/
old_diffract_tools.py
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old_diffract_tools.py
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import numpy as np
import matplotlib.pyplot as plt
import pyfits as pf
from scipy.interpolate import RectBivariateSpline as interp
from frebin import spaxel_scale
from swiftmask import swiftpupil
shift = np.fft.fftshift
fft = np.fft.fft2
ifft = np.fft.ifft2
fftfreq = np.fft.fftfreq
dtor = np.pi/180.0
'''------------------------------------------------
old_diffract_tools.py
code to simulate a narrowband image
------------------------------------------------'''
# =========================================================================
# =========================================================================
def mas2rad(x):
''' Convenient little function to convert milliarcsec to radians '''
return x*np.pi/(180*3600*1000)
# =========================================================================
# =========================================================================
def rad2mas(x):
''' Convenient little function to convert radians to milliarcseconds '''
return x/np.pi*(180*3600*1000)
# =========================================================================
# =========================================================================
def kolmogorov_spectrum(sz,r0 = 0.01,cutoff=None,inner=None):
xs, ys = np.linspace(-5./r0,5./r0,sz), np.linspace(-5./r0,5./r0,sz)
xx, yy = np.meshgrid(xs,ys)
rr = np.sqrt(xx**2+yy**2)
newspec = 0.0229*r0**(5./3.)*(rr**(-11./3.))
if cutoff is not None:
newspec[rr>cutoff] = 0
print 'cut off', cutoff
if inner is not None:
newspec[rr<inner] = np.nanmax(newspec[rr>inner])
newspec = shift(newspec)
newspec[~np.isfinite(newspec)] = 0
return newspec
# =========================================================================
# =========================================================================
def kolmogorov_scint(sz,height=5e4,wavel=1e-6,r0=1e-2,inner=5e-3):
xs, ys = np.linspace(-5./r0,5./r0,sz), np.linspace(-5./r0,5./r0,sz)
xx, yy = np.meshgrid(xs,ys)
rr = np.sqrt(xx**2+yy**2)
kf = (4*np.pi/wavel/height)**0.5
newspec = 4*0.0229*r0**(5./3.)*(rr**(-11./3.)) * np.sin(rr**2./kf**2.)**2.
newspec[rr>(1/inner)] = 0
newspec = shift(newspec)
newspec[~np.isfinite(newspec)] = 0
return newspec
# =========================================================================
# =========================================================================
def screen(seeingfile,xs=None,cutoff=None,mode='amp'):
'''Generate a phase screen'''
try:
seeing = pf.getdata(seeingfile)
except:
if mode == 'amp':
seeing = kolmogorov_scint(2080)
else:
seeing = kolmogorov_spectrum(2080,cutoff=None)
seeing = np.sqrt(shift(seeing)) + 0j # center and square root to get amplitudes; 0j to make it complex!
seeingx = np.arange(2080)*0.5
seeingx -= seeingx.max()
sxx,syy = np.meshgrid(seeingx,seeingx)
# #interpolate seeing to the correct basis
noise = np.random.standard_normal(np.shape(seeing))+0j # generate noise in pupil plane
noise = shift(fft(shift(noise)))
rprim = 5.093/2. # Palomar
seeing *= 2.*rprim*noise # multiply amplitudes by pupil plane noise
# remember seeing is normalised to the pupil diameter in metres!
seeing = shift(ifft(shift(seeing)))
if xs == None:
newx = np.linspace(-4*rprim,4*rprim,2080)
else:
newx = np.linspace(xs.min(),xs.max(),2080)
interpfun = interp(newx,newx,seeing)
return interpfun
# =========================================================================
# =========================================================================
def diffract(wavel,rprim,rsec,pos=[0,0],piston=100.e-9,spaxel=40.,seeing=False,verbose=True,
show_pupil=False,telescope=None,mode='amp',seeingamp=0.0,
perturbation='phase',amp=0.3,cutoff=None,sz=4096/2,final_sz=256):
'''Run a diffraction simulation!'''
# wavel = params[0]
# rprim = params[1]
# spacing = 3.
reso = rad2mas(wavel/(2*rprim))
if verbose:
print 'Lambda/D =',reso,'mas'
'''----------------------------------------
Calculate an input pupil.
----------------------------------------'''
pupil = np.ones((sz,sz),dtype='complex')
# get coordinates for the full un-cropped image
xs, ys = np.linspace(-sz/2,sz/2,sz), np.linspace(-sz/2,sz/2,sz)
xs *= 4*rprim/xs.max()
ys *= 4*rprim/ys.max()
th = pos[1]*np.pi/180.
poke = pos[0]*np.array([np.cos(th),np.sin(th)])
xx,yy = np.meshgrid(xs,ys)
rr = np.sqrt(xx**2 + yy**2)
rr2 = np.sqrt((xx-poke[0])**2 + (yy-poke[1])**2)
m2pix = sz/(xx.max()-xx.min())
pix2m = 1./m2pix
freqs = shift(fftfreq(sz,d=pix2m))
'''----------------------------------------
Apply a phase screen.
----------------------------------------'''
# seeing = np.exp(1.j*seeing)
# pupil *= seeing
# # where do you poke the phases?
# angle = 45
# dist = 0.5
# angle *= np.pi/180.
# poke = np.array([np.sin(angle),np.cos(angle)])
# poke = poke*(rprim-rsec)*dist + poke*rsec
# #phase piston a 1x1 m region cetred at the poke point
# pupil[np.sqrt((xx-poke[0])**2 +(yy-poke[1])**2)<3] *= np.exp(0+1j)
# display image
'''----------------------------------------
Apply the pupil mask.
----------------------------------------'''
# now limit the bandpass of the pupil
if telescope == 'swift':
mask,xs,m2pix=swiftpupil(sz=sz)
pix2m = 1./m2pix
freqs = shift(fftfreq(sz,d=pix2m))
else:
mask = np.ones(rr.shape,dtype='complex')
# mask *= np.exp(-(rr-(rprim+rsec)/2.)**2/2./gausswidth**2)
mask /= mask.max()
mask[rr>rprim] = 0
mask[rr<rsec] = 0
# if dust ==True:
# # mask*= 1 + 0.6*np.sin((rr-(rprim+rsec)/2.)*10.)
# interpfun = screen(seeing)
# seeing = interpfun(xs+xs.min(),ys+ys.min())
# seeing /= seeing.max()
# # seeing = np.exp(seeing)
# mask *= np.abs(seeing)
# mask /= mask.max()
# mask = np.ones(rr1.shape,dtype='complex')
# mask *= np.exp(-(rr-(rprim+rsec)/2.)**2/2./gausswidth**2)
# mask /= mask.max()
# mask[(rr1>rprim)* (rr2 > rprim)] = 0
if mode == 'amp':
interpfun = screen(None,xs=xs+xs.min(),cutoff=cutoff,mode='amp')
scintillation = interpfun(xs+xs.min(),ys+ys.min())
scintillation = (scintillation-scintillation.min())/(scintillation.max()-scintillation.min())
scintillation *= np.abs(mask)
keep = np.isfinite(scintillation) * (scintillation>0)
scintillation -= np.median(scintillation[keep])
pupil *= (1+amp*scintillation)
elif mode == 'phase':
interpfun = screen(None,xs=xs+xs.min(),cutoff=cutoff,mode='phase')
phasescreen = interpfun(xs+xs.min(),ys+ys.min())
phasescreen = (phasescreen-phasescreen.min())/(phasescreen.max()-phasescreen.min())
phasescreen *= np.abs(mask)
keep = np.isfinite(phasescreen)
phasescreen *= seeingamp
phasescreen -= np.median(phasescreen)
pupil *= np.exp(1.j*phasescreen)
pupil *= mask
if perturbation == 'phase':
if verbose:
print 'perturbing phase'
pupil[rr2<0.5] *= np.exp(2.*np.pi*1.j*piston/wavel)
elif perturbation == 'amplitude':
if verbose:
print 'perturbing amplitude'
pupil[rr2<0.5] *= 1.03
# plt.figure(0)
# plt.clf()
# plt.imshow(np.abs(pupil),extent=[xx.min(),xx.max(),xx.min(),xx.max()],
# cmap=plt.cm.gray,interpolation='none')
# cbar = plt.colorbar()
# # plt.scatter(poke[0],poke[1],s=5)
# plt.xlim(xx.min(),xx.max())
# plt.ylim(xx.min(),xx.max())
# plt.xlabel('m')
# plt.ylabel('m')
# plt.title('Input Pupil')
# plt.show()
if show_pupil:
toy = np.copy(pupil)
toy[mask==0] = np.nan
plt.figure()
plt.clf()
plt.imshow(np.abs(toy),extent=[xs.min(),xs.max(),xs.min(),xs.max()],
interpolation='none')
# plt.colorbar(ticks=np.linspace(0.98,1.03,11))
# plt.clim([0.98,1.03])
plt.colorbar()
plt.xlim([-4,4])
plt.ylim([-4,4])
plt.xlabel('m')
plt.ylabel('m')
plt.savefig('ampscreen.png')
# plt.title('Input Pupil')
# cbar = plt.colorbar()
plt.show()
if seeingamp >= 0.01:
plt.figure(1)
plt.clf()
plt.imshow(np.angle(pupil),extent=[xs.min(),xs.max(),xs.min(),xs.max()],
interpolation='none',origin='lower')
plt.xlabel('m')
plt.ylabel('m')
# plt.title('Input Phase Screen')
cbar = plt.colorbar()
pplt.savefig('phasescreen.png')
plt.draw()
plt.show()
if verbose:
rmsphase = np.sqrt(np.mean(np.angle(pupil[np.abs(pupil)>0]))**2)
print 'RMS Phase %.3g rad' %rmsphase
# insert in a padded array
# newpupil = np.zeros((sz*4,sz*4),dtype='complex')
# newpupil[3*sz/2:5*sz/2,3*sz/2:5*sz/2] = pupil
# pupil = newpupil
'''----------------------------------------
Propagate to the first focal plane.
----------------------------------------'''
focal = shift(fft(shift(pupil)))
# get coordinates for the full un-cropped image
focx = rad2mas(freqs*wavel)
focxx,focyy = np.meshgrid(focx,focx)
focrr = np.sqrt(focxx**2 + focyy**2)
image = focal.real**2 + focal.imag**2
imsz = image.shape[0]
# image = image[3*imsz/8:5*imsz/8,3*imsz/8:5*imsz/8]
# imagex = focx[3*imsz/8:5*imsz/8]
# display image
# plt.figure(1)
# plt.clf()
# plt.imshow(image**0.2,extent=[focx.min(),focx.max(),focx.min(),focx.max()],
# cmap=plt.cm.gray,interpolation='none')
# plt.xlabel('mas')
# plt.ylabel('mas')
# plt.title('HARMONI input PSF')
# cbar = plt.colorbar()
# plt.show()
'''----------------------------------------
Rebin
----------------------------------------'''
pscale = (focx.max()-focx.min())/focx.size
rescale = 1.0#wavel/centre_wavel
if verbose:
print 'Image dimension', imsz
print 'pscale',pscale
print 'rescale', rescale
print 'virtual spaxel size',spaxel*rescale
# try:
# rebin = fits_spaxel_scale(image2,pscale,spaxel,'config3.fits')
# rebinx = focx/pscale*spaxel
# print 'saved!'
# except:
rebin = spaxel_scale(image,pscale,spaxel*rescale,verbose=verbose)
rebin = rebin[rebin.shape[0]/2-(final_sz/2):rebin.shape[0]/2+(final_sz/2),rebin.shape[0]/2-(final_sz/2):rebin.shape[0]/2+(final_sz/2)]
rebinx = float(spaxel)*np.arange(256)
rebinx -= rebinx.max()/2.
return rebin, rebinx