def compare_interpolated_spectrum():
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
out = fft(ifftshift(f_full))
freqs = fftfreq(len(f_full), d=0.01) # spacing, Ang
sfreqs = fftshift(freqs)
taper = gauss_taper(freqs, sigma=0.0496) #Ang, corresponds to 2.89 km/s at 5150A.
tout = out * taper
ax.plot(sfreqs, fftshift(tout))
wl_h, fl_h = np.abs(np.load("PH6.8kms_0.01ang.npy"))
wl_l, fl_l = np.abs(np.load("PH2.5kms.npy"))
#end edges
wl_he = wl_h[200:-200]
fl_he = fl_h[200:-200]
interp = Sinc_w(wl_l, fl_l, a=5, window='kaiser')
fl_hi = interp(wl_he)
d = wl_he[1] - wl_he[0]
out = fft(ifftshift(fl_hi))
freqs = fftfreq(len(out), d=d)
ax.plot(fftshift(freqs), fftshift(out))
plt.show()
def pseudofrosch(x,k,tmax,dt):
global potential, psi0
ti=[0]
fi=[psi0(x)]
mmax=int((tmax)/dt+1)
for m in range(1,mmax,1):
tn=ti[m-1]
fn=fi[m-1]
fn=np.array(fn)
dp1=e**(-1j*potential(x)*dt/2)*fn #
ft_fn=ft.fft(dp1) #falschrum
ft_fn=ft.ifftshift(ft_fn)
dp2=e**(-1j*1/2*k**2*dt)*ft_fn
ift_fn=ft.ifft(dp2)
ift_fn=ft.ifftshift(ift_fn)
dp3=e**(-1j*potential(x)*dt/2)*ift_fn
dp3=list(dp3)
ti+=[tn+dt]
fi=fi+[dp3]
return [ti,fi]
def odddftups(inp,nor=None,noc=None,usfac=1,roff=0,coff=0):
from numpy.fft import ifftshift
from numpy import pi,newaxis,floor
nr,nc=np.shape(inp);
# Set defaults
if noc is None: noc=nc;
if nor is None: nor=nr;
if nr % 2 == 1:
oddr = True
nrnew = nr+1
else:
oddr = False
if nr % 2 == 1:
oddr = True
nrnew = nr+1
else:
oddr = False
# Compute kernels and obtain DFT by matrix products
term1c = ( ifftshift(np.arange(nc) - floor(nc/2)).T[:,newaxis] )
term2c = ( np.arange(noc) - coff )[newaxis,:]
kernc=np.exp((-1j*2*pi/(nc*usfac))*term1c*term2c);
term1r = ( np.arange(nor).T - roff )[:,newaxis]
term2r = ( ifftshift(np.arange(nr)) - floor(nr/2) )[newaxis,:]
kernr=np.exp((-1j*2*pi/(nr*usfac))*term1r*term2r);
#kernc=exp((-i*2*pi/(nc*usfac))*( ifftshift([0:nc-1]).' - floor(nc/2) )*( [0:noc-1] - coff ));
#kernr=exp((-i*2*pi/(nr*usfac))*( [0:nor-1].' - roff )*( ifftshift([0:nr-1]) - floor(nr/2) ));
out=np.dot(np.dot(kernr,inp),kernc);
#return np.roll(np.roll(out,+1,axis=0),+1,axis=1)
return out
def whiten_olsh_lee_inner(image, f_0=None, central_clip=(None, None), normalize_pre=True, normalize_post=True,
no_filter=False):
height, width = image.shape
assert height % 2 == 0 and width % 2 == 0, "image must have even size!"
if normalize_pre:
image = image - image.mean() # I personally think this is useless, since rho will make (0,0) freq compoenent 0.
std_im = image.std(ddof=1)
assert std_im != 0, "constant image unsupported!"
image /= std_im
fx, fy = np.meshgrid(np.arange(-height / 2, height / 2), np.arange(-width / 2, width / 2), indexing='ij')
rho = np.sqrt(fx * fx + fy * fy)
if f_0 is None:
f_0 = 0.4 * (height + width) / 2
filt = rho * np.exp(-((rho / f_0) ** 4))
im_f = fft2(image)
if not no_filter:
fft_filtered_old = im_f * ifftshift(filt)
else: # hack to only lower frequency response.
print('no real filtering!')
fft_filtered_old = im_f
fft_filtered_old = fftshift(fft_filtered_old)
if central_clip != (None, None):
fft_filtered_old = fft_filtered_old[height // 2 - central_clip[0] // 2:height // 2 + central_clip[0] // 2,
width // 2 - central_clip[1] // 2:width // 2 + central_clip[1] // 2]
im_out = np.real(ifft2(ifftshift(fft_filtered_old)))
# I believe since the rho at the (0,0) frequency part is zero, then the whole image should be zero as well.
# so explicit DC removing is useless.
if normalize_post:
assert abs(im_out.mean()) < 1e-6 # should be extremely small.
std_im_out = im_out.std(ddof=1)
else:
std_im_out = 1
return im_out / std_im_out
def _simulate_image(self):
"""
Generates the fake output.
"""
with self._acquisition_init_lock:
pos = self.align.position.value
logging.debug("Simulating image shift by %s", pos)
ac, bc = pos.get("a"), pos.get("b")
ang = math.radians(135)
# AB->XY
xc = -(ac * math.sin(ang) + bc * math.cos(ang))
yc = -(ac * math.cos(ang) - bc * math.sin(ang))
pixelSize = self.fake_img.metadata[model.MD_PIXEL_SIZE]
self.fake_img.metadata[model.MD_ACQ_DATE] = time.time()
x_pxs = xc / pixelSize[0]
y_pxs = yc / pixelSize[1]
# Image shifted based on LensAligner position
z = 1j # imaginary unit
self.deltar = x_pxs
self.deltac = y_pxs
nr, nc = self.fake_img.shape
array_nr = numpy.arange(-numpy.fix(nr / 2), numpy.ceil(nr / 2))
array_nc = numpy.arange(-numpy.fix(nc / 2), numpy.ceil(nc / 2))
Nr = fft.ifftshift(array_nr)
Nc = fft.ifftshift(array_nc)
[Nc, Nr] = numpy.meshgrid(Nc, Nr)
sim_img = fft.ifft2(fft.fft2(self.fake_img) * numpy.power(math.e,
z * 2 * math.pi * (self.deltar * Nr / nr + self.deltac * Nc / nc)))
output = model.DataArray(abs(sim_img), self.fake_img.metadata)
return output
def test_axes_keyword(self):
freqs = [[ 0, 1, 2], [ 3, 4, -4], [-3, -2, -1]]
shifted = [[-1, -3, -2], [ 2, 0, 1], [-4, 3, 4]]
assert_array_almost_equal(fftshift(freqs, axes=(0, 1)), shifted)
assert_array_almost_equal(fftshift(freqs, axes=0), fftshift(freqs, axes=(0,)))
assert_array_almost_equal(ifftshift(shifted, axes=(0, 1)), freqs)
assert_array_almost_equal(ifftshift(shifted, axes=0), ifftshift(shifted, axes=(0,)))
def fft_g2r(self, fg, fg_ishifted=False):
"""
FFT of array ``fg`` given in G-space.
"""
ndim, shape = fg.ndim, fg.shape
if ndim == 1:
fg = np.reshape(fg, self.shape)
return self.fft_g2r(fg, fg_ishifted=fg_ishifted).flatten()
if ndim == 3:
assert self.size == np.prod(shape[-3:])
if fg_ishifted: fg = ifftshift(fg)
fr = ifftn(fg)
elif ndim > 3:
assert self.size == np.prod(shape[-3:])
axes = np.arange(ndim)[-3:]
if fg_ishifted: fg = ifftshift(fg, axes=axes)
fr = ifftn(fg, axes=axes)
else:
raise NotImplementedError("ndim < 3 are not supported")
return fr * self.size
def _UpsampledDFT(data, nor, noc, precision=1, roff=0, coff=0):
"""
Upsampled DFT by matrix multiplies.
data (numpy.array): 2d array
nor, noc (ints): Number of pixels in the output upsampled DFT, in units
of upsampled pixels
precision (int): Calculate drift within 1/precision of a pixel
roff, coff (ints): Row and column offsets, allow to shift the output array
to a region of interest on the DFT
returns (tuple of floats): Drift in pixels
"""
z = 1j # imaginary unit
nr, nc = data.shape
# Compute kernels and obtain DFT by matrix products
kernc = numpy.power(math.e, (-z * 2 * math.pi / (nc * precision)) *
((fft.ifftshift(arange(0, nc))[:, None]).T - nc // 2) *
(arange(0, noc) - coff)[:, None]
)
kernr = numpy.power(math.e, (-z * 2 * math.pi / (nr * precision)) *
(fft.ifftshift(arange(0, nr))[:, None] - nr // 2) *
((arange(0, nor)[:, None]).T - roff)
)
return numpy.dot(numpy.dot((kernr.transpose()), data), kernc.transpose())
def gs_mod_gpu(idata,itera=10,osize=256):
cut=osize//2
pl=cl.get_platforms()[0]
devices=pl.get_devices(device_type=cl.device_type.GPU)
ctx = cl.Context(devices=[devices[0]])
queue = cl.CommandQueue(ctx)
plan = Plan(idata.shape, queue=queue,dtype=complex128) #no funciona con "complex128"
src = str(Template(KERNEL).render(
double_support=all(
has_double_support(dev) for dev in devices),
amd_double_support=all(
has_amd_double_support(dev) for dev in devices)
))
prg = cl.Program(ctx,src).build()
idata_gpu=cl_array.to_device(queue, ifftshift(idata).astype("complex128"))
fdata_gpu=cl_array.empty_like(idata_gpu)
rdata_gpu=cl_array.empty_like(idata_gpu)
plan.execute(idata_gpu.data,fdata_gpu.data)
mask=exp(2.j*pi*random(idata.shape))
mask[512-cut:512+cut,512-cut:512+cut]=0
idata_gpu=cl_array.to_device(queue, ifftshift(idata+mask).astype("complex128"))
fdata_gpu=cl_array.empty_like(idata_gpu)
rdata_gpu=cl_array.empty_like(idata_gpu)
error_gpu=cl_array.to_device(ctx, queue, zeros(idata_gpu.shape).astype("double"))
plan.execute(idata_gpu.data,fdata_gpu.data)
e=1000
ea=1000
for i in range (itera):
prg.norm(queue, fdata_gpu.shape, None,fdata_gpu.data)
plan.execute(fdata_gpu.data,rdata_gpu.data,inverse=True)
#~ prg.norm1(queue, rdata_gpu.shape,None,rdata_gpu.data,idata_gpu.data,error_gpu.data, int32(cut))
norm1=prg.norm1
norm1.set_scalar_arg_dtypes([None, None, None, int32])
norm1(queue, rdata_gpu.shape,None,rdata_gpu.data,idata_gpu.data,error_gpu.data, int32(cut))
e= sqrt(cl_array.sum(error_gpu).get())/(2*cut)
#~ if e>ea:
#~
#~ break
#~ ea=e
plan.execute(rdata_gpu.data,fdata_gpu.data)
fdata=fdata_gpu.get()
fdata=ifftshift(fdata)
fdata=exp(1.j*angle(fdata))
return fdata
def dftups(inp,nor=None,noc=None,usfac=1,roff=0,coff=0):
"""
Translated from matlab:
* `Original Source <http://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation/content/html/efficient_subpixel_registration.html>`_
* Manuel Guizar - Dec 13, 2007
* Modified from dftus, by J.R. Fienup 7/31/06
Upsampled DFT by matrix multiplies, can compute an upsampled DFT in just
a small region.
This code is intended to provide the same result as if the following
operations were performed:
* Embed the array "in" in an array that is usfac times larger in each
dimension. ifftshift to bring the center of the image to (1,1).
* Take the FFT of the larger array
* Extract an [nor, noc] region of the result. Starting with the
[roff+1 coff+1] element.
It achieves this result by computing the DFT in the output array without
the need to zeropad. Much faster and memory efficient than the
zero-padded FFT approach if [nor noc] are much smaller than [nr*usfac nc*usfac]
Parameters
----------
usfac : int
Upsampling factor (default usfac = 1)
nor,noc : int,int
Number of pixels in the output upsampled DFT, in units of upsampled
pixels (default = size(in))
roff, coff : int, int
Row and column offsets, allow to shift the output array to a region of
interest on the DFT (default = 0)
"""
# this function is translated from matlab, so I'm just going to pretend
# it is matlab/pylab
from numpy.fft import ifftshift,fftfreq
from numpy import pi,newaxis,floor
nr,nc=np.shape(inp);
# Set defaults
if noc is None: noc=nc;
if nor is None: nor=nr;
# Compute kernels and obtain DFT by matrix products
term1c = ( ifftshift(np.arange(nc,dtype='float') - floor(nc/2)).T[:,newaxis] )/nc # fftfreq
term2c = (( np.arange(noc,dtype='float') - coff )/usfac)[newaxis,:] # output points
kernc=np.exp((-1j*2*pi)*term1c*term2c);
term1r = ( np.arange(nor,dtype='float').T - roff )[:,newaxis] # output points
term2r = ( ifftshift(np.arange(nr,dtype='float')) - floor(nr/2) )[newaxis,:] # fftfreq
kernr=np.exp((-1j*2*pi/(nr*usfac))*term1r*term2r);
#kernc=exp((-i*2*pi/(nc*usfac))*( ifftshift([0:nc-1]).' - floor(nc/2) )*( [0:noc-1] - coff ));
#kernr=exp((-i*2*pi/(nr*usfac))*( [0:nor-1].' - roff )*( ifftshift([0:nr-1]) - floor(nr/2) ));
out=np.dot(np.dot(kernr,inp),kernc);
#return np.roll(np.roll(out,-1,axis=0),-1,axis=1)
return out
def test_definition(self):
x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
y = [-4, -3, -2, -1, 0, 1, 2, 3, 4]
assert_array_almost_equal(fft.fftshift(x), y)
assert_array_almost_equal(fft.ifftshift(y), x)
x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
y = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4]
assert_array_almost_equal(fft.fftshift(x), y)
assert_array_almost_equal(fft.ifftshift(y), x)
def plot_sinc_windows():
fig, ax = plt.subplots(nrows=2, figsize=(8, 8))
xs = np.linspace(-2, 2., num=200)
xs4 = np.linspace(-5, 5, num=500)
y2s = sinc_w(xs, 'lanczos')
y4s = sinc_w(xs4, 'lanczos', a=5)
yks = sinc_w(xs4, 'kaiser', a=5, alpha=5)
yks2 = sinc_w(xs, 'kaiser', a=2, alpha=5)
ax[0].plot(xs, y2s, "b", label='Lanczos, a=2')
ax[0].plot(xs4, y4s, 'g', label='Lanczos, a=5')
ax[0].plot(xs4, yks, "r", label='Kaiser 5, a=5')
ax[0].plot(xs, yks2, "c", label='Kaiser 5, a=2')
#ax[0].plot(xs,sinc_w(xs, 'hann'),label='Hann')
#ax[0].plot(xs,sinc_w(xs, 'kaiser',alpha=5),label='Kaiser=5')
#ax[0].plot(xs,sinc_w(xs, 'kaiser',alpha=10),label='Kaiser=10')
#xs4 = np.linspace(-4,4,num=100)
#ax[0].plot(xs4,sinc_w(xs4, 'lanczos', a = 4), label='Lanczos,a=4')
ax[0].legend()
ax[0].set_xlabel(r"$\pm a$")
#n=400 #zeropadd FFT
#freqs2 = fftfreq(len(y2s),d=xs[1]-xs[0])
#freqs4 =fftfreq(400,d=xs4[1]-xs4[0])
ysh = ifftshift(y2s)
pady = np.concatenate((ysh[:100], np.zeros((1000,)), ysh[100:]))
freq2 = fftshift(fftfreq(len(pady), d=0.02))
ys4h = ifftshift(y4s)
pad4y = np.concatenate((ys4h[:250], np.zeros((2000,)), ys4h[250:]))
freq4 = fftshift(fftfreq(len(pad4y), d=0.02))
fpady = fft(pady)
fpad4y = fft(pad4y)
ax[1].plot(freq2, 10 * np.log10(np.abs(fftshift(fpady / fpady[0]))))
ax[1].plot(freq4, 10 * np.log10(np.abs(fftshift(fpad4y / fpad4y[0]))))
ysk = ifftshift(yks)
padk = np.concatenate((ysk[:250], np.zeros((2000,)), ysk[250:]))
fpadk = fft(padk)
ax[1].plot(freq4, 10 * np.log10(np.abs(fftshift(fpadk / fpadk[0]))))
ysk2 = ifftshift(yks2)
padk2 = np.concatenate((ysk2[:100], np.zeros((1000,)), ysk2[100:]))
fpadk2 = fft(padk2)
ax[1].plot(freq2, 10 * np.log10(np.abs(fftshift(fpadk2 / fpadk2[0]))))
#ax[1].plot(freqs4, fft(ifftshift(
#ax[1].plot(freqs, get_db_response(xs, 'hann'),label='Hann')
#ax[1].plot(freqs, get_db_response(xs, 'kaiser',alpha=5),label='Kaiser=5')
#ax[1].plot(freqs, get_db_response(xs, 'kaiser',alpha=10),label='Kaiser=10')
#ax[1].legend()
ax[1].set_ylabel("dB")
ax[1].set_xlabel("cycles/a")
plt.show()
def apply_filter(data_array, filter_array,
fft_multiplier=None, ifft_multiplier=None,
output_multiplier=None, apply_window_func=False,
window_shift=None, invert_filter=False):
"""FFT image cube, apply mask and iFFT the output back to image domain.
Parameters
----------
data_array : ndarray
Image cube.
filter_array : ndarray
Filter to multiply to FFT(data_array). Same shape as data_array.
Assume (min, max) = (0, 1).
fft_multiplier : float, optional
Scalar to multiply to FFT output before masking.
ifft_multiplier : float, optional
Scalar to multiply to the masked array before iFFT back.
output_multiplier : float, optional
Scalar to multiply to output
apply_window_func : bool, optional
Apply blackman-nuttall window function to the first dimension of
the data_array before FFT.
window_shift : int
Shift window function by these many pixels.
Negative will shift to the left.
invert_filter: bool, optional
Invert the filter (1 - filter_array) before applying. Default is False.
Returns
-------
out: ndarray
Masked image cube.
"""
if apply_window_func:
k = nuttall(data_array.shape[0])
if window_shift:
k = np.roll(k, window_shift)
w = (np.ones_like(data_array).T * k).T
else:
w = np.ones_like(data_array)
data_fft = fftshift(fftn(ifftshift(data_array * w)))
if fft_multiplier is not None:
data_fft *= fft_multiplier
if invert_filter:
filter_array = 1 - filter_array
data_fft *= filter_array
out = fftshift(ifftn(ifftshift(data_fft))) / w
if ifft_multiplier is not None:
out *= ifft_multiplier
if output_multiplier is not None:
out *= output_multiplier
return out.real
def fast_hessian(img, sigma=3.0):
"""Calculates Hessian in *frequency space* via fft2
-4π [ μ^2 iL(μ,ν) μν iL(μ,ν) ]
[ μν iL(μ,ν) ν^2 iL(μ,ν) ]
where iL(μ,ν) is the inverse 2D FFT of the image
"""
#ffx = partial(rfft2, s=img.shape)
#iffx = partial(irfft2, s=img.shape)
ffx = fft2
iffx = ifft2
iL = ffx(img)
SHIFT = False
# coordinate matrices [[ u^2, uv], [uv, v^2]]
cxx = np.fromfunction(lambda i,j: i**2, iL.shape, dtype='float')
cxy = np.fromfunction(lambda i,j: i*j, iL.shape, dtype='float')
cyy = np.fromfunction(lambda i,j: j**2, iL.shape, dtype='float')
if SHIFT:
cxx = fftshift(cxx)
cxy = fftshift(cxy)
cyy = fftshift(cyy)
# elementwise multiplication
hxx = -4*np.pi**2 * cxx * iL
hxy = -4*np.pi**2 * cxy * iL
hyy = -4*np.pi**2 * cyy * iL
exparg = -(cxx + cyy) / (2*np.pi**2 * sigma**2)
#A = 1 / (2*np.pi*sigma**2)
A = 1
fgauss = A*np.exp(exparg)
hxx = fgauss * hxx
hxy = fgauss * hxy
hyy = fgauss * hyy
Hxx = iffx(hxx)
Hxy = iffx(hxy)
Hyy = iffx(hyy)
if SHIFT:
Hxx = ifftshift(Hxx)
Hxy = ifftshift(Hxy)
Hyy = ifftshift(Hyy)
return Hxx, Hxy, Hyy
def setUp(self):
# Input
self.data = hdf5.read_data("example_input.h5")
C, T, Z, Y, X = self.data[0].shape
self.data[0].shape = Y, X
self.small_data = self.data[0][350:400, 325:375]
# Input drifted by known value
self.data_drifted = hdf5.read_data("example_drifted.h5")
C, T, Z, Y, X = self.data_drifted[0].shape
self.data_drifted[0].shape = Y, X
# Input drifted by random value
z = 1j # imaginary unit
self.deltar = numpy.random.uniform(-100, 100)
self.deltac = numpy.random.uniform(-100, 100)
nr, nc = self.data[0].shape
array_nr = numpy.arange(-numpy.fix(nr / 2), numpy.ceil(nr / 2))
array_nc = numpy.arange(-numpy.fix(nc / 2), numpy.ceil(nc / 2))
Nr = fft.ifftshift(array_nr)
Nc = fft.ifftshift(array_nc)
[Nc, Nr] = numpy.meshgrid(Nc, Nr)
self.data_random_drifted = fft.ifft2(fft.fft2(self.data[0]) * numpy.power(math.e,
z * 2 * math.pi * (self.deltar * Nr / nr + self.deltac * Nc / nc)))
# Noisy inputs
noise = random.normal(0, 3000, self.data[0].size)
noise_array = noise.reshape(self.data[0].shape[0], self.data[0].shape[1])
self.data_noisy = self.data[0] + noise_array
self.data_drifted_noisy = self.data_drifted[0] + noise_array
self.data_random_drifted_noisy = self.data_random_drifted + noise_array
# Small input drifted by random value
self.small_deltar = numpy.random.uniform(-10, 10)
self.small_deltac = numpy.random.uniform(-10, 10)
nr, nc = self.small_data.shape
array_nr = numpy.arange(-numpy.fix(nr / 2), numpy.ceil(nr / 2))
array_nc = numpy.arange(-numpy.fix(nc / 2), numpy.ceil(nc / 2))
Nr = fft.ifftshift(array_nr)
Nc = fft.ifftshift(array_nc)
[Nc, Nr] = numpy.meshgrid(Nc, Nr)
self.small_data_random_drifted = fft.ifft2(fft.fft2(self.small_data) * numpy.power(math.e,
z * 2 * math.pi * (self.small_deltar * Nr / nr + self.small_deltac * Nc / nc)))
# Small noisy inputs
small_noise = random.normal(0, 3000, self.small_data.size)
small_noise_array = small_noise.reshape(self.small_data.shape[0], self.small_data.shape[1])
self.small_data_noisy = self.small_data + small_noise_array
self.small_data_random_drifted_noisy = self.small_data_random_drifted + small_noise_array
def gs_mod(idata,itera=10,osize=256):
"""Modiffied Gerchberg-Saxton algorithm to calculate DOEs
Calculates the phase distribution in a object plane to obtain an
specific amplitude distribution in the target plane. It uses a
FFT to calculate the field propagation.
The wavefront at the DOE plane is assumed as a plane wave.
This algorithm leaves a window around the image plane to allow the
noise to move there. It only optimises the center of the image.
**ARGUMENTS:**
========== ======================================================
idata numpy array containing the target amplitude distribution
itera Maximum number of iterations
osize Size of the center of the image to be optimized
It should be smaller than the image itself.
========== ======================================================
"""
M,N=idata.shape
cut=osize//2
zone=zeros_like(idata)
zone[M/2-cut:M/2+cut,N/2-cut:N/2+cut]=1
zone=zone.astype(bool)
mask=exp(2.j*pi*random(idata.shape))
mask[zone]=0
#~ imshow(abs(mask)),colorbar()
fdata=fftshift(fft2(ifftshift(idata+mask))) #Nota, colocar esta mascara es muy importante, por que si no no converge tan rapido
e=1000
ea=1000
for i in range (itera):
fdata=exp(1.j*angle(fdata))
rdata=ifftshift(ifft2(fftshift(fdata)))
#~ e= (abs(rdata[zone])-idata[zone]).std()
#~ if e>ea:
#~
#~ break
ea=e
rdata[zone]=exp(1.j*angle(rdata[zone]))*(idata[zone])
fdata=fftshift(fft2(ifftshift(rdata)))
fdata=exp(1.j*angle(fdata))
return fdata
def delayseq(x, delay_sec:float, fs:int):
"""
x: input 1-D signal
delay_sec: amount to shift signal [seconds]
fs: sampling frequency [Hz]
xs: time-shifted signal
"""
assert x.ndim == 1, 'only 1-D signals for now'
delay_samples = delay_sec*fs
delay_int = round(delay_samples)
nfft = nextpow2(x.size+delay_int)
fbins = 2*pi*ifftshift((arange(nfft)-nfft//2))/nfft
X = fft(x,nfft)
Xs = ifft(X*exp(-1j*delay_samples*fbins))
if isreal(x[0]):
Xs = Xs.real
xs = zeros_like(x)
xs[delay_int:] = Xs[delay_int:x.size]
return xs
def gen_wedge_psf(nx, ny, nf, dx, dy, df, z, out, threads=None):
u = fftshift(fftfreq(nx, dx * np.pi / 180))
v = fftshift(fftfreq(ny, dy * np.pi / 180))
e = fftshift(fftfreq(nf, df))
E = np.sqrt(Cosmo.Om0 * (1 + z) ** 3 +
Cosmo.Ok0 * (1 + z) ** 2 + Cosmo.Ode0)
D = Cosmo.comoving_transverse_distance(z).value
H0 = Cosmo.H0.value * 1e3
c = const.c.value
print(E, D, H0)
kx = u * 2 * np.pi / D
ky = v * 2 * np.pi / D
k_perp = np.sqrt(kx ** 2 + ky[np.newaxis, ...].T ** 2)
k_par = e * 2 * np.pi * H0 * f21 * E / (c * (1 + z) ** 2)
arr = np.ones((nf, nx, ny), dtype='complex128')
for i in range(nf):
mask = (k_perp > np.abs(k_par[i]) * c * (1 + z) / (H0 * E * D))
arr[i][mask] = 0
np.save('kx.npy', kx)
np.save('ky.npy', ky)
np.save('kpar.npy', k_par)
np.save('wedge_window.npy', arr.real)
fft_arr = fftshift(fftn(ifftshift(arr))).real
hdu = fits.PrimaryHDU(data=fft_arr)
hdr_dict = dict(cdelt1=dx, cdelt2=dy, cdelt3=df,
crpix1=nx/2, crpix2=ny/2, crpix3=nf/2,
crval1=0, crval2=0, crval3=0,
ctype1='RA---SIN', ctype2='DEC--SIN', ctype3='FREQ',
cunit1='deg', cunit2='deg', cunit3='Hz')
for k, v in hdr_dict.items():
hdu.header[k] = v
hdu.writeto(out, clobber=True)
def filterDFT(imageMatrix, filterMatrix):
shiftedDFT = fftshift(fft2(imageMatrix))
misc.imsave("dft.png", scaleSpectrum(shiftedDFT))
filteredDFT = shiftedDFT * filterMatrix
misc.imsave("filtered-dft.png", scaleSpectrum(filteredDFT))
return ifft2(ifftshift(filteredDFT))
def _load(self, path, fft, maxnorm):
try:
img = astimage.open(path, "r", eat_warnings=True)
except Exception as e:
die("can't open path “%s”: %s", path, e)
try:
img = img.simple()
except Exception as e:
print("blink: can't convert “%s” to simple 2D sky image; taking " "first plane" % path, file=sys.stderr)
data = img.read(flip=True)[tuple(np.zeros(img.shape.size - 2))]
toworld = None
else:
data = img.read(flip=True)
toworld = img.toworld
if fft:
from numpy.fft import ifftshift, fft2, fftshift
data = np.abs(ifftshift(fft2(fftshift(data.filled(0)))))
data = np.ma.MaskedArray(data)
toworld = None
if maxnorm:
data /= np.ma.max(data)
return data, toworld
def create_matching_kernel(source_psf, target_psf, window=None):
"""
Create a kernel to match 2D point spread functions (PSF) using the
ratio of Fourier transforms.
Parameters
----------
source_psf : 2D `~numpy.ndarray`
The source PSF. The source PSF should have higher resolution
(i.e. narrower) than the target PSF. ``source_psf`` and
``target_psf`` must have the same shape and pixel scale.
target_psf : 2D `~numpy.ndarray`
The target PSF. The target PSF should have lower resolution
(i.e. broader) than the source PSF. ``source_psf`` and
``target_psf`` must have the same shape and pixel scale.
window : callable, optional
The window (or taper) function or callable class instance used
to remove high frequency noise from the PSF matching kernel.
Some examples include:
* `~photutils.psf.matching.HanningWindow`
* `~photutils.psf.matching.TukeyWindow`
* `~photutils.psf.matching.CosineBellWindow`
* `~photutils.psf.matching.SplitCosineBellWindow`
* `~photutils.psf.matching.TopHatWindow`
For more information on window functions and example usage, see
:ref:`psf_matching`.
Returns
-------
kernel : 2D `~numpy.ndarray`
The matching kernel to go from ``source_psf`` to ``target_psf``.
The output matching kernel is normalized such that it sums to 1.
"""
# inputs are copied so that they are not changed when normalizing
source_psf = np.copy(np.asanyarray(source_psf))
target_psf = np.copy(np.asanyarray(target_psf))
if source_psf.shape != target_psf.shape:
raise ValueError('source_psf and target_psf must have the same shape '
'(i.e. registered with the same pixel scale).')
# ensure input PSFs are normalized
source_psf /= source_psf.sum()
target_psf /= target_psf.sum()
source_otf = fftshift(fft2(source_psf))
target_otf = fftshift(fft2(target_psf))
ratio = target_otf / source_otf
# apply a window function in frequency space
if window is not None:
ratio *= window(target_psf.shape)
kernel = np.real(fftshift((ifft2(ifftshift(ratio)))))
return kernel / kernel.sum()
def hg_conv(f, g): ub = tuple(array(f.shape) + array(g.shape) - 1); fh = rfftn(cpad(f,ub)); gh = rfftn(cpad(g,ub)); res = ifftshift(irfftn(fh * sp.conjugate(gh))); del fh, gh; return res;
def partial( x, order=1, length=None, axis=0):
"""Numerically differentiate `x` using the pseudo-spectral method.
Parameters
----------
x : array_like
The periodic data to be differentiated.
order : int
The order of the derivative to be computed.
length : float
The length of the domain on which the signal was sampled.
axis : int
The axis of `x` containing the data to be differentiated.
Returns
-------
dx : array, with the same shape as `x`
The differentiated data.
"""
if length is None:
length = 2 * pi;
if axis is None:
axis = -1;
N = x.shape[axis];
y = fft(x, axis=axis);
numvals = shape(y)[0];
preserveVals = ones(numvals/6);
downfilter = exp((arange(numvals/6+1, (numvals/2)+1) -
numvals/2.0))[::-1];
upfilter = exp(-(arange(numvals/2, (5*numvals/6)+1) -
numvals/2.0))[::-1];
#print 0, 'to' , numvals/6
#print len(preserveVals);
#print numvals/6+1, 'to', numvals/2 +1
#print len(downfilter);
#print numvals/2 + 1, 'to', (5*numvals/6)+1
#print len(upfilter)
#print (5*numvals/6)+1, 'to', numvals;
#print len(preserveVals)
#downfilter = slopeDown*(arange(numvals/6+1, (numvals/2)+1) - numvals/2.0);
#upfilter = slopeUp*(arange(numvals/2, (5*numvals/6)+1) - numvals/2.0);
fftFilter = concatenate((preserveVals, downfilter, upfilter, preserveVals))
y = (fftFilter * y.transpose()).transpose();
k = array(range(N), dtype=complex128) - N/2;
k *= 2*pi*1j / length;
k = k**order;
shp = ones(len(x.shape));
shp[axis] = N;
k.shape = shp;
dy = ifftshift(k) * y;
dx = ifft(dy, axis=axis).real;
# print 'NUMPY'
# print dx;
return dx;
def compute(self, scene: Scene):
""" Compute optical irradiance map
Computation proccedure:
1) convert radiance to irradiance
2) apply lens and macular transmittance
3) apply off-axis fall-off (cos4th)
4) apply optical transfert function
Args:
scene (pyEyeBall.Scene): instance of Scene class, containing the radiance and other scene information
Examples:
>>> oi = Optics()
>>> oi.compute(Scene())
"""
# set field of view and wavelength samples
self.fov = scene.fov
scene.wave = self._wave
self.dist = scene.dist
# compute irradiance
self.photons = pi / (1 + 4 * self.f_number**2 * (1 + abs(self.magnification))**2) * scene.photons
# apply ocular transmittance
self.photons *= self.ocular_transmittance
# apply the relative illuminant (off-axis) fall-off: cos4th function
x, y = self.spatial_support
s_factor = np.sqrt(self.image_distance**2 + x**2 + y**2)
self.photons *= (self.image_distance / s_factor[:, :, None])**4
# apply optical transfer function of the optics
for ii in range(self.wave.size):
otf = fftshift(self.otf(self._wave[ii], self.frequency_support_x, self.frequency_support_y))
self.photons[:, :, ii] = np.abs(ifftshift(ifft2(otf * fft2(fftshift(self.photons[:, :, ii])))))
def plot_pulse(A_t,A_w,t,w, l0 = 1.550 * micr, t_zoom = pico, l_zoom = 10*nano):
## Fix maximum
if 'A_max' not in plot_pulse.__dict__:
plot_pulse.A_max = amax(A_t)
plot_pulse.A_w_max = amax(A_w)
w0 = 2 * pi * C_SPEED / l0
## Plot Time domain
fig = pl.gcf()
fig.add_subplot(211)
pl.plot(t / t_zoom, absolute(A_t/plot_pulse.A_max), hold = False)
pl.axis([amin(t) / t_zoom*0.4,amax(t) / t_zoom*0.4, 0, 1.1])
pl.xlabel(r'$time\ (%s s)$'%units[t_zoom])
atten_win = 0.01
npoints = len(w)
apod = arange(npoints)
apod = exp(-apod/(npoints*atten_win)) + exp(-(npoints-apod)/(npoints*atten_win))
apod = ifftshift(apod)
## Plot Freq domain
fig.add_subplot(212)
pl.plot((2 * pi * C_SPEED)/(w+w0)/micr, log10(absolute(A_w)**2/absolute(plot_pulse.A_w_max)**2) * 10, hold=False)
#pl.plot((2 * pi * C_SPEED)/(w+w0) / micr, log10(absolute(apod)**2/absolute(amax(apod))**2 ) *10, hold=True)
#pl.semilogy()
pl.axis([(l0-l_zoom)/micr, (l0+l_zoom)/micr, -60, 5])
pl.xlabel(r'$wavelength\ (\mu m)$')
pl.ylabel(r'$spectrum (db)$')
pl.show()
def laplacian_filter(in_file, in_mask=None, out_file=None):
import numpy as np
import nibabel as nb
import os.path as op
from math import pi
from numpy.fft import fftn, ifftn, fftshift, ifftshift
if out_file is None:
fname, fext = op.splitext(op.basename(in_file))
if fext == '.gz':
fname, _ = op.splitext(fname)
out_file = op.abspath('./%s_smooth.nii.gz' % fname)
im = nb.load(in_file)
data = im.get_data()
if in_mask is not None:
mask = nb.load(in_mask).get_data()
mask[mask > 0] = 1.0
mask[mask <= 0] = 0.0
data *= mask
dataft = fftshift(fftn(data))
x = np.linspace(0, 2 * pi, dataft.shape[0])[:, None, None]
y = np.linspace(0, 2 * pi, dataft.shape[1])[None, :, None]
z = np.linspace(0, 2 * pi, dataft.shape[2])[None, None, :]
lapfilt = 2.0 * np.squeeze((np.cos(x) + np.cos(y) + np.cos(z))) - 5.0
dataft *= fftshift(lapfilt)
imfilt = np.real(ifftn(ifftshift(dataft)))
nb.Nifti1Image(imfilt.astype(np.float32), im.get_affine(),
im.get_header()).to_filename(out_file)
return out_file
def symmetrize(self, C_N):
"""Symmetrize force constant matrix."""
# Number of atoms
natoms = len(self.indices)
# Number of unit cells
N = np.prod(self.N_c)
# Reshape force constants to (l, m, n) cell indices
C_lmn = C_N.reshape(self.N_c + (3 * natoms, 3 * natoms))
# Shift reference cell to center index
if self.offset == 0:
C_lmn = fft.fftshift(C_lmn, axes=(0, 1, 2)).copy()
# Make force constants symmetric in indices -- in case of an even
# number of unit cells don't include the first
i, j, k = np.asarray(self.N_c) % 2 - 1
C_lmn[i:, j:, k:] *= 0.5
C_lmn[i:, j:, k:] += \
C_lmn[i:, j:, k:][::-1, ::-1, ::-1].transpose(0, 1, 2, 4, 3).copy()
if self.offset == 0:
C_lmn = fft.ifftshift(C_lmn, axes=(0, 1, 2)).copy()
# Change to single unit cell index shape
C_N = C_lmn.reshape((N, 3 * natoms, 3 * natoms))
return C_N
def frp_to_fir(frp, fbins=None):
'''Transform a fringe rate profile to a fir filter.'''
frp = ifftshift(frp,axes=-1)
fir = ifft(frp, axis=-1)
fir = fftshift(fir, axes=-1)
if fbins is not None: return fir, fftshift(fftfreq(fbins.size, fbins[1] - fbins[0]))
else: return fir
def real_space(self):
"""Fourier transform the dynamical matrix to real-space."""
if not self.assembled:
self.assemble()
# Shape of q-point grid
N_c = self.N_c
# Reshape before Fourier transforming
shape = self.D_k.shape
Dq_lmn = self.D_k.reshape(N_c + shape[1:])
DR_lmn = fft.ifftn(fft.ifftshift(Dq_lmn, axes=(0, 1, 2)), axes=(0, 1, 2))
if debug:
# Check that D_R is real enough
assert np.all(DR_lmn.imag < 1e-8)
DR_lmn = DR_lmn.real
# Corresponding R_m vectors in units of the basis vectors
R_cm = np.indices(N_c).reshape(3, -1)
N1_c = np.array(N_c)[:, np.newaxis]
R_cm += N1_c // 2
R_cm %= N1_c
R_cm -= N1_c // 2
R_clmn = R_cm.reshape((3,) + N_c)
return DR_lmn, R_clmn
def inverse_spectrogram(spec, s_len,
sample_rate, spec_sample_rate, freq_spacing, min_freq=0, max_freq=None, nstd=6, log=True, noise_level_db=80, rectify=True):
"""turns the complex spectrogram into a signal
inverts by repeating the process on a string-of-ones
"""
spec_copy = spec.copy()
if log:
spec_copy = 10**(spec_copy)
spec_tranpose = spec.transpose() # spec_tranpose[time][frequency]
hnwinlen = len(spec) - 1
nincrement = int(np.round(float(sample_rate)/spec_sample_rate))
gauss_t = np.arange(-hnwinlen, hnwinlen+1, 1.0)
gauss_std = float(2*hnwinlen) / float(nstd)
gauss_window = np.exp(-gauss_t**2 / (2.0*gauss_std**2)) / (gauss_std*np.sqrt(2*np.pi))
s = np.zeros(s_len + 2*hnwinlen+1)
w = np.zeros(s_len + 2*hnwinlen+1)
for i in range(len(spec_tranpose)):
sample = i * nincrement
spec_slice = np.concatenate((spec_tranpose[i][:0:-1].conj(), spec_tranpose[i]))
s[sample:sample+2*hnwinlen+1] += gauss_window * ifft(ifftshift(spec_slice))
w[sample:sample+2*hnwinlen+1] += gauss_window ** 2
s /= w
return s[hnwinlen:hnwinlen+s_len]
def inverse_mps(mps):
"Inverts a MPS back to a spectrogram"
spec = ifft2(ifftshift(mps))
return spec
def retrieve_phase(data, params, max_iters=200, pupil_tol=1e-8, mse_tol=1e-8, phase_only=False):
"""Retrieve the phase across the objective's back pupil from an
experimentally measured PSF.
NOTE: If all that is needed is phase, e.g. for adaptive optical correction, then most normal
ways of estimating the background should be sufficient and you can use the `phase_only`
keyword. However, if you want to properly model your PSF for something like deconvolution
then you should be aware that the magnitude estimate is _incredibly_ sensitive to the background
correction applied to the data prior to running the algorithm, and multiple background
methods/parameters should be tried.
Follows: [Hanser, B. M.; Gustafsson, M. G. L.; Agard, D. A.;
Sedat, J. W. Phase Retrieval for High-Numerical-Aperture Optical Systems.
Optics Letters 2003, 28 (10), 801.](dx.doi.org/10.1364/OL.28.000801)
Parameters
----------
data : ndarray (3 dim)
The experimentally measured PSF of a subdiffractive source
params : dict
Parameters to pass to HanserPSF, size and zsize will be automatically
updated from data.shape
max_iters : int
The maximum number of iterations to run, default is 200
pupil_tol : float
the tolerance in percent change in change in pupil, default is 1e-8
mse_tol : float
the tolerance in percent change for the mean squared error between
data and simulated data, default is 1e-8
phase_only : bool
True means only the phase of the back pupil is retrieved while the
amplitude is not.
Returns
-------
PR_result : PhaseRetrievalResult
An object that contains the phase retrieval result
"""
# make sure data is square
assert max_iters > 0, "Must have at least one iteration"
assert data.shape[1] == data.shape[2], "Data is not square in x/y"
assert data.ndim == 3, "Data doesn't have enough dims"
# make sure the user hasn't screwed up the params
params.update(
dict(vec_corr="none", condition="none", zsize=data.shape[0], size=data.shape[-1])
)
# assume that data prep has been handled outside function
# The field magnitude is the square root of the intensity
mag = psqrt(data)
# generate a model from parameters
model = HanserPSF(**params)
# generate coordinates
model._gen_kr()
# start a list for iteration
mse = np.zeros(max_iters)
mse_diff = np.zeros(max_iters)
pupil_diff = np.zeros(max_iters)
# generate a pupil to start with
new_pupil = model._gen_pupil()
# save it as a mask
mask = new_pupil.real
# initialize
old_mse = old_pupil = np.nan
# iterate
for i in range(max_iters):
# generate new mse and add it to the list
model.apply_pupil(new_pupil)
new_mse = _calc_mse(data, model.PSFi)
mse[i] = new_mse
if i > 0:
# calculate the difference in mse to test for convergence
mse_diff[i] = abs(old_mse - new_mse) / old_mse
# calculate the difference in pupil
pupil_diff[i] = (abs(old_pupil - new_pupil) ** 2).mean() / (abs(old_pupil) ** 2).mean()
else:
mse_diff[i] = np.nan
pupil_diff[i] = np.nan
# check tolerances, how much has the pupil changed, how much has the mse changed
# and what's the absolute mse
logger.info(
f"Iteration {i}, mse_diff = {mse_diff[i]:.2g}, pupil_diff = {pupil_diff[i]:.2g}"
)
if pupil_diff[i] < pupil_tol or mse_diff[i] < mse_tol or mse[i] < mse_tol:
break
# update old_mse
old_mse = new_mse
# retrieve new pupil
old_pupil = new_pupil
# keep phase
phase = np.angle(model.PSFa.squeeze())
# replace magnitude with experimentally measured mag
new_psf = mag * np.exp(1j * phase)
# generate the new pupils
new_pupils = fftn(ifftshift(new_psf, axes=(1, 2)), axes=(1, 2))
# undo defocus and take the mean
new_pupils /= model._calc_defocus()
new_pupil = new_pupils.mean(0) * mask
# if phase only discard magnitude info
if phase_only:
new_pupil = np.exp(1j * np.angle(new_pupil)) * mask
else:
logger.warning("Reach max iterations without convergence")
mse = mse[: i + 1]
mse_diff = mse_diff[: i + 1]
pupil_diff = pupil_diff[: i + 1]
# shift mask
mask = fftshift(mask)
# shift phase then unwrap and mask
phase = unwrap_phase(fftshift(np.angle(new_pupil))) * mask
# shift magnitude
magnitude = fftshift(abs(new_pupil)) * mask
return PhaseRetrievalResult(magnitude, phase, mse, pupil_diff, mse_diff, model)
def M(vk, H_fft):
return np.real(fft.fftshift(fft.ifft2(fft.fft2(fft.ifftshift(vk)) *
H_fft)))
def Filter(img, filter_matrix):
shifted_dft_img = fftshift(fft2(img))
filter_img = shifted_dft_img * filter_matrix
return ifft2(ifftshift(filter_img))
im = cv2.imread(
'bricks.jpg'
) # path needs to be channged all input images are available in the input folder
im = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY)
cv2.imwrite("input.jpg",
im) # output images in the output folder can be used for refrence
sampled_1 = block_reduce(im, (1, 1))
sampled_2 = block_reduce(im, (2, 2))
sampled_4 = block_reduce(im, (4, 4))
sampled_8 = block_reduce(im, (8, 8))
sampled_16 = block_reduce(im, (16, 16))
sampled1_fft = fftshift(fft2(sampled_1))
sampled1_mag = abs(sampled1_fft)
res1 = ifft2(ifftshift(sampled1_fft)).astype("uint8")
cv2.imwrite(
"res1.jpg",
res1) # output images in the output folder can be used for refrence
cv2.imwrite(
"fft1.jpg",
10 * log(sampled1_mag +
1)) # output images in the output folder can be used for refrence
sampled2_fft = fftshift(fft2(sampled_2))
sampled2_mag = abs(sampled2_fft)
res2 = ifft2(ifftshift(sampled2_fft)).astype("uint8")
cv2.imwrite(
"res2.jpg",
res2) # output images in the output folder can be used for refrence
cv2.imwrite(
def process_card(cardname, expansion=None):
time.sleep(0.05)
# try/except in case the search doesn't return anything
try:
# If the card specifies which set to retrieve the scan from, do that
if expansion:
# Set specified from set formatter
query = "!\"" + cardname + "\" set=" + expansion
print("Processing: " + cardname + ", set: " + expansion)
else:
query = "!\"" + cardname + "\""
print("Processing: " + cardname)
card = scrython.cards.Search(q=query).data()[0]
except scrython.foundation.ScryfallError:
print("Couldn't find card: " + cardname)
return
# Handle cards with multiple faces
if card["layout"] == "transform":
cards = [x for x in card["card_faces"]]
else:
cards = [
card,
]
for card_obj in cards:
name = card_obj["name"].replace(
"//", "&") # should work on macOS & windows now
name = name.replace(":", "") # case for Circle of Protection: X
# Process with waifu2x
r = requests.post("https://api.deepai.org/api/waifu2x",
data={
'image': card_obj["image_uris"]["large"],
},
headers={'api-key': config.TOKEN})
output_url = r.json()['output_url']
im = imageio.imread(output_url)
# Read in filter image
filterimage = np.copy(imageio.imread("./filterimagenew.png"))
# Resize filter to shape of input image
filterimage = resize(filterimage, [im.shape[0], im.shape[1]],
anti_aliasing=True,
mode="edge")
# Initialise arrays
im_filtered = np.zeros(im.shape, dtype=np.complex_)
im_recon = np.zeros(im.shape, dtype=np.float_)
# Apply filter to each RGB channel individually
for i in range(0, 3):
im_filtered[:, :, i] = np.multiply(fftshift(fft2(im[:, :, i])),
filterimage)
im_recon[:, :, i] = ifft2(ifftshift(im_filtered[:, :, i])).real
# Scale between 0 and 255 for uint8
minval = np.min(im_recon)
maxval = np.max(im_recon)
im_recon_sc = (255 * ((im_recon - minval) / (maxval - minval))).astype(
np.uint8)
# TODO: pre-m15, post-8ed cards
# TODO: pre-8ed cards (?)
# Borderify image
pad = 57 # Pad image by 1/8th of inch on each edge
bordertol = 16 # Overfill onto existing border by 16px to remove white corners
im_padded = np.zeros([im.shape[0] + 2 * pad, im.shape[1] + 2 * pad, 3])
# Get border colour from left side of image
bordercolour = np.median(im_recon_sc[200:(im_recon_sc.shape[0] - 200),
0:bordertol],
axis=(0, 1))
# Pad image
for i in range(0, 3):
im_padded[pad:im.shape[0] + pad, pad:im.shape[1] + pad,
i] = im_recon_sc[:, :, i]
# Overfill onto existing border to remove white corners
# Left
im_padded[0:im_padded.shape[0], 0:pad + bordertol, :] = bordercolour
# Right
im_padded[0:im_padded.shape[0], im_padded.shape[1] -
(pad + bordertol):im_padded.shape[1], :] = bordercolour
# Top
im_padded[0:pad + bordertol, 0:im_padded.shape[1], :] = bordercolour
# Bottom
im_padded[im_padded.shape[0] - (pad + bordertol):im_padded.shape[0],
0:im_padded.shape[1], :] = bordercolour
# Remove copyright line
if card["frame"] == "2015":
# Modern frame
leftPix = 735
rightPix = 1140
topPix = 1550
bottomPix = 1585
# creatures have a shifted legal line
try:
power = card_obj["power"]
toughness = card_obj["toughness"]
topPix = 1575
bottomPix = 1615
# Creature card
except KeyError:
pass
# planeswalkers have a shifted legal line too
try:
loyalty = card_obj["loyalty"]
topPix = 1575
bottomPix = 1615
except KeyError:
pass
im_padded[topPix:bottomPix, leftPix:rightPix, :] = bordercolour
elif card["frame"] == "2003":
# 8ED frame
try:
loyalty = card_obj["loyalty"]
leftPix = 300
rightPix = 960
topPix = 1570
bottomPix = 1600
im_padded[topPix:bottomPix, leftPix:rightPix, :] = bordercolour
except KeyError:
# TODO: Content aware fill?
pass
# Remove holostamp
if card["frame"] == "2015" and (card["rarity"] == "rare" or card["rarity"] == "mythic") \
and "/large/front/" in card_obj["image_uris"]["large"]:
# Need to remove holostamp
# Define bounds of ellipse to fill with border colour
leftE = 575
rightE = 690
topE = 1520
bottomE = 1575
cx = (leftE + rightE) / 2
cy = (topE + bottomE) / 2
h = (bottomE - topE) / 2
w = (rightE - leftE) / 2
for x in range(leftE, rightE + 1):
for y in range(topE, bottomE + 1):
# determine if point is in the holostamp area
if pow(x - cx, 2) / pow(w, 2) + pow(y - cy, 2) / pow(
h, 2) <= 1:
# point is inside ellipse
im_padded[y, x, :] = bordercolour
# Write image to disk
imageio.imwrite("formatted/" + name + ".png",
im_padded.astype(np.uint8))
import numpy as np
import numpy.fft as fft
import pylab as plt
import iris
plt.ion()
FILE_LOC = '/home/markmuetz/mirrors/archer/work/cylc-run/u-ax548/share/data/history/m500_large_dom_no_wind/w072.nc'
w = iris.load(FILE_LOC)[0]
k = fft.fftshift(fft.fftfreq(w.shape[-1], d=0.5))
l = k.copy()
K, L = np.meshgrid(k, l)
fts = fft.fftshift(fft.fft2(w[:, 15].data), axes=(1, 2))
angle = np.angle(fts[0, 257, 256]) - np.angle(fts[:, 257, 256])
fts_trans = fts * np.exp(
1j * angle[:, None, None] * L[None, :, :] / L[257, 256])
w_trans = fft.ifft2(fft.ifftshift(fts_trans, axes=(1, 2)))
for i in range(24):
plt.clf()
plt.imshow(w_trans[i].real)
plt.pause(0.3)
def space_propagate(self, wave: np.ndarray, dz: float):
spatial_propagator = np.exp(-1j * self.wave_length * np.pi * dz *
self.q_mgrid**2)
return ifft2(ifftshift(spatial_propagator) * fft2(wave))
def dfi_reconstruction(sinogram,
center,
angles=None,
ratio=1.0,
filter_name="hann",
pad_rate=0.25,
pad_mode="edge",
apply_log=True):
"""
Apply the DFI (direct Fourier inversion) reconstruction method to a
sinogram image (Ref. [1]). The method is a practical and direct
implementation of the Fourier slice theorem (Ref. [2]).
Parameters
----------
sinogram : array_like
2D array. Sinogram image.
center : float
Center of rotation.
angles : array_like
1D array. List of angles (in radian) corresponding to the sinogram.
ratio : float
To apply a circle mask to the reconstructed image.
filter_name : {None, "hann", "bartlett", "blackman", "hamming", "nuttall",\\
"parzen", "triang"}
Apply a smoothing filter.
pad_rate : float
To apply padding before the FFT. The padding width equals to
(pad_rate * image_width).
pad_mode : str
Padding method. Full list can be found at numpy.pad documentation.
apply_log : bool
Apply the logarithm function to the sinogram before reconstruction.
Returns
-------
array_like
Square array. Reconstructed image.
References
----------
.. [1] https://doi.org/10.1364/OE.418448
.. [2] https://doi.org/10.1071/PH560198
"""
if apply_log is True:
sinogram = -np.log(sinogram)
(nrow, ncol) = sinogram.shape
if ncol % 2 == 0:
sinogram = np.pad(sinogram, ((0, 0), (0, 1)), mode="edge")
ncol1 = sinogram.shape[1]
xshift = (ncol1 - 1) / 2.0 - center
sinogram = shift(sinogram, (0, xshift), mode='nearest')
if angles is not None:
t_ang = np.sum(np.abs(np.diff(angles * 180.0 / np.pi)))
if abs(t_ang - 360) < 10:
nrow = nrow // 2 + 1
sinogram = (sinogram[:nrow] + np.fliplr(sinogram[-nrow:])) / 2
step = np.mean(np.abs(np.diff(angles)))
b_ang = angles[0] - (angles[0] // (2 * np.pi)) * (2 * np.pi)
sino_360 = np.vstack((sinogram[:nrow - 1], np.fliplr(sinogram)))
sinogram = shift(sino_360, (b_ang / step, 0), mode='wrap')[:nrow]
if angles[-1] < angles[0]:
sinogram = np.flipud(np.fliplr(sinogram))
num_pad = int(pad_rate * ncol1)
sinogram = np.pad(sinogram, ((0, 0), (num_pad, num_pad)), mode=pad_mode)
ncol2 = sinogram.shape[1]
mask = util.make_circle_mask(ncol2, 1.0)
(r_mat, theta_mat) = generate_mapping_coordinate(ncol2, nrow, ncol2, ncol2)
sino_fft = fft.fftshift(fft.fft(fft.ifftshift(sinogram, axes=1)), axes=1)
if filter_name is not None:
window = make_smoothing_window(filter_name, ncol2)
sino_fft = sino_fft * np.tile(window, (nrow, 1))
mat_real = np.real(sino_fft)
mat_imag = np.imag(sino_fft)
reg_real = util.mapping(
mat_real, r_mat, theta_mat, order=5, mode="reflect") * mask
reg_imag = util.mapping(
mat_imag, r_mat, theta_mat, order=5, mode="reflect") * mask
recon = np.real(
fft.fftshift(fft.ifft2(
fft.ifftshift(reg_real + 1j * reg_imag))))[num_pad:ncol + num_pad,
num_pad:ncol + num_pad]
if ratio is not None:
if ratio == 0.0:
ratio = min(center, ncol - center) / (0.5 * ncol)
mask = util.make_circle_mask(ncol, ratio)
recon = recon * mask
return recon
def FROG_ifft(Ewsig):
return fft.ifft(fft.ifftshift(Ewsig, axes=0), axis=0)
pl.subplot(1,3,3)
pl.imshow( angle(imgFFT) ) # Phase
pl.title('Phase')
# Most power in images is concentrated around zero frequency
# (which represents the mean). This stands out when the amplitude
# is plotted, frustrating our view of the other frequencies.
# Log helps visualizing data with many different orders of magnitude.
pl.show()
##### 2.c
img2 = real(ifft2( ifftshift( imgFFT ) ))
pl.figure(2)
pl.subplot( 1, 2, 1)
pl.imshow(img)
pl.subplot( 1, 2, 2)
pl.imshow(img2)
pl.show()
print 'The squared error is: ', ((img - img2)**2).sum()
# Yes, they're the same!
##### 2.d
def calculate_grappa_unmixing(source_data, acc_factor, kernel_size=(4,5), data_mask=None, csm=None, regularization_factor=0.001, target_data=None):
'''Calculates unmixing coefficients for a 2D image using a GRAPPA algorithm
:param source_data: k-space source data ``[coils, y, x]``
:param acc_factor: Acceleration factor, e.g. 2
:param kernel_shape: Shape of the k-space kernel ``(ky-lines, kx-points)`` (default ``(4,5)``)
:param data_mask: Mask of where calibration data is located in source_data (defaults to all of source_data)
:param csm: Coil sensitivity map, ``[coil, y, x]`` (used for b1-weighted combining. Will be estimated from calibratino data if not supplied)
:param regularization_factor: adds tychonov regularization (default ``0.001``)
- 0 = no regularization
- set higher for more aggressive regularization.
:param target_data: If target data differs from source data (defaults to source_data)
:returns unmix: Image unmixing coefficients for a single ``x`` location, ``[coil, y, x]``
:returns gmap: Noise enhancement map, ``[y, x]``
'''
ny = source_data.shape[1]
nc_source = source_data.shape[0]
if target_data is None:
target_data = source_data
if data_mask is None:
data_mask = np.ones((ny, nc_source))
nc_target = target_data.shape[0]
if csm is None:
#Assume calibration data is in the middle
f = np.asarray(np.asmatrix(np.hamming(np.max(np.sum(data_mask,0)))).T * np.asmatrix(np.hamming(np.max(np.sum(data_mask,1)))))
fmask = np.zeros((source_data.shape[1],source_data.shape[2]),dtype=np.complex64)
idx = np.argwhere(data_mask==1)
fmask[idx[:,0],idx[:,1]] = f.reshape(idx.shape[0])
fmask = np.tile(fmask[None,:,:],(nc_source,1,1))
csm = fftshift(ifftn(ifftshift(source_data * fmask, axes=(1,2)), axes=(1,2)), axes=(1,2))
(csm,rho) = coils.calculate_csm_walsh(csm)
kernel = np.zeros((nc_target,nc_source,kernel_size[0]*acc_factor,kernel_size[1]),dtype=np.complex64)
sampled_indices = np.nonzero(data_mask)
kx_cal = (sampled_indices[1][0],sampled_indices[1][-1])
ky_cal = (sampled_indices[0][0],sampled_indices[0][-1])
for s in range(0,acc_factor):
kernel_mask = np.zeros((kernel_size[0]*acc_factor, kernel_size[1]),dtype=np.int8)
kernel_mask[s:kernel_mask.shape[0]:acc_factor,:] = 1
s_data = source_data[:,ky_cal[0]:ky_cal[1],kx_cal[0]:kx_cal[1]]
t_data = target_data[:,ky_cal[0]:ky_cal[1],kx_cal[0]:kx_cal[1]]
k = estimate_convolution_kernel(s_data,kernel_mask,regularization_factor=regularization_factor,target_data=t_data)
kernel = kernel + k
#return kernel
kernel = kernel[:,:,::-1,::-1] #flip kernel in preparation for convolution
csm_ss = np.sum(csm * np.conj(csm),0)
csm_ss = csm_ss + 1.0*(csm_ss < np.spacing(1)).astype('float32')
unmix = np.zeros(source_data.shape,dtype=np.complex64)
for c in range(0,nc_target):
kernel_pad = _pad_kernel(kernel[c,:,:,:],unmix.shape)
kernel_pad = fftshift(ifftn(ifftshift(kernel_pad, axes=(1,2)), axes=(1,2)), axes=(1,2))
kernel_pad *= unmix.shape[1]*unmix.shape[2]
unmix = unmix + (kernel_pad * np.tile(np.conj(csm[c,:,:]) /csm_ss,(nc_source,1,1)))
unmix /= acc_factor
gmap = np.squeeze(np.sqrt(np.sum(abs(unmix) ** 2, 0))) * np.squeeze(np.sqrt(np.sum(abs(csm) ** 2, 0)))
return (unmix,gmap)
y = np.linspace(0, int(img.shape[0]), img.shape[0])
x = np.linspace(0, int(img.shape[1]), img.shape[1])
xx, yy = np.meshgrid(x, y)
fft = np.empty([img.shape[0], img.shape[1], img.shape[2]],
dtype=np.complex64)
ifft = np.empty([img.shape[0], img.shape[1], img.shape[2]],
dtype=np.complex64)
for c in range(3):
#phase[:, :, c] = fillPhase(xx, yy, phaseSteps[0][c], phaseSteps[1][c])
phase[:, :, c] = circPhase(xx, yy, i, j, c)
#pass
#plt.imshow(phase/np.amax(phase))
#plt.show()
for c in range(3):
img1 = np.array(img * np.exp(1j * phase))
fft[:, :, c] = fftshift(fft2(ifftshift(img1[:, :, c])))
thetaX = np.arctan(
i * ledSpace / ledSep) * (M * inPixSize /
(wls[c] * 2 * np.pi * mag))
thetaY = np.arctan(
j * ledSpace / ledSep) * (M * inPixSize /
(wls[c] * 2 * np.pi * mag))
fftTrans = h.translate(fft[:, :, c], -thetaX, -thetaY)
fft[:, :, c] = pupil[:, :, c] * fftTrans
ifft[:, :, c] = fftshift(ifft2(fftshift(fft[:, :, c])))
#plt.imshow(np.log(np.abs(fft))[:, :, 0])
#plt.show()
#plt.imshow(np.array(np.abs(ifft)*255, dtype=np.int64))
#plt.show()
imgName = "./Imgs/img_" + str(i) + "_" + str(j) + "_.jpg"
cv.imwrite(imgName, np.array(np.abs(ifft) * 255, dtype=np.int64))
def IFFT_t_shift(self, A):
if PYFFTW_AVAILABLE:
self.ifft_input[:] = fftshift(A)
return ifftshift(self.ifft())
else:
return ifftshift(scipy.fftpack.fft(fftshift(A)))
T_PRI,
window=False,
debug=False)
# # phase correction based on range frequency
# time.count()
# print("phase correction based on range frequency")
# tau_0 = 2*R_t0/c
# for i in range(0, m_prime.size):
# for k in range(FT_FFT_freq_RangeBin.size):
# m_p = m_prime[i]
# F_k = FT_FFT_freq_RangeBin[k]
# FT_FFT_RangeBin[i, k] = (FT_FFT_RangeBin[i, k]*np.exp(1j*2*pi*F_k*tau_0))**(F_0/(F_0+F_k))*np.exp(-1j*2*pi*F_k*tau_0)
# ifft back to time domain after phase correction and remove zero padding
PhaseCorrected_RangeBin = ifftn(ifftshift(FT_FFT_RangeBin, axes=(1, )),
s=(RangeBin[0, :].size, ),
axes=(1, ))
# PhaseCorrected_RangeBin = ifftn(ifftshift(FT_FFT_RangeBin, axes=(1,)), axes=(1,))
time.count()
print("Doppler Processing")
# Doppler processing to extract target speed
Doppler = fftshift(
fftn(PhaseCorrected_RangeBin, axes=(0, )),
axes=(0, )) # n dimensional FFT, only FFT over column (over pulses)
DopplerFreq = fftshift(fftfreq(pulse_num, T_PRI))
DopplerVelocity = DopplerFreq * wave_len / 2
time.count()
def Recover(self,
xi,
*,
code='',
pb=('', 0, 1, 0, 0, 0, 0, 0, 0, 0, 0),
vis=False,
error=None,
err=None):
## Initialization ##
# Hard-code the random seed to make it reproducible #
np.random.seed(0)
# Pass xi into the goal image `y`, but pass it through the selection matrix `sig` first #
y = np.zeros((np.shape(self.sig)[0], np.size(xi)))
y[0, ...] = xi.reshape(np.size(xi), order="F")
self.y[:] = np.reshape(self.sig @ y, self.sz, order="F")
self.y_ = self.y.copy()
# Reinitialize psi and the slack variables #
self.Psi[:] = fftw.zeros_aligned(self.sz, dtype='complex64')
self.S_0[:] = fftw.zeros_aligned(self.sz, dtype='complex64')
self.S_1[:] = fftw.zeros_aligned(self.sz, dtype='complex64')
self.S_2[:] = fftw.zeros_aligned(self.sz, dtype='complex64')
# Localization error #
if (vis or (error is not None)):
pts = np.zeros([0, 3])
if (error is not None):
tru = OP._LoadMot(code)
pts = tru[tru[:, :, 3] == pb[1], :]
temp = []
temp[:] = pts[:, 0]
pts[:, 0] = pts[:, 1] # Swap X & Y #
pts[:, 1] = temp[:]
H_A, H_S = _IDFilters(self.sz[1:])
else:
tru = OP._LoadTruth(code)
for p in range(len(tru)):
if (pb[1] in tru[p].frm):
f = np.nonzero(pb[1] == tru[p].frm)[0]
pts = np.concatenate((pts, tru[p].res[f, :]), axis=0)
## Iterate Through ADMM ##
stpwch = time.time()
timers = np.zeros((USER.REC_ITER))
for i in range(USER.REC_ITER):
# Separate the result of this iteration from the previous solution `self.Psi`. This allows us to build Psi incrementally, modularizing the regularization.
Psi = fftw.zeros_aligned(self.sz, dtype='complex64')
# Perform Regularizations #
Psi = self.Reg_Accuracy(Psi, i)
Psi = self.Reg_Sparcity(
Psi, 1) #np.minimum(np.maximum(2*i/USER.REC_ITER, 1/2), 3/2))
Psi = self.Reg_Temporal(Psi)
# Copy in the new result #
self.Psi[:] = Psi.copy()
# Alert us if we have an issue! #
if (np.any(np.isnan(Psi))): raise ValueError("Psi has NaN values!")
# Visualization #
if (vis and (np.mod(i, USER.REC_ITER // 20) == 0)):
self.BT_Psi()
plt.clf()
plt.gca(position=[0, 0, 1, 1])
plt.imshow(np.log10(
npf.fftshift(np.sum(np.abs(self.psi), axis=(0, 1)))),
cmap='gray')
plt.plot(pts[:, 0],
pts[:, 1],
color='r',
marker='o',
linewidth=0,
fillstyle='none')
plt.clim(-3, 0)
plt.draw()
plt.pause(0.1)
if ((error is not None) and (np.mod(i, 3) == 0) and (i > 60)):
# Get psi #
self.BT_Psi()
# Find where psi is important #
psi_f = npf.fftshift(np.abs(self.psi), axes=(-2, -1))
# Identify points in the cloud #
Psi_f = npf.fftn(psi_f)
psi_a = np.real_if_close(
npf.ifftshift(npf.ifftn(Psi_f * H_A), axes=(-2, -1)))
psi_s = np.real_if_close(
npf.ifftshift(npf.ifftn(Psi_f * H_S), axes=(-2, -1)))
lhs = psi_a
rhs = psi_s * (1 + 1) + np.mean(psi_f)
idx = np.nonzero(lhs > rhs)
pos = np.array([idx[3], idx[2], idx[1], idx[0] / USER.KER_T]).T
wgt = np.round(
np.sqrt(psi_f**2 + ((psi_a + psi_s) / 2)**2)[idx], 3)
if (0 < len(wgt) < 10000):
# Attempt a triangulation #
# Create a point cloud based on the points #
pnts = np.concatenate([pos, wgt[:, None]], axis=1)
# Segment the point cloud to find clusters #
cloud = PointCloud(pnts, seg=True)
# Why?? # vvv #
# Weight threshold #
clust = _CloudThr(cloud.clust)
# # ^^^ #
clust = _Separate(clust)
if (len(clust) == 0): continue
# Evaluate the average minimum error per particle #
dist_x = np.zeros([np.shape(pts)[0], len(clust)])
dist_y = np.zeros([np.shape(pts)[0], len(clust)])
dist_z = np.zeros([np.shape(pts)[0], len(clust)])
# Evaluate the distance between each point and all clusters #
for c in range(len(clust)):
diff = (pts[:, :3] - clust[c].res) * [
*USER.RES, USER.DOF[0] / USER.KER_Z
]
dist_x[:, c] = np.abs(diff[:, 0])
dist_y[:, c] = np.abs(diff[:, 1])
dist_z[:, c] = np.abs(diff[:, 2])
# Get the minimum error per cluster, average over all particles #
error[int(i // 3), pb[1], 0] = np.mean(np.min(dist_x,
1)) # X
error[int(i // 3), pb[1], 1] = np.mean(np.min(dist_y,
1)) # Y
error[int(i // 3), pb[1], 2] = np.mean(np.min(dist_z,
1)) # Z
#if((err is not None) and (np.mod(i, 3) == 0)):
# err[pb(1),i,:] = ComputeError(xi)
# Progress Bar #
timers[i] = time.time() - stpwch
if (i > 0):
prefix = '(%s):\t%8.3f sec' % (pb[0], pb[-2] + timers[i])
#suffix = '(Remain: %5.0f sec)' % (pb[-1])
suffix = '(Remain: %3.0f:%2.0f:%2.0f) ' % (pb[-1] // 3600,
(pb[-1] % 3600) //
60, pb[-1] % 60)
if (pb[4] > 1): # Show Z progress #
VIS._ProgressBar(pb[1] + 1,
pb[2],
sub_i=pb[3] + 1,
sub_I=pb[4],
prefix=prefix,
suffix=suffix)
elif (pb[6] > 1
or pb[8] > 1): # Show chunked iteration progress #
i_ = i + 1 + (pb[5] * pb[8] + pb[7]) * USER.REC_ITER
I_ = pb[6] * pb[8] * USER.REC_ITER
VIS._ProgressBar(pb[1] + 1,
pb[2],
sub_i=i_,
sub_I=I_,
prefix=prefix,
suffix=suffix)
else:
VIS._ProgressBar(pb[1] + 1,
pb[2],
sub_i=i,
sub_I=USER.REC_ITER,
prefix=prefix,
suffix=suffix)
if (vis):
plt.ioff()
plt.show()
## Output ##
self.BT_Psi()
return np.abs(self.psi), error
def reconstruct(DATA, iterations):
## Define Parameters
# Define Optical Parameters
wavelength = DATA['wavelength']
LED_spacing = DATA['LED_spacing']
matrix_spacing = DATA['matrix_spacing']
x_offset = DATA['x_offset']
y_offset = DATA['y_offset']
NA_obj = DATA['NA_obj']
px_size = DATA['px_size']
Images = DATA['Images']
m_s, n_s = Images[0][0].shape
array_dimensions = Images.shape
arraysize = array_dimensions[0]
## Define Calculated Parameters
LED_limit = LED_spacing * (arraysize - 1) / 2
LED_positions = np.linspace(float(-LED_limit), float(LED_limit),
int(2 * (LED_limit / LED_spacing) + 1))
k = 2 * np.pi / wavelength
# wavevector magnitude
# lists of transverse wavevectors
kx_list = -k * np.sin(
np.arctan((LED_positions + x_offset) / matrix_spacing))
ky_list = -k * np.sin(
np.arctan((LED_positions + y_offset) / matrix_spacing))
kx_list = kx_list[0]
ky_list = ky_list[0]
# Pixel Size and NA calculations
px_size_synth = px_size / 4
# calculate subimage size
# size of sub images in pixels
m_r = m_s * (px_size / px_size_synth)
n_r = m_r
# maximum spatial frequency for sub-image
kt_max_sub = k * NA_obj
# maximum spatial frequency for reconstructed image
# Use synthetic NA plus only the margin needed for subimage oversampling.
# also take matrix offset into account
max_offset = np.max(np.abs([x_offset, y_offset]))
NA_matrix = np.sin(np.arctan((LED_limit + max_offset) / matrix_spacing))
kt_max_rec = k * (NA_matrix + NA_obj)
# spatial frequency axes for spectrums of images
kx_axis_sub = np.linspace(-kt_max_sub[0], kt_max_sub[0], n_s)
ky_axis_sub = np.linspace(-kt_max_sub[0], kt_max_sub[0], m_s)
# grid of spatial frequencies for each pixel of reconstructed spectrum
# same for subimage spectrum
[kx_g_sub, ky_g_sub] = np.meshgrid(kx_axis_sub, ky_axis_sub)
## retrieve phase iteratively
# initialize object
dtype = np.complex64
'''
objectFT = np.zeros(shape=[int(m_r),int(n_r)]).astype(dtype)
'''
img = Images[int(np.floor(arraysize / 2)), int(np.floor(arraysize / 2))]
objectFTguess = fftshift(fftn(img))
pad_width = int((m_r - img.shape[0]) / 2)
objectFT = np.pad(objectFTguess, pad_width=pad_width,
mode='constant').astype(dtype)
# only need to generate one CTF, since it will be applied to the
# sub-images after they are extracted from the reconstructed image
# spectrum, and thus will not move around (relative to the sub-image).
CTF = (kx_g_sub**2 + ky_g_sub**2) < kt_max_rec**2
# define convergence tolerance:
for iters in range(iterations):
print("Iteration: " + str(iters))
for i in range(arraysize): # one per row of LEDs
for j in range(arraysize): # one per column of LEDs
kx_center = np.round(
(kx_list[j] + kt_max_rec) / 2 / kt_max_rec * (n_r - 1)) + 1
ky_center = np.round(
(ky_list[i] + kt_max_rec) / 2 / kt_max_rec * (m_r - 1)) + 1
kx_low = np.round(kx_center - (n_s) / 2)
kx_high = np.round(kx_center + (n_s) / 2)
ky_low = np.round(ky_center - (m_s) / 2)
ky_high = np.round(ky_center + (m_s) / 2)
# extract piece of spectrum
kx = np.array([np.arange(int(kx_low), int(kx_high))],
dtype=int)
ky = np.array([np.arange(int(ky_low), int(ky_high))],
dtype=int)
pieceFT = objectFT[ky.T, kx]
#apply CTF and digital correction
pieceFT_constrained = (m_s / m_r)**2 * np.multiply(
pieceFT, CTF)
# iFFT
piece = ifftn(ifftshift(pieceFT_constrained))
# Replace intensity with intensity of sampled Images
piece_replaced = (m_r / m_s)**2 * np.sqrt(np.abs(
Images[i, j])) * np.exp(1j * np.angle(piece))
# FFT
piece_replacedFT = fftshift(fftn(piece_replaced)) * CTF
# place updated intensity back into frequency space object
#objectFT[ky.T,kx] += piece_replacedFT
objectFT[ky.T,
kx] = piece_replacedFT + pieceFT - pieceFT_constrained
# compute reconstructed object
object = ifftn(ifftshift(objectFT))
return object, objectFT
def TEST_LIMITS(img, ker, eps, *, code='', visual=False):
# Test runs for limitations only - 64x64! #
## Initialize ##
F = np.shape(img)[0]
Z = np.shape(img)[1]
Y = np.shape(img)[2]
X = np.shape(img)[3]
pos = [None] * F
wgt = [None] * F
H_A, H_S = _IDFilters([Z * np.shape(ker)[1], Y, X])
tru = OP._LoadTruth(code)
error = np.full([int(USER.REC_ITER // 3), F, 3], np.nan)
# Progress #
stpwch = time.time()
timers = np.zeros((F))
t_remain = np.nan
## Recover Emitter Positions ##
admm = ADMM(ker)
for f in np.arange(F):
psi_f = np.zeros((np.shape(ker)[0], Z * np.shape(ker)[1], Y, X))
for z in range(Z):
pb = (code, f, F, z, Z, 0, 1, 0, 1,
timers[f - (1 if (f > 0) else 0)], t_remain)
zrng = [z * USER.KER_Z, (z + 1) * USER.KER_Z]
# Split the image into each plane #
img_ = img[f, z, :, :] / eps[f, z, :, :]
eps_ = eps[f, z, :, :] / np.max(eps)
# Obtain the point clouds per frame #
psi_f[:, zrng[0]:zrng[1], ...], error = admm.Recover(img_,
code=code,
pb=pb,
vis=visual,
error=error)
# Identify points in the cloud #
Psi_f = npf.fftn(psi_f)
psi_a = np.real_if_close(
npf.ifftshift(npf.ifftn(Psi_f * H_A), axes=(-2, -1)))
psi_s = np.real_if_close(
npf.ifftshift(npf.ifftn(Psi_f * H_S), axes=(-2, -1)))
# Determine where the smaller blur is bigger than the larger one #
lhs = psi_a
rhs = psi_s * (1 + 1 / eps_) + np.mean(psi_f)
idx = np.nonzero(lhs > rhs)
pos[f] = np.array([idx[3], idx[2], idx[1], idx[0] / USER.KER_T + f]).T
wgt[f] = np.round(np.sqrt(psi_f**2 + ((psi_a + psi_s) / 2)**2)[idx], 3)
# Progress Display #
timers[f] = time.time() - stpwch
if (sum(timers > 0) > 1):
t_remain = (F - (f + 1)) * np.mean(np.diff(timers[timers > 0]))
prefix = '(%s):\t%8.3f sec' % (code, timers[f])
suffix = '(Remain: %5.0f sec)' % (t_remain)
VIS._ProgressBar(f + 1, F, prefix=prefix, suffix=suffix)
#if(error is not None):
spi.savemat(OP.FOLD_MAT + code + ' error.mat', {'error': error})
print(code + ' done!')
def conditional_ifftshift(self, x):
if global_variables.PRE_FFTSHIFT:
x[:] = ifftshift(x)
return x
else:
return x
def _Recover(img, ker, eps, *, code='', step=1, vis=False):
## Initialize ##
f0 = 0
F = np.shape(img)[0]
Z = np.shape(img)[1]
Y = np.shape(img)[2]
X = np.shape(img)[3]
C = np.minimum(X, Y) if ((not USER.REC_CHUNK) or ((X <= 128) and
(Y <= 128))) else 64
pos = [None] * F
wgt = [None] * F
H_A, H_S = _IDFilters([np.shape(ker)[0], Z * np.shape(ker)[1], Y, X])
tru = OP._LoadTruth(code)
# Progress #
stpwch = time.time()
timers = np.zeros((F))
t_remain = np.nan
# Truth #
#error = np.full([int(USER.REC_ITER//3), F], np.nan)
## Recover Emitter Positions ##
ker_ = ker[..., (Y - C) // 2:(Y + C) // 2, :][...,
(X - C) // 2:(X + C) // 2]
admm = ADMM(ker_)
for f in np.arange(F, step=step):
psi_f = np.zeros((np.shape(ker)[0], Z * np.shape(ker)[1], Y, X))
for z in range(Z):
zrng = [z * USER.KER_Z, (z + 1) * USER.KER_Z]
# Split the image into each plane #
img_ = img[f + f0, z, :, :] / eps[
f + f0,
z, :, :] # << ------------------------------------------------------------ #
eps_ = eps[f + f0, z, :, :] / np.max(eps)
# Chunk the image and obtain point clouds per frame #
img_chunks, xrng, yrng, overlay = _Chunk(img_, C=C)
M = np.shape(xrng)[0]
N = np.shape(yrng)[0]
for m in range(M):
for n in range(N):
pb = (code, f, F, z, Z, m, M, n, N,
timers[f -
(1 if (M == 1 and N == 1 and f > 0) else 0)],
t_remain)
if (np.ptp(img_chunks[n, m, ...]) > 2 * np.std(img_)):
psi, _ = admm.Recover(img_chunks[n, m, ...],
code=code,
pb=pb,
vis=False)
psi = np.fft.fftshift(psi, axes=(-2, -1))
psi_f[:, zrng[0]:zrng[1],
...][...,
yrng[n,
0]:yrng[n,
1], :][...,
xrng[m,
0]:xrng[m,
1]] += psi
timers[f] = time.time() - stpwch
psi_f[:, zrng[0]:zrng[1], ...] /= np.maximum(overlay, 1)
# Identify points in the cloud #
Psi_f = npf.fftn(psi_f)
psi_a = np.real_if_close(
npf.ifftshift(npf.ifftn(Psi_f * H_A), axes=(-2, -1)))
psi_s = np.real_if_close(
npf.ifftshift(npf.ifftn(Psi_f * H_S), axes=(-2, -1)))
# Determine where the smaller blur is bigger than the larger one #
lhs = psi_a
rhs = psi_s * (1 + 1 / eps_) + np.mean(psi_f) * (
1 + (USER.KER_T > 1)) #eps_ * np.std(psi_f)/np.mean(psi_f)
idx = np.nonzero(lhs > rhs)
pos[f] = np.array([idx[3], idx[2], idx[1], idx[0] / USER.KER_T + f]).T
wgt[f] = np.round(np.sqrt(psi_f**2 + ((psi_a + psi_s) / 2)**2)[idx], 3)
# Visualization #
if (vis):
plt.figure(figsize=(15, 5))
ax = plt.axes(position=[0, 0, 1 / 3, 0.9])
ax.imshow(img_, cmap='gray')
ax.set_title('Input image #%i/%i' % (f + 1, F + 1))
ax = plt.axes(position=[1 / 3, 0, 1 / 3, 0.9])
ax.imshow(np.sum(psi_f, axis=(0, 1)), cmap='gray')
ax.set_title('Deconvolution')
ax = plt.axes(position=[2 / 3, 0, 1 / 3, 0.9])
ax.imshow(img_, cmap='gray')
if (len(wgt[f]) > 0):
ax.scatter(pos[f][:, 0],
pos[f][:, 1],
s=100 * (wgt[f] / np.max(wgt[f])),
c='r')
ax.set_title('Point Cloud')
if (USER.KER_Z > 1):
plt.figure(figsize=(6, 6))
ax = plt.axes(projection='3d',
position=[-0.05, -0.07, 1.1, 1.1])
if (len(wgt[f]) > 0):
ax.scatter(pos[f][:, 0],
pos[f][:, 1],
pos[f][:, 2],
s=100 * (wgt[f] / np.max(wgt[f])))
ax.view_init(azim=30, elev=10)
ax.set_xlim(0, np.shape(img)[3])
ax.set_ylim(0, np.shape(img)[2])
ax.set_zlim(0, USER.KER_Z)
plt.show()
# Progress Display #
timers[f] = time.time() - stpwch
if (sum(timers > 0) > 1):
t_remain = (F - (f + 1)) * np.mean(np.diff(timers[timers > 0]))
prefix = '(%s):\t%8.3f sec' % (code, timers[f])
#suffix = '(Remain: %5.0f sec)' % (t_remain)
suffix = '(Remain: %3.0f:%2.0f:%2.0f)' % (t_remain // 3600,
(t_remain % 3600) // 60,
t_remain % 60)
VIS._ProgressBar(f + 1, F, prefix=prefix, suffix=suffix)
#import scipy.io as spi
#spi.savemat(OP.FOLD_MAT + code + ' error.mat', {'error': error})
## Output ##
return pos, wgt
def setup_fftw(self, pulse_in, fiber, output_power, raman_plots=False):
''' Call immediately before starting Propagate. This function does two
things:\n
1) it sets up byte aligned arrays for fftw\n
2) it fftshifts betas, omegas, and the Raman response so that no further\n
shifts are required during integration. This saves lots of time.'''
self.n = pulse_in.NPTS
if PYFFTW_AVAILABLE:
self.fft_input = pyfftw.empty_aligned(self.n, dtype='complex128')
self.fft_output = pyfftw.empty_aligned(self.n, dtype='complex128')
self.ifft_input = pyfftw.empty_aligned(self.n, dtype='complex128')
self.ifft_output = pyfftw.empty_aligned(self.n, dtype='complex128')
self.fft_input_2 = pyfftw.empty_aligned(self.n, dtype='complex128')
self.fft_output_2 = pyfftw.empty_aligned(self.n,
dtype='complex128')
self.ifft_input_2 = pyfftw.empty_aligned(self.n,
dtype='complex128')
self.ifft_output_2 = pyfftw.empty_aligned(self.n,
dtype='complex128')
self.ifft_input_3 = pyfftw.empty_aligned(self.n,
dtype='complex128')
self.ifft_output_3 = pyfftw.empty_aligned(self.n,
dtype='complex128')
# To be double sure that there are no problems, also make 2 copies of
# the FFT objects. This lets us nest ifft_2 around a function using ifft
# without worrying about potential problems.
#self.fft = pyfftw.builders.fft(self.fft_input)
#self.fft_2 = pyfftw.builders.fft(self.fft_input_2)
#self.ifft = pyfftw.builders.fft(self.ifft_input)
#self.ifft_2 = pyfftw.builders.fft(self.ifft_input_2)
self.fft = pyfftw.FFTW(self.fft_input,
self.fft_output,
direction='FFTW_BACKWARD')
self.fft_2 = pyfftw.FFTW(self.fft_input_2,
self.fft_output_2,
direction='FFTW_BACKWARD')
self.ifft = pyfftw.FFTW(self.ifft_input,
self.ifft_output,
direction='FFTW_FORWARD')
self.ifft_2 = pyfftw.FFTW(self.ifft_input_2,
self.ifft_output_2,
direction='FFTW_FORWARD')
self.ifft_3 = pyfftw.FFTW(self.ifft_input_3,
self.ifft_output_3,
direction='FFTW_FORWARD')
else:
self.fft_input = np.ndarray((self.n, ), dtype='complex128')
self.fft_output = np.ndarray((self.n, ), dtype='complex128')
self.ifft_input = np.ndarray((self.n, ), dtype='complex128')
self.ifft_output = np.ndarray((self.n, ), dtype='complex128')
self.fft_input_2 = np.ndarray((self.n, ), dtype='complex128')
self.fft_output_2 = np.ndarray((self.n, ), dtype='complex128')
self.ifft_input_2 = np.ndarray((self.n, ), dtype='complex128')
self.ifft_output_2 = np.ndarray((self.n, ), dtype='complex128')
# self.fft_input = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
# self.fft_output = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
# self.ifft_input = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
# self.ifft_output = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
#
# self.fft_input_2 = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
# self.fft_output_2 = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
# self.ifft_input_2 = pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
# self.ifft_output_2= pyfftw.empty_aligned(self.n, fft_n, dtype='complex128')
self.A_I = np.ndarray((self.n, ), dtype='complex128')
self.A2 = np.ndarray((self.n, ), dtype='complex128')
self.exp_D = np.ndarray((self.n, ), dtype='complex128')
self.k1 = np.ndarray((self.n, ), dtype='complex128')
self.k2 = np.ndarray((self.n, ), dtype='complex128')
self.k3 = np.ndarray((self.n, ), dtype='complex128')
self.k4 = np.ndarray((self.n, ), dtype='complex128')
self.temp = np.ndarray((self.n, ), dtype='complex128')
self.Aw = np.ndarray((self.n, ), dtype='complex128')
self.A2w = np.ndarray((self.n, ), dtype='complex128')
self.dA = np.ndarray((self.n, ), dtype='complex128')
self.dA2 = np.ndarray((self.n, ), dtype='complex128')
self.R_A2 = np.ndarray((self.n, ), dtype='complex128')
self.dR_A2 = np.ndarray((self.n, ), dtype='complex128')
self.omegas = np.ndarray((self.n, ), dtype='complex128')
self.alpha = np.ndarray((self.n, ), dtype='complex128')
self.betas = np.ndarray((self.n, ), dtype='complex128')
self.LinearStep_output = np.ndarray((self.n, ), dtype='complex128')
self.A = np.ndarray((self.n, ), dtype='complex128')
self.R = np.ndarray((self.n, ), dtype='complex128')
self.R0 = np.ndarray((self.n, ), dtype='complex128')
self.Af = np.ndarray((self.n, ), dtype='complex128')
self.Ac = np.ndarray((self.n, ), dtype='complex128')
self.A_I[:] = 0.0
self.A2[:] = 0.0
self.Af[:] = 0.0
self.Ac[:] = 0.0
self.A[:] = 0.0
self.R[:] = 0.0
self.R0[:] = 0.0
self.omegas[:] = pulse_in.V_THz
self.alpha[:] = -fiber.get_gain(pulse_in, output_power)
self.gamma = fiber.gamma
self.w0 = pulse_in.center_frequency_THz * 2.0 * np.pi
self.last_h = None
# if not self.disable_Raman:
self.CalculateRamanResponseFT(pulse_in)
if raman_plots:
plt.subplot(221)
plt.plot(self.omegas / (2 * np.pi),
np.abs(self.R - (1 - self.f_R)), 'bo')
plt.plot(self.omegas / (2 * np.pi),
np.abs(self.R0 - (1 - self.f_R0)), 'r')
#plt.xlim([0,25])
plt.title('Abs[R(w)]')
plt.xlabel('THz')
plt.subplot(222)
plt.plot(self.omegas / (2 * np.pi),
np.unwrap(np.angle(self.R - (1 - self.f_R))), 'bo')
plt.plot(self.omegas / (2 * np.pi),
np.unwrap(np.angle(self.R0 - (1 - self.f_R0))), 'r')
plt.title('Angle[R(w)]')
plt.xlabel('THz')
plt.subplot(223)
plt.plot(pulse_in.T*1000, ifftshift(np.real(self.IFFT_t(\
self.R - (1-self.f_R)))), 'bo')
plt.plot(pulse_in.T*1000, ifftshift(np.real(self.IFFT_t(\
self.R0 - (1-self.f_R0)))), 'r')
plt.title('Abs[R[t]]')
plt.xlim([0, 1000])
plt.xlabel('fs')
plt.subplot(224)
plt.plot(self.omegas / (2 * np.pi), abs(self.FFT_t(self.A)))
plt.title('Abs[A[w]]')
plt.xlabel('THz')
plt.show()
# Load up parameters
self.A[:] = self.conditional_fftshift(pulse_in.AT)
self.omegas[:] = self.conditional_fftshift(self.omegas)
# self.betas[:] = self.conditional_fftshift(self.betas)
self.alpha[:] = self.conditional_fftshift(self.alpha)
self.R[:] = self.conditional_fftshift(self.R)
self.R0[:] = self.conditional_fftshift(self.R0)
print('pulse energy in ', np.sum(abs(pulse_in.AT)))
print('copied as ', np.sum(abs(self.A)))
def fftGS(z, target, estimate=None, iterations=20, error=None, flagRand=True):
"""
Far field Gerchberg - Saxton Algorithm
Calculates the phase distribution in a object plane (for a given
amplitude constrain) to obtain an specific amplitude distribution in
the target plane.
It uses the Gerchberg - Saxton algorithm for far-field propagation,
using a standard FFT.
**ARGUMENTS:**
========== ======================================================
z Propagation distance. This is used to calculate the
resolution needed in the object plane, for a given
target resolution.
target :class:`Field` instance whose amplitude distribution
is used to represent the amplitude constrain to be
applied in the target plane. The phase of this field
is not used.
estimate :class:`Field` instance used as initial estimate for
the problem. The amplitude of this field is taken as
the reference amplitude and the phase is obtained. The
resolution used to define this field must match the
value needed to obtain the required target resolution
when the FFT-Fraunhoffer transform is used. If the
wrong value is given an exception is raised.
If not given, a unitary amplitude wave, with random
phase and the correct resolution, is used.
iterations Maximum number of iterations
error Expected error
========== ======================================================
.. note:: target and object must have the same wavelength
**RETURN VALUE:**
(holo,err)
==== ==========================================================
holo Field instance, containing the reference amplitude
information and the phase obtained from the iterative
algorithm. The holo.res attribute contains the
resolution of the calculated hologram for the given
propagation distance. The holo.l attribute contains the
wavelength used to calculate the hologram.
err Final error obtained
==== ==========================================================
"""
if estimate == None:
if flagRand:
edata = exp(2.0j * pi * random(target.shape))
else:
edata = exp(2.0j * pi * ones(target.shape))
sx, sy = target.size
dxe = target.l * z / sx
dye = target.l * z / sy
estimate = Field(data=edata, psize=(dxe, dye), l=target.l)
assert (
estimate.shape == target.shape
), "The estimate field, and the target field, must have the same shape"
assert (
target.l == estimate.l
), "The wave lengths for the reference beam, and the target must be equal"
sx, sy = target.size
dxe = target.l * z / sx
dye = target.l * z / sy
dx, dy = estimate.res
assert (dxe == dx) and (
dye == dy
), "The resolution for the reference beam, and the target must be equal"
holo = estimate.data
eabs = estimate.abs()
# Normalized Target amplitude
ntarget = target.abs() / target.abs().max()
for n in range(iterations):
if n != 0:
holo = fftshift(fft2(ifftshift(imp)))
# Keep only the phase in the hologram plane
holo = exp(1.0j * angle(holo))
holo = holo * eabs
# Calculate the new image plane
imp = ifftshift(ifft2(fftshift(holo)))
err = (ntarget - abs(imp) / abs(imp).max()).std()
if error != None and err < error:
break
d = exp(1.0j * angle(imp))
imp = d * target.abs()
holo = Field(data=holo, psize=(dxe, dye), l=target.l)
return holo, err
def remove_stripe(img, level, wname='db5', sigma=1.5):
"""
Suppress horizontal stripe in a sinogram using the Fourier-Wavelet based
method by Munch et al. [2]_.
Parameters
----------
img : 2d array
The two-dimensional array representig the image or the sinogram to de-stripe.
level : int
The highest decomposition level.
wname : str, optional
The wavelet type. Default value is ``db5``
sigma : float, optional
The damping factor in the Fourier space. Default value is ``1.5``
Returns
-------
out : 2d array
The resulting filtered image.
References
----------
.. [2] B. Munch, P. Trtik, F. Marone, M. Stampanoni, Stripe and ring artifact removal with
combined wavelet-Fourier filtering, Optics Express 17(10):8567-8591, 2009.
"""
nrow, ncol = img.shape
# wavelet decomposition.
cH = []
cV = []
cD = []
for i in range(0, level):
img, (cHi, cVi, cDi) = pywt.dwt2(img, wname)
cH.append(cHi)
cV.append(cVi)
cD.append(cDi)
# FFT transform of horizontal frequency bands
for i in range(0, level):
# FFT
fcV = fftshift(fft(cV[i], axis=0))
my, mx = fcV.shape
# damping of vertical stripe information
yy2 = (np.arange(-np.floor(my / 2), -np.floor(my / 2) + my))**2
damp = -np.expm1(-yy2 / (2.0 * (sigma**2)))
fcV = fcV * np.tile(damp.reshape(damp.size, 1), (1, mx))
#inverse FFT
cV[i] = np.real(ifft(ifftshift(fcV), axis=0))
# wavelet reconstruction
for i in range(level - 1, -1, -1):
img = img[0:cH[i].shape[0], 0:cH[i].shape[1]]
img = pywt.idwt2((img, (cH[i], cV[i], cD[i])), wname)
return img[0:nrow, 0:ncol]
def test_inverse(self):
for n in [1, 4, 9, 100, 211]:
x = random((n, ))
assert_array_almost_equal(ifftshift(fftshift(x)), x)
def updateNoise(self):
"""Updates the noise sample. Does not change any of the noise parameters
but choses a new random sample given the previously set parameters.
"""
if not (self.noiseType in [
'binary', 'Binary', 'normal', 'Normal', 'uniform', 'Uniform'
]):
if (self.noiseType in [
'image', 'Image'
]) and (self.imageComponent in ['amplitude', 'Amplitude']):
self.noiseTex = numpy.random.uniform(0, 1, int(self._size**2))
self.noiseTex = numpy.reshape(
self.noiseTex, (int(self._size), int(self._size)))
if self.filter in ['Butterworth', 'butterworth']:
self.noiseTex = fftshift(self._filter(self.noiseTex))
elif self.filter in ['Gabor', 'gabor']:
self.noiseTex = fftshift(self._gabor(self.noiseTex))
elif self.filter in ['Isotropic', 'isotropic']:
self.noiseTex = fftshift(self._isotropic(self.noiseTex))
self.noiseTex[0][0] = 0
In = self.noiseTex * exp(1j * self.noisePh)
Im = numpy.real(ifft2(In))
else:
Ph = numpy.random.uniform(0, 2 * numpy.pi, int(self._size**2))
Ph = numpy.reshape(Ph, (int(self._size), int(self._size)))
In = self.noiseTex * exp(1j * Ph)
Im = numpy.real(ifft2(In))
Im = ifftshift(Im)
gsd = filters.getRMScontrast(Im)
factor = gsd * self.noiseClip
numpy.clip(Im, -factor, factor, Im)
self.tex = Im / factor
elif self.noiseType in ['normal', 'Normal']:
self.noiseTex = numpy.random.randn(int(
self._sideLength[1]), int(
self._sideLength[0])) / self.noiseClip
elif self.noiseType in ['uniform', 'Uniform']:
self.noiseTex = 2.0 * numpy.random.rand(int(
self._sideLength[1]), int(self._sideLength[0])) - 1.0
else:
numpy.random.shuffle(
self.noiseTex) # pick random noise sample by shuffleing values
self.noiseTex = numpy.reshape(
self.noiseTex,
(int(self._sideLength[1]), int(self._sideLength[0])))
if self.noiseType in [
'binary', 'Binary', 'normal', 'Normal', 'uniform', 'Uniform'
]:
if self.filter in [
'butterworth', 'Butterworth', 'Gabor', 'gabor',
'Isotropic', 'isotropic'
]:
if self.units == 'pix':
if self._size[0] == self._size[1]:
baseImage = numpy.array(
Image.fromarray(self.noiseTex).resize(
(int(self._size[0]), int(self._size[1])),
Image.NEAREST))
else:
msg = (
'NoiseStim can only apply filters to square noise images'
)
raise ValueError(msg)
else:
baseImage = numpy.array(
Image.fromarray(self.noiseTex).resize(
(int(self._size), int(self._size)), Image.NEAREST))
baseImage = numpy.array(baseImage).astype(
numpy.float32) * 0.0078431372549019607 - 1.0
FT = fft2(baseImage)
spectrum = numpy.absolute(fftshift(FT))
angle = numpy.angle(FT)
if self.filter in ['butterworth', 'Butterworth']:
spectrum = fftshift(self._filter(spectrum))
elif self.filter in ['isotropic', 'Isotropic']:
spectrum = fftshift(self._isotropic(spectrum))
elif self.filter in ['gabor', 'Gabor']:
spectrum = fftshift(self._gabor(spectrum))
spectrum[0][0] = 0 # set DC to zero
FT = spectrum * exp(1j * angle)
Im = numpy.real(ifft2(FT))
gsd = filters.getRMScontrast(Im)
factor = gsd * self.noiseClip
numpy.clip(Im, -factor, factor, Im)
self.tex = Im / factor
else:
if not (self.noiseType in ['image', 'Image']):
self.tex = self.noiseTex
def INFFT(input):
return fft.fftshift(fft.ifft2(fft.ifftshift(input)))
def double_wedge_filter(sinogram,
center=0,
sino_type="180",
iteration=5,
mask=None,
ratio=1.0,
pad=250):
"""
Apply double-wedge filter to a sinogram image (Ref. [1]_).
Parameters
----------
sinogram : array_like
2D array. 180-degree sinogram or 360-degree sinogram.
center : float, optional
Center-of-rotation. No need for a 360-sinogram.
sino_type : {"180", "360"}
Sinogram type : 180-degree or 360-degree.
iteration : int
Number of iteration.
mask : array_like, optional
Double-wedge binary mask.
ratio : float, optional
Define the cut-off angle of the double-wedge filter.
pad : int
Padding width.
Returns
-------
array_like
2D array. Filtered sinogram.
References
----------
.. [1] https://doi.org/10.1364/OE.418448
"""
if not (sino_type == "180" or sino_type == "360"):
raise ValueError("!!! Use only one of two options: '180' or '360'!!!")
if sino_type == "180":
nrow0 = sinogram.shape[0]
if center == 0:
raise ValueError(
"Please provide the location of the rotation axis")
sinogram = conv.convert_sinogram_180_to_360(sinogram, center)
(nrow, ncol) = sinogram.shape
ncol_pad = ncol + 2 * pad
if mask is None:
mask = make_double_wedge_mask(nrow, ncol_pad, ratio * ncol / 2.0)
else:
if mask.shape != (nrow, ncol_pad):
raise ValueError(
"Shape of the left-right padded sinogram {0} and the mask "
"{1} is not the same!!!".format((nrow, ncol_pad), mask.shape))
sino_filt = np.copy(sinogram)
for i in range(iteration):
sino_filt = np.pad(sino_filt, ((0, 0), (pad, pad)), mode="edge")
sino_filt = np.real(
fft.ifft2(fft.ifftshift(fft.fftshift(fft.fft2(sino_filt)) * mask)))
sino_filt = sino_filt[:, pad:ncol + pad]
if sino_type == "180":
sino_filt = sino_filt[:nrow0]
return sino_filt
# evanescent_idx = np.isnan(kz)
ATF0[cut_idx] = 0 # exclude evanescent k
PSF3D = np.zeros(((Nz, Npixels - 1, Npixels - 1)))
for idx, z in enumerate(zs):
angular_spectrum_propagator = np.exp(1.j * 2 * np.pi * kz * z)
ATF = ATF0 * angular_spectrum_propagator
evanescent_idx = (k_rho > k_cut_off)
ATF[evanescent_idx] = 0
ASF = ifftshift(ifft2(ATF)) #* k**2/f**2 # Amplitude Spread Function
ASF = ASF[1:, 1:]
PSF = np.abs(ASF)**2 # Point Spread Function
PSF3D[idx, :, :] = PSF
print('The numerical aperture of the system is:', NA)
print('The transverse resolution is:', DeltaXY, 'um')
print('The axial resolution is:', DeltaZ, 'um')
print('The pixel size is:', dr, 'um')
print('The voxel depth is:', dz, 'um')
print(f'The displacement z from the focus is: {displacementZ} um')
print(f'The displacement y from the optical axis is: {displacementY} um')
# %% figure 1
def gs_gpu(idata, itera=100):
"""Gerchberg-Saxton algorithm to calculate DOEs using the GPU
Calculates the phase distribution in a object plane to obtain an
specific amplitude distribution in the target plane. It uses a
FFT to calculate the field propagation.
The wavefront at the DOE plane is assumed as a plane wave.
**ARGUMENTS:**
========== ======================================================
idata numpy array containing the target amplitude distribution
itera Maximum number of iterations
========== ======================================================
"""
pl = cl.get_platforms()[0]
devices = pl.get_devices(device_type=cl.device_type.GPU)
ctx = cl.Context(devices=[devices[0]])
queue = cl.CommandQueue(ctx)
plan = Plan(idata.shape, queue=queue,
dtype=complex128) #no funciona con "complex128"
src = str(
Template(KERNEL).render(
double_support=all(has_double_support(dev) for dev in devices),
amd_double_support=all(
has_amd_double_support(dev) for dev in devices)))
prg = cl.Program(ctx, src).build()
idata_gpu = cl_array.to_device(queue,
ifftshift(idata).astype("complex128"))
fdata_gpu = cl_array.empty_like(idata_gpu)
rdata_gpu = cl_array.empty_like(idata_gpu)
plan.execute(idata_gpu.data, fdata_gpu.data)
e = 1000
ea = 1000
for i in range(itera):
prg.norm(queue, fdata_gpu.shape, None, fdata_gpu.data)
plan.execute(fdata_gpu.data, rdata_gpu.data, inverse=True)
tr = rdata_gpu.get()
rdata = ifftshift(tr)
#TODO: This calculation should be done in the GPU
e = (abs(rdata) - idata).std()
if e > ea:
break
ea = e
prg.norm2(queue, rdata_gpu.shape, None, rdata_gpu.data, idata_gpu.data)
plan.execute(rdata_gpu.data, fdata_gpu.data)
fdata = fdata_gpu.get()
#~ prg.norm(queue, fdata_gpu.shape, None,fdata_gpu.data)
fdata = ifftshift(fdata)
fdata = exp(1.j * angle(fdata))
#~ fdata=fdata_gpu.get()
return fdata
def lens_propagate(self, wave_in, cs_mm, defocus, aperture):
h = mtf(self.wave_length, cs_mm, defocus)(self.q_mgrid)
aper = np.where(self.q_mgrid < aperture / self.wave_length, 1., 0.)
h *= aper
return ifft2(ifftshift(h) * fft2(wave_in))