def reference_object(obj):
ft = matrixDFT.MatrixFourierTransform()
obj_transform = ft.perform(obj, narray, narray)
cropped_obj_transform = np.zeros(narray * narray).reshape(narray, narray)
cropped_obj_transform[439:450, 439:450] = obj_transform[439:450, 439:450]
ref_obj = ft.inverse(cropped_obj_transform, narray, narray)
detector_ref_obj = rebin(ref_obj, ov)
return detector_ref_obj
def check_object(a,b,thresh_percent,pup,opd,ff,NL,C): ft = matrixDFT.MatrixFourierTransform() narray = a.shape[0] CV = ft.perform(a,narray,narray) OTF = ft.perform(b,narray,narray) thresh = abs(OTF).max()*thresh_percent idx = np.where(abs(OTF)>=thresh) objtfm = np.zeros(narray*narray).reshape(narray,narray) objtfm[idx] = CV[idx]/OTF[idx] ant_alias = makedisk(narray,ctr = (40,40),radius = 20) new_obj = ft.inverse(objtfm*ant_alias,narray,narray) return new_obj, CV
import plotly
import plotly.graph_objs as go
import complex_demo
plotly.offline.init_notebook_mode()
shift = 10
sigma = 10
narray = 101
#generate a Gaussian function
x, gaussian_array = complex_demo.make1DGaussian(narray, sigma, x0=shift)
#Fourier transform
#instantiate an mft object:
#make it as 2D array matrixDFT takes 2D
gaussian_array = np.array([gaussian_array])
ft = matrixDFT.MatrixFourierTransform()
ft_gaussian = ft.perform(gaussian_array, 9, (1, 81))
xx = np.linspace(-40, 40, 81)
#plot the result
complex_demo.complex_3dplot(xx,
ft_gaussian[0],
real_color='purple',
plot=True,
filename='example_gauss')
def find_centroid(a, thresh, verbose=False):
"""
input a: input array (real, square), considered 'image space'
input thresh: normalize abs(cv = ft(a)) and define support of good cv when this is above threshold
then find phase slope only in this support area.
returns centroid of a, as offset from array center, in pythonese as calculated by DFT's and so on..
Original domain a, Fourier domain cv
sft square image a to cv array, no loss or oversampling - like an fft.
Normalize peak of abs(cv) to unity
Create 'live area' mask from abs(cv) with slight undersizing
(allow for 1 pixel shifts to live data still)
(splodges, or full image a la KP)
Calculate phase slopes using cv.angle() phase array
Calculate mean of phase slopes over mask
Normalize phase slopes to reflect image centroid location in pixels
By eye, looking at smoothness of phase slope array...
JWST NIRISS F480 F430M F380M 0.02
JWST NIRISS F277 0.02 - untested
GPI - untested
XY conventions meshed to LG_Model conventions:
if you simulate a psf with pixel_offset = ( (0.2, 0.4), ) then blind application
centroid = utils.find_centroid()
returns the image centroid (0.40036, 0.2000093) pixels in image space. To use this
in LG_Model, nrm_core,... you will want to calculate the new image center using
image_center = utils.centerpoint(s) + np.array((centroid[1], centroid[0])
and everything holds together sensibly looking at DS9 images of a.
[email protected] 2018.02
"""
ft = matrixDFT.MatrixFourierTransform()
cv = ft.perform(a, a.shape[0], a.shape[0])
cvmod, cvpha = np.abs(cv), np.angle(cv)
cvmod = cvmod/cvmod.max() # normalize to unity peak
#import matplotlib.pyplot as plt
#plt.imshow(a)
#plt.show()
#print(np.isnan(cvmod))
#print(np.isnan(thresh))
cvmask = np.where(cvmod >= thresh)
cvmask_edgetrim = trim(cvmask, a.shape[0])
htilt, vtilt = findslope(cvpha, cvmask_edgetrim, verbose)
M = np.zeros(a.shape)
print(">>> utils.find_centroid(): M.shape {0}, a.shape {1}".format(M.shape, a.shape))
print(cvmask_edgetrim)
M[cvmask_edgetrim] = 1
print(">>> utils.find_centroid(): M.shape {0}, cvpha.shape {1}".format(M.shape, cvpha.shape))
if 0:
fits.PrimaryHDU(data=a).writeto("/Users/anand/gitsrc/nrm_analysis/rundir/3_test_LGmethods_data/img.fits", overwrite=True)
fits.PrimaryHDU(data=cvmod).writeto("/Users/anand/gitsrc/nrm_analysis/rundir/3_test_LGmethods_data/cvmod.fits", overwrite=True)
fits.PrimaryHDU(data=M*cvpha*180.0/np.pi).writeto("/Users/anand/gitsrc/nrm_analysis/rundir/3_test_LGmethods_data/cvpha.fits", overwrite=True)
print("cv abs max = {}".format(cvmod.max()))
print("utils.find_centroid: {0} locations of CV array in CV mask for this data".format(len(cvmask[0])))
return htilt, vtilt
def example_FT_properties(plot_line=False, **kwargs):
sigma = 10
narray = 101
#define the figure object
fig = tools.make_subplots(rows=8,
cols=2,
specs=[[{
'is_3d': True
}, {
'is_3d': True
}] for i in range(8)],
print_grid=False)
ft = matrixDFT.MatrixFourierTransform()
#subplot 1: real, even
x, gaussian_array = make1DGaussian(narray, sigma, x0=10)
gaussian_array = np.array([gaussian_array])
ft_gaussian = ft.perform(gaussian_array, 9, (1, 81))
x_data = np.linspace(-40, 40, 81)
func1 = lambda x, x0, sigma: np.exp(-(x - x0)**2. / (2. * sigma**2.))
func2 = lambda x, x0, sigma: x * np.exp(-(x - x0)**2. / (2. * sigma**2.))
x_input = np.linspace(-50, 50, 101)
y = func1(x_input, 0., sigma)
#generate the complex_3dplot plot
trace = complex_3dplot(x_input, y, to_plot=False, return_traces=True)
#put the 3d objects into the subplot
fig.append_trace(trace[0], 1, 1)
fig.append_trace(trace[1], 1, 1)
if plot_line:
fig.append_trace(trace[2], 1, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 1, 2)
fig.append_trace(trace[1], 1, 2)
if plot_line:
fig.append_trace(trace[2], 1, 2)
y = func2(x_input, 0., sigma)
trace = complex_3dplot(x, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 2, 1)
fig.append_trace(trace[1], 2, 1)
if plot_line:
fig.append_trace(trace[2], 2, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 2, 2)
fig.append_trace(trace[1], 2, 2)
if plot_line:
fig.append_trace(trace[2], 2, 2)
y = func1(x_input, 0., sigma) * 1j
trace = complex_3dplot(x_input, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 3, 1)
fig.append_trace(trace[1], 3, 1)
if plot_line:
fig.append_trace(trace[2], 3, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 3, 2)
fig.append_trace(trace[1], 3, 2)
if plot_line:
fig.append_trace(trace[2], 3, 2)
y = func2(x_input, 0., sigma) * 1j
trace = complex_3dplot(x, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 4, 1)
fig.append_trace(trace[1], 4, 1)
if plot_line:
fig.append_trace(trace[2], 4, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 4, 2)
fig.append_trace(trace[1], 4, 2)
if plot_line:
fig.append_trace(trace[2], 4, 2)
y = func1(x_input, 0., sigma) * (1. + 1j)
trace = complex_3dplot(x_input, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 5, 1)
fig.append_trace(trace[1], 5, 1)
if plot_line:
fig.append_trace(trace[2], 5, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 5, 2)
fig.append_trace(trace[1], 5, 2)
if plot_line:
fig.append_trace(trace[2], 5, 2)
y = func2(x_input, 0., sigma) * (1. + 1j)
trace = complex_3dplot(x, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 6, 1)
fig.append_trace(trace[1], 6, 1)
if plot_line:
fig.append_trace(trace[2], 6, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 6, 2)
fig.append_trace(trace[1], 6, 2)
if plot_line:
fig.append_trace(trace[2], 6, 2)
y = func1(x_input, 10., sigma)
trace = complex_3dplot(x_input, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 7, 1)
fig.append_trace(trace[1], 7, 1)
if plot_line:
fig.append_trace(trace[2], 7, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 7, 2)
fig.append_trace(trace[1], 7, 2)
if plot_line:
fig.append_trace(trace[2], 7, 2)
y = func1(x_input, 10., sigma) * 1j
trace = complex_3dplot(x, y, to_plot=False, return_traces=True)
fig.append_trace(trace[0], 8, 1)
fig.append_trace(trace[1], 8, 1)
if plot_line:
fig.append_trace(trace[2], 8, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], to_plot=False, return_traces=True)
fig.append_trace(trace[0], 8, 2)
fig.append_trace(trace[1], 8, 2)
if plot_line:
fig.append_trace(trace[2], 8, 2)
fig['layout'].update(title='Properties of Fourier Transform',
height=1600,
width=600,
showlegend=False)
if kwargs.get('filename'):
plotly.offline.plot(fig, filename=kwargs['filename'])
else:
plotly.offline.iplot(fig)
def example_FT_properties():
sigma = 10
narray = 101
fig = tools.make_subplots(rows=8, cols=2,
specs=[[{'is_3d': True}, {'is_3d': True}] for i in range(8)])
ft = matrixDFT.MatrixFourierTransform()
x, gaussian_array = make1DGaussian(narray, sigma, x0 = 10)
gaussian_array = np.array([gaussian_array])
ft_gaussian = ft.perform(gaussian_array, 9, (1, 81))
x_data = np.linspace(-40, 40, 81)
func1 = lambda x, x0, sigma: np.exp(-(x-x0)**2./(2.*sigma**2.))
func2 = lambda x, x0, sigma: x * np.exp(-(x-x0)**2./(2.*sigma**2.))
x_input = np.linspace(-50, 50, 101)
y = func1(x_input, 0., sigma)
trace = complex_3dplot(x_input, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 1, 1)
fig.append_trace(trace[1], 1, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 1, 2)
fig.append_trace(trace[1], 1, 2)
y = func2(x_input, 0., sigma)
trace = complex_3dplot(x, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 2, 1)
fig.append_trace(trace[1], 2, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 2, 2)
fig.append_trace(trace[1], 2, 2)
y = func1(x_input, 0., sigma) * 1j
trace = complex_3dplot(x_input, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 3, 1)
fig.append_trace(trace[1], 3, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 3, 2)
fig.append_trace(trace[1], 3, 2)
y = func2(x_input, 0., sigma) * 1j
trace = complex_3dplot(x, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 4, 1)
fig.append_trace(trace[1], 4, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 4, 2)
fig.append_trace(trace[1], 4, 2)
y = func1(x_input, 0., sigma) * (1. + 1j)
trace = complex_3dplot(x_input, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 5, 1)
fig.append_trace(trace[1], 5, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 5, 2)
fig.append_trace(trace[1], 5, 2)
y = func2(x_input, 0., sigma) * (1. + 1j)
trace = complex_3dplot(x, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 6, 1)
fig.append_trace(trace[1], 6, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 6, 2)
fig.append_trace(trace[1], 6, 2)
y = func1(x_input, 10., sigma)
trace = complex_3dplot(x_input, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 7, 1)
fig.append_trace(trace[1], 7, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 7, 2)
fig.append_trace(trace[1], 7, 2)
y = func1(x_input, 10., sigma) * 1j
trace = complex_3dplot(x, y, plot=False, return_traces=True)
fig.append_trace(trace[0], 8, 1)
fig.append_trace(trace[1], 8, 1)
ft_y = ft.perform(np.array([y]), 9, (1, 81))
trace = complex_3dplot(x_data, ft_y[0], plot=False, return_traces=True)
fig.append_trace(trace[0], 8, 2)
fig.append_trace(trace[1], 8, 2)
fig['layout'].update(title='Properties of Fourier Transform',
height=1600, width=600)
plotly.offline.iplot(fig)