psf_and_imageconv_dragonfly_obs.py

# -*- coding: utf-8 -*-
"""psf_and_imageconv_dragonfly_obs.py -- determine zeropoint for airmass of 1 and embed ZPSPACE in header

Usage:
    psf_and_imageconv_dragonfly_obs [-h] [-v] [-k KERNEL] [-p PIXANGLE] [-c CENTRE] [-a ANGLE] <npzfile>
Options:
    -h, --help                                  Show this screen
    -v, --verbose                               Show extra information [default: False]
    -k KERNEL, --kernel KERNEL                  Name of the kernel to use. [default: Airy]
    -p PIXANGLE, --pixangle PIXANGLE            angle subtended by an image pixel
    -c CENTRE, --centre CENTRE                  centre on chip (pixel coordinates)
    -a ANGLE, --angle ANGLE                     angle of chip long axis wrt image x-axis (radians)
Examples:
    psf_and_imageconv_dragonfly_obs -v emission.npz

Created on Thu Feb  2 14:12:22 2017, modified Tue Sept 26 2017
@author: wijers, modified by lokhorst

Description:
takes a .npz box (region) projection from make_maps, convolves with a PSF, 
selects a region if needed

input: 
 - 2D array repesenting emission
 - angle subtended by an image pixel
 - centre on chip (pixel coordinates)
 - angle of chip long axis wrt image x-axis (radians)
output:
 - photon counts or ergs per second (as in input file) per pixel
"""

import docopt
import numpy as np
import astropy as asp
import astropy.convolution as cnv
import os.path

import eagle_constants_and_units as cons
#import loadnpz_and_plot as lnp
from cosmo_utils import comoving_distance_cm # loading all of make_maps means the entire read_eagle machinary too 

# working units: cgs, radians

radians = 1.
degrees = np.pi/180.
arcmin = 1./60. * degrees 
arcsec = 1./3600. * degrees

g = 1.
kg = 10.**3 * g

s = 1.
Hz = 1/s

cm = 1.
nm = 10.**-7 * cm
mum = 10**-4 * cm

erg = 1.

Jy = 10**-23 * erg/(s*cm**2) *1/Hz  

# Dragonfly CCD data (current)
data_version = 1
saved_kernels = 'dragonfly_kernels_dataversion%s' %str(data_version)
saved_abr_fftkernels = 'dragonfly_abr_fftkernels_dataversion%s' %str(data_version)

FOV = (2.6*degrees, 1.9*degrees)
numpix_dr = (3326,2504)
pix_size_phys = 5.4 *mum
pix_size_angle = 2.8 * arcsec
seeing_limit = 1.5*arcsec #typically 1.5--2.0 in long exposures according to the dragonfly paper

def diffraction_limit(wavelength):
    return 0.65*arcsec * wavelength/(450.*nm)
def airy_size(wavelength): #3.1 mum diamater of Airy disc; used as distance to first Airy zero
    return 3.1*mum/2. * wavelength/(450.*nm)

wavelengths = {'halpha': 656.28*nm}

def SB_photonscgs_to_ABmagarcsec(sb):
    fld = sb * cons.planck * (4*np.pi)/3600**2 # flux density: energy / (m**2 s)  /frequency (/arcmin**2)  sufrace brightness: photons / (cm**2 s) /sr       
    return -2.5*np.log10(fld/(3631.*Jy))

def print_verbose_string(printme):
    print >> sys.stderr, "VERBOSE: %s" % printme


# attempt: use kernel in projection. 
# For a given CCD pixel, sample a few points and use 
# image_pixel_S_B * PSF_normed * subsample_area
 
# image: input grid of surface brightness values (can be ergs or photons, assumded cgs and log)
# image_angle_per_pixel: angular size subtended by an image pixel
# centre: where to put the CCD centre on the image (pixel coordinates, fractional value are fine)
# angle: angle between CCD long edge and x-axis
# z: image redshift (needed for wavelength -> Airy disk size)
# proj_dens: how densly to sample each grid cell for projection onto the CCD    
# psf_rad: sample PSF out to psf_rad*airy disk size
 
 
 
# Calculate kernels on first call, then reuse
# kernels dict contains kernels labeled by:
#     boxlength, number of pixels, redshift, spectral line, and psf radius (in units of max(Airy disk, seeing limit))  
# added and updated by generate_kernel
# added to an npz file by save_kernels, retrieved from npz file by load_kernelsf




########################################
# Deborah: Bob Abraham suggests 2-Moffat + power law as the 'best' solution, 
# with the power law probably being unnecessary for these purposes.  
########################################

# From Rob Abraham's ipython notebook (mangled version):


# Baseline profiles; normalised to 1 (checked). 
# FWHM is for the Moffat profile alone

# default beta: kolmogorov turbulence for single Moffat
#               2.0 and 7.0 for 2-moffat Racine (1996) fit
def moffat(theta, fwhm, beta=4.765):
    """Profile with default beta suggested by Trujillo et al. 2001. This
    value of beta corresponds to Kolmogorov turbulence."""
    ibeta = 1.0/beta
    alpha = fwhm/(2.0*np.sqrt(2.0**ibeta - 1.0))
    coefficient = (beta-1.0)/(np.pi*(alpha**2))
    firstMoffat = coefficient * (1 + (theta/alpha)**2)**(-beta)
    return firstMoffat

def aureole_profile(theta, fwhm, d0=50):
        """Analytical function suggested by Racine (1996) for modelling the full
        PSF aureole. The default value of d0 matches the photographic data of
        King (1971). Note that d0 is specified in units of the FWHM. (It is 50
        and not 100 as in the Racine paper because it is in units of FWHM and
        not HW). Note that constructing a PSF with an Aureole will change the
        effective PSF (likely by a very small amount, assuming only a small
        fraction of the light is in the aureole) but this will not be correctly
        captured by the fwhm property of the PSF."""
        
        d = d0 * fwhm
        coeff = 1./(8*np.pi*d**2)
        cosfac = np.cos(np.arctan(theta/(2*d)))
        return coeff*(cosfac**3.0)


#####################################################
# Machinery for generating and saving these kernels #
#####################################################

abr_fftkernels = {}

def save_abr_fftkernels(skernels = abr_fftkernels):
    if os.path.isfile(saved_abr_fftkernels +'.npz'): # npz file already exists
        if verbose:
            print_verbose_string("npz kernel file already exists.")
        current = np.load(saved_kernels +'.npz')
        current_dict = {key: current[key] for key in current.keys()}
        current_dict.update(skernels)
        np.savez(saved_kernels,**current_dict)
    else:
        np.savez(saved_abr_fftkernels,**skernels)
    return 0

def load_abr_fftkernels(version = data_version):
    stored = np.load('dragonfly_abr_fftkernels_dataversion%s.npz' %str(version))
    stored_dict = {key: stored[key] for key in stored.keys()}
    abr_fftkernels.update(stored_dict)
    return 0

# stripped-down verion of the loadnpz_and_plot function
# used for oversampling grids
def imreduce(img, factor):
    """
    img: 2D image array
    factor: factor by which to reduce the number of array elements along each axis
    """

    inimg = img
    inshape = np.array(img.shape)
    
    inimg = np.array(np.split(inimg,inshape[0]/factor,axis=0))
    inimg = np.array(np.split(inimg,inshape[1]/factor,axis=-1))
    
    inimg = np.sum(inimg,axis=-1)
    inimg = np.sum(inimg,axis=-1)
    
    inimg = inimg/np.float(factor**2)        

    return inimg.T

    
def generate_abr_fftkernel(boxlength,numpix,z,kernel,fwhm,beta,d0,tag = ''):
    '''
    Input parameters: 
    
    input image description: used to calculate angle/pixel and required fft kernel size
        boxlength   [Mpc] (float)
        numpix      number of image pixels (int) 
        z           redshift (float): 
    kernel desciption: basic kernels and combinations thereof
        kernel      (string) one of ['Moffat', 'Aureole']                   
        beta1       beta parameter of the (first) Moffat profile (float)
        beta2       beta parameter of the second Moffat profile (float)
    The beta parameters are unused if the (second) Moffat profile is not used.
    
    Output:
    
    psf             (float array, 2d)
    updates dict of the individual psf models required
        
    '''
        
    # angle_per_pix in input and ouput images
    comdist = comoving_distance_cm(z)
    longlen = float(boxlength) * cons.cm_per_mpc  
    if comdist > longlen/2.: # even at larger values, the projection along z-axis = projection along sightline approximation will break down
        adist = comdist/(1.+z)
    else: 
        adist = longlen/2./(1.+z) 
    image_angle_per_pixel = longlen/(1.+z)/numpix *1./adist * radians # these functions work in units of angles

    # fft, ifft checked: correct behaviour on constant and delta functions; 
    # slight errors occur in normalisation
    # in product of delta functions, the peak does shift, but the sum and shape are intact
    # oversample functions and take averages to get the pixel kernel values
    basegrid = np.indices((10*numpix,10*numpix)) - 10*numpix/2 #(not exactly centered to avoid artifical smearing over at least 4 pixels)
    theta = np.sqrt(basegrid[0]**2 + basegrid[1]**2)*image_angle_per_pixel/10.    
    del basegrid
    
    # should be periodic; no light is lost, and all light contributes to each point. 
    print("Calculting PSF.\n")    
    if kernel == 'Moffat':
        psf = imreduce(moffat(theta, fwhm, beta),10)
        psf  = psf/np.sum(psf)
        print("Fourier transforming PSF.\n")
        ftpsf = np.fft.rfft2(psf)
        abr_fftkernels.update({'(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm),str(beta)) + tag: ftpsf})
        
    elif kernel == 'Aureole':
        psf = imreduce(aureole_profile(theta, fwhm, d0),10)
        psf = np.sum(psf)
        print("Fourier transforming PSF.\n")
        ftpsf = np.fft.rfft2(psf)
        abr_fftkernels.update({'(%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm*d0)) + tag: ftpsf})
    
    else:
        print('%s is not a valid kernel'%str(kernel))
    
    return ftpsf
    




def conv_image_abr(img,boxlength,numpix,z,kernel,fwhm,beta1='auto',beta2='auto',d0='auto',m1f = 'auto',mf='auto',af = 'auto',pf = 0.,tag = ''):
    '''
    Input parameters: 
    
    input image description: used to calculate angle/pixel and required fft kernel size
        image       (float array, 2d)
        boxlength   [cMpc] (float)
        numpix      number of image pixels (int) 
        z           redshift (float): 
    kernel desciption: basic kernels and combinations thereof
        kernel      (string) one of
                    ['Moffat', '2Moffat', 'Aureole', 'Point', '2MoffatAureole']
                    The 'Point' option does nothing, and is just a way to get
                    a full fft that only smears part of the light.
        beta1       beta parameter of the (first) Moffat profile (float)
        beta2       beta parameter of the second Moffat profile (float)
        mr1         fraction of the Moffat light in the first profile (float)
        mf          fraction of light in the Moffat profile(s)
        af          fraction of light in the Aureole profile
        pf          fraction of light not spread out (float or 'auto')
        tag         kernel dict entry tag (string)
    The beta parameters are unused if the (second) Moffat profile is not used;
    the fraction parameters are always used, so that only a part of the light 
    can be spread. (The remainder is only put into the point fraction if it is
    set to 'auto'.)
    No check is performed on whether the fractions add up to one.

    Output:
    
    image convolved with the chosen psf model (float array, 2d)   
    abr_fftkernels updated with the individual psf models required
    
    '''
    # check kernel choice and point fraction:
    if kernel not in ['Moffat', '2Moffat', 'Aureole', 'Point', '2MoffatAureole']:
        print('Invalid kernel choice.')
        return None
    
    # set default values for the chosen profile (following Arbraham ipython)
    if kernel == 'Moffat':
        if verbose:
            print_verbose_string("Chose Moffat profile.")
        # only normalisation parameter is mf; mr, af are ignored except for auto pf setting     
        if mf == 'auto':
            mf = 1.
        af = 0.
        if beta1 == 'auto':
            beta1 = 4.765 # kolmogorov turbulence
    
    elif kernel == '2Moffat':
        if verbose:
            print_verbose_string("Chose 2Moffat profile.")
        if mf == 'auto':
            mf =1.
        if m1f == 'auto':
            m1f = 0.8
        if beta1 == 'auto':
            beta1 = 7.0
        if beta2 == 'auto':
            beta2 = 2.0
        af = 0. 
    
    elif kernel == 'Aureole':
        if verbose:
            print_verbose_string("Chose Aureole profile.")
        if d0 == 'auto':
            d0 = 50.
        if af == 'auto':
            af = 1.            
        mf = 0.

    elif kernel == 'Point':
        if verbose:
            print_verbose_string("Chose Point profile.")
        if pf == 'auto':
            pf = 1.

    elif kernel == '2MoffatAureole':
        # default is the optimistic case from the ipython notebook
        # optimistic:  af = 0.02  pessimistic:   af = 0.1   (cirrus)
        # optimistic: fwhm = 3.0  pessimistic:  fwhm = 6.0 in arcsec
        if verbose:
            print_verbose_string("Chose 2MoffatAureole profile.")
        
        if af == 'auto' and mf =='auto':
            af = 0.02
            mf = 0.98
        elif mf == 'auto':
            mf = 1.- af
        elif af == 'auto':
            af = 1. - mf
            
        if beta1 == 'auto':
            beta1 = 7.0
        if beta2 == 'auto':
            beta2 = 2.0
        if d0 == 'auto':
            d0 = 50.
        
    if fwhm == 'auto':
        fwhm = 3.0*arcsec # working units are radians
        
    if pf == 'auto' and kernel != 'Point':
        pf = 1. - af - mf
               
    # generate the kernels, or take from earlier calculations
    if kernel == 'Moffat':
        if '(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),'Moffat',str(fwhm),str(beta1)) + tag in abr_fftkernels.keys():
            ftpsf = abr_fftkernels['(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm),str(beta1)) + tag]
        else:
            ftpsf = generate_abr_fftkernel(boxlength,numpix,z,'Moffat',fwhm,beta1,d0,tag = tag)
        ftpsf = ftpsf*mf
    
    elif kernel == '2Moffat'  or kernel == '2MoffatAureole': 
        if '(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),'Moffat',str(fwhm),str(beta1)) + tag in abr_fftkernels.keys():
            ftpsf1 = abr_fftkernels['(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm),str(beta1)) + tag]
        else:
            ftpsf1 = generate_abr_fftkernel(boxlength,numpix,z,'Moffat',fwhm,beta1,d0,tag = tag)
        
        if '(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),'Moffat',str(fwhm),str(beta2)) + tag in abr_fftkernels.keys():
            ftpsf2 = abr_fftkernels['(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm),str(beta2)) + tag]
        else:        
            ftpsf2 = generate_abr_fftkernel(boxlength,numpix,z,'Moffat',fwhm,beta2,d0,tag = tag)
        
        ftpsf = mf*(m1f*ftpsf1 + (1.-m1f)*ftpsf2)
        del ftpsf1
        del ftpsf2
        
        if kernel == '2MoffatAureole':
            if '(%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm*d0)) + tag in abr_fftkernels.keys():
                ftpsf += af* abr_fftkernels['(%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm*d0)) + tag]
            else:
                ftpsf += af*generate_abr_fftkernel(boxlength,numpix,z,'Aureole',fwhm,beta1,d0,tag = tag)

    elif kernel == 'Aureole':
        if '(%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm*d0)) + tag in abr_fftkernels.keys():
            ftpsf = abr_fftkernels['(%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),kernel,str(fwhm*d0)) + tag]
        else:
            ftpsf = generate_abr_fftkernel(boxlength,numpix,z,'Aureole',fwhm,beta1,d0,tag = tag)
        ftpsf = af*ftpsf
    
    elif kernel == 'Point':
        dim2 = numpix/2 + 1
        ftpsf = np.ones((numpix,dim2)) # FT of a delta function
    else: 
        print('Some error in kernel selection for generation. Time to debug.')    

    if pf > 1e-5:
        dim2 = numpix/2 + 1
        ftpsf += pf* np.ones((numpix,dim2))
        
    if np.abs(mf+pf+af -1.)>1e-5:
        print('Total flux is changed by a factor of %f!'%(mf+pf+af))
            
    out = np.fft.irfft2(np.fft.rfft2(img)*ftpsf)            
    return out

















# uses the key to determine an images box size and number of pixels -> pixel angular size
# generates kernel if not already in dict, then uses it to convolve the image with
# updates global dict <kernels> and returns log10 convolved image    
def conv_image(image,key,kernel,z=0.,psf_rad=None,kernel_tag = '',fft=False):
    # box size
    if '12' in key:
        (L_x,L_y,L_z) = (12.5,)*3
    if '25' in key:
        (L_x,L_y,L_z) = (25.,)*3

    if '_h' in key:
        L_z = L_z/2.
    if '_q' in key:
        L_z = L_z/4.
    
    boxlength = L_x
        
    # wavelength
    if 'halpha' in key:
         line = 'halpha' 
    
    # numpix
    if '_8_' in key or key[-2:] =='_8':
        numpix = 8000
    if '_4_' in key or key[-2:] =='_4':
        numpix = 4000
    if '_2_' in key or key[-2:] =='_2':
        numpix = 2000
    if psf_rad == None:
        if kernel == 'gauss':
            psf_rad = 10
        if kernel == 'airy':
            psf_rad = 300
            
    kernel_key = '(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),line,str(psf_rad),kernel) + kernel_tag
    if kernel_key not in kernels.keys():
        kernels.update(generate_kernel(line,boxlength,numpix,kernel,z,psf_rad=psf_rad,tag = kernel_tag))
    conv_kernel = kernels[kernel_key]
    if fft:
        return np.log10(cnv.convolve_fft(10**image,conv_kernel,boundary = 'wrap'))
    else:    
        return np.log10(cnv.convolve(10**image,conv_kernel,boundary = 'wrap'))


    
def dict_conv(dict_in,kernel,z=0.,psf_rad=None,kernel_tag = '',dict_tag='',fft=False):
        return {key+ dict_tag: conv_image(dict_in[key],key,kernel,z=z,psf_rad=psf_rad,kernel_tag = kernel_tag,fft=fft) for key in dict_in.keys()}

 
 
def generate_kernel2(line,boxlength,numpix,kernel,z,psf_rad=None,tag = ''):
    if psf_rad == None:
        if kernel == 'gauss':
            psf_rad = 10
        if kernel == 'airy':
            psf_rad = 300
    # angle_per_pix
    comdist = comoving_distance_cm(z)
    longlen = float(boxlength) * cons.cm_per_mpc  
    if comdist > longlen: # even at larger values, the projection along z-axis = projection along sightline approximation will break down
        adist = comdist/(1.+z)
    else: 
        adist = longlen/(1.+z) 
    image_angle_per_pixel =longlen/numpix *1./adist * radians
    
    wavelength = wavelengths[line]*(1.+z) 
    R_airy_zero = airy_size(wavelength)  
    pix_size_image_phys = image_angle_per_pixel/pix_size_angle * pix_size_phys
    seeing_limit_phys = seeing_limit/pix_size_angle * pix_size_phys
    
    kernel_radius = int(np.ceil(psf_rad*max(R_airy_zero,seeing_limit_phys)/pix_size_image_phys))
    if not kernel_radius %2: #if kernel radius is even
        kernel_radius +=1
        
    if kernel == 'gauss':
        
        sigma =np.sqrt((0.42/1.22*R_airy_zero)**2 + seeing_limit_phys**2/2.3548**2) # using the smaller of two approximations for sigma corresponding to an Airy disk radius
        # For now: use a Gaussian PSF, with the seeing limit as FWHM
        psf = cnv.Gaussian2DKernel(sigma/pix_size_image_phys, x_size = 6*kernel_radius +1, y_size = 6*kernel_radius+1, mode = 'oversample')
        psf.normalize(mode='integral')
    
    if kernel == 'airy':
        airy_disk_psf = cnv.AiryDisk2DKernel(R_airy_zero/pix_size_image_phys, x_size = 4*kernel_radius+1, y_size = 4*kernel_radius+1, mode = 'oversample')
    
        # For now: use a Gaussian PSF, with the seeing limit as FWHM
        seeing_psf = cnv.Gaussian2DKernel(seeing_limit_phys/pix_size_image_phys/2.3548, x_size = 6*kernel_radius +1, y_size = 6*kernel_radius+1, mode = 'oversample')
    
        # watch out for effects of extending out to larger radii at the corners than edge middles; just include the weird edges for now
        psf = cnv.convolve_fft(seeing_psf.array,airy_disk_psf,boundary = 'fill',fill_value = 0.)
        psf= psf/np.sum(psf)
    
    return {'(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),line,str(psf_rad),kernel) + tag: psf}
    


# uses the key to determine an images box size and number of pixels -> pixel angular size
# generates kernel if not already in dict, then uses it to convolve the image with
# updates global dict <kernels> and returns log10 convolved image    
def conv_image2(image,key,kernel,z=0.,psf_rad=None,kernel_tag = '',fft=False):
    # box size
    if '12' in key:
        (L_x,L_y,L_z) = (12.5,)*3
    if '25' in key:
        (L_x,L_y,L_z) = (25.,)*3

    if '_h' in key:
        L_z = L_z/2.
    if '_q' in key:
        L_z = L_z/4.
    
    boxlength = L_x
        
    # wavelength
    if 'halpha' in key:
         line = 'halpha' 
    
    # numpix
    if '_8_' in key or key[-2:] =='_8':
        numpix = 8000
    if '_4_' in key or key[-2:] =='_4':
        numpix = 4000
    if '_2_' in key or key[-2:] =='_2':
        numpix = 2000
    if psf_rad == None:
        if kernel == 'gauss':
            psf_rad = 10
        if kernel == 'airy':
            psf_rad = 300
            
    kernel_key = '(%s,%s,%s,%s,%s,%s)'%(str(boxlength),str(numpix),str(z),line,str(psf_rad),kernel) + kernel_tag
    if kernel_key not in kernels.keys():
        kernels.update(generate_kernel(line,boxlength,numpix,kernel,z,psf_rad=psf_rad,tag = kernel_tag))
    conv_kernel = kernels[kernel_key]
    if fft:
        return np.log10(cnv.convolve_fft(10**image,conv_kernel,boundary = 'wrap'))
    else:    
        return np.log10(cnv.convolve(10**image,conv_kernel,boundary = 'wrap'))
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
def conv_kernel_and_CCD_project_Airy(image,image_angle_per_pixel,z=0.,proj_dens=10,psf_rad=15):
    wavelength = wavelengths['halpha']*(1.+z) 
    R_airy_zero = airy_size(wavelength)  
    pix_size_image_phys = image_angle_per_pixel/pix_size_angle * pix_size_phys
    seeing_limit_phys = seeing_limit/pix_size_angle * pix_size_phys
    
    kernel_radius = int(np.ceil(psf_rad*R_airy_zero/pix_size_image_phys))
    if not kernel_radius %2: #if kernel radius is even
        kernel_radius +=1
        
    #for_kernel = np.indices((2*kernel_radius+1,)*2) - kernel_radius 
    #for_kernel = np.sqrt(for_kernel[0]**2 + for_kernel[1]**2)*pix_size_image_phys
    
    # centre mode should be the same approach as for the smoothing kernels
    #automatically normalised so sum =1.0, Airy zero radius given in pixels 
    airy_disk_psf = cnv.AiryDisk2DKernel(R_airy_zero/pix_size_image_phys, x_size = 4*kernel_radius+1, y_size = 4*kernel_radius+1, mode = 'oversample')
    
    # For now: use a Gaussian PSF, with the seeing limit as FWHM
    seeing_psf = cnv.Gaussian2DKernel(seeing_limit_phys/pix_size_image_phys/2.3548, x_size = 6*kernel_radius +1, y_size = 6*kernel_radius+1, mode = 'oversample')
    
    # watch out for effects of extending out to larger radii at the corners than edge middles; just include the weird edges for now
    psf_tot = cnv.convolve(seeing_psf,airy_disk_psf,boundary = 'fill',fill_value = 0.)
    
    
    # calculate psf inside the kernel_radius 
    psf_image = cnv.convolve(10**image,psf_tot,boundary = 'wrap')
    
    #proj_grid = np.indices((image.shape[0]*proj_dens,image.shape[1]*proj_dens))
    
    return psf_image


def conv_kernel_and_CCD_project_Gauss(image,image_angle_per_pixel,z=0.,proj_dens=10,psf_rad=10):
    wavelength = wavelengths['halpha']*(1.+z) 
    R_airy_zero = airy_size(wavelength)  
    pix_size_image_phys = image_angle_per_pixel/pix_size_angle * pix_size_phys
    seeing_limit_phys = seeing_limit/pix_size_angle * pix_size_phys
    
    kernel_radius = int(np.ceil(psf_rad*R_airy_zero/pix_size_image_phys))
    if not kernel_radius %2: #if kernel radius is even
        kernel_radius +=1
        
    sigma =np.sqrt((0.42/1.22*R_airy_zero)**2 + seeing_limit_phys**2/2.3548**2) # using the smaller of two approximations for sigma corresponding to an Airy disk radius
    # For now: use a Gaussian PSF, with the seeing limit as FWHM
    psf = cnv.Gaussian2DKernel(sigma/pix_size_image_phys, x_size = 6*kernel_radius +1, y_size = 6*kernel_radius+1, mode = 'oversample')
    

    # calculate psf inside the kernel_radius 
    psf_image = cnv.convolve(10**image,psf,boundary = 'wrap')
    
    #proj_grid = np.indices((image.shape[0]*proj_dens,image.shape[1]*proj_dens))
    
    return psf_image


# assumes full projected boxes
def conv_airy(image,key,z=0.,proj_dens=10,psf_rad=15):
    # box size
    if '12' in key:
        (L_x,L_y,L_z) = (12.5,)*3
    if '25' in key:
        (L_x,L_y,L_z) = (25.,)*3

    if '_h' in key:
        L_z = L_z/2.
    if '_q' in key:
        L_z = L_z/4.
        
    # wavelength
    if 'halpha' in key:
         wavelength = wavelengths['halpha']*(1.+z) 
    
    # numpix
    if '_8_' in key or key[-2:] =='_8':
        npix = 8000
    if '_4_' in key or key[-2:] =='_4':
        npix = 4000
    if '_2_' in key or key[-2:] =='_2':
        npix = 2000
        

    # angle_per_pix
    comdist = comoving_distance_cm(z)
    longlen = max(L_x,L_y,L_z)/2. * cons.cm_per_mpc  
    if comdist > longlen: # even at larger values, the projection along z-axis = projection along sightline approximation will break down
        adist = comdist/(1.+z)
    else: 
        adist = longlen/(1.+z) 
    angle_per_pix = L_x/npix * cons.cm_per_mpc/adist * radians
    
    return conv_kernel_and_CCD_project_Airy(image,angle_per_pix,z=z,proj_dens = proj_dens,psf_rad = psf_rad)
   
   
def angle_per_pix_calc(key,z=0.):
     # box size
    if '12' in key:
        (L_x,L_y,L_z) = (12.5,)*3
    if '25' in key:
        (L_x,L_y,L_z) = (25.,)*3

    if '_h' in key:
        L_z = L_z/2.
    if '_q' in key:
        L_z = L_z/4.
    
    # numpix
    if '_8_' in key or key[-2:] =='_8':
        npix = 8000
    if '_4_' in key or key[-2:] =='_4':
        npix = 4000
    if '_2_' in key or key[-2:] =='_2':
        npix = 2000
        

    # angle_per_pix
    comdist = comoving_distance_cm(z)
    longlen = max(L_x,L_y,L_z)/2. * cons.cm_per_mpc  
    if comdist > longlen: # even at larger values, the projection along z-axis = projection along sightline approximation will break down
        adist = comdist/(1.+z)
    else: 
        adist = longlen/(1.+z) 
    angle_per_pix = L_x/npix * cons.cm_per_mpc/adist * radians
    
    return angle_per_pix
    

# assumes full projected boxes
def conv_gauss(image,key,z=0.,proj_dens=10,psf_rad=10):
    # box size
    if '12' in key:
        (L_x,L_y,L_z) = (12.5,)*3
    if '25' in key:
        (L_x,L_y,L_z) = (25.,)*3
    if '100' in key:
        (L_x,L_y,L_z) = (100.,)*3
        
    if '_h' in key:
        L_z = L_z/2.
    if '_q' in key:
        L_z = L_z/4.
    if '_five' in key:
        L_z = L_z/20.
        
    # wavelength
    if 'halpha' in key:
         wavelength = wavelengths['halpha']*(1.+z) 
    
    # numpix
    if '_32_' in key or key[-2:] =='_32':
        npix = 32000    
    if '_8_' in key or key[-2:] =='_8':
        npix = 8000
    if '_4_' in key or key[-2:] =='_4':
        npix = 4000
    if '_2_' in key or key[-2:] =='_2':
        npix = 2000
        

    # angle_per_pix
    comdist = comoving_distance_cm(z)
    longlen = max(L_x,L_y,L_z)/2. * cons.cm_per_mpc  
    if comdist > longlen: # even at larger values, the projection along z-axis = projection along sightline approximation will break down
        adist = comdist/(1.+z)
    else: 
        adist = longlen/(1.+z) 
    angle_per_pix = L_x/npix * cons.cm_per_mpc/adist * radians
    
    return conv_kernel_and_CCD_project_Gauss(image,angle_per_pix,z=z,proj_dens = proj_dens,psf_rad = psf_rad)


def dict_conv_old(dict_in,kernel,z=0.,proj_dens=10):
    if kernel == 'gauss':
        return {key: conv_gauss(dict_in[key],key,z=z,proj_dens=proj_dens,psf_rad=10) for key in dict_in.keys()}
    if kernel == 'airy':
        return {key: conv_airy(dict_in[key],key,z=z,proj_dens=proj_dens,psf_rad=150) for key in dict_in.keys()}


####################### BODY OF PROGRAM STARTS HERE ########################

if __name__ == "__main__":
    
    arguments   = docopt.docopt(__doc__)

    npzfile     = arguments['<npzfile>']
    verbose     = arguments['--verbose']
    
    kernel      = arguments['--kernel']
    pixangle    = arguments['--pixangle']
    centrecoord = arguments['--centre']
    axangle     = arguments['--angle']
    
    if verbose:
        print arguments
        
    boxlength   = '100'
    numpix      = '32'
    zlength_clue= 'five'
    wavelenth   = 'halpha'
    key = '('+boxlength+','+wavelength+','+'_'+numpix+'_'+')'
    if verbose:
        print_verbose_string(key)
        
    psf_image = conv_gauss(npzfile,key)