def calculate2dfrom1d(q,I,Nx,Ny,bcx,bcy,dist,energy,pixelsize,noise=False):
"""Create a 2D scattering image from a scattering curve.
Inputs:
q: q-values
I: intensities
Nx: number of rows
Ny: number of columns
bcx: beam center row coordinate (counting from 1)
bcy: beam center column coordinate (counting from 1)
dist: sample-detector distance
energy: photon energy
pixelsize: size of a pixel
noise: True if you want to add noise (re-sample the scattering image
from a Poisson distribution). False if not. Or give a number for
relative error.
Outputs:
the scattering image itself.
"""
A=np.zeros((Nx,Ny))
D=calculateDmatrix(A,pixelsize,bcx,bcy)
q1=4*np.pi*np.sin(0.5*np.arctan(D/dist))*energy/HC
A=np.interp(q1,q,I,left=0,right=0)
if noise:
if type(noise)==type(True):
A=np.random.poisson(A)
else:
A=A*(1+(np.random.random(A.shape)*2-1)*noise)
return A
def calculatetwothetamatrix(mat,dist,res,bcx,bcy):
"""Calculate two-theta values for detector pixels
Inputs:
mat: scattering image (or mask) matrix, only its shape is needed
dist: sample-detector distance, in mm.
res: pixel size (mm)
bcx, bcy: beam positions (row, column) in pixel coordinates,
counting starts from 1.
Output:
a matrix of the same shape as mat, containing twotheta values for
the pixels.
"""
return np.arctan(calculateDmatrix(mat.astype(np.uint8),res,bcx,bcy)/dist)
def calculateqmatrix(mat,dist,energy,res,bcx,bcy):
"""Calculate q values for detector pixels
Inputs:
mat: scattering image (or mask) matrix, only its shape is needed
energy: true (calibrated) photon energy
dist: sample-detector distance, in mm.
res: pixel size (mm)
bcx, bcy: beam positions (row, column) in pixel coordinates,
counting starts from 1.
Output:
a matrix of the same shape as mat, containing q values for the
individual pixels.
"""
return 4*np.pi*np.sin(0.5*np.arctan(calculateDmatrix(mat,res,bcx,bcy)/dist))*energy/HC
def qrangefrommask(mask,energy,distance,res,bcx,bcy,fullyunmasked=False):
"""Calculate q-range from mask matrix
Inputs:
mask: mask matrix (1 unmasked, 0 masked)
energy: calibrated energy
distance: sample-to-detector distance
res: pixel size
bcx: row coordinate of beam center (starting from 1)
bcy: column coordinate of beam center (starting from 1)
fullyunmasked: if the q-range should be fully unmasked (only the
beginning and the end is checked). Set it to True if you want only
full circles (eg. for azimuthal averaging). False gives you the
entire unmasked q-range (ti. including partially covered q rings)
Outputs: qmin,qmax,Nq
qmin: smallest q-value (smallest distance of unmasked points from
the origin)
qmax: largest q-value (largest distance of unmasked points from
the origin)
Nq: number of q-bins (approx. one q-bin for one pixel)
"""
D=calculateDmatrix(mask,res,bcx,bcy)
dmin=np.nanmin(D[mask!=0])
dmax=np.nanmax(D[mask!=0])
qmin=4*np.pi*np.sin(0.5*np.arctan(dmin/distance))*energy/HC
qmax=4*np.pi*np.sin(0.5*np.arctan(dmax/distance))*energy/HC
Nq=np.ceil(dmax-dmin)
if fullyunmasked:
# the smallest of the border elements in D
Dbordermin=min(D[:,0].min(),D[0,:].min(),D[-1,:].min(),D[:,-1].min())
qbordermin=4*np.pi*np.sin(0.5*np.arctan(Dbordermin/distance))*energy/HC
qmax=min(qmax,qbordermin)
return qmin,qmax,Nq
