Creatgraphy

import numpy as np
import matplotlib.pyplot as plt
import cmath as cm
from angles import r2d,normalize,d2r    
from scipy.stats import multivariate_normal

"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

Title: Gerchberg-Saxton-Algorithm with 2 and 4 Phase-Discretisation
Author: Dominik Doellerer


The Algorithm computes iterative the phase-shift for a given output image 
as shown in "A Practical Algorithm for the Determination of Phase from Image 
and Diffraction Plane Pictures" in Optik Vol. 35 No. 2 (1972) 
by R. W. Gerchberg and W. O. Saxton
Today, its not easy to machine a continous phase-shift into a material. 
The program computes a discrete phase-shift by simply dividing into 2 or 4 parts.


The Project is under the Attribution-NonCommercial-ShareAlike 4.0 International
(CC BY-NC-SA 4.0) License. This means you are free to copy the model or adapt
it for non-commercial purposes.

"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

IMAGE_FILE = '/YOURFOLDER/IMAGE.png' # input image 
INTERATIONS = 5 # iterations of the gerchberg-saxton algorithm default 30
NUMBER_OF_PHASES = 2 #1 no discretisation 2 discrete Phases  or 4 discrete Phases
SOURCE = 'gauss' #amplitude of lightsource 'gauss' or 'constant'
FAC_MU = 4 # width of the target gauss-curve if in use 1 equals normal, higher than 1 flattens the curve


DISCRETE_2PHASE = '/YOURFOLDER/DISCRETE_2PHASE.jpg'
DISCRETE_4PHASE_1 = '/YOURFOLDER/DISCRETE_4PHASE_1.jpg'
DISCRETE_4PHASE_2 = '/YOURFOLDER/DISCRETE_4PHASE_2.jpg'
DISCRETE_4PHASE_3 = '/YOURFOLDER/DISCRETE_4PHASE_3.jpg'
DISCRETE_4PHASE_4 = '/YOURFOLDER/DISCRETE_4PHASE_4.jpg'
CONTINUOUS_PHASE = '/YOURFOLDER/CONTINUOUS_PHASE.jpg'


#=======================math==============================================
def ampl(x):
    return np.sqrt(x.real*x.real+x.imag*x.imag)

def absdiff(array1,array2):
    #returns the absolut difference of two arrays in form of a new array
    diff = np.zeros_like(array1)
    for i in range(len(diff)):
        for j in range(len(diff[1])):
            diff[i][j]= array1[i][j]-array2[i][j]
    plt.figure()
    plt.imshow(diff)
    plt.colorbar()
    plt.title("Diff")
    return diff

def gaussian(x, mu,sig):
    return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))
  
def gauss(sizey,sizex,fac_mu):
    
    x = np.linspace(0, sizex, sizex)
    y = np.linspace(0, sizey, sizey)
    X, Y = np.meshgrid(x, y)
    pos = np.dstack((X, Y))
    mu = np.array([sizex/2, sizey/2])
    cov = np.array([[sizex*fac_mu,0],[0, sizey*fac_mu]])
    rv = multivariate_normal(mu, cov)
    Z = rv.pdf(pos)

    return Z


#=======================image==============================================

def con2bw(image):
    image_gray = np.mean(image, -1)

    image_bw = np.zeros_like(image_gray)
    for i in range(len(image_gray)):
            for j in range(len(image_gray[i])):
                if image_gray[i][j]<0.5: image_bw [i][j]= 0
                if image_gray[i][j]>=0.5: image_bw[i][j] = 1
                
    return image_bw

def plot_amplitude(im):
    plt.figure()
    from matplotlib.colors import LogNorm
    plt.imshow(np.abs(im), norm=LogNorm(vmin=5))
    plt.colorbar
    plt.title("FFT Amplitude Image")
    
def argand(a):
    plt.figure()
    for i in range (len(a)):
        for x in range(len(a[i])):
            plt.polar([0,normalize(r2d(cm.phase(a[i][x])),0,360)],[0,abs(a[i][x])],marker='o')
    plt.title("Phase")
    plt.show()

def plot3D(array):
    import matplotlib.pyplot as plt
    import numpy as np
    
    np.random.seed(1234)
    fig = plt.figure()
    ax1 = fig.add_subplot(111, projection='3d')
    
    A = array-3.0
    
    x = np.array([[i] * len(array[1]) for i in range(len(array))]).ravel() 
    y = np.array([i for i in range(len(array[1]))] * len(array)) 
    z = np.zeros(len(array)*len(array[1])) 
    dx = np.ones(len(array)*len(array[1]))
    dy = np.ones(len(array)*len(array[1]))
    dz = A.ravel()
    
    ax1.bar3d(x, y, z, dx, dy, dz)


#=======================GSA==============================================

def gsa(source,target,n):
    
    a = np.fft.ifftshift(np.fft.ifft2(np.fft.fftshift(target))) 
    phase_a = np.zeros_like(target)
    b = np.complex128(np.zeros_like(target))
    phase_c = np.zeros_like(target)
    c = np.complex128(np.zeros_like(target))
    d = np.complex128(np.zeros_like(target))
    retrieved_phase = np.zeros_like(target)

    for z in range(n):
                
        
        for i in range(len(source)):
            for j in range(len(source[i])):
                phase_a[i][j] = cm.phase(a[i][j])
        
        b = np.multiply(source, np.exp(1j*phase_a))
        c = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(b)))
     
        for i in range(len(source)):
            for j in range(len(source[i])):
                phase_c[i][j] = cm.phase(c[i][j])
                
        d = np.multiply(ampl(target), np.exp(1j*phase_c))
        
        a = np.fft.ifftshift(np.fft.ifft2(np.fft.fftshift(d)))
        
        print(z)
        
    for i in range(len(source)):
        for j in range(len(source[i])):
            retrieved_phase[i][j] = normalize(r2d(cm.phase(a[i][j])),0,360)
     
    return retrieved_phase

#=======================quantisation==============================================

def storeSeperate(retrieved_phase,n_sep):
    plt.figure() 
    if(n_sep==1):
        plt.imsave(CONTINUOUS_PHASE,retrieved_phase, cmap='gray')
        plt.imshow(retrieved_phase)            

    if(n_sep==2):
        phase = np.zeros_like(retrieved_phase)
        for i in range(len(retrieved_phase)):
            for j in range(len(retrieved_phase[i])):
                
                if( abs(retrieved_phase[i][j]) > 180):
                    phase[i][j]=1
                else:
                    phase[i][j]=0
        plt.imshow(phase)            
        plt.imsave(DISCRETE_2PHASE,phase, cmap='gray')

    if(n_sep==4):
        phase1 = np.zeros_like(retrieved_phase)
        phase2 = np.zeros_like(retrieved_phase)
        phase3 = np.zeros_like(retrieved_phase)
        phase4 = np.zeros_like(retrieved_phase)
        
        
        for i in range(len(retrieved_phase)):
            for j in range(len(retrieved_phase[i])):
                
                if( abs(retrieved_phase[i][j]) > 270):
                    phase4[i][j]=1
                elif(abs(retrieved_phase[i][j]) > 180):
                    phase3[i][j]=1
                elif(abs(retrieved_phase[i][j]) > 90):
                    phase2[i][j]=1
                else:
                    phase1[i][j]=1
                    
        plt.imshow(phase1)
        plt.imsave(DISCRETE_4PHASE_4,phase4, cmap='gray')
        plt.imsave(DISCRETE_4PHASE_3,phase3, cmap='gray')
        plt.imsave(DISCRETE_4PHASE_2,phase2, cmap='gray')
        plt.imsave(DISCRETE_4PHASE_1,phase1, cmap='gray')

    plt.title("saved discretisation")
#=======================main==============================================

image = plt.imread(IMAGE_FILE).astype(float)

plt.figure()
plt.imshow(image)
plt.title("original")

target = con2bw(image)
if(SOURCE=='gauss'):
    source = gauss(len(target),len(target[1]),FAC_MU) 
else:
    source = np.ones_like(target)/(len(target)*len(target))

plt.figure() 
plt.imshow(source)
plt.title("source")

retrieved_phase = gsa(source,target,INTERATIONS)

plt.figure() 
plt.imshow(retrieved_phase)
plt.title("retrieved phase / no discretisation")

#=======================holores==============================================
out = np.zeros_like(source)

if(NUMBER_OF_PHASES==2):
    phase = np.zeros_like(retrieved_phase)
    for i in range(len(retrieved_phase)):
        for j in range(len(retrieved_phase[i])):
                    
            if( abs(retrieved_phase[i][j]) > 180):
                phase[i][j]=180
            else:
                phase[i][j]=0
      
    
    holo1 =  np.complex128(source)
    for i in range(len(source)):
        for j in range(len(source[i])):
            holo1[i][j]= source[i][j] * np.exp(1j*phase[i][j]/360*cm.pi*2) 
                    
    holo2 = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(holo1)))
    
    for i in range(len(holo1)):
                for j in range(len(holo2[i])):
                    out[i][j] = ampl(holo2[i][j])


if(NUMBER_OF_PHASES==4):
    phase1 = np.zeros_like(retrieved_phase)
    phase2 = np.zeros_like(retrieved_phase)
    phase3 = np.zeros_like(retrieved_phase)
    phase4 = np.zeros_like(retrieved_phase)
    
    
    for i in range(len(retrieved_phase)):
        for j in range(len(retrieved_phase[i])):
            
            if( abs(retrieved_phase[i][j]) > 270):
                phase4[i][j]=1
            elif(abs(retrieved_phase[i][j]) > 180):
                phase3[i][j]=1
            elif(abs(retrieved_phase[i][j]) > 90):
                phase2[i][j]=1
            else:
                phase1[i][j]=1
    
    holo = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(source*np.exp(1j*(((phase1*90)+phase2*180+phase3*270+phase4*360)/360*3.1415*2)))))
    for i in range(len(holo)):
        for j in range(len(holo[i])):
            out[i][j] = np.sqrt(holo[i][j].real*holo[i][j].real+holo[i][j].imag*holo[i][j].imag)

storeSeperate(retrieved_phase,NUMBER_OF_PHASES) 
   
if(NUMBER_OF_PHASES==4 or NUMBER_OF_PHASES==2):
    plt.figure() 
    plt.imshow(out)
    plt.title("output of discretisation")
else:   
    holo1 =  np.complex128(source)
    for i in range(len(source)):
        for j in range(len(source[i])):
            holo1[i][j]= source[i][j] * np.exp(1j*retrieved_phase[i][j]/360*cm.pi*2) 
                    
    holo2 = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(holo1)))
    
    for i in range(len(holo1)):
                for j in range(len(holo2[i])):
                    out[i][j] = ampl(holo2[i][j])
    plt.figure() 
    plt.imshow(out)
    plt.title("output without discretisation")

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import numpy as np

import matplotlib.pyplot as plt

import cmath as cm

from angles import r2d,normalize,d2r

from scipy.stats import multivariate_normal

"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

Title: Gerchberg-Saxton-Algorithm with 2 and 4 Phase-Discretisation

Author: Dominik Doellerer

The Algorithm computes iterative the phase-shift for a given output image

as shown in "A Practical Algorithm for the Determination of Phase from Image

and Diffraction Plane Pictures" in Optik Vol. 35 No. 2 (1972)

by R. W. Gerchberg and W. O. Saxton

Today, its not easy to machine a continous phase-shift into a material.

The program computes a discrete phase-shift by simply dividing into 2 or 4 parts.

The Project is under the Attribution-NonCommercial-ShareAlike 4.0 International

(CC BY-NC-SA 4.0) License. This means you are free to copy the model or adapt

it for non-commercial purposes.

"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

IMAGE_FILE = '/YOURFOLDER/IMAGE.png' # input image

INTERATIONS = 5 # iterations of the gerchberg-saxton algorithm default 30

NUMBER_OF_PHASES = 2 #1 no discretisation 2 discrete Phases or 4 discrete Phases

SOURCE = 'gauss' #amplitude of lightsource 'gauss' or 'constant'

FAC_MU = 4 # width of the target gauss-curve if in use 1 equals normal, higher than 1 flattens the curve

DISCRETE_2PHASE = '/YOURFOLDER/DISCRETE_2PHASE.jpg'

DISCRETE_4PHASE_1 = '/YOURFOLDER/DISCRETE_4PHASE_1.jpg'

DISCRETE_4PHASE_2 = '/YOURFOLDER/DISCRETE_4PHASE_2.jpg'

DISCRETE_4PHASE_3 = '/YOURFOLDER/DISCRETE_4PHASE_3.jpg'

DISCRETE_4PHASE_4 = '/YOURFOLDER/DISCRETE_4PHASE_4.jpg'

CONTINUOUS_PHASE = '/YOURFOLDER/CONTINUOUS_PHASE.jpg'

#=======================math==============================================

def ampl(x):

return np.sqrt(x.real*x.real+x.imag*x.imag)

def absdiff(array1,array2):

#returns the absolut difference of two arrays in form of a new array

diff = np.zeros_like(array1)

for i in range(len(diff)):

for j in range(len(diff[1])):

diff[i][j]= array1[i][j]-array2[i][j]

plt.figure()

plt.imshow(diff)

plt.colorbar()

plt.title("Diff")

return diff

def gaussian(x, mu,sig):

return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))

def gauss(sizey,sizex,fac_mu):

x = np.linspace(0, sizex, sizex)

y = np.linspace(0, sizey, sizey)

X, Y = np.meshgrid(x, y)

pos = np.dstack((X, Y))

mu = np.array([sizex/2, sizey/2])

cov = np.array([[sizex*fac_mu,0],[0, sizey*fac_mu]])

rv = multivariate_normal(mu, cov)

Z = rv.pdf(pos)

return Z

#=======================image==============================================

def con2bw(image):

image_gray = np.mean(image, -1)

image_bw = np.zeros_like(image_gray)

for i in range(len(image_gray)):

for j in range(len(image_gray[i])):

if image_gray[i][j]<0.5: image_bw [i][j]= 0

if image_gray[i][j]>=0.5: image_bw[i][j] = 1

return image_bw

def plot_amplitude(im):

plt.figure()

from matplotlib.colors import LogNorm

plt.imshow(np.abs(im), norm=LogNorm(vmin=5))

plt.colorbar

plt.title("FFT Amplitude Image")

def argand(a):

plt.figure()

for i in range (len(a)):

for x in range(len(a[i])):

plt.polar([0,normalize(r2d(cm.phase(a[i][x])),0,360)],[0,abs(a[i][x])],marker='o')

plt.title("Phase")

plt.show()

def plot3D(array):

import matplotlib.pyplot as plt

import numpy as np

np.random.seed(1234)

fig = plt.figure()

ax1 = fig.add_subplot(111, projection='3d')

A = array-3.0

x = np.array([[i] * len(array[1]) for i in range(len(array))]).ravel()

y = np.array([i for i in range(len(array[1]))] * len(array))

z = np.zeros(len(array)*len(array[1]))

dx = np.ones(len(array)*len(array[1]))

dy = np.ones(len(array)*len(array[1]))

dz = A.ravel()

ax1.bar3d(x, y, z, dx, dy, dz)

#=======================GSA==============================================

def gsa(source,target,n):

a = np.fft.ifftshift(np.fft.ifft2(np.fft.fftshift(target)))

phase_a = np.zeros_like(target)

b = np.complex128(np.zeros_like(target))

phase_c = np.zeros_like(target)

c = np.complex128(np.zeros_like(target))

d = np.complex128(np.zeros_like(target))

retrieved_phase = np.zeros_like(target)

for z in range(n):

for i in range(len(source)):

for j in range(len(source[i])):

phase_a[i][j] = cm.phase(a[i][j])

b = np.multiply(source, np.exp(1j*phase_a))

c = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(b)))

for i in range(len(source)):

for j in range(len(source[i])):

phase_c[i][j] = cm.phase(c[i][j])

d = np.multiply(ampl(target), np.exp(1j*phase_c))

a = np.fft.ifftshift(np.fft.ifft2(np.fft.fftshift(d)))

print(z)

for i in range(len(source)):

for j in range(len(source[i])):

retrieved_phase[i][j] = normalize(r2d(cm.phase(a[i][j])),0,360)

return retrieved_phase

#=======================quantisation==============================================

def storeSeperate(retrieved_phase,n_sep):

plt.figure()

if(n_sep==1):

plt.imsave(CONTINUOUS_PHASE,retrieved_phase, cmap='gray')

plt.imshow(retrieved_phase)

if(n_sep==2):

phase = np.zeros_like(retrieved_phase)

for i in range(len(retrieved_phase)):

for j in range(len(retrieved_phase[i])):

if( abs(retrieved_phase[i][j]) > 180):

phase[i][j]=1

else:

phase[i][j]=0

plt.imshow(phase)

plt.imsave(DISCRETE_2PHASE,phase, cmap='gray')

if(n_sep==4):

phase1 = np.zeros_like(retrieved_phase)

phase2 = np.zeros_like(retrieved_phase)

phase3 = np.zeros_like(retrieved_phase)

phase4 = np.zeros_like(retrieved_phase)

for i in range(len(retrieved_phase)):

for j in range(len(retrieved_phase[i])):

if( abs(retrieved_phase[i][j]) > 270):

phase4[i][j]=1

elif(abs(retrieved_phase[i][j]) > 180):

phase3[i][j]=1

elif(abs(retrieved_phase[i][j]) > 90):

phase2[i][j]=1

else:

phase1[i][j]=1

plt.imshow(phase1)

plt.imsave(DISCRETE_4PHASE_4,phase4, cmap='gray')

plt.imsave(DISCRETE_4PHASE_3,phase3, cmap='gray')

plt.imsave(DISCRETE_4PHASE_2,phase2, cmap='gray')

plt.imsave(DISCRETE_4PHASE_1,phase1, cmap='gray')

plt.title("saved discretisation")

#=======================main==============================================

image = plt.imread(IMAGE_FILE).astype(float)

plt.figure()

plt.imshow(image)

plt.title("original")

target = con2bw(image)

if(SOURCE=='gauss'):

source = gauss(len(target),len(target[1]),FAC_MU)

else:

source = np.ones_like(target)/(len(target)*len(target))

plt.figure()

plt.imshow(source)

plt.title("source")

retrieved_phase = gsa(source,target,INTERATIONS)

plt.figure()

plt.imshow(retrieved_phase)

plt.title("retrieved phase / no discretisation")

#=======================holores==============================================

out = np.zeros_like(source)

if(NUMBER_OF_PHASES==2):

phase = np.zeros_like(retrieved_phase)

for i in range(len(retrieved_phase)):

for j in range(len(retrieved_phase[i])):

if( abs(retrieved_phase[i][j]) > 180):

phase[i][j]=180

else:

phase[i][j]=0

holo1 = np.complex128(source)

for i in range(len(source)):

for j in range(len(source[i])):

holo1[i][j]= source[i][j] * np.exp(1j*phase[i][j]/360*cm.pi*2)

holo2 = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(holo1)))

for i in range(len(holo1)):

for j in range(len(holo2[i])):

out[i][j] = ampl(holo2[i][j])

if(NUMBER_OF_PHASES==4):

phase1 = np.zeros_like(retrieved_phase)

phase2 = np.zeros_like(retrieved_phase)

phase3 = np.zeros_like(retrieved_phase)

phase4 = np.zeros_like(retrieved_phase)

for i in range(len(retrieved_phase)):

for j in range(len(retrieved_phase[i])):

if( abs(retrieved_phase[i][j]) > 270):

phase4[i][j]=1

elif(abs(retrieved_phase[i][j]) > 180):

phase3[i][j]=1

elif(abs(retrieved_phase[i][j]) > 90):

phase2[i][j]=1

else:

phase1[i][j]=1

holo = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(source*np.exp(1j*(((phase1*90)+phase2*180+phase3*270+phase4*360)/360*3.1415*2)))))

for i in range(len(holo)):

for j in range(len(holo[i])):

out[i][j] = np.sqrt(holo[i][j].real*holo[i][j].real+holo[i][j].imag*holo[i][j].imag)

storeSeperate(retrieved_phase,NUMBER_OF_PHASES)

if(NUMBER_OF_PHASES==4 or NUMBER_OF_PHASES==2):

plt.figure()

plt.imshow(out)

plt.title("output of discretisation")

else:

holo1 = np.complex128(source)

for i in range(len(source)):

for j in range(len(source[i])):

holo1[i][j]= source[i][j] * np.exp(1j*retrieved_phase[i][j]/360*cm.pi*2)

holo2 = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(holo1)))

for i in range(len(holo1)):

for j in range(len(holo2[i])):

out[i][j] = ampl(holo2[i][j])

plt.figure()

plt.imshow(out)

plt.title("output without discretisation")