effects.py

import galsim
from matplotlib.pyplot import flag
import numpy as np
from numpy.core.fromnumeric import mean, size
from numpy.random import Generator, PCG64
import math
import copy
from numba import jit
from astropy import stats


def AddOverscan(GSImage, overscan=1000, gain=1, widthl=27, widthr=27, widtht=8, widthb=8, read_noise=5):
    """
    Add overscan/gain; gain=e-/ADU
    widthl: left pre-scan width
    widthr: right pre-scan width
    widtht: top over-scan width (the top of nd-array with small row-index)
    widthb: bottom over-scan width (the bottom of nd-array with large row-index)
    """
    imgshape = GSImage.array.shape
    newimg = galsim.Image(imgshape[1]+widthl+widthr, imgshape[0]+widtht+widthb, init_value=0)
    rng = galsim.UniformDeviate()
    NoiseOS = galsim.GaussianNoise(rng, sigma=read_noise)
    newimg.addNoise(NoiseOS)
    newimg = (newimg+overscan)/gain
    newimg.array[widtht:(widtht+imgshape[0]), widthl:(widthl+imgshape[1])] = GSImage.array
    newimg.wcs = GSImage.wcs
    # if GSImage.wcs is not None:
    #     newwcs = GSImage.wcs.withOrigin(galsim.PositionD(widthl,widtht))
    #     newimg.wcs = newwcs
    # else:
    #     pass
    return newimg


def DefectivePixels(GSImage, IfHotPix=True, IfDeadPix=True, fraction=1E-4, seed=20210304, biaslevel=0):
    # Also called bad pixels, including hot pixels and dead pixels
    # Hot Pixel > 20e-/s
    # Dead Pixel < 70%*Mean
    rgf = Generator(PCG64(int(seed*1.1)))
    if IfHotPix is True and IfDeadPix is True:
        HotFraction = rgf.random()             # fraction in total bad pixels
    elif IfHotPix is False and IfDeadPix is False:
        return GSImage
    elif IfHotPix is True:
        HotFraction = 1
    else:
        HotFraction = 0

    NPix = GSImage.array.size
    NPixBad = int(NPix*fraction)
    NPixHot = int(NPix*fraction*HotFraction)
    NPixDead = NPixBad-NPixHot

    NPix_y, NPix_x = GSImage.array.shape
    mean = np.mean(GSImage.array)
    rgp = Generator(PCG64(int(seed)))
    yxposfrac = rgp.random((NPixBad, 2))
    YPositHot = np.array(NPix_y*yxposfrac[0:NPixHot, 0]).astype(np.int32)
    XPositHot = np.array(NPix_x*yxposfrac[0:NPixHot, 1]).astype(np.int32)
    YPositDead = np.array(NPix_y*yxposfrac[NPixHot:, 0]).astype(np.int32)
    XPositDead = np.array(NPix_x*yxposfrac[NPixHot:, 1]).astype(np.int32)

    rgh = Generator(PCG64(int(seed*1.2)))
    rgd = Generator(PCG64(int(seed*1.3)))
    if IfHotPix is True:
        GSImage.array[YPositHot, XPositHot] += rgh.gamma(2, 25*150, size=NPixHot)
    if IfDeadPix is True:
        GSImage.array[YPositDead, XPositDead] = rgd.random(NPixDead)*(mean-biaslevel)*0.7+biaslevel+rgp.standard_normal()*5
    return GSImage


def BadColumns(GSImage, seed=20240309, chipid=1, logger=None):
    # Set bad column values
    ysize, xsize = GSImage.array.shape
    subarr = GSImage.array[int(ysize*0.1):int(ysize*0.12), int(xsize*0.1):int(xsize*0.12)]
    subarr = stats.sigma_clip(subarr, sigma=4, cenfunc='median', maxiters=3, masked=False)
    meanimg = np.median(subarr)
    stdimg = np.std(subarr)
    seed += chipid
    rgn = Generator(PCG64(int(seed)))
    rgcollen = Generator(PCG64(int(seed*1.1)))
    rgxpos = Generator(PCG64(int(seed*1.2)))
    rgdn = Generator(PCG64(int(seed*1.3)))

    nbadsecA, nbadsecD = rgn.integers(low=1, high=5, size=2)
    collen = rgcollen.integers(low=int(ysize*0.1), high=int(ysize*0.7), size=(nbadsecA+nbadsecD))
    xposit = rgxpos.integers(low=int(xsize*0.05), high=int(xsize*0.95), size=(nbadsecA+nbadsecD))
    if logger is not None:
        logger.info(xposit+1)
    else:
        print(xposit+1)
    # signs = 2*rgdn.integers(0,2,size=(nbadsecA+nbadsecD))-1
    # if meanimg>0:
    dn = rgdn.integers(low=np.abs(meanimg)*1.3+50, high=np.abs(meanimg)*2+150, size=(nbadsecA+nbadsecD))  # *signs
    # elif meanimg<0:
    #     dn = rgdn.integers(low=meanimg*2-150, high=meanimg*1.3-50, size=(nbadsecA+nbadsecD)) #*signs
    for badcoli in range(nbadsecA):
        GSImage.array[(ysize-collen[badcoli]):ysize, xposit[badcoli]:(xposit[badcoli]+1)] = (np.abs(np.random.normal(0, stdimg*2, (collen[badcoli], 1)))+dn[badcoli])
    for badcoli in range(nbadsecD):
        GSImage.array[0:collen[badcoli+nbadsecA], xposit[badcoli+nbadsecA]:(xposit[badcoli+nbadsecA]+1)] = (np.abs(np.random.normal(0, stdimg*2, (collen[badcoli+nbadsecA], 1)))+dn[badcoli+nbadsecA])
    return GSImage


def AddBiasNonUniform16(GSImage, bias_level=500, nsecy=2, nsecx=8, seed=202102, logger=None):
    # Generate Bias and its non-uniformity, and add the 16 bias values to the GS-Image
    rg = Generator(PCG64(int(seed)))
    Random16 = (rg.random(nsecy*nsecx)-0.5)*20
    if int(bias_level) == 0:
        BiasLevel = np.zeros((nsecy, nsecx))
    elif bias_level > 0:
        BiasLevel = Random16.reshape((nsecy, nsecx)) + bias_level
    if logger is not None:
        msg = str(" Biases of 16 channels: " + str(BiasLevel))
        logger.info(msg)
    else:
        print(" Biases of 16 channels:\n", BiasLevel)
    arrshape = GSImage.array.shape
    secsize_x = int(arrshape[1]/nsecx)
    secsize_y = int(arrshape[0]/nsecy)
    for rowi in range(nsecy):
        for coli in range(nsecx):
            GSImage.array[rowi*secsize_y:(rowi+1)*secsize_y, coli*secsize_x:(coli+1)*secsize_x] += BiasLevel[rowi, coli]
    return GSImage


def MakeBiasNcomb(npix_x, npix_y, bias_level=500, ncombine=1, read_noise=5, gain=1, seed=202102, logger=None):
    # Start with 0 value bias GS-Image
    ncombine = int(ncombine)
    BiasSngImg0 = galsim.Image(npix_x, npix_y, init_value=0)
    BiasSngImg = AddBiasNonUniform16(BiasSngImg0,
                                     bias_level=bias_level,
                                     nsecy=2, nsecx=8,
                                     seed=int(seed),
                                     logger=logger)
    BiasCombImg = BiasSngImg*ncombine
    rng = galsim.UniformDeviate()
    NoiseBias = galsim.GaussianNoise(rng=rng, sigma=read_noise*ncombine**0.5)
    BiasCombImg.addNoise(NoiseBias)
    if ncombine == 1:
        BiasTag = 'Single'
        pass
    elif ncombine > 1:
        BiasCombImg /= ncombine
        BiasTag = 'Combine'
    # BiasCombImg.replaceNegative(replace_value=0)
    # BiasCombImg.quantize()
    return BiasCombImg, BiasTag


def ApplyGainNonUniform16(GSImage, gain=1, nsecy=2, nsecx=8, seed=202102, logger=None):
    # Generate Gain non-uniformity, and multipy the different factors (mean~1 with sigma~1%) to the GS-Image
    rg = Generator(PCG64(int(seed)))
    Random16 = (rg.random(nsecy*nsecx)-0.5)*0.04+1   # sigma~1%
    Gain16 = Random16.reshape((nsecy, nsecx))/gain
    gain_array = np.ones(nsecy*nsecx)*gain
    if logger is not None:
        msg = str("Gain of 16 channels: " + str(Gain16))
        logger.info(msg)
    else:
        print("Gain of 16 channels: ", Gain16)
    arrshape = GSImage.array.shape
    secsize_x = int(arrshape[1]/nsecx)
    secsize_y = int(arrshape[0]/nsecy)
    for rowi in range(nsecy):
        for coli in range(nsecx):
            GSImage.array[rowi*secsize_y:(rowi+1)*secsize_y, coli*secsize_x:(coli+1)*secsize_x] *= Gain16[rowi, coli]
            gain_array[rowi*nsecx+coli] = 1/Gain16[rowi, coli]
    return GSImage, gain_array


def GainsNonUniform16(GSImage, gain=1, nsecy=2, nsecx=8, seed=202102, logger=None):
    # Generate Gain non-uniformity, and multipy the different factors (mean~1 with sigma~1%) to the GS-Image
    rg = Generator(PCG64(int(seed)))
    Random16 = (rg.random(nsecy*nsecx)-0.5)*0.04+1   # sigma~1%
    Gain16 = Random16.reshape((nsecy, nsecx))/gain
    if logger is not None:
        msg = str(seed-20210202, "Gains of 16 channels: " + str(Gain16))
        logger.info(msg)
    else:
        print(seed-20210202, "Gains of 16 channels:\n", Gain16)
    # arrshape = GSImage.array.shape
    # secsize_x = int(arrshape[1]/nsecx)
    # secsize_y = int(arrshape[0]/nsecy)
    # for rowi in range(nsecy):
    #     for coli in range(nsecx):
    #         GSImage.array[rowi*secsize_y:(rowi+1)*secsize_y,coli*secsize_x:(coli+1)*secsize_x] *= Gain16[rowi,coli]
    # return GSImage
    return Gain16


def MakeFlatSmooth(GSBounds, seed):
    rg = Generator(PCG64(int(seed)))
    r1, r2, r3, r4 = rg.random(4)
    a1 = -0.5 + 0.2*r1
    a2 = -0.5 + 0.2*r2
    a3 = r3+5
    a4 = r4+5
    xmin, xmax, ymin, ymax = GSBounds.getXMin(), GSBounds.getXMax(), GSBounds.getYMin(), GSBounds.getYMax()
    Flty, Fltx = np.mgrid[ymin:(ymax+1), xmin:(xmax+1)]
    rg = Generator(PCG64(int(seed)))
    p1, p2, bg = rg.poisson(1000, 3)
    Fltz = 0.6*1e-7*(a1 * (Fltx-p1) ** 2 + a2 * (Flty-p2) ** 2 - a3*Fltx - a4*Flty) + bg*20
    FlatImg = galsim.ImageF(Fltz)
    return FlatImg


def MakeFlatNcomb(flat_single_image, ncombine=1, read_noise=5, gain=1, overscan=500, biaslevel=500, seed_bias=20210311, logger=None):
    ncombine = int(ncombine)
    FlatCombImg = flat_single_image*ncombine
    rng = galsim.UniformDeviate()
    NoiseFlatPoi = galsim.PoissonNoise(rng=rng, sky_level=0)
    FlatCombImg.addNoise(NoiseFlatPoi)
    NoiseFlatReadN = galsim.GaussianNoise(rng=rng, sigma=read_noise*ncombine**0.5)
    FlatCombImg.addNoise(NoiseFlatReadN)
    # NoiseFlat = galsim.CCDNoise(rng, gain=gain, read_noise=read_noise*ncombine**0.5, sky_level=0)
    for i in range(ncombine):
        FlatCombImg = AddBiasNonUniform16(
            FlatCombImg,
            bias_level=biaslevel,
            nsecy=2, nsecx=8,
            seed=seed_bias,
            logger=logger)
    if ncombine == 1:
        FlatTag = 'Single'
        pass
    elif ncombine > 1:
        FlatCombImg /= ncombine
        FlatTag = 'Combine'
    # FlatCombImg.replaceNegative(replace_value=0)
    # FlatCombImg.quantize()
    return FlatCombImg, FlatTag


def MakeDarkNcomb(npix_x, npix_y, overscan=500, bias_level=500, seed_bias=202102, darkpsec=0.02, exptime=150, ncombine=10, read_noise=5, gain=1, logger=None):
    ncombine = int(ncombine)
    darkpix = darkpsec*exptime
    DarkSngImg = galsim.Image(npix_x, npix_y, init_value=darkpix)
    rng = galsim.UniformDeviate()
    NoiseDarkPoi = galsim.PoissonNoise(rng=rng, sky_level=0)
    NoiseReadN = galsim.GaussianNoise(rng=rng, sigma=read_noise*ncombine**0.5)
    DarkCombImg = DarkSngImg*ncombine
    DarkCombImg.addNoise(NoiseDarkPoi)
    DarkCombImg.addNoise(NoiseReadN)
    for i in range(ncombine):
        DarkCombImg = AddBiasNonUniform16(
            DarkCombImg,
            bias_level=bias_level,
            nsecy=2, nsecx=8,
            seed=int(seed_bias),
            logger=logger)
    if ncombine == 1:
        DarkTag = 'Single'
        pass
    elif ncombine > 1:
        DarkCombImg /= ncombine
        DarkTag = 'Combine'
    # DarkCombImg.replaceNegative(replace_value=0)
    # DarkCombImg.quantize()
    return DarkCombImg, DarkTag


def PRNU_Img(xsize, ysize, sigma=0.01, seed=202101):
    rg = Generator(PCG64(int(seed)))
    prnuarr = rg.normal(1, sigma, (ysize, xsize))
    prnuimg = galsim.ImageF(prnuarr)
    return prnuimg


def NonLinear_f(x, beta_1, beta_2):
    return x - beta_1 * x * x + beta_2 * x * x * x


def NonLinearity(GSImage, beta1=5E-7, beta2=0):
    # NonLinear_f = lambda x, beta_1, beta_2: x - beta_1*x*x + beta_2*x*x*x
    GSImage.applyNonlinearity(NonLinear_f, beta1, beta2)
    return GSImage


# Saturation & Bleeding Start#
def BleedingTrail(aa, yy):
    if aa < 0.2:
        aa = 0.2
    else:
        pass
    try:
        fy = 0.5*(math.exp(math.log(yy+1)**3/aa)+np.exp(-1*math.log(yy+1)**3/aa))
        faa = 0.5*(math.e+1/math.e)
        trail_frac = 1-0.1*(fy-1)/(faa-1)
    except Exception as e:
        print(e)
        trail_frac = 1

    return trail_frac


def MakeTrail(imgarr, satuyxtuple, charge, fullwell=9e4, direction='up', trailcutfrac=0.9):
    '''
    direction: "up" or "down". For "up", bleeds along Y-decreasing direction; for "down", bleeds along Y-increasing direction.
    '''
    yi, xi = satuyxtuple
    aa = np.log(charge/fullwell)**3              # scale length of the bleeding trail
    yy = 1

    while charge > 0:
        if yi < 0 or yi > imgarr.shape[0]-1:
            break
        if yi == 0 or yi == imgarr.shape[0]-1:
            imgarr[yi, xi] = fullwell
            break

        if direction == 'up':
            if imgarr[yi-1, xi] >= fullwell:
                imgarr[yi, xi] = fullwell
                yi -= 1
                # [TEST] charge in the middle
                if yi == (imgarr.shape[0] // 2 - 1):
                    break
                continue
        elif direction == 'down':
            if imgarr[yi+1, xi] >= fullwell:
                imgarr[yi, xi] = fullwell
                yi += 1
                if yi == (imgarr.shape[0] // 2):
                    break
                continue
        if aa <= 1:
            while imgarr[yi, xi] >= fullwell:
                imgarr[yi, xi] = fullwell
                if direction == 'up':
                    imgarr[yi-1, xi] += charge
                    charge = imgarr[yi-1, xi]-fullwell
                    yi -= 1
                    # if yi < 0:
                    if yi < 0 or yi == (imgarr.shape[0]//2 - 1):
                        break
                elif direction == 'down':
                    imgarr[yi+1, xi] += charge
                    charge = imgarr[yi+1, xi]-fullwell
                    yi += 1
                    # if yi > imgarr.shape[0]:
                    if yi > imgarr.shape[0]  or yi == (imgarr.shape[0]//2):
                        break
        else:
            # calculate bleeding trail:
            trail_frac = BleedingTrail(aa, yy)

            # put charge upwards
            if trail_frac >= 0.99:
                imgarr[yi, xi] = fullwell
                if direction == 'up':
                    yi -= 1
                elif direction == 'down':
                    yi += 1
                yy += 1
            else:
                if trail_frac < trailcutfrac:
                    break
                charge = fullwell*trail_frac
                imgarr[yi, xi] += charge
                if imgarr[yi, xi] > fullwell:
                    imgarr[yi, xi] = fullwell

                if direction == 'up':
                    yi -= 1
                elif direction == 'down':
                    yi += 1
                yy += 1

    return imgarr


def ChargeFlow(imgarr, fullwell=9E4):
    size_y, size_x = imgarr.shape
    satupos_y, satupos_x = np.where(imgarr > fullwell)

    if satupos_y.shape[0] == 0:
        # make no change for the image array
        return imgarr
    elif satupos_y.shape[0]/imgarr.size > 0.5:
        imgarr.fill(fullwell)
        return imgarr

    chargedict = {}
    imgarrorig = copy.deepcopy(imgarr)

    for yi, xi in zip(satupos_y, satupos_x):
        yxidx = ''.join([str(yi), str(xi)])
        chargedict[yxidx] = imgarrorig[yi, xi]-fullwell

    for yi, xi in zip(satupos_y, satupos_x):
        yxidx = ''.join([str(yi), str(xi)])
        satcharge = chargedict[yxidx]
        chargeup = ((np.random.random()-0.5)*0.05+0.5)*satcharge
        chargedn = satcharge - chargeup

        try:
            # Charge Clump moves up
            if yi >= 0 and yi < imgarr.shape[0]:
                imgarr = MakeTrail(imgarr, (yi, xi), chargeup, fullwell=9e4, direction='up', trailcutfrac=0.9)
                # Charge Clump moves down
                imgarr = MakeTrail(imgarr, (yi, xi), chargedn, fullwell=9e4, direction='down', trailcutfrac=0.9)
        except Exception as e:
            print(e, '@pix ', (yi+1, xi+1))
            return imgarr
    return imgarr


def SaturBloom(GSImage, nsect_x=1, nsect_y=1, fullwell=9e4):
    """
    To simulate digital detector's saturation and blooming effect. The blooming is along the read-out direction, perpendicular to the charge transfer direction. Charge clumpy overflows the pixel well will flow to two oposite directions with nearly same charges.
    Work together with chargeflow() function.
    Parameters:
      GSImage: a GalSim Image of a chip;
      nsect_x: number of sections divided along x direction;
      nsect_y: number of sections divided along y direction.
    Return: a saturated image array with the same size of input.
    """
    imgarr = GSImage.array
    size_y, size_x = imgarr.shape
    subsize_y = int(size_y/nsect_y)
    subsize_x = int(size_x/nsect_x)

    for i in range(nsect_y):
        for j in range(nsect_x):
            subimg = imgarr[subsize_y*i:subsize_y*(i+1), subsize_x*j:subsize_x*(j+1)]

            subimg = ChargeFlow(subimg, fullwell=fullwell)

            imgarr[subsize_y*i:subsize_y*(i+1), subsize_x*j:subsize_x*(j+1)] = subimg

    return GSImage

#    Saturation & Bleeding End    #


def readout16(GSImage, rowi=0, coli=0, overscan_value=0):
    # readout image as 16 outputs of sub-images plus prescan & overscan.
    # assuming image width and height sizes are both even.
    # assuming image has 2 columns and 8 rows of output channels.
    # 00  01
    # 10  11
    # 20  21
    # ...
    # return: GS Image Object
    npix_y, npix_x = GSImage.array.shape
    subheight = int(8+npix_y/2+8)
    subwidth = int(16+npix_x/8+27)
    OutputSubimg = galsim.ImageUS(subwidth, subheight, init_value=overscan_value)
    if rowi < 4 and coli == 0:
        subbounds = galsim.BoundsI(1, int(npix_x/2),  int(npix_y/8*rowi+1), int(npix_y/8*(rowi+1)))
        subbounds = subbounds.shift(galsim.PositionI(GSImage.bounds.getXMin()-1, GSImage.bounds.getYMin()-1))
        subimg = GSImage[subbounds]
        OutputSubimg.array[27:int(npix_y/8)+27, 8:int(npix_x/2)+8] = subimg.array
    elif rowi < 4 and coli == 1:
        subbounds = galsim.BoundsI(npix_x/2+1, npix_x,  npix_y/8*rowi+1, npix_y/8*(rowi+1))
        subbounds = subbounds.shift(galsim.PositionI(GSImage.bounds.getXMin()-1, GSImage.bounds.getYMin()-1))
        subimg = GSImage[subbounds]
        OutputSubimg.array[27:int(npix_y/8)+27, 8:int(npix_x/2)+8] = subimg.array
    elif rowi >= 4 and rowi < 8 and coli == 0:
        subbounds = galsim.BoundsI(1, npix_x/2,  npix_y/8*rowi+1, npix_y/8*(rowi+1))
        subbounds = subbounds.shift(galsim.PositionI(GSImage.bounds.getXMin()-1, GSImage.bounds.getYMin()-1))
        subimg = GSImage[subbounds]
        OutputSubimg.array[16:int(npix_y/8)+16, 8:int(npix_x/2)+8] = subimg.array
    elif rowi >= 4 and rowi < 8 and coli == 1:
        subbounds = galsim.BoundsI(npix_x/2+1, npix_x,  npix_y/8*rowi+1, npix_y/8*(rowi+1))
        subbounds = subbounds.shift(galsim.PositionI(GSImage.bounds.getXMin()-1, GSImage.bounds.getYMin()-1))
        subimg = GSImage[subbounds]
        OutputSubimg.array[16:int(npix_y/8)+16, 8:int(npix_x/2)+8] = subimg.array
    else:
        print("\n\033[31mError: "+"Wrong rowi or coli assignment. Permitted: 0<=rowi<=7, 0<=coli<=1."+"\033[0m\n")
        return OutputSubimg
    return OutputSubimg


def CTE_Effect(GSImage, threshold=27, direction='column'):
    # Devide the image into 4 sections and apply CTE effect with different trail directions.
    # GSImage: a GalSim Image object.
    size_y, size_x = GSImage.array.shape
    size_sect_y = int(size_y/2)
    size_sect_x = int(size_x/2)
    imgarr = GSImage.array
    if direction == 'column':
        imgarr[0:size_sect_y, :] = CTEModelColRow(imgarr[0:size_sect_y, :], trail_direction='down', direction='column', threshold=threshold)
        imgarr[size_sect_y:size_y, :] = CTEModelColRow(imgarr[size_sect_y:size_y, :], trail_direction='up', direction='column', threshold=threshold)
    elif direction == 'row':
        imgarr[:, 0:size_sect_x] = CTEModelColRow(imgarr[:, 0:size_sect_x], trail_direction='right', direction='row', threshold=threshold)
        imgarr[:, size_sect_x:size_x] = CTEModelColRow(imgarr[:, size_sect_x:size_x], trail_direction='left', direction='row', threshold=threshold)
    return GSImage


@jit()
def CTEModelColRow(img, trail_direction='up', direction='column', threshold=27):

    # total trail flux vs (pixel flux)^1/2 is approximately linear
    # total trail flux = trail_a * (pixel flux)^1/2 + trail_b
    # trail pixel flux = pow(0.5,x)/0.5, normalize to 1
    trail_a = 5.651803799619966
    trail_b = -2.671933068990729

    sh1 = img.shape[0]
    sh2 = img.shape[1]
    n_img = img*0
    idx = np.where(img < threshold)
    if len(idx[0]) == 0:
        pass
    elif len(idx[0]) > 0:
        n_img[idx] = img[idx]

    yidx, xidx = np.where(img >= threshold)
    if len(yidx) == 0:
        pass
    elif len(yidx) > 0:
        # print(index)
        for i, j in zip(yidx, xidx):
            f = img[i, j]
            trail_f = (np.sqrt(f)*trail_a + trail_b)*0.5
            # trail_f=5E-5*f**1.5
            xy_num = 10
            all_trail = np.zeros(xy_num)

            xy_upstr = np.arange(1, xy_num, 1)

            # all_trail_pix = np.sum(pow(0.5,xy_upstr)/0.5)
            all_trail_pix = 0
            for m in xy_upstr:
                a1 = 12.97059491
                b1 = 0.54286652
                c1 = 0.69093105
                a2 = 2.77298856
                b2 = 0.11231055
                c2 = -0.01038675
                # t_pow = 0
                am = 1
                bm = 1
                t_pow = am*np.exp(-bm*m)
                # if m < 5:
                #     t_pow = a1*np.exp(-b1*m)+c1
                # else:
                #     t_pow = a2*np.exp(-b2*m)+c2
                if t_pow < 0:
                    t_pow = 0

                all_trail_pix += t_pow
                all_trail[m] = t_pow
            trail_pix_eff = trail_f/all_trail_pix
            all_trail = trail_pix_eff*all_trail
            all_trail[0] = f - trail_f

            for m in np.arange(0, xy_num, 1):
                if direction == 'column':
                    if trail_direction == 'down':
                        y_pos = i + m
                    elif trail_direction == 'up':
                        y_pos = i - m
                    if y_pos < 0 or y_pos >= sh1:
                        break
                    n_img[y_pos, j] = n_img[y_pos, j] + all_trail[m]
                elif direction == 'row':
                    if trail_direction == 'left':
                        x_pos = j - m
                    elif trail_direction == 'right':
                        x_pos = j + m
                    if x_pos < 0 or x_pos >= sh2:
                        break
                    n_img[i, x_pos] = n_img[i, x_pos] + all_trail[m]

    return n_img


# ---------- For Cosmic-Ray Simulation ------------
# ---------- Zhang Xin ----------------------------
def getYValue(collection, x):
    index = 0
    if (collection.shape[1] == 2):
        while (x > collection[index, 0] and index < collection.shape[0]):
            index = index + 1
        if (index == collection.shape[0] or index == 0):
            return 0

        deltX = collection[index, 0] - collection[index-1, 0]
        deltY = collection[index, 1] - collection[index-1, 1]

        if deltX == 0:
            return (collection[index, 1] + collection[index-1, 1])/2.0
        else:
            a = deltY/deltX
            return a * (x - collection[index-1, 0]) + collection[index-1, 1]
    return 0


def selectCosmicRayCollection(attachedSizes, xLen, yLen, cr_pixelRatio, CR_max_size):

    normalRay = 0.90
    nnormalRay = 1-normalRay
    max_nrayLen = 100
    pixelNum = int(xLen * yLen * cr_pixelRatio * normalRay)
    pixelNum_n = int(xLen * yLen * cr_pixelRatio * nnormalRay)
    CRPixelNum = 0

    maxValue = max(attachedSizes[:, 1])
    maxValue += 0.1

    cr_event_num = 0
    CRs = np.zeros(pixelNum)
    while (CRPixelNum < pixelNum):
        x = CR_max_size * np.random.random()
        y = maxValue * np.random.random()
        if (y <= getYValue(attachedSizes, x)):
            CRs[cr_event_num] = np.ceil(x)
            cr_event_num = cr_event_num + 1
            CRPixelNum = CRPixelNum + round(x)

    while (CRPixelNum < pixelNum + pixelNum_n):
        nx = np.random.random()*(max_nrayLen-CR_max_size)+CR_max_size
        CRs[cr_event_num] = np.ceil(nx)
        cr_event_num = cr_event_num + 1
        CRPixelNum = CRPixelNum + np.ceil(nx)

    return CRs[0:cr_event_num]


def defineEnergyForCR(cr_event_size, seed=12345):
    import random
    sigma = 0.6 / 2.355
    mean = 3.3
    random.seed(seed)
    energys = np.zeros(cr_event_size)
    for i in np.arange(cr_event_size):
        energy_index = random.normalvariate(mean, sigma)
        energys[i] = pow(10, energy_index)
    return energys


def convCR(CRmap=None, addPSF=None, sp_n=4):
    sh = CRmap.shape

    # sp_n = 4
    subCRmap = np.zeros(np.array(sh)*sp_n)
    pix_v0 = 1/(sp_n*sp_n)
    for i in np.arange(sh[0]):
        i_st = sp_n*i
        for j in np.arange(sh[1]):
            if CRmap[i, j] == 0:
                continue
            j_st = sp_n*j
            pix_v1 = CRmap[i, j]*pix_v0
            for m in np.arange(sp_n):
                for n in np.arange(sp_n):
                    subCRmap[i_st+m, j_st + n] = pix_v1

    m_size = addPSF.shape[0]

    subCRmap_n = np.zeros(np.array(subCRmap.shape) + m_size - 1)

    for i in np.arange(subCRmap.shape[0]):
        for j in np.arange(subCRmap.shape[1]):
            if subCRmap[i, j] > 0:
                convPix = addPSF*subCRmap[i, j]
                subCRmap_n[i:i+m_size, j:j+m_size] += convPix

    CRmap_n = np.zeros((np.array(subCRmap_n.shape)/sp_n).astype(np.int32))
    sh_n = CRmap_n.shape

    for i in np.arange(sh_n[0]):
        i_st = sp_n*i
        for j in np.arange(sh_n[1]):
            p_v = 0
            j_st = sp_n*j
            for m in np.arange(sp_n):
                for n in np.arange(sp_n):
                    p_v += subCRmap_n[i_st+m, j_st + n]

            CRmap_n[i, j] = p_v

    return CRmap_n


def produceCR_Map(xLen, yLen, exTime, cr_pixelRatio, gain, attachedSizes, seed=20210317):
    # Return: an 2-D numpy array
    # attachedSizes = np.loadtxt('./wfc-cr-attachpixel.dat');
    np.random.seed(seed)
    CR_max_size = 20.0
    cr_size = selectCosmicRayCollection(attachedSizes, xLen, yLen, cr_pixelRatio, CR_max_size)

    cr_event_size = cr_size.shape[0]
    cr_energys = defineEnergyForCR(cr_event_size, seed=seed)

    CRmap = np.zeros([yLen, xLen])

    # produce conv kernel
    from astropy.modeling.models import Gaussian2D
    o_size = 4
    sp_n = 8

    m_size = o_size*sp_n+1
    m_cen = o_size*sp_n/2
    sigma_psf = 0.2*sp_n
    addPSF_ = Gaussian2D(1, m_cen, m_cen, sigma_psf, sigma_psf)
    yp, xp = np.mgrid[0:m_size, 0:m_size]
    addPSF = addPSF_(xp, yp)
    convKernel = addPSF/addPSF.sum()

    # ---------------------------------
    for i in np.arange(cr_event_size):
        xPos = round((xLen - 1) * np.random.random())
        yPos = round((yLen - 1) * np.random.random())
        cr_lens = int(cr_size[i])
        if cr_lens == 0:
            continue
        pix_energy = cr_energys[i]/gain/cr_lens
        pos_angle = 1/2*math.pi*np.random.random()

        crMatrix = np.zeros([cr_lens+1, cr_lens + 1])

        for j in np.arange(cr_lens):
            x_n = int(np.cos(pos_angle)*j - np.sin(pos_angle)*0)
            if x_n < 0:
                x_n = x_n + cr_lens+1
            y_n = int(np.sin(pos_angle)*j + np.cos(pos_angle)*0)
            if x_n < 0 or x_n > cr_lens or y_n < 0 or y_n > cr_lens:
                continue
            crMatrix[y_n, x_n] = pix_energy

        crMatrix_n = convCR(crMatrix, convKernel, sp_n)
        # crMatrix_n = crMatrix

        xpix = np.arange(crMatrix_n.shape[0]) + int(xPos)
        ypix = np.arange(crMatrix_n.shape[1]) + int(yPos)

        sh = CRmap.shape
        okx = (xpix >= 0) & (xpix < sh[1])
        oky = (ypix >= 0) & (ypix < sh[0])

        sly = slice(ypix[oky].min(), ypix[oky].max()+1)
        slx = slice(xpix[okx].min(), xpix[okx].max()+1)
        CRmap[sly, slx] += crMatrix_n[oky, :][:, okx]
    return CRmap.astype(np.int32), cr_event_size


def ShutterEffectArr(GSImage, t_exp=150, t_shutter=1.3, dist_bearing=735, dt=1E-3):
    # Generate Shutter-Effect normalized image
    # t_shutter: time of shutter movement
    # dist_bearing: distance between two bearings of shutter leaves
    # dt: delta_t of sampling

    from scipy import interpolate

    SampleNumb = int(t_shutter/dt+1)
    DistHalf = dist_bearing/2

    t = np.arange(SampleNumb)*dt
    a_arr = 5.84*np.sin(2*math.pi/t_shutter*t)
    v = np.zeros(SampleNumb)
    theta = np.zeros(SampleNumb)
    x = np.arange(SampleNumb)/(SampleNumb-1)*dist_bearing
    s = np.zeros(SampleNumb)
    s1 = np.zeros(SampleNumb)
    s2 = np.zeros(SampleNumb)
    brt = np.zeros(SampleNumb)
    idx = np.arange(SampleNumb)
    sidx = np.zeros(SampleNumb)
    s1idx = np.zeros(SampleNumb)
    s2idx = np.zeros(SampleNumb)

    v[0] = 0
    theta[0] = 0

    for i in range(SampleNumb-1):
        v[i+1] = v[i]+a_arr[i]*dt
        theta[i+1] = theta[i]+v[i]*dt
        s1[i] = DistHalf*np.cos(theta[i])
        s2[i] = dist_bearing-DistHalf*np.cos(theta[i])
        s1idx[i] = int(s1[i]/dist_bearing*(SampleNumb))
        s2idx[i] = int(s2[i]/dist_bearing*(SampleNumb))
        brt[(idx > s1idx[i]) & (idx < s2idx[i])] += dt

    if t_exp > t_shutter*2:
        brt = brt*2+(t_exp-t_shutter*2)
    else:
        brt = brt*2

    x = (x-dist_bearing/2)*100

    intp = interpolate.splrep(x, brt, s=0)

    xmin = GSImage.bounds.getXMin()
    xmax = GSImage.bounds.getXMax()
    ymin = GSImage.bounds.getYMin()
    ymax = GSImage.bounds.getYMax()
    if xmin < np.min(x) or xmax > np.max(x):
        raise LookupError("Out of focal-plane bounds in X-direction.")
    if ymin < -25331 or ymax > 25331:
        raise LookupError("Out of focal-plane bounds in Y-direction.")
    sizex = xmax-xmin+1
    sizey = ymax-ymin+1
    xnewgrid = np.mgrid[xmin:(xmin+sizex)]
    expeffect = interpolate.splev(xnewgrid, intp, der=0)
    expeffect /= t_exp
    exparrnormal = np.tile(expeffect, (sizey, 1))
    # GSImage *= exparrnormal

    return exparrnormal