Source code for jscatter.smallanglescattering

# -*- coding: utf-8 -*-
# written by Ralf Biehl at the Forschungszentrum Jülich ,
# Jülich Center for Neutron Science 1 and Institute of Complex Systems 1
#    jscatter is a program to read, analyse and plot data
#    Copyright (C) 2015  Ralf Biehl
#
#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.
#
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
#
#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.
# 

"""
This module allows smearing/desmearing of SAXS/SANS data.

Smearing is for line collimation as in Kratky SAXS cameras and for point collimation for SANS.
For SANS the resolution smearing a la Pedersen is realised (resFunct).

For desmearing the Lake algorithm is an iterative procedure to desmear smeared data.
We follow here the improvements according to Vad using a convergence criterion and smoothing.

As references the waterXray scattering and a AgBe reference spectrum are available.

For form factors and structure factors see the respective modules.


"""
from __future__ import print_function
from __future__ import division

import copy
import fnmatch

import math
import os
import re
import numpy as np
import scipy
import shutil
import sys
import xml.etree.ElementTree
from scipy import interpolate,special,constants
from scipy.integrate import simps as integrate
import scipy.signal
from .graceplot import GracePlot as grace
from .dataarray import zeros
from .dataarray import dataArray as dA
from .dataarray import dataList as dL
from .formel import voigt,Elements,felectron,waterdensity,watercompressibility,loglist,smooth


_beamProfType={0:'no',1:'sig',2:'trap'}

# normalized gaussian function
_gauss=lambda x,A,mean,sigma,bgr:A*np.exp(-0.5*(x-mean)**2/sigma**2)/sigma/np.sqrt(2*np.pi) + bgr

[docs]def readpdh(pdhFileName): """ Opens and reads a SAXS data file in the .pdh (Primary Data Handling) format. If data contain X values <0 it is assumed that the primary beam is included as for SAXSpace instruments. In this case the primary beam with max value as .transmission and the peak center as centerTransmissionPeak are extracted. Parameters ---------- pdhFileName : string file name Returns ------- dataArray Notes ----- Alternativly the files can be read ignoring the information in the header (it is stored in the comments) :: data=dA(pdhFileName,lines2parameter=[2,3,4]) **PDH format** used in the PCG SAXS software suite developed by the Glatter group at the University of Graz, Austria. This format is described in the appendix of the PCG manual (below from version 4.05.12 page 159). In the PDH format, lines 1-5 contain header information, followed by the SAXS data. :: line 1: format A80 -> description line 2: format 16(A4,1X) -> description in 16x4 character groups (1X = space separated) line 3: format 8(I9,1X) -> 8 integers (1X = space separated) line 4: format 5(E14.6,1X) -> 5 float (1X = space separated) line 5: format 5(E14.6,1X -> 5 float(1X = space separated) line 6+ format 3(E14.6,1X) - SAXS data x,y,error (1X = space separated) with: - line 3 field 0 : number of points - line 4 field 4 : normalization constant (default 1, never zero!!) Anything else can have different meanings. The SAXSpace and SAXSess (AntonPaar) format add: - line 4 field 2 : detector distance in mm - line 4 field 5 : wavelength - line 5 field 2 : detector slit length (equivalent to width of integration area) in q units Additional xml parameter as in the SAXSPACE format appended can be extracted to attributes by addXMLParameter. Mainly this is "Exposure" time. Example data for SAXSpace :: <emptyline> SAXS BOX 2057 0 0 0 0 0 0 0 0.000000E+00 3.052516E+02 0.000000E+00 1.000000E+00 1.541800E-01 0.000000E+00 1.332843E+00 0.000000E+00 0.000000E+00 0.000000E+00 -1.033335E-01 2.241656E+03 1.024389E+00 -1.001430E-01 2.199972E+03 1.052537E+00 ... """ data=dA(pdhFileName,lines2parameter=[2,3,4]) if np.isnan(data.eY.min()): data.setColumnIndex(iey=None) #forth line if data.line_3[4]!=0: data.wavelength=data.line_3[4] if data.line_3[1]!=0: data.detectordistance=data.line_3[1] #detector slit length (equivalent to width of integration area if data.line_4[1]!=0: data.dIW = data.line_4[3] if data.X.min()<0: #get transmission if primary beam is in data data.transmission=data.prune(-0.05,0.05).Y.max() temp=data.prune(-0.05,0.05) data.centerTransmissionPeak=(temp.X*temp.Y/temp.Y.sum()).mean() return data
[docs]def fitdarkcurrent(darkfile): """ Fits dark current with 5th order polynom + cosine. This is dangerous as the darkcurrent has a noise that is not random but depends on used detector and count time. """ dark=dA(darkfile,lines2parameter=[2,3,4]) darkp=dark.prune(0.01,6.3,100) #modeldark=lambda x,a0,a1,a2,a3,a4,a5,b0,b1,b2: a0+a1*x+a2*x**2+a3*x**3+a4*x**4+a5*x**4 + b0*np.cos(((x-b1)/b2)) modeldark=lambda x,a0,a1,a2,a3,a4,a5,b0,b1,b2: a0+a1*(x-b1)+a2*(x-b1)**2+a3*(x-b1)**3+a4*(x-b1)**4+a5*(x-b1)**5+b0*np.cos(((x-b1)/b2)) darkp.setlimit(a0=[2010,2050],b2=[0,10],b0=[0,100],b1=[2,4]) darkp.fit(modeldark, {'a0':2030,'a1':4.5,'a2':5.5,'a3':-1,'b0':36,'b1':2.9,'b2':0.88}, {'a4':0,'a5':0,}, mapNames={'x':'X'}) newdark=darkp.modelValues(x=dark.X) newdark.setattr(dark) return newdark
#smearing Functions #################################################################### def _wBLength(beam): """ Weight at beam length y due to detector integration width. The relevant integration width is detected automatically from beamProfile. Parameters ---------- beam : beamProfile beam profile with attributes see prepareBeamProfile Returns ------- weight at Beam Length position y after integration over detector integration width dIW as array [y,weight] """ dIW = beam.dIW if beam.a==0 and dIW==0: return None if beam.beamProfType[0] =='m' : # a measured beam profile stored in beam y=np.r_[0:3*abs(beam.X).max():100j] # estimate if dIW==0: weight = beam.interp(y) else : interval=(beam.X[:,None]>y-dIW/2) & (beam.X[:,None]<y+dIW/2) weight=np.trapz(np.repeat(beam.Y[:, None],interval.shape[1] , axis=1)*(interval*1),interval ,axis=0) elif beam.beamProfType[0] =='t' : # a trapezoidal profile y=np.r_[0:3*abs(beam.X).max():100j] # estimate if dIW==0: weight = beam.interp(y) else : def _integral(yy): # define trapez respecting integration boundaries ymi=yy-dIW/2. # integration boundaries yma=yy+dIW/2. X=beam.X.copy() Y=beam.Y.copy() ibmi=np.searchsorted(X,ymi)-1 # index position in beam ibma=np.searchsorted(X,yma) if ibmi>=len(X) or ibma==0: return 0. X[X<ymi]=ymi # set the boundary x value Y[X<ymi]=0. # values outside are zero Y[ibmi]=beam.interp(ymi) # set boundary y value as interpolated value at boundary X[X>yma]=yma # same for other side Y[X>yma]=0. if ibma<len(Y): Y[ibma]=beam.interp(yma) w=np.trapz(Y,X) # integrate return w weight=[_integral(yy) for yy in y] else: raise TypeError('No beam profile given.') # normalize normweight=weight/integrate(weight,y) # return only the nonzero values return np.c_[y[normweight>1e-5],normweight[normweight>1e-5]].T def _wBWidth(beam): """ weighting beam width from +-2.5*sigma for Gaussian The integral is 0.99958 """ if isinstance(beam.bxw,float): if beam.bxw==0: return None # normalized Gaussian sigma = beam.bxw/np.sqrt(2*np.log(2.0)) # sigma from hwhm # points with maximum width 2.5*sigma x=np.r_[-2.5*sigma:2.5*sigma:21j] return np.c_[x,_gauss(x,1,0,sigma,0)].T elif hasattr(beam.bxw,'_isdataArray'): # experimental data interpolated x=np.r_[beam.bxw.X[0]:beam.bxw.X[-1]:27j] return np.c_[x,beam.bxw.interp(x) ].T def _smear(q,data): """ Calculates smeared intensity for q array Defining a cubic spline representing the unsmeared scattering curve, Integrates all of the contributions to the observed scattering intensity at a nominal q-value Parameters ---------- q : array wavevectors data : dataset here the beam parameters a,b,dIW are taken Notes ----- Contributions of scattering of other q-values are determined by the beam geometry and the detector slit width. """ tckUnsm = data.tckUnsm # spline coefficients of data q=np.atleast_1d(q) # guarantee a ndarray # get weighting functions as arrays wx=_wBWidth(data.beamProfile) wy=_wBLength(data.beamProfile) # for qxy>q.max() the spline delivers wrong extrapolated results, so we use there a mean average from the largest q # generate mean value for qxy > q.max as last 10 values qmaxmean=interpolate.splev(q[-10:],tckUnsm,der=0).mean() if wx is None: if wy is None: # there is no smearing! Just return interpolated value valq = interpolate.splev(q,tckUnsm,der=0) else: # smear only y qy=np.sqrt((q[:,None]**2)+wy[0]**2) val=interpolate.splev(qy.flatten(),tckUnsm,der=0).reshape(qy.shape) val[qy > q.max()] = qmaxmean valwy=val*wy[1][None,:] valq=integrate(valwy,wy[0],axis=-1) else: # smear x if wy is None: # only x qx=q[:,None]+wx[0] val=interpolate.splev(qx.flatten(),tckUnsm,der=0).reshape(qx.shape) val[qx > q.max()] = qmaxmean valwx=val*wx[1][:,None] valq=integrate(valwx,wx[0],axis=-1) else: # smear over both x and y qxy=np.sqrt(((q[:,None]+wx[0])**2)[:,:,None]+wy[0]**2) val=interpolate.splev(qxy.flatten(),tckUnsm,der=0).reshape(qxy.shape) val[qxy>q.max()]=qmaxmean valwxwy=val*wx[1][:,None]*wy[1][None,None,:] valwx=integrate(valwxwy,wy[0],axis=-1) valq=integrate(valwx,wx[0],axis=-1) return valq
[docs]def smear(data,beamProfile,**kwargs): r""" Smearing data for line-collimated SAXS (Kratky camera) or as point collimation SANS/SAXS. The full resolution for point collimation SAXS/SANS is described in resFunct. Parameters ---------- data : dataArray Data to be smeared. beamProfile : beamProfile or 'trap', 'SANS', 'explicit', dataArray Beam profile as prepared from prepareBeamProfile or type as 'trapezoidal', 'SANS','explicit' or a measured beam profile as dataArray for line collimation. Measured Profile is treated by prepareBeamProfile. kwargs : See prepareBeamProfile for kwargs. Returns ------- dataArray Notes ----- - If data has attributes a, b, dIW, bxw, detDist these are used, if not given in function call. - If wavelength is missing in data a default of 0.155418 nm for Xray :math:`K_{\alpha}` line is assumed. For SANS 0.6 A. - During smearing for Kratky camera an integration over the beam width and beam length are performed. In this integration :math:`q_{w,l}= ((q+q_{w})^2)+q_{l}^2)^{1/2}` is used with :math:`q_{w}` along the beam width and :math:`q_{l}` along the beam length. in regions :math:`q_{w,l} > max(q_{data})` we estimate the measured scattering intensity by the mean of the last 10 points of the measured spectra to allow for a maximum in :math:`q` range. The strictly valid q range can be estimated by calculating :math:`q_{x,y} < max(q)` with 2 times the used beam width and beam length. As the smearing for larger :math:`q` has no real effect the estimate might be still ok. Examples -------- :: # use as # prepare measured line collimation beamprofile mbeam = js.sas.prepareBeamProfile(beam, bxw=0.01, dIW=1.) # prepare profile with trapezoidal shape (a,b can be fitted above) tbeam = js.sas.prepareBeamProfile('trapz', a=mbeam.a, b=mbeam.b, bxw=0.01, dIW=1) # prepare profile SANS (missing parameters get defaults, see resFunct) Sbeam = js.sas.prepareBeamProfile('SANS', detDist=2000,wavelength=0.4,wavespread=0.15) # prepare profile with explicit given Gaussian width in column 3 as e.g. KWS2@JCNS Gbeam = js.sas.prepareBeamProfile(measurement,explicit=3) # smear datasm= js.sas.smear(data,mbeam) datast= js.sas.smear(data,tbeam) datasS= js.sas.smear(data,Sbeam) datasG= js.sas.smear(data,Gbeam) """ dataa=data.copy() dataa.beamProfile=prepareBeamProfile(beamProfile,**kwargs) # smear data if dataa.beamProfile.beamProfType[0] == 'S': # calculate parameters for cubic spline representation of the data dataa.tckUnsm = interpolate.splrep(dataa.X, dataa.Y, s=0) dataa=resFunct(dataa,**beamProfile.resFunctAttr) elif dataa.beamProfile.beamProfType[0] == 'e': dataa=resFunctExplicit(dataa,beamProfile) else: # calculate parameters for cubic spline representation of the data dataa.tckUnsm = interpolate.splrep(dataa.X, dataa.Y, s=0) dataa.Y=_smear(dataa.X,dataa) dataa.setColumnIndex(iey=None) return dataa
[docs]def desmear(Ios, beamProfile, NIterations=-15, windowsize=4, qmax=4, **kwargs): """ Desmearing according to Lake algorithm with posibility to stop recursion at best desmearing. For negative NIterations the iterations are stopped if a convergence criterion reaches a minimum as described by Vad [2]_. In each step a smoothing based on the ratio desmeared/observed as described in [2]_ is used (point average with windowsize). Parameters ---------- Ios : dataArray Original smeared data beamProfile : dataArray Beam profile as prepeared with prepareBeamProfile NIterations : int, default=-15 Number of iterations to stop. Negative values indicate to use the convergence criterion described by Vad [2]_ and abs(NIterations) gives the maximum iterations to stop. qmax : float, default=4 Maximum in scattering vector q up to where the convergence criterion is evaluated. This reduces the influence of the noise at larger a. windowsize : odd int , default=4 Window size for smoothing in each step of desmearing (running average). Returns ------- dataArray References ---------- .. [1] Lake, J. A. (1967). Acta Cryst. 23, 191–194. .. [2] Comparison of iterative desmearing procedures for one-dimensional small-angle scattering data Vad and Sager, J. Appl. Cryst. (2011) 44,32-42 """ beamProfile=prepareBeamProfile(beamProfile,**kwargs) #lists of desmeared data start from os (original smeared) for iterations Idesmeared = dL(Ios.copy()) Idesmeared[-1].convergence=1 Idesmeared[-1].decreasing =True Idesmeared[-1].chi2=1 # Iterations of Lake desmearing while True: Idesmeared.append(Idesmeared[-1].copy()) # just generate new dataArray Ismeared=smear(Idesmeared[-2],beamProfile) # smear it gamman=Idesmeared[0].Y/Ismeared.Y # generate convergence criterion Idesmeared[-1].Y=Idesmeared[0].Y*smooth(Idesmeared[-2].Y/Idesmeared[0].Y,windowsize)* gamman # calc iteration with smoothing meangamma=np.abs(gamman[Idesmeared[0].X < qmax].mean()-1) # calc convergence criterion Idesmeared[-1].chi2=((Ismeared.Y-Idesmeared[0].Y)**2).mean() # chi**2 distance #does convergence increase again then we finish and stop Idesmeared[-1].decreasing = (meangamma <= Idesmeared.convergence.array.min()) Idesmeared[-1].convergence=meangamma # store convergence criterion close to zero #smooth the last step in iteration print(len(Idesmeared), meangamma, Idesmeared.convergence.array.min(), Idesmeared[-1].decreasing) if len(Idesmeared)>=abs(NIterations): print('len(Idesmeared) = NIterations', len(Idesmeared)) return Idesmeared[-1] elif (NIterations<0) and (Idesmeared[-1].decreasing == False) and (Idesmeared[-2].decreasing == False): return Idesmeared[Idesmeared.convergence.array.argmin()] return 'Error' # should be never reached
[docs]def prepareBeamProfile(data=None,**kwargs): """ Prepare beam profile from Beam Profile measurement or according to given parameters. Parameters ---------- data : dataArray,'trapez','SANS' Contains measured beam profile, explicit Gaussian width list or type 'SANS', 'trapz'. - dataArray Line collimation as measured can be given and will be smoothed and made symmetric. - dataArray with explicit given Gaussian width for each Q values, missing values will be interpolated. - 'trapez' : Line collimation with trapezoidal parameters a, b, bxw, dIW. - 'SANS' : Smearing a la Pedersen; see resFunct for parameters collDist,collAperture,detDist,sampleAperture,wavelength,wavespread,dpixelWidth,dringwidth,zeroextrapolfunc : Parameters as described in resFunct for SANS These are determined from the experimental setup. a : float Larger full length of trapezoidal profile in detector q units b : float Shorter full length of trapezoidal profile in detector q units If a=b ==> a=a*(1+1e-7), b=b*(1-1e-7) bxw : float,dataArray Beam width profile. Use getBeamWidth to cut the primary beam and fit a Gaussian. A float describes the beam half-width at half maximum (hwhm of Gaussian). If bxw is the profile prepared by getBeamWidth the experiemntal profile is used. dIW : float Detector slit width in detector q units. Length on detector to integrate parallel to beam length for line collimation. On my SAXspace this is 1.332 as given in the header if the file. wavelength : float, Wavelength in nm default 0.155418 nm for SAXS 0.5 for SANS detDist : float, default 305.3558 Detectordistance in units mm Default is SAXS detector distance of SAXSpace explicit : int For explicit given Gaussian width the index of the column with the width. For merged dataFiles of KWS2@MLZ this is the forth column with index 3. Returns ------- beam profile as dataArray Notes ----- - For measured beam profiles parameters a,b are determined from the flanks for trapezoidal profile. - Detector q units are equivalent to the pixel distance as expressed in a corrected measurement. - For 'explicit' Gaussian width a SANS measurement as on KWS2 can be used which has sigma as 4th column. Missing values are interpolated. Examples -------- :: # use as # prepare measured beamprofile mbeam = js.sas.prepareBeamProfile(beam, bxw=0.01, dIW=1.) # prepare profile with trapezoidal shape (a,b are fitted above) tbeam = js.sas.prepareBeamProfile('trapz', a=mbeam.a, b=mbeam.b, bxw=0.01, dIW=1) # prepare profile SANS (missing parameters get defaults) Sbeam = js.sas.prepareBeamProfile('SANS', detDist=2000,wavelength=0.4,wavespread=0.15) # prepare profile with explicit given Gaussian width in column 3 as e.g. KWS2@MLZ Gbeam = js.sas.prepareBeamProfile(measurement,explicit=3) """ if hasattr(data,'isBeamProfile'): # fast return if it is already beamprofile return data elif hasattr(data,'_isdataArray') and 'explicit' in kwargs: beam=data[np.r_[0,kwargs['explicit']]] beam.beamProfType = 'explicit' elif hasattr(data,'_isdataArray'): beam=data[:2].prune(number=100) # cut 3rd column as it contains NANs for SAXSpace beam.beamProfType = 'measured' else: # an empty array beam=zeros((2,6)) beam.beamProfType = data for attr in ['collDist','collAperture','detDist','sampleAperture','wavespread','dpixelWidth', 'dringwidth','zeroextrapolfunc','highQextrapolfunc','wavelength','a','b','dIW','bxw']: if attr in kwargs: setattr(beam,attr,kwargs[attr]) if beam.beamProfType[0] == 'm': # make it symmetric as it was measured if not hasattr(beam,'wavelength'): beam.wavelength=0.155418 # K_alpha in nm as default if not hasattr(beam,'detDist'): beam.detDist =305.3558 # distance for SAXSpace in mm if not hasattr(beam,'dIW'):beam.dIW=0 if not hasattr(beam,'bxw'):beam.bxw=0 beam.qscale=2*np.pi/beam.wavelength/beam.detDist #factor for q units beam.Y=beam.Y-beam.Y.min() center=beam.X[beam.Y>(beam.Y.max()*0.8)].mean() beam.X-=center ml=min((beam.X<0).sum(),(beam.X>0).sum()) if (beam.X<0).sum() > (beam.X>0).sum(): beam.Y[-2*ml:]=(beam.Y[-2*ml:]+beam.Y[-2*ml:][::-1])/2. else: beam.Y[:2*ml]=(beam.Y[:2*ml]+beam.Y[:2*ml][::-1])/2. # normalize to integral=1 beam.Y/=np.trapz(beam.Y,beam.X) highflanc=beam.where(lambda a:(a.Y<beam.Y.max()*0.9) & (a.X>0)) top=beam.where(lambda a:(a.Y>beam.Y.max()*0.9) ) topmean=top.where(lambda a: abs(a.X)<abs(a.X).max()*0.9).Y.mean() pf=np.polyfit(highflanc.X, highflanc.Y, 1) beam.a=-2*pf[1]/pf[0] beam.b=2*(topmean-pf[1])/pf[0] elif beam.beamProfType[0] == 't': # For trapezoidal beam profile, make sure that a > b if not hasattr(beam,'wavelength'): beam.wavelength=0.155418 # K_alpha in nm as default if not hasattr(beam,'detDist'): beam.detDist =305.3558 # distance for SAXSpace in mm if not hasattr(beam,'dIW'): beam.dIW=0 if not hasattr(beam,'bxw'): beam.bxw=0 elif hasattr(beam.bxw,'_isdataArray'): # use the extracted parameter from measured data beam.bxw=beam.bxw.hwhm beam.qscale=2*np.pi/beam.wavelength/beam.detDist #factor for q units if beam.a==beam.b: beam.a*=1+1e-7 beam.b*=1-1e-7 if beam.a < beam.b: beam.a,beam.b=beam.b,beam.a beam.X=[-beam.a,-beam.a/2.,-beam.b/2.,beam.b/2.,beam.a/2.,beam.a] beam.Y=[0,0,1,1,0,0] beam.Y/=np.trapz(beam.Y,beam.X) elif beam.beamProfType[0] == 'S': # SANS with Pedersen smearing, only parameters needed beam.resFunctAttr=dict() for attr in ['collDist','collAperture','detDist','sampleAperture','wavelength','wavespread','dpixelWidth', 'dringwidth','zeroextrapolfunc','highQextrapolfunc']: if attr in kwargs: beam.resFunctAttr[attr]=kwargs[attr] beam.isBeamProfile=True return beam
[docs]def getBeamWidth(empty,minmax='auto',show=False): """ Extract primary beam of empty cell or buffer measurement. The primary beam is searched and cut between the next minima found, then normalized. Additionally a Gaussian fit is done and hwhm is included in result profile. Parameters ---------- empty : dataArray Empty cell measurement with the transmitted beam included. minmax : 'auto',[float,float] Automatic or interval for search of primary beam. E.g. [-0.03,0.03] allow for explicitly setting the interval. show : bool Show the fit result Returns ------- dataArray with beam width profile .sigma sigma of fit with Gaussian .hwhm half width half maximum """ if minmax[0]=='a': # auto # for normal empty cell or buffer measurement the primary beam is the maximum imax=imin=empty.Y.argmax() while empty.Y[imax+1]<empty.Y[imax]: imax+=1 while empty.Y[imin-1]<empty.Y[imin]: imin-=1 xmax=empty.X[imax] xmin=empty.X[imin] else: xmin=minmax[0] xmax=minmax[1] primarybeam=empty.prune(lower=xmin,upper=xmax) primarybeam.Y-=primarybeam.Y.min() norm= scipy.integrate.simps(primarybeam.Y, primarybeam.X) primarybeam.Y/=norm try: primarybeam.eY /= norm except:pass primarybeam.fit(_gauss,{'mean':0,'sigma':0.015,'bgr':0,'A':1},{},{'x':'X'}) primarybeam.hwhm=primarybeam.sigma*np.sqrt(np.log(2.0)) if show: primarybeam.showlastErrPlot() return primarybeam
[docs]def plotBeamProfile(beam,p=None): """ Plots beam profile and weight function according to parameters in beam. Parameters ---------- beam beam with parameters """ wY =_wBLength(beam) wX =_wBWidth(beam) if p is None: p=grace() p.multi(2,1) p[0].plot(wY,li=[1,3,1],sy=0,legend='Y profile a=%.3g b=%.3g ' %(beam.a,beam.b)) p[0].plot(wX[0],wX[1]/(wX[1].max()),li=[1,3,2],sy=0,legend='X profile hw=%.4g max %.3g ' %(beam.bxw,wX[1].max())) p[1].plot(beam,li=[1,3,2],sy=0,legend='weight function ') p[0].yaxis(label='weight') p[0].xaxis(label='x,y') p[1].yaxis(label='profile') p[1].xaxis(label='x,y') p[0].title("Beam Length Profile and Weighting Function") p[0].legend(x=1,y=0.9) p[1].legend(x=4,y=beam.Y.max()) return p
[docs]def AgBeReference(q,wavelength,n=np.r_[1:10],ampn=[1]*10,domainsize=100,udw=0.1,asym=0,lg=1): """ The scattering intensity expected from AgBe as a reference for wavelength calibration. The intensities assume a d-spacing of 5.8378 nm and a reduction of the intensity as q**-2. The domain size determines the width according to Scherrer equation [2]_. The first peak is at 1.076 1/nm. The result needs to be convoluted with the instrument resolution by resFunct or smear. Parameters ---------- q : array Wavevector wavelength : float Wavelength n : array of int Order of the peaks. ampn : list of float Amplitudes of the peaks domainsize : float Domainsize of AgBe crystals in nm. default 100 nm as is given in [1]_. udw : float Displacement u in Debye Waller factor exp(-u**2*q**2/3) asym : float Factor asymmetry in Voigt function describing the peaks. lg : float Lorenzian/gaussian fraction of both FWHM, describes the contributions of gaussian and lorenzian shape. See Voigt for details. Returns ------- dataArray References ---------- .. [1] T. C. Huang, H. Toraya, T. N. Blanton and Y. Wu X-ray Powder Diffraction Analysis of Silver Behenate, a Possible Low-Angle Diffraction Standard J. Appl.Cryst.(1993).26,180-184 .. [2] Patterson, A. The Scherrer Formula for X-Ray Particle Size Determination Phys. Rev. 56 (10): 978–982 (1939) doi:10.1103/PhysRev.56.978. """ dspacing=5.8378 # nm braggAngle=2*np.arcsin(n*wavelength/2./dspacing) # as 2*Theta theta=lambda q:2*np.arcsin(q/4/np.pi*wavelength) # Scherer equation for broadening due to finite size beta=0.9*wavelength/(domainsize*np.cos(braggAngle)) # beta is FWHM in rad # the peaks are described as Gaussians in theta peaks=np.c_[[voigt(theta(q),center=m,lg=lg,fwhm=fw,asym=asym).Y*a for m,fw,a in zip(braggAngle,beta,ampn) ]].sum(axis=0)/q**2*np.exp(-q**2*udw**2/3.) result=dA(np.c_[q,peaks].T) result.setColumnIndex(iey=None) result.columnname='wavevector; intensity' result.rf_modelname=sys._getframe().f_code.co_name return result
[docs]def resFunct(S,collDist=8000.,collAperture=10,detDist=8000.,sampleAperture=10, wavelength=0.5,wavespread=0.2,dpixelWidth=10,dringwidth=1, zeroextrapolfunc=2,highQextrapolfunc=2): """ Resolution smearing of small angle scattering for SANS or SAXS according to Pedersen for radial averaged data. I(q0)= Integral{(R(q,q0)*S(q)}dq with Kernel R(q,q0) of equ. 33 in [1]_ including wavelength spread, finite collimation and detector resolution. Default parameters are typical for a SANS machine like KWS2@JCNS with rectangular apertures. Low Q can be extrapolated as power law or Guinier like or constant. Parameters ---------- S : array like dataArray with X. and .Y theoretical Scattering function q in nm^-1 .Y can be arbitrary unit collDist : float, default 8000 collimation distance in mm collAperture : float, default 10 collimation rectangular aperture size in mm detDist : float, default 8000 detector distance in mm sampleAperture : float, default 10 sample rectangular aperture size in mm wavelength : float, default 0.5 wavelength in nm wavespread : float, default 0.1 FWHM wavelengthspread dlambda/lambda dpixelWidth : float, default 10 Detector pixel width in mm dringwidth : integer, default 1 number of pixel for averaging zeroextrapolfunc : , default 2 Type of extrapolation at low X edge for better handling of the border: - guinier : Low X data are log scaled, then X**2 extrapolated as Guinier like extrapolation. - float : Power law extrapolation of low X e.g. -4 for X**-4 for Porod scaling. - None : A constant value as Y(X.min()). highQextrapolfunc : float, default 2 Type of extrapolation at high X edge for better handling of the border: - float : Power law extrapolation of low X e.g. -4 for X**-4 for Porod scaling. - None : A constant value as Y(X.max()). Returns ------- dataArray columns ['wavevector; smeared scattering; unsmeared scattering; half width smearing function'] Notes ----- - HalfWidthSmearingFunction is the FWHM the Gaussian used for smearing including all effects. - The resolution is assumed to be equal in direction parallel and perpendicular to q on a 2D detector as described in chap. 2.5 in [1]_. - We neglect additional smearing due to radial averaging (last paragraph in chap 2.5 of [1]_). - Defaults correspond to a typical medium resolution measurement. - zeroextrapolfunc, highQextrapolfuncallow extrapolation at both edges to reduce edge effects. The best values depends on the measured signal shape at the edge and may change. The optimal way is to calculate the used model for the whole Q range, smear it and prune to the needed range. This is demonstated in example 2. - An example for SANS fitting with resFunc is given in example_SANSsmearing.py. Examples -------- Reproducing Table 1 of [1]_ :: import jscatter as js q=js.loglist(0.1,10,500) S=js.ff.sphere(q,6) # this is the direct call of resFunc, use smear instead as shown in next example Sr=js.sas.resFunct(S, collDist=2000.0, collAperture=20, detDist=2000.0, sampleAperture=10, wavelength=0.5, wavespread=0.2,dpixelWidth=0,dringwidth=0) # plot it p=js.grace() p.plot( S,sy=[1,0.3],li=1,legend='sphere') p.plot( Sr,sy=[2,0.3,2],li=2,legend='smeared sphere') p.plot(Sr.X,Sr[-1],li=4,sy=0,legend='FWHM in nm\S-1 ') p.yaxis(min=1e-3,scale='l',charsize=1.5,label='I(q) / a.u.',tick=[10,9]) p.yaxis(min=1e-1,tick=[10,9]) p.xaxis(scale='l',charsize=1.5,label='q / nm\S-1',tick=[10,9]) p.legend(x=0.8,y=5e5) Example 2:: # smear model over full range and interpolate to needed data # this is the best way to smear a model for fitting, but is not possible for desmearing meas=js.dA('measureddata.dat') # load data # define profile resol2m = js.sas.prepareBeamProfile('SANS', detDist=2000,collDist=2000.,wavelength=0.4,wavespread=0.15) q=np.r_[0.01:5:0.01] # or np.r_[0:meas.X.min():0.01,meas.X,meas.X.max():meas.X.max()*2:0.1] # calc model temp=js.ff.ellipsoid(q,2,3) # smear it smearedmodel=js.sas.smear(temp,resol2m).interpolate(X=meas.X) References ---------- .. [1] Analytical Treatment of the Resolution Function for Small-Angle Scattering JAN SKOV PEDERSEN, DORTHE POSSELTAND KELL MORTENSEN J. Appl. Cryst. (1990). 23, 321-333 """ L=collDist r1=collAperture l=detDist r2=sampleAperture dq=dpixelWidth*dringwidth/l # wave vector of incomming neutrons k0=2*np.pi/wavelength # maximum angles of aperture edge a1=r1/(L+l) a2=r2/l # dbeta estimate at low q for extrapolation to low q if a1>=a2: dbeta=2*r1/L else: dbeta=2*r2*(1/L+1/l) # number of points to extrapolate per sigma nn=8 X=S.X # sigma squared width q independent part at low q and maximum wavespread # finite collimation + detector resolution dq sigma=(((k0*dbeta)**2+(k0*dq)**2)/8/math.log(2)+(X.max()*wavespread)**2/(8*math.log(2)))**0.5 # extent by 3 sigma to low and high q xexl=loglist( max(0,X.min()-3*sigma) , X.min() ,3*nn)[:-1] # low q xexh=loglist( X.max() , X.max()+3*sigma ,3*nn)[:-1] # high q # extrapolate the Y values in xexl region if zeroextrapolfunc is None: # this uses smallest value to extrapolate Y=np.r_[np.interp(xexl,S.X,S.Y),S.Y] elif isinstance(zeroextrapolfunc,(float,int)): q=zeroextrapolfunc # apply inverse power and reverse it after polyfit Y=np.r_[S.prune(upper=X.min()*3).polyfit(xexl,1,lambda yy:yy**(1/q)).Y**q,S.Y] else: # Guinier like after log it should be quadratic Y=np.r_[np.exp(S.prune(upper=X.min()*3).polyfit(xexl,2,np.log).Y),S.Y] # extrapolate the Y values in xexh region if highQextrapolfunc is None: # this uses largest value to extrapolate Y=np.r_[Y,np.interp(xexh,S.X,S.Y)] elif isinstance(highQextrapolfunc,(float,int)): q=highQextrapolfunc # apply inverse power and reverse it after polyfit Y=np.r_[Y,S.prune(lower=X.max()-sigma).polyfit(xexh,1,lambda yy:yy**(1/q)).Y**q] # make this 2dim for later XT=np.r_[xexl,X,xexh][:,None] # now the real dbeta 1+2 # 8*math.log(2) scales as FWHM**2= 8*math.log(2) * sigma**2 # 2*theta theta2=2*np.arcsin(X/(2*k0)) cos2theta=np.cos(theta2) # dbeta if a1>=a2: dbeta1=2*r1/L-0.5*r2*r2/(r1*l*l*L)*cos2theta**4*(L+l/cos2theta**2)**2 dbeta2=2*r1/L-0.5*r2*r2/(r1*l*l*L)*cos2theta**2*(L+l/cos2theta)**2 else: dbeta1=2*r2*(1/L+cos2theta**2/l)-0.5*r1*r1/r2*l/L/(cos2theta**2*(L+l/cos2theta**2)) dbeta2=2*r2*(1/L+cos2theta/l)-0.5*r1*r1/r2*l/L/(cos2theta*(L+l/cos2theta)) # sigmas finite collimation sigma2c1=k0**2*np.cos(theta2/2)**2*dbeta1**2/(8*math.log(2)) sigma2c2=k0**2*dbeta2**2/(8*math.log(2)) # sigmas detector resolution sigma2d1=k0**2*np.cos(theta2/2)**2*cos2theta**2*dq**2/(8*math.log(2)) sigma2d2=k0**2*cos2theta**2*dq**2/(8*math.log(2)) # wavelength dependent part of sigma**2 + collimation part + detector resolution sigma2=(X*wavespread)**2/(8*math.log(2))+sigma2c1+sigma2d1 # equation 33 in [1]_ for all q # R is Kernel for convolution as 2D matrix # with axis=1 for q_average and axis=0 for the q integration over gaussian resolution with width sigma # modified Besselfunction of first kind zeroth order =>>> scipy.special.i0e exp scaled # np.abs(XT*X/sigma2) is related to rescale the exp scaled bessel func R=(XT/sigma2)*np.exp(-0.5*((XT**2+X**2)/sigma2)+np.abs(XT*X/sigma2))*\ special.i0e(XT*X/sigma2) # this consumes the main computing time 385 ms of 410ms # width dx between Q values for integration; first and last are taken full as kind of extrapolation with value of border dx=XT*0 dx[1:-1]=((XT[2:]-XT[:-2])/2.) dx[0]=(XT[1]-XT[0])/2 # above zero dx[-1]=XT[-1]-XT[-2] # assume extend to inf # integrate over kernel dx*R*Y and normalize integral dx*R SR=(dx*R*Y[:,None]).sum(axis=0)/(R*dx).sum(axis=0) result=dA(np.c_[S.X,SR,S.Y,2*(2*math.log(2))**0.5*sigma2**0.5].T) result.setColumnIndex(iey=None) result.columnname='wavevector; smeared scattering; unsmeared scattering; half width smearing function' result.rf_collDist=collDist result.rf_collAperture=collAperture result.rf_detDist=detDist result.rf_sampleAperture=sampleAperture result.rf_detectorResolution=dq result.rf_modelname=sys._getframe().f_code.co_name result.rf_extrapolX=XT.T[0] result.rf_extrapolY=Y result.rf_wavelength=wavelength result.rf_wavespread=wavespread result.rf_zeroextrapolfunc=zeroextrapolfunc result.rf_highQextrapolfunc=highQextrapolfunc return result
[docs]def resFunctExplicit(S,beamprofile,zeroextrapolfunc=2,highQextrapolfunc=2): """ Resolution smearing of small angle scattering for SANS or SAXS according to explict given Gaussian width. I(q0)= Integral{(R(q,q0)*S(q)}dq with Gaussian kernel R(q,q0). E.g. for merged dataFiles of KWS2@MLZ the explicit width is given in the 4th column. Parameters ---------- S : array like dataArray with X. and .Y theoretical Scattering function q in nm^-1 .Y can be arbitrary unit beamProfile : beamProfile 'explicit' Beam profile as prepared from prepareBeamProfile 'explicit' zeroextrapolfunc : , default 2 Type of extrapolation at low X edge for better handling of the border: - guinier : Low X data are log scaled, then X**2 extrapolated as Guinier like extrapolation. - float : Power law extrapolation of low X e.g. -4 for X**-4 for Porod scaling. - None : A constant value as Y(X.min()). highQextrapolfunc : float, default 2 Type of extrapolation at high X edge for better handling of the border: - float : Power law extrapolation of low X e.g. -4 for X**-4 for Porod scaling. - None : A constant value as Y(X.max()). Returns ------- dataArray columns ['wavevector; smeared scattering; unsmeared scattering; half width smearing function'] Notes ----- - HalfWidthSmearingFunction is the FWHM the Gaussian used for smearing including all effects. """ # number of points to extrapolate per sigma nn=8 X=S.X # extent by 3 sigma to low and high q xexl=loglist( max(0,X.min()-3*beamprofile.Y.min()) , X.min() ,3*nn)[:-1] # low q xexh=loglist( X.max() , X.max()+3*beamprofile.Y.max() ,3*nn)[:-1] # high q # extrapolate the Y values in xexl region if zeroextrapolfunc is None: # this uses smallest value to extrapolate Y=np.r_[np.interp(xexl,S.X,S.Y),S.Y] elif isinstance(zeroextrapolfunc,(float,int)): q=zeroextrapolfunc # apply inverse power and reverse it after polyfit Y=np.r_[S.prune(upper=X.min()*3).polyfit(xexl,1,lambda yy:yy**(1/q)).Y**q,S.Y] else: # Guinier like after log it should be quadratic Y=np.r_[np.exp(S.prune(upper=X.min()*3).polyfit(xexl,2,np.log).Y),S.Y] # extrapolate the Y values in xexh region if highQextrapolfunc is None: # this uses largest value to extrapolate Y=np.r_[Y,np.interp(xexh,S.X,S.Y)] elif isinstance(highQextrapolfunc,(float,int)): q=highQextrapolfunc # apply inverse power and reverse it after polyfit Y=np.r_[Y,S.prune(lower=X.max()-2*beamprofile.Y.max()).polyfit(xexh,1,lambda yy:yy**(1/q)).Y**q] # make this 2dim for later XT=np.r_[xexl,X,xexh][:,None] # R is Kernel for convolution as 2D matrix # with axis=1 for q_average and axis=0 for the q integration over gaussian resolution with width sigma sigma=beamprofile.interp(X) R=np.exp(-0.5*((XT-X)**2/sigma)) / (np.sqrt(2*np.pi)*sigma) # this consumes the main computing time # width dx between Q values for integration; first and last are taken full as kind of extrapolation with value of border dx=XT*0 dx[1:-1]=((XT[2:]-XT[:-2])/2.) dx[0]=(XT[1]-XT[0])/2 # above zero dx[-1]=XT[-1]-XT[-2] # assume extend to inf # integrate over kernel dx*R*Y and normalize integral dx*R SR=(dx*R*Y[:,None]).sum(axis=0)/(R*dx).sum(axis=0) result=dA(np.c_[S.X,SR,S.Y,sigma].T) result.setColumnIndex(iey=None) result.columnname='wavevector; smeared scattering; unsmeared scattering; sigma smearing function' result.rf_modelname=sys._getframe().f_code.co_name result.rf_extrapolX=XT.T[0] result.rf_extrapolY=Y result.rf_zeroextrapolfunc=zeroextrapolfunc result.rf_highQextrapolfunc=highQextrapolfunc return result
# noinspection PyAugmentAssignment
[docs]def waterXrayScattering(composition='h2o1',T=293,units='mol'): """ Absolute scattering of water with components (salt, buffer) at Q=0 as reference for X-ray. According to [2]_ a buffer of water with components might be used. Ions need to be given separatly as ['55.51h2o1','0.15Na','0.15Cl'] for 0.15 M NaCl solution. It is accounted for the temperature dependence of water density and compressibility. Parameters ---------- composition : string Buffer composition as in scatteringLengthDensityCalc give dissosiated ions separatly as ['1Na','1Cl'] with concentration in mol prepended the additional scattering as ionic liquid of the ions in water is taken into account see [2]_ mass in g; 1000g water are 55.508 mol T : float temperature in °K units : 'mol' anything except 'mol' prepended unit is mass fraction 'mol' prepended units is mol and mass fraction is calculated as :math:`mass=[mol] mass_{molecule}` e.g. 1l Water with 123mmol NaCl ['55.508H2O1','0.123Na1Cl1'] Returns ------- float absolute scattering length in Units 1/cm References ---------- .. [1] SAXS experiments on absolute scale with Kratky systems using water as a secondary standard Doris Orthaber et al. J. Appl. Cryst. (2000). 33, 218±225 .. [2] A high sensitivity pinhole camera for soft condensed matter T. Zemb, O. Tache, F. Né, and O. Spalla, J. Appl. Crystallogr. 36, 800 (2003). Notes ----- :math:`I(0)=(\sigma_{water}^2f_e^2 n_{ew}^2 k_B T \chi + \sum_{ci} n_i N_A 1000 n_{ei}^2 f_e^2 )/100` with :math:`\sigma_{water}` water density :math:`\chi` compressibility :math:`n_{ew}` number of electrons per water molecule :math:`f_e` cross section of electron in nm :math:`k_B` Boltzman constant :math:`n_i` concentration component i :math:`n_{ei}` number of electrons per molecule component i in Mol :math:`\sum_{ci}` is done for all ions separately if given """ # Units is MMTK kMMTK=0.00831447086363271 # in kJ/mol/K k=1.3806488e-23 # J/K mw=18.01528 I0=0 ch2o=0 cd2o=0 if isinstance(composition,str): composition=[composition] for compo in composition: compo=compo.lower() # decompose in numbers and characters decomp=re.findall('\d+\.\d+|\d+|\D+',compo) if not re.match('\d+\.\d+|\d+',decomp[-1]): raise KeyError('last %s Element missing following number '%decomp[-1]) if not re.match('\d',decomp[0]): # add a 1 as concentration in front if not there decomp=[1]+decomp mass=np.sum([Elements[ele][1]*float(num) for ele,num in zip(decomp[1:][::2],decomp[1:][1::2])]) nei=np.sum([Elements[ele][0]*float(num) for ele,num in zip(decomp[1:][::2],decomp[1:][1::2])]) if units.lower()=='mol': ci=float(decomp[0]) else: # if units!=mol we convert here from mass to mol fraction ci=float(decomp[0])/mass if ''.join(decomp[1:])=='h2o1': ch2o+=ci elif ''.join(decomp[1:])=='d2o1': cd2o+=ci else: # units in m I0+=ci*constants.N_A*1000*(felectron*1e-9)**2*nei**2 # in mol/m**3... dhfraction=cd2o/(ch2o+cd2o) if ch2o+cd2o!=0 else 0 I0/=(ch2o+cd2o)/(1000/mw) # from g/ml to m**-3 water_density=waterdensity(['%.4f'%(1-dhfraction)+'h2o1','%.4f'%dhfraction+'d2o1'],T=T)*1e6/mw*constants.N_A chi=watercompressibility(d2ofract=dhfraction,T=T,units='bar')*1e-5 # in 1/Pa I0+=water_density**2*(felectron*1e-9*10)**2*k*T*chi return I0/100. # in 1/cm
[docs]def transmissionCorrection(data, dark, emptybeam=None, edge=0.03, exposure=None): r""" Subtract dark current, find primary beam, get transmission and normalize by transmission and exposure time. For measurements including the primary beam from a semitransparent beamstop as from SAXSpace. Transmission is the maximum of the primary beam peak after dark subtraction. Allows easier comaprison of measurements with aged source (primary intensity change). Parameters ---------- data : dataArray A measurement from a SAXSpace instrument read by js.dA('filename.pdh',lines2parameter=[2,3,4]) dark : dataArray Dark current measurement. emptybeam : dataArray,float, default=None Empty beam measurement or count rate at primary peak maximum of emty peak. - dark will be subtracted. - If not provided the empty beam transmission is set to 1. - If float the empty beam is not subtracted and only transmission is calculated as :math:`T=\frac{I(q=0)_{sample}}{I(q=0)_{emptybeam}}`. edge : float, default 0.03 Wavevector value below beam stop edge. The primary beam is searched below this value. exposure : float, default None Esposure time in unit 's'. If not given the xml description at the end of the file is examined. Returns ------- dataArray with corrected data as :math:`\frac{I_S-I_{dark}}{T_S}` (see Notes) Notes ----- Files from SAXSpace instrument (.pdh) can be read by :: js.dA('filename.pdh',lines2parameter=[2,3,4]) **Correction** Brulet at al [1]_ describe the data correction for SANS, which is in principle also valid for SAXS, if incoherent contributions are neglected. The difference is, that SAXS has typical transmission around ~0.3 for 1mm water sample in quartz cell due to absorption, while in SANS typical values are around ~0.9 for D2O. Larger volume fractions in the sample play a more important rule for SANS as hydrogenated ingredients reduce the transmission significantly, while in SAXS still the water and the cell (quartz) dominate. One finds for a sample inside of a container with thicknesses (:math:`z`) for sample, buffer (solvent), empty cell and emty beam measurement (omitting the overall q dependence): .. math:: I_s = \frac{1}{z_S}\big((\frac{I_S-I_{dark}}{T_S}-I_{b}T_S\big) -\big(\frac{I_{EC}-I_{dark}}{T_{EC}}-I_{b}T_{EC})\big) - \frac{1}{z_B}\big((\frac{I_B-I_{dark}}{T_B}-I_{b}T_B\big) -\big(\frac{I_{EC}-I_{dark}}{T_{EC}}-I_{b}T_{EC})\big) where - :math:`I_s` is the interesting species - :math:`I_S` is the sample of species in solvent (buffer) - :math:`I_B` is the pure solvent (describing a constant background) - :math:`I_{dark}` is the dark current measurement - :math:`I_b` is the empty beam measurement - :math:`I_{EC}` is the empty cell measurement - :math:`z_x` corresponding sample thickness - :math:`T_x` corresponding transmission The reccuring pattern :math:`\big((\frac{I-I_{dark}}{T}-I_{b}T\big)` shows that the the beam tail (border of primary beam not absorbed by the beam stop) is attenuated by the corresponding sample. For equal sample thickness :math:`z` the empty beam is included in subtraction of :math:`I_B`: .. math:: I_s = \frac{1}{z} \big((\frac{I_S-I_{dark}}{T_S}-I_{b}T_S) - (\frac{I_B-I_{dark}}{T_B}-I_{b}T_B)\big) **The simple case** If the transmissions are nearly equal as for e.g. protein samples with low concentration (:math:`T_S \approx T_B`) we only need to subtract the transmission and dark current corrected buffer measurement from the sample. .. math:: I_s = \frac{1}{z} \big((\frac{I_S-I_{dark}}{T_S}) - (\frac{I_B-I_{dark}}{T_B}\big) **Higher accuracy for large volume fractions** For larger volume fractions :math:`\Phi` the transmission might be different and we have to take into account that only :math:`1-\Phi` of solvent contributes to :math:`I_S`. We may incorporate this in the sense of an optical density changing the effective thickness :math:`\frac{1}{z_B}\rightarrow\frac{1-\Phi}{z_B}` resulting in different thicknesses :math:`z_S \neq z_B` **Transmission** The transmission is measured as the ratio :math:`T=\frac{I(q=0)_{sample}}{I(q=0)_{emptybeam}}` with :math:`I(q=0)` as the primary beam intensity. If the primary beam tail is neglected in the above equation :math:`I(q=0)_{emptybeam}` only gives a common scaling factor and can be omitted if arbitrary units are used. Alternatively one can scale to the EC transmission with :math:`T_{EC}=1` For absolute calibration the same needs to be done. One finds :math:`T_{sample in cell}=T_{empty cell}T_{sample without cell}`. References ---------- .. [1] Improvement of data treatment in small-angle neutron scattering Brûlet et al Journal of Applied Crystallography 40, 165-177 (2007) """ if hasattr(data, 'transmission'): raise Warning('data has .transmission. It was already corrected and keept as it is.') return if emptybeam is None: ebtransmission=1 elif isinstance(emptybeam,(int, float)): # only peak value given ebtransmission=emptybeam elif hasattr(emptybeam,'ebtransmission'): # only do it one time for emptybeam ebtransmission=emptybeam.ebtransmission else: # take care of eb if not hasattr(emptybeam,'Exposure'): addXMLParameter(emptybeam) emptybeam.Y-=dark.Y # dark subtraction try: emptybeam.eY = (emptybeam.eY**2 + dark.eY**2)**0.5 except:pass imax=imin=emptybeam.Y[emptybeam.X<edge].argmax() emptybeam.ebtransmission=emptybeam.Y[imax-2:imax+3].mean() # search for minima around transmission peak while emptybeam.Y[imax+1]<emptybeam.Y[imax]: imax+=1 while emptybeam.Y[imin-1]<emptybeam.Y[imin]: imin-=1 xmax=emptybeam.X[imax] xmin=emptybeam.X[imin] temp=emptybeam[:,imin:imax] emptybeam.centerTransmissionPeak=(temp.X*temp.Y/temp.Y.sum()).mean() emptybeam.Y = emptybeam.Y /emptybeam.Exposure[0] emptybeam.eY = emptybeam.eY/emptybeam.Exposure[0] ebtransmission = emptybeam.ebtransmission if data.X.min()>0: raise Exception('data seem to have no transmission peak ') if exposure is None: addXMLParameter(data) else: data.Exposure=[exposure , 's'] if not hasattr(data, 'Exposure'): raise Exception('No exposure time found or given.') # dark subtraction data.Y-=dark.Y try: data.eY = (data.eY**2 + dark.eY**2)**0.5 except:pass imax=imin=data.Y[data.X<edge].argmax() data.transmission=data.Y[imax-2:imax+3].mean()/ebtransmission # search for minima around transmission peak while data.Y[imax+1]<data.Y[imax]: imax+=1 while data.Y[imin-1]<data.Y[imin]: imin-=1 xmax=data.X[imax] xmin=data.X[imin] temp=data[:,imin:imax] data.centerTransmissionPeak=(temp.X*temp.Y/temp.Y.sum()).mean() data.Y = data.Y /data.Exposure[0] /data.transmission data.eY = data.eY/data.Exposure[0] /data.transmission if hasattr(emptybeam,'ebtransmission'): # subtract emtybeam data.Y-=(data.transmission*emptybeam.Y) data.eY = (data.eY**2 + (data.transmission*emptybeam.eY)**2)**0.5
def _w2f(word): """converts string word if possible to float""" try: return float(word) except (ValueError,TypeError): return word
[docs]def autoscaleYinoverlapX(dataa,key=None,keep='lowest'): """ Scales elements of data to have same mean .Y value in the overlap region of .X . Parameters ---------- dataa : dataList data to scale key : string Data are grouped into unique values of attribute key before scaling. E.g. to do it for a series of concentrations for each concentration individually. keep : default 'l' If 'l' the lowest X are kept and higher X are scaled successively to next lower X. Anything else highest X are kept and other are scaled to next higher. Returns ------- dataList new scaled dataList Notes ----- First data are sorted along .X.mean() scaling value is stored in .autoscalefactor """ result=dL() if key is not None and hasattr(dataa,key): values=np.unique(getattr(dataa,key)) else: values=[None] for uniquevalues in values: if uniquevalues is not None: data=dataa.filter(lambda a:getattr(a,key)==uniquevalues).copy() else: data=dataa.copy() data.sort(key=lambda ee:ee.X.mean()) if keep[0] in ('l',0): d=-1 for i in range(len(data)-1,0,-1): meani0=data[i].where(lambda a:a.X<data[i+d].X.max()).Y.mean() meani1=data[i+d].where(lambda a:a.X>data[i].X.min()).Y.mean() data[i+d][1]*=meani0/meani1 data[i+d].autoscalefactor=meani0/meani1 data[-1].autoscalefactor=1 else: d=1 for i in range(len(data)-1): meani0=data[i].where(lambda a:a.X>data[i+d].X.min()).Y.mean() meani1=data[i+d].where(lambda a:a.X<data[i].X.max()).Y.mean() data[i+d][1]*=meani0/meani1 data[i+d].autoscalefactor=meani0/meani1 data[0].autoscalefactor=1 result.append(data) return result
[docs]def removespikesminmaxmethod(dataa,order=7,sigma=2,nrepeat=1,removePoints=None): """ Takes a dataset and removes single spikes from data by substitution with spline. Find minima and maxima of data including double point spikes; no 3 point spikes scipy.signal.argrelextrema with np.greater and np.less are used to find extrema Parameters ---------- dataa : dataArray Dataset with eY data. order : int Number of points see scipy.signal.argrelextrema. Distance between extrema. sigma : float Deviation factor from std dev; from eY. If datapoint -spline> sigma*std its a spike. nrepeat : int Repeat the procedure nrepeat times. removePoints : list of integer Instrument related points to remove because of dead pixels. 'JCNS' results in a list for SAXSPACE at JCNS Jülich. Returns ------- data with spikes removed """ SAXSPACE=[0,1,134,135,530,539,540,1011,1012,1091,1092,1287,1312,1451,1452,1502,1503,1606,1607,1810,1811,1893,1912,1913,1933,1934] if removePoints=='JCNS': removePoints=SAXSPACE elif not isinstance(removePoints,list): removePoints=[] # make copy data=dataa.copy() takepoints=np.array([i not in removePoints for i in range(len(data.Y))]) data=data[:,takepoints] def getpeaklist(data,order=7): """ find minima and maxima of data including double spikes no 3 point spikes """ # find minima and maxima llgreater=scipy.signal.argrelextrema(data.Y,np.greater,order=order,mode='wrap')[0] llless=scipy.signal.argrelextrema(data.Y,np.less,order=order,mode='wrap')[0] doubles=[] # list of neighbouring pixel # check in between llgreater intervals if edges are also spikes for i,j in zip(llgreater[:-1],llgreater[1:]): intervalmax=scipy.signal.argrelextrema(data.Y[i+1:j],np.greater,order=order,mode='wrap')[0] if len(intervalmax)>0: # if an max is found check edges if min(intervalmax)==0: doubles.append(min(intervalmax)+i+1) if max(intervalmax)==len(data.Y[i+1:j]): doubles.append(max(intervalmax)+i+1) for i,j in zip(llless[:-1],llless[1:]): intervalmax=scipy.signal.argrelextrema(data.Y[i+1:j],np.less,order=order,mode='wrap')[0] if len(intervalmax)>0: if min(intervalmax)==0: doubles.append(min(intervalmax)+i+1) if max(intervalmax)==len(data.Y[i+1:j]): doubles.append(max(intervalmax)+i+1) return np.r_[llgreater,llless,np.array(doubles)] def reldif2(data,spline,sigma=1): # check if distance is larger than sigma return abs( (data.Y-spline(data.X))/data.eY)>sigma while nrepeat>0: peaklist=getpeaklist(data,order=order) # which point is peak peaks=np.array([i in peaklist for i in range(len(data.Y))]) # spline without the peaks '~' is 'not' spline=scipy.interpolate.UnivariateSpline(data.X[~peaks],data.Y[~peaks],s=0) # remove the spikes and substitute with spline of surrounding if peak and > sigma # removespikes=lambda data,n,sigma:np.where(reldif2(data,spline,n,sigma=sigma) & peaks,meansurrounding(data,n),data.Y) removespikes=lambda data,sigma:np.where(reldif2(data,spline,sigma=sigma)&peaks,spline(data.X),data.Y) data.Y=removespikes(data,sigma=sigma) nrepeat-=1 return data
[docs]def removespikes(dataa,xmin=None,xmax=None,medwindow=5,SGwindow=None,sigma=0.2,SGorder=2): """ Takes a dataset and removes single spikes. A median filter is used to find single spikes. If abs(data.Y-medianY)/data.eY>sigma then the medianY value is used. If SGwindow!=None Savitzky-Golay filtered values are used. If sigma is 0 then new values (median or Savitzky-Golay filtered) are used everywhere. Parameters ---------- dataa : dataArray dataset with eY data medwindow : odd integer window size of scipy.signal.medfilt SGwindow : odd int, None Savitzky-Golay filter see scipy.signal.savgol_filter without the spikes; window should be smaller than instrument resolution order : int polynominal order of scipy.signal.savgol_filter needs to be smaller than SGwindow SGsigma : float relative deviation from eY if datapoint-median> sigma*eY its a spike Returns ------- Filtered and smoothed dataArray """ # make copy data=copy.deepcopy(dataa) if not isinstance(sigma,(int,float)): sigma=0. if xmin is None: xmin=min(data.X) if xmax is None: xmax=max(data.X) if SGwindow==0: SGwindow=None # median filter to remove spikes Ynew=scipy.signal.medfilt(data.Y,medwindow) # decide where a spike is found --> if difference is larger than sigma spikesat=abs(data.Y-Ynew)/data.eY>sigma # logical limits limits=np.logical_and(data.X>xmin,data.X<xmax) if isinstance(SGwindow,int): # Savgol as smoothed signal # window smaller than resolution Ynew=scipy.signal.savgol_filter(np.where(spikesat,Ynew,data.Y),SGwindow,order) else: # remove only the spikes and substitute with Ynew Ynew=np.where(spikesat,Ynew,data.Y) # data.Y=np.where(np.logical_and(spikesat,limits),Ynew,data.Y) data.Y=np.where(limits,Ynew,data.Y) data.smoothed_SGwindow=SGwindow data.smoothed_sigma=sigma data.smoothed_medwindow=medwindow data.smoothed_SGorder=SGorder return data
[docs]def addXMLParameter(data): """ Adds the parameters stored in xml part of a .pdh file as eg. in SAXSPACE .pdh files. Parameters ---------- data : dataArray Already read pdh file. XML content is found in comments of the read files and starts with '<'. """ if hasattr(data,'_isdataArray'): datalist=[data] elif hasattr(dataa,'_isdataList'): datalist=data else: raise Exception(data,' is not dataArray or dataList') for dat in datalist: lines=filter(lambda a: (a[:1]=='<'),dat.comment) try: root=xml.etree.ElementTree.fromstringlist(lines) for par in root.iter('parameter'): setattr(dat,par[2].text,[_w2f(par[ii].text) for ii in (3,1) ]) except: raise Warning('No xml data found. Go on.')
[docs]def locatefiles(pattern,root=os.curdir): """ Locate all files matching supplied filename pattern in and below supplied root directory. Parameters ---------- pattern : file pattern Pattern used in fnmatch.filter root : directory, default is os.curdir Directory where to start Returns ------- file list """ matchfiles=[] for path,dirs,files in os.walk(os.path.abspath(root)): for filename in fnmatch.filter(files,pattern): matchfiles.append(os.path.join(path,filename)) return matchfiles
[docs]def copyfiles(pattern,root=os.curdir,destination='copy',link=False): """ Copies all files matching pattern in tree below root to destination directory Parameters ---------- pattern : file pattern Pattern used in fnmatch.filter root : directory, default is os.curdir Directory where to start destination : dirname Destination link : bool If True links are created. """ files=locatefiles(pattern,root=root) if not os.path.exists(destination): os.mkdir(destination) for ff in files: newname=os.path.join(destination,os.path.basename(ff)) print( newname) if not link: shutil.copy2(ff,newname) else: os.symlink(ff,newname) return
[docs]def moveSAXSPACE(pattern,root='./',destination='./despiked',skip='BeamProfile',medwindow=5,SGwindow=5,sigma=0.2, order=2): """ Read SAXSPACE .pdh files and removes spikes by removespikes. This is mainly for use at JCNS SAXSPACE with CCD camera as detector :-)))) Parameters ---------- pattern : string Search pattern for filenames destination : string Where to save the files skip : string Words in filename to skip the file medwindow : odd integer Window size of scipy.signal.medfilt SGwindow : odd int, None Savitzky-Golay filter see scipy.signal.savgol_filter order : int Polynominal order of scipy.signal.savgol_filter sigma : float Deviation factor of eY If datapoint-median> sigma*std its a spike Notes ----- Default values are adjusted to typical SAXSPACE measurement. """ files=locatefiles(pattern,root=root) if not os.path.exists(destination): os.mkdir(destination) for file1 in files: if 'BeamProfile' in file1: continue newname=os.path.join(destination,os.path.basename(file1)) print( file1,'->',newname) f=open(file1,'rU') filecontent=f.readlines() f.close() header=filecontent[:2+3] nlines=int(header[2].split()[0]) numbers=filecontent[2+3:2+3+nlines] footer=filecontent[2+3+nlines:] data=dA(numbers) datanew=removespikes(data,xmin=None,medwindow=medwindow,SGwindow=SGwindow,sigma=sigma,SGorder=order) f=open(newname,'w') f.writelines(header) np.savetxt(f,datanew.T,delimiter=' ',fmt='%10.6E') f.writelines(footer) f.close() return