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
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==True and IfDeadPix==True:
        HotFraction = rgf.random()             # fraction in total bad pixels
    elif IfHotPix==False and IfDeadPix==False:
        return GSImage
    elif IfHotPix==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==True:
        GSImage.array[YPositHot,XPositHot] += rgh.gamma(2,25*150,size=NPixHot)
    if IfDeadPix==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):
    # 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))
    print(xposit+1)
    # signs = 2*rgdn.integers(0,2,size=(nbadsecA+nbadsecD))-1
    if meanimg>0:
        dn = rgdn.integers(low=meanimg*1.3+50, high=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):
    # 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
    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):
    # 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))
    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):
    # 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
    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]
    return GSImage


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 = 1e-6*(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):
    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)
    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):
    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))
    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 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


def chargeflow(ndarr, fullwell=10E4):
    size_y,size_x = ndarr.shape
    satpos_y = np.where(ndarr>=fullwell)[0]
    satpos_x = np.where(ndarr>=fullwell)[1]
    Nsatpix = len(satpos_y)

    if Nsatpix==0:
        # make no change for the image array
        return ndarr

    else:    
        for i in range(Nsatpix):
            ClumpFullwell=True
            satcharge = ndarr[satpos_y[i],satpos_x[i]]-fullwell
            ndarr[satpos_y[i],satpos_x[i]] = fullwell
            
            satpos_yi0 = satpos_y[i]

            # Define the x,y=0,0 element of image array is the lower-left corner. So y decreases being downward.

            # print('Charge Clump moves down')
            chargedn = ((np.random.random()-0.5)*0.05+0.5)*satcharge
            chargeup = satcharge - chargedn
            fwi = 1
            aa = np.log(chargedn/fullwell)**3*0.9   # blooming length begin to has e- less than fullwell
            if aa < 0.05:
                ClumpFullwell=False
            # Test
            try:
                while ClumpFullwell==True:
                    if satpos_y[i]<=0:
                        break
                    if ndarr[satpos_y[i]-1,satpos_x[i]]<fullwell:
                        ndarr[satpos_y[i]-1,satpos_x[i]] = ndarr[satpos_y[i]-1,satpos_x[i]] + chargedn
                        if ndarr[satpos_y[i]-1,satpos_x[i]]>=fullwell:
                            fx = 0.5*(math.exp(math.log(fwi)**3/aa)+np.exp(-1*math.log(fwi)**3/aa))
                            if fx>5:
                                fx=5
                            faa= 0.5*(math.exp(aa/aa)+np.exp(-1*aa/aa))
                            rand_frac = 1-0.1*(fx-1)/(faa-1)

                            chargedn = ndarr[satpos_y[i]-1,satpos_x[i]] - fullwell
                            ndarr[satpos_y[i]-1,satpos_x[i]] = fullwell*rand_frac
                            satpos_y[i] = satpos_y[i]-1
                            if satpos_y[i]<0:
                                ClumpFullwell=False
                                break
                        else:
                            ClumpFullwell=False
                        fwi += 1
                    else:
                        satpos_y[i] = satpos_y[i]-1
                        if satpos_y[i]<0:
                            ClumpFullwell=False
                            break
                  
                
                # print('Charge Clump moves up')
                ClumpFullwell=True
                satpos_y[i] = satpos_yi0
                fwi = 1
                aa = np.log(chargeup/fullwell)**3*0.9   # blooming length at which it begins to have e- less than fullwell
                if aa < 0.05:
                    ClumpFullwell=False
                while ClumpFullwell==True:
                    if satpos_y[i]>=size_y-1:
                        break
                    if ndarr[satpos_y[i]+1,satpos_x[i]]<fullwell:
                        ndarr[satpos_y[i]+1,satpos_x[i]] = ndarr[satpos_y[i]+1,satpos_x[i]] + chargeup
                        if ndarr[satpos_y[i]+1,satpos_x[i]]>=fullwell:
                            fx = 0.5*(math.exp(math.log(fwi)**3/aa)+np.exp(-1*math.log(fwi)**3/aa))
                            if fx>5:
                                fx=5
                            faa= 0.5*(math.exp(aa/aa)+np.exp(-1*aa/aa))
                            rand_frac = 1-0.1*(fx-1)/(faa-1)
                            chargeup = ndarr[satpos_y[i]+1,satpos_x[i]] - fullwell
                            ndarr[satpos_y[i]+1,satpos_x[i]] = fullwell*rand_frac
                            satpos_y[i] = satpos_y[i]+1
                            if satpos_y[i]>=size_y-1:
                                ClumpFullwell=False
                                break
                        else:
                            ClumpFullwell=False
                        fwi += 1
                    else:
                        satpos_y[i] = satpos_y[i]+1
                        if satpos_y[i]>=size_y-1:
                            ClumpFullwell=False
                            break
            except Exception as e:
                print(e)
                print(fwi, aa)
                pass
          
    return ndarr


def SaturBloom(GSImage, nsect_x=1, nsect_y=1, fullwell=10e4):
    """
    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


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):
    import random
    sigma = 0.6 / 2.355;
    mean = 3.3;

    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);

    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_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

    brt = brt*2+(150-t_shutter*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 /= np.max(expeffect)
    exparrnormal = np.tile(expeffect, (sizey,1))
    # GSImage *= exparrnormal

    return exparrnormal