspond to the
            ``sources_is_astropy`` argument.
        image_mask : `lsst.afw.image.Mask`, optional
            Mask image that may be used to compute distance-to-nearest-star
            metrics.
        sources_is_astropy : `bool`, optional
            Whether ``sources`` is an `astropy.table.Table` instance instead
            of an `lsst.afw.table.Catalog` instance.  Default is `False` (the
            latter).
        """
        nan = float("nan")
        summary.psfSigma = nan
        summary.psfIxx = nan
        summary.psfIyy = nan
        summary.psfIxy = nan
        summary.psfArea = nan
        summary.nPsfStar = 0
        summary.psfStarDeltaE1Median = nan
        summary.psfStarDeltaE2Median = nan
        summary.psfStarDeltaE1Scatter = nan
        summary.psfStarDeltaE2Scatter = nan
        summary.psfStarDeltaSizeMedian = nan
        summary.psfStarDeltaSizeScatter = nan
        summary.psfStarScaledDeltaSizeScatter = nan
        summary.maxDistToNearestPsf = nan
        summary.psfTraceRadiusDelta = nan
        summary.psfApFluxDelta = nan
        summary.psfApCorrSigmaScaledDelta = nan
        summary.starEMedian = nan
        summary.starUnNormalizedEMedian = nan
        summary.starComa1Median = nan
        summary.starComa2Median = nan
        summary.starTrefoil1Median = nan
        summary.starTrefoil2Median = nan
        summary.starKurtosisMedian = nan
        summary.starE41Median = nan
        summary.starE42Median = nan
 
        if psf is None:
            return
        shape = psf.computeShape(bbox.getCenter())
        summary.psfSigma = shape.getDeterminantRadius()
        summary.psfIxx = shape.getIxx()
        summary.psfIyy = shape.getIyy()
        summary.psfIxy = shape.getIxy()
        im = psf.computeKernelImage(bbox.getCenter())
        # The calculation of effective psf area is taken from
        # ls.st/srd Equation 1.
        summary.psfArea = float(np.sum(im.array)**2./np.sum(im.array**2.))
 
        if image_mask is not None:
            psfApRadius = max(self.config.minPsfApRadiusPix, 3.0*summary.psfSigma)
            self.log.debug("Using radius of %.3f (pixels) for psfApFluxDelta metric", psfApRadius)
            psfTraceRadiusDelta, psfApFluxDelta = compute_psf_image_deltas(
                image_mask,
                psf,
                sampling=self.config.psfGridSampling,
                ap_radius_pix=psfApRadius,
                bad_mask_bits=self.config.psfBadMaskPlanes
            )
            summary.psfTraceRadiusDelta = float(psfTraceRadiusDelta)
            summary.psfApFluxDelta = float(psfApFluxDelta)
            if image_ap_corr_map is not None:
                if self.config.psfApCorrFieldName not in image_ap_corr_map.keys():
                    self.log.warning(f"{self.config.psfApCorrFieldName} not found in "
                                     "image_ap_corr_map.  Setting psfApCorrSigmaScaledDelta to NaN.")
                    psfApCorrSigmaScaledDelta = nan
                else:
                    image_ap_corr_field = image_ap_corr_map[self.config.psfApCorrFieldName]
                    psfApCorrSigmaScaledDelta = compute_ap_corr_sigma_scaled_delta(
                        image_mask,
                        image_ap_corr_field,
                        summary.psfSigma,
                        sampling=self.config.psfGridSampling,
                        bad_mask_bits=self.config.psfBadMaskPlanes,
                    )
                summary.psfApCorrSigmaScaledDelta = float(psfApCorrSigmaScaledDelta)
 
        if sources is None:
            # No sources are available (as in some tests and rare cases where
            # the selection criteria in finalizeCharacterization lead to no
            # good sources).
            return
 
        # Count the total number of psf stars used (prior to stats selection).
        nPsfStar = sources[self.config.starSelection].sum()
        summary.nPsfStar = int(nPsfStar)
 
        psf_mask = self.starSelector.run(sources).selected
        nPsfStarsUsedInStats = psf_mask.sum()
 
        if nPsfStarsUsedInStats == 0:
            # No stars to measure statistics, so we must return the defaults
            # of 0 stars and NaN values.
            return
 
        if sources_is_astropy:
            psf_cat = sources[psf_mask]
        else:
            psf_cat = sources[psf_mask].copy(deep=True)
 
        starXX = psf_cat[self.config.starShape + "_xx"]
        starYY = psf_cat[self.config.starShape + "_yy"]
        starXY = psf_cat[self.config.starShape + "_xy"]
        psfXX = psf_cat[self.config.psfShape + "_xx"]
        psfYY = psf_cat[self.config.psfShape + "_yy"]
        psfXY = psf_cat[self.config.psfShape + "_xy"]
 
        # Use the trace radius for the star size.
        starSize = np.sqrt(starXX/2. + starYY/2.)
 
        starE1 = (starXX - starYY)/(starXX + starYY)
        starE2 = 2*starXY/(starXX + starYY)
        starSizeMedian = np.median(starSize)
 
        starE = np.sqrt(starE1**2.0 + starE2**2.0)
        starUnNormalizedE = np.sqrt((starXX - starYY)**2.0 + (2.0*starXY)**2.0)
        starEMedian = np.median(starE)
        starUnNormalizedEMedian = np.median(starUnNormalizedE)
        summary.starEMedian = float(starEMedian)
        summary.starUnNormalizedEMedian = float(starUnNormalizedEMedian)
 
        # Use the trace radius for the psf size.
        psfSize = np.sqrt(psfXX/2. + psfYY/2.)
        psfE1 = (psfXX - psfYY)/(psfXX + psfYY)
        psfE2 = 2*psfXY/(psfXX + psfYY)
 
        e1Residuals = starE1 - psfE1
        e2Residuals = starE2 - psfE2
 
        psfStarDeltaE1Median = np.median(e1Residuals)
        psfStarDeltaE1Scatter = sigmaMad(e1Residuals, scale='normal')
        psfStarDeltaE2Median = np.median(e2Residuals)
        psfStarDeltaE2Scatter = sigmaMad(e2Residuals, scale='normal')
 
        psfStarDeltaSizeMedian = np.median(starSize - psfSize)
        psfStarDeltaSizeScatter = sigmaMad(starSize - psfSize, scale="normal")
        psfStarScaledDeltaSizeScatter = psfStarDeltaSizeScatter/starSizeMedian
 
        summary.psfStarDeltaE1Median = float(psfStarDeltaE1Median)
        summary.psfStarDeltaE2Median = float(psfStarDeltaE2Median)
        summary.psfStarDeltaE1Scatter = float(psfStarDeltaE1Scatter)
        summary.psfStarDeltaE2Scatter = float(psfStarDeltaE2Scatter)
        summary.psfStarDeltaSizeMedian = float(psfStarDeltaSizeMedian)
        summary.psfStarDeltaSizeScatter = float(psfStarDeltaSizeScatter)
        summary.psfStarScaledDeltaSizeScatter = float(psfStarScaledDeltaSizeScatter)
 
        # Higher-order moments and derived metrics.
        if sources_is_astropy:
            columnNames = psf_cat.colnames
        else:
            columnNames = psf_cat.schema.getNames()
        if self.config.starHigherOrderMomentBase + "_03" in columnNames:
            starM03 = psf_cat[self.config.starHigherOrderMomentBase + "_03"]
            starM12 = psf_cat[self.config.starHigherOrderMomentBase + "_12"]
            starM21 = psf_cat[self.config.starHigherOrderMomentBase + "_21"]
            starM30 = psf_cat[self.config.starHigherOrderMomentBase + "_30"]
            starM04 = psf_cat[self.config.starHigherOrderMomentBase + "_04"]
            starM13 = psf_cat[self.config.starHigherOrderMomentBase + "_13"]
            starM22 = psf_cat[self.config.starHigherOrderMomentBase + "_22"]
            starM31 = psf_cat[self.config.starHigherOrderMomentBase + "_31"]
            starM40 = psf_cat[self.config.starHigherOrderMomentBase + "_40"]
 
            starComa1Median = np.nanmedian(starM30 + starM12)
            starComa2Median = np.nanmedian(starM21 + starM03)
            starTrefoil1Median = np.nanmedian(starM30 - 3.0*starM12)
            starTrefoil2Median = np.nanmedian(3.0*starM21 - starM03)
            starKurtosisMedian = np.nanmedian(starM40 + 2.0*starM22 + starM04)
            starE41Median = np.nanmedian(starM40 - starM04)
            starE42Median = np.nanmedian(2.0*(starM31 + starM13))
 
            summary.starComa1Median = float(starComa1Median)
            summary.starComa2Median = float(starComa2Median)
            summary.starTrefoil1Median = float(starTrefoil1Median)
            summary.starTrefoil2Median = float(starTrefoil2Median)
            summary.starKurtosisMedian = float(starKurtosisMedian)
            summary.starE41Median = float(starE41Median)
            summary.starE42Median = float(starE42Median)
        else:
            self.log.warning("Higher-order moments with base column name %s not found in source "
                             "catalog. Setting the derived metrics (i.e. coma1[2], trefoil1[2], "
                             "kurtosis, e4_1, and e4_2) to nan.", self.config.starHigherOrderMomentBase)
 
        if image_mask is not None:
            maxDistToNearestPsf = maximum_nearest_psf_distance(
                image_mask,
                psf_cat,
                sampling=self.config.psfSampling,
                bad_mask_bits=self.config.psfBadMaskPlanes
            )
            summary.maxDistToNearestPsf = float(maxDistToNearestPsf)
 
    def comp_psf_TEX_visit_level(self, summary, sources, sources_is_astropy=False):
        """Compute all summary-statistic fields at visit level for TEx metric of PSF.
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        sources : `lsst.afw.table.SourceCatalog` or `astropy.table.Table`
            Catalog for quantities that are computed from source table columns.
            If `None`, these quantities will be reset (generally to NaN).
            The type of this table must correspond to the
            ``sources_is_astropy`` argument.
        sources_is_astropy : `bool`, optional
            Whether ``sources`` is an `astropy.table.Table` instance instead
            of an `lsst.afw.table.Catalog` instance.
        """
 
        if self._isTEXComputationDone:
 
            summary.psfTE1e1 = self.psfTE1e1
            summary.psfTE1e2 = self.psfTE1e2
            summary.psfTE1ex = self.psfTE1ex
            summary.psfTE2e1 = self.psfTE2e1
            summary.psfTE2e2 = self.psfTE2e2
            summary.psfTE2ex = self.psfTE2ex
            summary.psfTE3e1 = self.psfTE3e1
            summary.psfTE3e2 = self.psfTE3e2
            summary.psfTE3ex = self.psfTE3ex
            summary.psfTE4e1 = self.psfTE4e1
            summary.psfTE4e2 = self.psfTE4e2
            summary.psfTE4ex = self.psfTE4ex
 
        else:
 
            self._isTEXComputationDone = True
 
            nan = float("nan")
            summary.psfTE1e1, self.psfTE1e1 = nan, nan
            summary.psfTE1e2, self.psfTE1e2 = nan, nan
            summary.psfTE1ex, self.psfTE1ex = nan, nan
            summary.psfTE2e1, self.psfTE2e1 = nan, nan
            summary.psfTE2e2, self.psfTE2e2 = nan, nan
            summary.psfTE2ex, self.psfTE2ex = nan, nan
            summary.psfTE3e1, self.psfTE3e1 = nan, nan
            summary.psfTE3e2, self.psfTE3e2 = nan, nan
            summary.psfTE3ex, self.psfTE3ex = nan, nan
            summary.psfTE4e1, self.psfTE4e1 = nan, nan
            summary.psfTE4e2, self.psfTE4e2 = nan, nan
            summary.psfTE4ex, self.psfTE4ex = nan, nan
 
            psf_mask = self.starSelector.run(sources).selected
 
            nPsfStarsUsedInStats = psf_mask.sum()
 
            if nPsfStarsUsedInStats == 0:
                # No stars to measure statistics, so we must return the defaults
                # of 0 stars and NaN values.
                return
 
            if sources_is_astropy:
                psf_cat = sources[psf_mask]
            else:
                psf_cat = sources[psf_mask].copy(deep=True)
 
            starXX = psf_cat[self.config.starShape + '_xx']
            starYY = psf_cat[self.config.starShape + '_yy']
            starXY = psf_cat[self.config.starShape + '_xy']
            psfXX = psf_cat[self.config.psfShape + '_xx']
            psfYY = psf_cat[self.config.psfShape + '_yy']
            psfXY = psf_cat[self.config.psfShape + '_xy']
 
            starE1 = (starXX - starYY)/(starXX + starYY)
            starE2 = 2*starXY/(starXX + starYY)
 
            psfE1 = (psfXX - psfYY)/(psfXX + psfYY)
            psfE2 = 2*psfXY/(psfXX + psfYY)
 
            e1Residuals = starE1 - psfE1
            e2Residuals = starE2 - psfE2
 
            # Comp TEx
            ra = psf_cat["coord_ra"].to(units.deg)
            dec = psf_cat["coord_dec"].to(units.deg)
 
            psfTEx = {
                "TE1": self.psfTE1,
                "TE2": self.psfTE2,
            }
 
            gatherE12Stat = {
                "TE1": {"E1": np.nan, "E2": np.nan, "Ex": np.nan, },
                "TE2": {"E1": np.nan, "E2": np.nan, "Ex": np.nan, },
            }
 
            isNotNan = np.array([True] * len(ra))
            isNotNan &= np.isfinite(ra)
            isNotNan &= np.isfinite(dec)
            isNotNan &= np.isfinite(e1Residuals)
            isNotNan &= np.isfinite(e2Residuals)
 
            if np.sum(isNotNan) >= 2:
                # TE1 and TE2 computation, over visit.
                for TEX in ["TE1", "TE2"]:
 
                    output = psfTEx[TEX].run(
                        e1Residuals[isNotNan], e2Residuals[isNotNan],
                        ra[isNotNan], dec[isNotNan],
                        units="degree",
                    )
 
                    gatherE12Stat[TEX]["E1"] = output.metric_E1
                    gatherE12Stat[TEX]["E2"] = output.metric_E2
                    gatherE12Stat[TEX]["Ex"] = output.metric_Ex
 
                # TE3 and TE4 loop over detector and then median on visit.
 
                psfTEx = {
                    "TE3": self.psfTE3,
                    "TE4": self.psfTE4,
                }
 
                gatherE34Stat = {
                    "TE3": {"E1": [], "E2": [], "Ex": [], },
                    "TE4": {"E1": [], "E2": [], "Ex": [], },
                }
                # calibrateImage run at detector level,
                # need to wait second run of PSF to run this.
                if "detector" in psf_cat.colnames:
                    detectorIds = list(set(psf_cat["detector"]))
                    for TEX in ["TE3", "TE4"]:
                        for ccdId in detectorIds:
                            isccdId = (ccdId == psf_cat["detector"])
                            mask = (isccdId & isNotNan)
                            if np.sum(mask) >= 2:
                                output = psfTEx[TEX].run(
                                    e1Residuals[mask], e2Residuals[mask],
                                    ra[mask], dec[mask],
                                    units="degree",
                                )
                                gatherE34Stat[TEX]["E1"].append(output.metric_E1)
                                gatherE34Stat[TEX]["E2"].append(output.metric_E2)
                                gatherE34Stat[TEX]["Ex"].append(output.metric_Ex)
 
                self.psfTE1e1 = summary.psfTE1e1 = gatherE12Stat["TE1"]["E1"]
                self.psfTE1e2 = summary.psfTE1e2 = gatherE12Stat["TE1"]["E2"]
                self.psfTE1ex = summary.psfTE1ex = gatherE12Stat["TE1"]["Ex"]
                self.psfTE2e1 = summary.psfTE2e1 = gatherE12Stat["TE2"]["E1"]
                self.psfTE2e2 = summary.psfTE2e2 = gatherE12Stat["TE2"]["E2"]
                self.psfTE2ex = summary.psfTE2ex = gatherE12Stat["TE2"]["Ex"]
                self.psfTE3e1 = summary.psfTE3e1 = np.nanmedian(gatherE34Stat["TE3"]["E1"])
                self.psfTE3e2 = summary.psfTE3e2 = np.nanmedian(gatherE34Stat["TE3"]["E2"])
                self.psfTE3ex = summary.psfTE3ex = np.nanmedian(gatherE34Stat["TE3"]["Ex"])
                self.psfTE4e1 = summary.psfTE4e1 = np.nanmedian(gatherE34Stat["TE4"]["E1"])
                self.psfTE4e2 = summary.psfTE4e2 = np.nanmedian(gatherE34Stat["TE4"]["E2"])
                self.psfTE4ex = summary.psfTE4ex = np.nanmedian(gatherE34Stat["TE4"]["Ex"])
 
    def update_wcs_stats(self, summary, wcs, bbox, visitInfo):
        """Compute all summary-statistic fields that depend on the WCS model.
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        wcs : `lsst.afw.geom.SkyWcs` or `None`
            Astrometric calibration model.  If `None`, all fields that depend
            on the WCS will be reset (generally to NaN).
        bbox : `lsst.geom.Box2I`
            Bounding box of the image for which summary stats are being
            computed.
        visitInfo : `lsst.afw.image.VisitInfo`
            Observation information used in together with ``wcs`` to compute
            the zenith distance.
        """
        nan = float("nan")
        summary.raCorners = [nan]*4
        summary.decCorners = [nan]*4
        summary.ra = nan
        summary.dec = nan
        summary.pixelScale = nan
        summary.zenithDistance = nan
 
        if wcs is None:
            return
 
        sph_pts = wcs.pixelToSky(geom.Box2D(bbox).getCorners())
        summary.raCorners = [float(sph.getRa().asDegrees()) for sph in sph_pts]
        summary.decCorners = [float(sph.getDec().asDegrees()) for sph in sph_pts]
 
        sph_pt = wcs.pixelToSky(bbox.getCenter())
        summary.ra = sph_pt.getRa().asDegrees()
        summary.dec = sph_pt.getDec().asDegrees()
        summary.pixelScale = wcs.getPixelScale(bbox.getCenter()).asArcseconds()
 
        date = visitInfo.getDate()
 
        if date.isValid():
            # We compute the zenithDistance at the center of the detector
            # rather than use the boresight value available via the visitInfo,
            # because the zenithDistance may vary significantly over a large
            # field of view.
            observatory = visitInfo.getObservatory()
            loc = EarthLocation(lat=observatory.getLatitude().asDegrees()*units.deg,
                                lon=observatory.getLongitude().asDegrees()*units.deg,
                                height=observatory.getElevation()*units.m)
            obstime = Time(visitInfo.getDate().get(system=DateTime.MJD),
                           location=loc, format="mjd")
            coord = SkyCoord(
                summary.ra*units.degree,
                summary.dec*units.degree,
                obstime=obstime,
                location=loc,
            )
            with warnings.catch_warnings():
                warnings.simplefilter("ignore")
                altaz = coord.transform_to(AltAz)
 
            summary.zenithDistance = float(90.0 - altaz.alt.degree)
 
    def update_photo_calib_stats(self, summary, photo_calib):
        """Compute all summary-statistic fields that depend on the photometric
        calibration model.
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        photo_calib : `lsst.afw.image.PhotoCalib` or `None`
            Photometric calibration model.  If `None`, all fields that depend
            on the photometric calibration will be reset (generally to NaN).
        """
        if photo_calib is not None:
            summary.zeroPoint = float(2.5*np.log10(photo_calib.getInstFluxAtZeroMagnitude()))
        else:
            summary.zeroPoint = float("nan")
 
    def update_background_stats(self, summary, background):
        """Compute summary-statistic fields that depend only on the
        background model.
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        background : `lsst.afw.math.BackgroundList` or `None`
            Background model.  If `None`, all fields that depend on the
            background will be reset (generally to NaN).
 
        Notes
        -----
        This does not include fields that depend on the background-subtracted
        masked image; when the background changes, it should generally be
        applied to the image and `update_masked_image_stats` should be called
        as well.
        """
        if background is not None:
            bgStats = (bg[0].getStatsImage().getImage().array
                       for bg in background)
            summary.skyBg = float(sum(np.median(bg[np.isfinite(bg)]) for bg in bgStats))
        else:
            summary.skyBg = float("nan")
 
    def update_masked_image_stats(self, summary, masked_image):
        """Compute summary-statistic fields that depend on the masked image
        itself.
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        masked_image : `lsst.afw.image.MaskedImage` or `None`
            Masked image.  If `None`, all fields that depend
            on the masked image will be reset (generally to NaN).
        """
        nan = float("nan")
        if masked_image is None:
            summary.skyNoise = nan
            summary.meanVar = nan
            return
        statsCtrl = afwMath.StatisticsControl()
        statsCtrl.setNumSigmaClip(self.config.sigmaClip)
        statsCtrl.setNumIter(self.config.clipIter)
        statsCtrl.setAndMask(afwImage.Mask.getPlaneBitMask(self.config.badMaskPlanes))
        statsCtrl.setNanSafe(True)
 
        statObj = afwMath.makeStatistics(masked_image, afwMath.STDEVCLIP, statsCtrl)
        skyNoise, _ = statObj.getResult(afwMath.STDEVCLIP)
        summary.skyNoise = skyNoise
 
        statObj = afwMath.makeStatistics(masked_image.variance, masked_image.mask, afwMath.MEANCLIP,
                                         statsCtrl)
        meanVar, _ = statObj.getResult(afwMath.MEANCLIP)
        summary.meanVar = meanVar
 
    def update_effective_time_stats(self, summary, exposure):
        """Compute effective exposure time statistics to estimate depth.
 
        The effective exposure time is the equivalent shutter open
        time that would be needed under nominal conditions to give the
        same signal-to-noise for a point source as what is achieved by
        the observation of interest. This metric combines measurements
        of the point-spread function, the sky brightness, and the
        transparency. It assumes that the observation is
        sky-background dominated.
 
        .. _teff_definitions:
 
        The effective exposure time and its subcomponents are defined in [1]_.
 
        References
        ----------
 
        .. [1] Neilsen, E.H., Bernstein, G., Gruendl, R., and Kent, S. (2016).
               Limiting Magnitude, \tau, teff, and Image Quality in DES Year 1
               https://www.osti.gov/biblio/1250877/
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        exposure : `lsst.afw.image.ExposureF`
            Exposure to grab band and exposure time metadata
 
        """
        nan = float("nan")
        summary.effTime = nan
        summary.effTimePsfSigmaScale = nan
        summary.effTimeSkyBgScale = nan
        summary.effTimeZeroPointScale = nan
 
        exposureTime = exposure.getInfo().getVisitInfo().getExposureTime()
        filterLabel = exposure.getFilter()
        if (filterLabel is None) or (not filterLabel.hasBandLabel):
            band = None
        else:
            band = filterLabel.bandLabel
 
        if band is None:
            self.log.warning("No band associated with exposure; effTime not calculated.")
            return
 
        # PSF component
        if np.isnan(summary.psfSigma):
            self.log.debug("PSF sigma is NaN")
            f_eff = nan
        elif band not in self.config.fiducialPsfSigma:
            self.log.debug(f"Fiducial PSF value not found for {band}")
            f_eff = nan
        else:
            fiducialPsfSigma = self.config.fiducialPsfSigma[band]
            f_eff = (summary.psfSigma / fiducialPsfSigma)**-2
 
        # Transparency component
        # Note: Assumes that the zeropoint includes the exposure time
        if np.isnan(summary.zeroPoint):
            self.log.debug("Zero point is NaN")
            c_eff = nan
        elif band not in self.config.fiducialZeroPoint:
            self.log.debug(f"Fiducial zero point value not found for {band}")
            c_eff = nan
        else:
            fiducialZeroPoint = self.config.fiducialZeroPoint[band]
            zeroPointDiff = fiducialZeroPoint - (summary.zeroPoint - 2.5*np.log10(exposureTime))
            c_eff = min(10**(-2.0*(zeroPointDiff)/2.5), self.config.maxEffectiveTransparency)
 
        # Sky brightness component (convert to cts/s)
        if np.isnan(summary.skyBg):
            self.log.debug("Sky background is NaN")
            b_eff = nan
        elif band not in self.config.fiducialSkyBackground:
            self.log.debug(f"Fiducial sky background value not found for {band}")
            b_eff = nan
        else:
            fiducialSkyBackground = self.config.fiducialSkyBackground[band]
            b_eff = fiducialSkyBackground/(summary.skyBg/exposureTime)
 
        # Old effective exposure time scale factor
        # t_eff = f_eff * c_eff * b_eff
 
        # New effective exposure time (seconds) from magnitude limit
        if band not in self.config.fiducialMagLim:
            self.log.debug(f"Fiducial magnitude limit not found for {band}")
            effectiveTime = nan
        elif band not in self.config.fiducialExpTime:
            self.log.debug(f"Fiducial exposure time not found for {band}")
            effectiveTime = nan
        else:
            effectiveTime = compute_effective_time(summary.magLim,
                                                   self.config.fiducialMagLim[band],
                                                   self.config.fiducialExpTime[band])
 
        # Output quantities
        summary.effTime = float(effectiveTime)
        summary.effTimePsfSigmaScale = float(f_eff)
        summary.effTimeSkyBgScale = float(b_eff)
        summary.effTimeZeroPointScale = float(c_eff)
 
    def update_magnitude_limit_stats(self, summary, exposure):
        """Compute a summary statistic for the point-source magnitude limit at
        a given signal-to-noise ratio using exposure-level metadata.
 
        The magnitude limit is calculated at a given SNR from the PSF,
        sky, zeropoint, and readnoise in accordance with SMTN-002 [1]_,
        LSE-40 [2]_, and DMTN-296 [3]_.
 
        References
        ----------
 
        .. [1] "Calculating LSST limiting magnitudes and SNR" (SMTN-002)
        .. [2] "Photon Rates and SNR Calculations" (LSE-40)
        .. [3] "Calculations of Image and Catalog Depth" (DMTN-296)
 
 
        Parameters
        ----------
        summary : `lsst.afw.image.ExposureSummaryStats`
            Summary object to update in-place.
        exposure : `lsst.afw.image.ExposureF`
            Exposure to grab band and exposure time metadata
        """
        if exposure.getDetector() is None:
            summary.magLim = float("nan")
            return
 
        # Calculate the average readnoise [e-]
        readNoiseList = list(ipIsr.getExposureReadNoises(exposure).values())
        readNoise = np.nanmean(readNoiseList)
        if np.isnan(readNoise):
            readNoise = 0.0
            self.log.warning("Read noise set to NaN! Setting readNoise to 0.0 to proceed.")
 
        # Calculate the average gain [e-/ADU]
        gainList = list(ipIsr.getExposureGains(exposure).values())
        gain = np.nanmean(gainList)
        if np.isnan(gain):
            self.log.warning("Gain set to NaN! Setting magLim to NaN.")
            summary.magLim = float("nan")
            return
 
        # Get the image units (default to "adu" if metadata key absent)
        md = exposure.getMetadata()
        if md.get("LSST ISR UNITS", "adu") == "electron":
            gain = 1.0
 
        # Convert readNoise to image units
        readNoise /= gain
 
        # Calculate the limiting magnitude.
        # Note 1: Assumes that the image and readnoise have the same units
        # Note 2: Assumes that the zeropoint includes the exposure time
        magLim = compute_magnitude_limit(summary.psfArea, summary.skyBg,
                                         summary.zeroPoint, readNoise,
                                         gain, self.config.magLimSnr)
 
        summary.magLim = float(magLim)
 
 
def maximum_nearest_psf_distance(
    image_mask,
    psf_cat,
    sampling=8,
    bad_mask_bits=["BAD", "CR", "INTRP", "SAT", "SUSPECT", "NO_DATA", "EDGE"],
):
    """Compute the maximum distance of an unmasked pixel to its nearest PSF.
 
    Parameters
    ----------
    image_mask : `lsst.afw.image.Mask`
        The mask plane associated with the exposure.
    psf_cat : `lsst.afw.table.SourceCatalog` or `astropy.table.Table`
        Catalog containing only the stars used in the PSF modeling.
    sampling : `int`
        Sampling rate in each dimension to create the grid of points on which
        to evaluate the distance to the nearest PSF star. The tradeoff is
        between adequate sampling versus speed.
    bad_mask_bits : `list` [`str`]
        Mask bits required to be absent for a pixel to be considered
        "unmasked".
 
    Returns
    -------
    max_dist_to_nearest_psf : `float`
        The maximum distance (in pixels) of an unmasked pixel to its nearest
        PSF model star.
    """
    mask_arr = image_mask.array[::sampling, ::sampling]
    bitmask = image_mask.getPlaneBitMask(bad_mask_bits)
    good = ((mask_arr & bitmask) == 0)
 
    x = np.arange(good.shape[1]) * sampling
    y = np.arange(good.shape[0]) * sampling
    xx, yy = np.meshgrid(x, y)
 
    dist_to_nearest_psf = np.full(good.shape, np.inf)
    for psf in psf_cat:
        x_psf = psf["slot_Centroid_x"]
        y_psf = psf["slot_Centroid_y"]
        dist_to_nearest_psf = np.minimum(dist_to_nearest_psf, np.hypot(xx - x_psf, yy - y_psf))
        unmasked_dists = dist_to_nearest_psf * good
        max_dist_to_nearest_psf = np.max(unmasked_dists)
 
    return max_dist_to_nearest_psf
 
 
def compute_psf_image_deltas(
    image_mask,
    image_psf,
    sampling=96,
    ap_radius_pix=3.0,
    bad_mask_bits=["BAD", "CR", "INTRP", "SAT", "SUSPECT", "NO_DATA", "EDGE"],
):
    """Compute the delta between the maximum and minimum model PSF trace radius
    values evaluated on a grid of points lying in the unmasked region of the
    image.
 
    Parameters
    ----------
    image_mask : `lsst.afw.image.Mask`
        The mask plane associated with the exposure.
    image_psf : `lsst.afw.detection.Psf`
        The PSF model associated with the exposure.
    sampling : `int`, optional
        Sampling rate in each dimension to create the grid of points at which
        to evaluate ``image_psf``s trace radius value. The tradeoff is between
        adequate sampling versus speed.
    ap_radius_pix : `float`, optional
        Radius in pixels of the aperture on which to measure the flux of the
        PSF model.
    bad_mask_bits : `list` [`str`], optional
        Mask bits required to be absent for a pixel to be considered
        "unmasked".
 
    Returns
    -------
    psf_trace_radius_delta, psf_ap_flux_delta : `float`
        The delta (in pixels) between the maximum and minimum model PSF trace
        radius values and the PSF aperture fluxes (with aperture radius of
        max(2, 3*psfSigma)) evaluated on the x,y-grid subsampled on the
        unmasked detector pixels by a factor of ``sampling``.  If both the
        model PSF trace radius value and aperture flux value on the grid
        evaluate to NaN, then NaNs are returned immediately.
    """
    psf_trace_radius_list = []
    psf_ap_flux_list = []
    mask_arr = image_mask.array[::sampling, ::sampling]
    bitmask = image_mask.getPlaneBitMask(bad_mask_bits)
    good = ((mask_arr & bitmask) == 0)
 
    x = np.arange(good.shape[1]) * sampling
    y = np.arange(good.shape[0]) * sampling
    xx, yy = np.meshgrid(x, y)
 
    for x_mesh, y_mesh, good_mesh in zip(xx, yy, good):
        for x_point, y_point, is_good in zip(x_mesh, y_mesh, good_mesh):
            if is_good:
                position = geom.Point2D(x_point, y_point)
                psf_trace_radius = image_psf.computeShape(position).getTraceRadius()
                psf_ap_flux = image_psf.computeApertureFlux(ap_radius_pix, position)
                if ~np.isfinite(psf_trace_radius) and ~np.isfinite(psf_ap_flux):
                    return float("nan"), float("nan")
                psf_trace_radius_list.append(psf_trace_radius)
                psf_ap_flux_list.append(psf_ap_flux)
 
    psf_trace_radius_delta = np.max(psf_trace_radius_list) - np.min(psf_trace_radius_list)
    if np.any(np.asarray(psf_ap_flux_list) < 0.0):  # Consider any -ve flux entry as "bad".
        psf_ap_flux_delta = float("nan")
    else:
        psf_ap_flux_delta = np.max(psf_ap_flux_list) - np.min(psf_ap_flux_list)
 
    return psf_trace_radius_delta, psf_ap_flux_delta
 
 
def compute_ap_corr_sigma_scaled_delta(
    image_mask,
    image_ap_corr_field,
    psfSigma,
    sampling=96,
    bad_mask_bits=["BAD", "CR", "INTRP", "SAT", "SUSPECT", "NO_DATA", "EDGE"],
):
    """Compute the delta between the maximum and minimum aperture correction
    values scaled (divided) by ``psfSigma`` for the given field representation,
    ``image_ap_corr_field`` evaluated on a grid of points lying in the
    unmasked region of the image.
 
    Parameters
    ----------
    image_mask : `lsst.afw.image.Mask`
        The mask plane associated with the exposure.
    image_ap_corr_field : `lsst.afw.math.ChebyshevBoundedField`
        The ChebyshevBoundedField representation of the aperture correction
        of interest for the exposure.
    psfSigma : `float`
        The PSF model second-moments determinant radius (center of chip)
        in pixels.
    sampling : `int`, optional
        Sampling rate in each dimension to create the grid of points at which
        to evaluate ``image_psf``s trace radius value. The tradeoff is between
        adequate sampling versus speed.
    bad_mask_bits : `list` [`str`], optional
        Mask bits required to be absent for a pixel to be considered
        "unmasked".
 
    Returns
    -------
    ap_corr_sigma_scaled_delta : `float`
        The delta between the maximum and minimum of the (multiplicative)
        aperture correction values scaled (divided) by ``psfSigma`` evaluated
        on the x,y-grid subsampled on the unmasked detector pixels by a factor
        of ``sampling``.  If the aperture correction evaluates to NaN on any
        of the grid points, this is set to NaN.
    """
    mask_arr = image_mask.array[::sampling, ::sampling]
    bitmask = image_mask.getPlaneBitMask(bad_mask_bits)
    good = ((mask_arr & bitmask) == 0)
 
    x = np.arange(good.shape[1], dtype=np.float64) * sampling
    y = np.arange(good.shape[0], dtype=np.float64) * sampling
    xx, yy = np.meshgrid(x, y)
 
    ap_corr = image_ap_corr_field.evaluate(xx.ravel(), yy.ravel()).reshape(xx.shape)
    ap_corr_good = ap_corr[good]
    if ~np.isfinite(ap_corr_good).all():
        ap_corr_sigma_scaled_delta = float("nan")
    else:
        ap_corr_sigma_scaled_delta = (np.max(ap_corr_good) - np.min(ap_corr_good))/psfSigma
 
    return ap_corr_sigma_scaled_delta
 
 
def compute_magnitude_limit(
        psfArea,
        skyBg,
        zeroPoint,
        readNoise,
        gain,
        snr
):
    """Compute the expected point-source magnitude limit at a given
    signal-to-noise ratio given the exposure-level metadata. Based on
    the signal-to-noise formula provided in SMTN-002 (see LSE-40 for
    more details on the calculation).
 
      SNR = C / sqrt( C/g + (B/g + sigma_inst**2) * neff )
 
    where C is the counts from the source, B is counts from the (sky)
    background, sigma_inst is the instrumental (read) noise, neff is
    the effective size of the PSF, and g is the gain in e-/ADU.  Note
    that input values of ``skyBg``, ``zeroPoint``, and ``readNoise``
    should all consistently be in electrons or ADU.
 
    Parameters
    ----------
    psfArea : `float`
        The effective area of the PSF [pix].
    skyBg : `float`
        The sky background counts for the exposure [ADU or e-].
    zeroPoint : `float`
        The zeropoint (includes exposure time) [ADU or e-].
    readNoise : `float`
        The instrumental read noise for the exposure [ADU or e-].
    gain : `float`
        The instrumental gain for the exposure [e-/ADU]. The gain should
         be 1.0 if the skyBg, zeroPoint, and readNoise are in e-.
    snr : `float`
        Signal-to-noise ratio at which magnitude limit is calculated.
 
    Returns
    -------
    magnitude_limit : `float`
        The expected magnitude limit at the given signal to noise.
    """
    # Effective number of pixels within the PSF calculated directly
    # from the PSF model.
    neff = psfArea
 
    # Instrumental noise (read noise only)
    sigma_inst = readNoise
 
    # Total background counts derived from Eq. 45 of LSE-40
    background = (skyBg/gain + sigma_inst**2) * neff
    # Source counts to achieve the desired SNR (from quadratic formula)
    # Note typo in gain exponent in Eq. 45 of LSE-40 (DM-53234)
    source = (snr**2)/(2*gain) + np.sqrt((snr**4)/(4*gain**2) + snr**2 * background)
 
    # Convert to a magnitude using the zeropoint.
    # Note: Zeropoint currently includes exposure time
    magnitude_limit = -2.5*np.log10(source) + zeroPoint
 
    return magnitude_limit
 
 
def psf_sigma_to_psf_area(psfSigma, pixelScale):
    """Convert psfSigma [pixels] to an approximate psfArea [pixel^2] as defined in LSE-40.
    This is the same implementation followed by SMTN-002 to estimate SNR=5 magnitude limits.
 
    Parameters
    ----------
    psfSigma : `float`
        The PSF sigma value [pix].
    pixelScale : `float`
        The pixel scale [arcsec/pix].
 
    Returns
    -------
    psf_area : `float`
        Approximation of the PSF area [pix^2]
    """
    # Follow SMTN-002 to convert to geometric and effective FWHM
    fwhm_geom = psfSigma * 2.355 * pixelScale
    fwhm_eff = (fwhm_geom - 0.052) / 0.822
    # Area prefactor comes from LSE-40
    psf_area = 2.266 * (fwhm_eff / pixelScale)**2
    return psf_area
 
 
def compute_effective_time(
        magLim,
        fiducialMagLim,
        fiducialExpTime
):
    """Compute the effective exposure time from m5 following the prescription described in SMTN-296.
 
      teff = 10**(0.8 * (magLim - fiducialMagLim) ) * fiducialExpTime
 
    where `magLim` is the magnitude limit, `fiducialMagLim` is the fiducial magnitude limit calculated from
    the fiducial values of the ``psfArea``, ``skyBg``, ``zeroPoint``, and ``readNoise``, and
    `fiducialExpTime` is the fiducial exposure time (s).
 
    Parameters
    ----------
    magLim : `float`
        The measured magnitude limit [mag].
    fiducialMagLim : `float`
        The fiducial magnitude limit [mag].
    fiducialExpTime : `float`
        The fiducial exposure time [s].
 
    Returns
    -------
    effectiveTime : `float`
        The effective exposure time.
    """
    effectiveTime = 10**(0.8 * (magLim - fiducialMagLim)) * fiducialExpTime
    return effectiveTime