routines.py 9.88 KB
 Nick Sauerwein committed Feb 27, 2017 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 ``````# -*- coding: utf-8 -*- """ Created on Mon Apr 25 20:27:42 2016 @author: Benedikt Hermann """ import numpy as np import matplotlib.pyplot as plt from scipy import misc from scipy import optimize import os import scipy as sp def sampleavg(path, Basler, g, N=500.): #return avg. Image of N Samples, g is an int indicating the summation: #g=1: 1, 3, 5, ... #g=2: 2, 4, 6, ... #g=3: all. N=np.double(N) i=1 if g==1: I1 = misc.imread(os.path.join(path,Basler+str(2*i-1).zfill(4)+'.bmp'), flatten= 0) I=I1/N for j in range(int(N)-1): i=j+2 print(i) I1 = misc.imread(os.path.join(path,Basler+str(2*i-1).zfill(4)+'.bmp'), flatten= 0) I=I+I1/N if g==2: I1 = misc.imread(os.path.join(path,Basler+str(2*i).zfill(4)+'.bmp'), flatten= 0) I=I1/N for j in range(int(N)-1): i=j+2 print(i) I1 = misc.imread(os.path.join(path,Basler+str(2*i).zfill(4)+'.bmp'), flatten= 0) I=I+I1/N if g==3: I1 = misc.imread(os.path.join(path,Basler+str(i).zfill(4)+'.bmp'), flatten= 0) I=I1/N for j in range(2*int(N)-1): i=j+2 print(i) I1 = misc.imread(os.path.join(path,Basler+str(i).zfill(4)+'.bmp'), flatten= 0) I=I+I1/N return I def savitzky_golay(y, window_size, order, deriv=0, rate=1): from math import factorial try: window_size = np.abs(np.int(window_size)) order = np.abs(np.int(order)) except ValueError as msg: raise ValueError("window_size and order have to be of type int") if window_size % 2 != 1 or window_size < 1: raise TypeError("window_size size must be a positive odd number") if window_size < order + 2: raise TypeError("window_size is too small for the polynomials order") order_range = range(order+1) half_window = (window_size -1) // 2 # precompute coefficients b = np.mat([[k**i for i in order_range] for k in range(-half_window, half_window+1)]) m = np.linalg.pinv(b).A[deriv] * rate**deriv * factorial(deriv) # pad the signal at the extremes with # values taken from the signal itself firstvals = y[0] - np.abs( y[1:half_window+1][::-1] - y[0] ) lastvals = y[-1] + np.abs(y[-half_window-1:-1][::-1] - y[-1]) y = np.concatenate((firstvals, y, lastvals)) return np.convolve( m[::-1], y, mode='valid') def smooth(Z1, ws=51, order=1):#in: profiles #smoothen ysg1 = savitzky_golay(Z1, ws, order) return ysg1 def normalize(Z, plot=0): # get G(x) gaussian profile of laser, then normalize #Fourier Analysis N = len(Z);a=0.;b=N t, step = np.linspace(a,b,N,endpoint=False,retstep=True) y = Z-np.mean(Z) f = 1./N*abs(np.fft.fft(y)) f2 = np.fft.fftshift(f) k = np.r_[-len(y)/2.:len(y)/2.]/(b-a) if plot: plt.plot(k,f2,"r-") plt.xlim((-0.05,0.05)) plt.ylabel("DFT \$I_{px="+"}-\$", fontsize=16) plt.title("Discrete Fourier Transform", fontsize=16) plt.xlabel("ky") plt.tight_layout() m=np.argmax(f2[N/2+2:]) f= (k[N/2+2+m]) if plot: plt.figure("n") plt.plot(Z) def GaussSin(x, p1, p2, p3, p4, p5,f): return p1*np.exp(-1*p2*(x-p3)**2)*np.sin(2.*np.pi*f/2*x+p4)**2+p5 p5=np.min(Z) p1=np.max(Z)-p5 p3=np.argmax(Z) if plot: plt.figure("n") plt.plot(t, GaussSin(t, p1,1e-5,p3,+0., p5,f), "k--") # find start params F=optimize.curve_fit(GaussSin,t,Z,p0=[p1,1e-5,p3,+0., p5,f])[0] if plot: plt.plot(t, GaussSin(t, F[0],F[1],F[2],F[3],F[4],F[5])) def Gauss(x,p1,p2,p3): return p1*np.exp(-1*p2*(x-p3)**2) if plot: plt.plot(t, Gauss(t, F[0],F[1],F[2])+F[4], "r--") # Normalisation NZ=(Z-F[4])/Gauss(t, F[0],F[1],F[2]) if plot: plt.figure() plt.plot(NZ) return NZ, t, F[5], F[3] #normalized profile, x interval, freq, konstant phase of undist. def alphafit2(Z1, Z2,B=0.015,m=550., b=150., s=50.): Z1, t, f1, dp1=normalize(Z1) Z2, t, f2, dp2=normalize(Z2) #fit for sin phase and freq def sin2(x, A, f, dp): return A*np.sin(2*np.pi*f/2.*x+dp)**2 Para=optimize.curve_fit(sin2, t, Z1, p0=[1., f1, dp1])[0] A1=Para[0]; f1=Para[1]; dp1=Para[2] Para=optimize.curve_fit(sin2, t, Z2, p0=[1., f2, dp2])[0] A2=Para[0] Z1=Z1/A1; Z2=Z2/A2 Dif=Z1-Z2 def alphaF(x, B, s, m, b): deg=2 return B*(-1*np.exp(-1./s**deg*(x-(m-b))**deg)+np.exp(-1./s**deg*(x-(m+b))**deg)) def fitF(x,B, s, m, b): A=1. return A*(np.sin(2*np.pi*f1/2.*x+dp1)**2-np.sin(2*np.pi*f1/2.*x+dp1+alphaF(x, B, s, m, b))**2) Para=optimize.curve_fit(fitF, t, Dif, p0=[B, s, m, b])[0] afit = alphaF(t, Para[0],Para[1],Para[2],Para[3]) Diffit = fitF(t, Para[0],Para[1],Para[2],Para[3]) return Dif,Diffit, afit def phaseunwrap(Z1, Z2): """ 1. Fourier transform 2. Gaussian window 3. shift oszillation peak to zero 3. inverse Fourier Transform -> A(x) 4. A(x)/Aref(x) """ #1 DFT N = len(Z1);a=0.;b=N t, step = np.linspace(a,b,N,endpoint=False,retstep=True) f = 1./N*(np.fft.fft(Z1)) f2 = np.fft.fftshift(f) k = np.r_[-len(Z1)/2.:len(Z1)/2.]/(b-a) #2 Gaussian Window def Ga(x): return np.exp(-1./x**2*(3.*(k[1]-k[0]))**2) W1=(f2)*Ga(k) W1[0:int(len(W1)/2)]=0. #3 shift oszillation peak to zero b=np.argmax(W1) m=int(b-len(W1)/2) S1=np.zeros(len(W1), dtype=np.complex64) #S1=np.roll(np.array(W1),-m) S1[int(len(W1)/2)-m:-m]=W1[int(len(W1)/2):] # plt.figure("test") # plt.plot(k, S1) # plt.plot(k, LP(k)) D1=np.fft.ifft(N*S1) #same for ref. signal f = 1./N*(np.fft.fft(Z2)) f2 = np.fft.fftshift(f) k = np.r_[-len(Z2)/2.:len(Z2)/2.]/(b-a) W2=(f2)*Ga(k) W2[0:int(len(W2)/2)]=0 m=int(np.argmax(W2)-len(W2)/2) S2=np.zeros(len(W1), dtype=np.complex64) #S2=np.roll(W2,-m) S2[int(len(W2)/2)-m:-m]=W2[int(len(W2)/2):] D2=np.fft.ifft(N*S2) #4 A(x)/Aref(x) E=D2/D1 P1=np.zeros(len(S1)) #print(E) P1=np.angle(E) # minus sign if I1 and I2 are interchanged (on<->off) #if np.argmax(smooth(P1[int(len(P1)/10):-int(len(P1)/10)]))4.: g=np.round(diff/np.pi) Pc[j:,i+1]+=g*np.pi return Pc def phase(A,As,shift=217): lx=len(A[:,0]) ly=len(A[0,:]) Ph=np.copy(A) Phs=np.copy(As) for i in range(lx): Ph[i,:]-=np.average(Ph[i,0:50]) Phs[i,:]-=np.average(Ph[i,0:50]) for j in range(shift,ly): Phs[i,j]=Phs[i,j]+Phs[i,j-shift] Ph[i,j]=Ph[i,j]+Phs[i,j-shift] return Ph def MLEM(X,theta, meas): from scipy import ndimage #rotate Xp=ndimage.rotate(X, -theta, reshape=False) Lxt=len(X[0,:]) X1=np.zeros((Lxt,Lxt)) ysim=np.sum(Xp,axis=0) ZZ=(len(ysim)-len(meas))/2 meas=np.append(ysim[:ZZ],meas) meas=np.append(meas,ysim[-ZZ:]) T=np.abs(meas/ysim) X1[:,Lxt/4:-Lxt/4]=Xp[:,Lxt/4:-Lxt/4]*T[Lxt/4:-Lxt/4] return ndimage.rotate(X1,theta, reshape=False) def iabel(dfdx, x): nx = len(x) integral = sp.zeros(nx-1, dtype=float) for i in range(0, nx-1): divisor = sp.sqrt(x[i:]**2 - x[i]**2) integrand = dfdx[i:] / divisor integrand[0] = integrand[1] # deal with the singularity at x=r integral[i] = - sp.trapz(integrand, x[i:]) / sp.pi return integral def abel(f,x): #f is the the distribution w.r.t. r nx=len(x) integral= sp.zeros(nx,dtype=float) for i in range(0, nx-1): divisor = sp.sqrt(x[i:]**2 - x[i]**2) integrand = f[i:]*x[i:] / divisor integrand[0] = integrand[1] # deal with the singularity at x=r integral[i] = 2*sp.trapz(integrand, x[i:]) return integral def periodic_gaussian_deriv(x, sigma): nx = len(x) # put the peak in the middle of the array: mu = x[nx/2] g = dgaussiandx(x, mu, sigma) # need to normalize, the discrete approximation will be a bit off: g = g / (-sp.sum(x * g)) # reorder to split the peak across the boundaries: return(sp.append(g[nx/2:nx], g[0:nx/2])) def dgaussiandx(x, mu, sigma): return( -(x-mu)*sp.exp(-(x-mu)**2/sigma**2/2.0)/(sigma**2*sp.sqrt(2*sp.pi*sigma**2)) ) def noise_img(img): nx=len(img[:,0]) ny=len(img[0,:]) sx=20 sy=20 noise=np.zeros((nx/sx-2, ny/sy-1)) for i in range(ny/sx-1): p=img[:,i*sx+sx/2] n=p-smooth(p, ws=21, order=3) for j in range(nx/sy-2): noise[j,i]=np.std(n[j*sy:(j+1)*sy]) return noise def gauss(x,a,x0,sigma): return a*np.exp(-(x-x0)**2/(2*sigma**2)) def gauss_fit(x, y): n = len(x) mean = n/2 sigma = n/4 popt,pcov = sp.optimize.curve_fit(gauss,x,y,p0=[1,mean,sigma]) return popt, pcov``````