"""
inspired by these seminal references:
[1] G. N. Ramachandran and R. Srinivasan, "An apparent paradox in crystal structure analysis," Nature 190, 159-161 (1961)
<https://dx.doi.org/10.1038/190159a0>
[2] A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proceedings of the IEEE 69, 529-541 (1981)
<https://dx.doi.org/10.1109/PROC.1981.12022>
[3] R. J. Read, "Model phases: probabilities and bias," Methods in Enzymology 277, 110-128 (1997)
<https://dx.doi.org/10.1016/S0076-6879(97)77009-5>
for a slightly contrarian view on the relative importance of phases vs. amplitudes, see:
[4] I. Juvells et al, "The role of amplitude and phase of the Fourier transform in the digital image processing," Am. J. Phys. 59, 744 (1991)
<https://dx.doi.org/10.1119/1.16754>
[5] A. W. Lohmann et al, "Significance of phase and amplitude in the Fourier domain," J. Opt. Soc. Am. A 14, 2901 (1997)
<https://dx.doi.org/10.1364/JOSAA.14.002901>
note that the "counterexamples" cited in references [4] and [5] seem cherrypicked and certainly irrelevant to crystallography
"""
# generate random uniform distributions of amplitudes and phases using min/max of genuine arrays as upper and lower bounds
random_amps1 = np.random.uniform(low=np.min(img1_amplitude), high=np.max(img1_amplitude), size=np.shape(img1_amplitude))
random_amps2 = np.random.uniform(low=np.min(img2_amplitude), high=np.max(img2_amplitude), size=np.shape(img2_amplitude))
random_phases1 = np.random.uniform(low=np.min(img1_phase), high=np.max(img1_phase), size=np.shape(img1_phase))
random_phases2 = np.random.uniform(low=np.min(img2_phase), high=np.max(img2_phase), size=np.shape(img2_phase))
"""
# generate random gaussian distributions of amplitudes and phases using mean/std dev of genuine arrays as input parameters
random_amps1 = np.random.normal(loc=np.mean(img1_amplitude), scale=np.std(img1_amplitude), size=np.shape(img1_amplitude))
random_amps2 = np.random.normal(loc=np.mean(img2_amplitude), scale=np.std(img2_amplitude), size=np.shape(img2_amplitude))
random_phases1 = np.random.normal(loc=np.mean(img1_phase), scale=np.std(img1_phase), size=np.shape(img1_phase))
random_phases2 = np.random.normal(loc=np.mean(img2_phase), scale=np.std(img2_phase), size=np.shape(img2_phase))
"""
# reconstruct image from amplitudes of image 1 and random phases
img1_rand1_comb = np.multiply(img1_amplitude, np.exp(1j * random_phases1))
img1amp_rand1phase = np.abs(np.fft.ifft2(np.fft.ifftshift(img1_rand1_comb)))
shift5 = img1amp_rand1phase + np.min(img1amp_rand1phase)
shift5[shift5 > 255] = 255
img1amp_rand1phase[img1amp_rand1phase > 255] = 255
img1amp_rand1phase[img1amp_rand1phase < 0] = 0
# reconstruct image from phases of image 1 and random amplitudes
img1_rand2_comb = np.multiply(random_amps1, np.exp(1j * img1_phase))
rand1amp_img1phase = np.abs(np.fft.ifft2(np.fft.ifftshift(img1_rand2_comb)))
shift6 = rand1amp_img1phase + np.min(rand1amp_img1phase)
shift6[shift6 > 255] = 255
rand1amp_img1phase[rand1amp_img1phase > 255] = 255
rand1amp_img1phase[rand1amp_img1phase < 0] = 0
# reconstruct image from amplitudes of image 2 and random phases
img2_rand1_comb = np.multiply(img2_amplitude, np.exp(1j * random_phases2))
img2amp_rand2phase = np.abs(np.fft.ifft2(np.fft.ifftshift(img2_rand1_comb)))
shift7 = img2amp_rand2phase + np.min(img2amp_rand2phase)
shift7[shift7 > 255] = 255
img2amp_rand2phase[img2amp_rand2phase > 255] = 255
img2amp_rand2phase[img2amp_rand2phase < 0] = 0
# reconstruct image from phases of image 2 and random amplitudes
img2_rand2_comb = np.multiply(random_amps2, np.exp(1j * img2_phase))
rand2amp_img2phase = np.abs(np.fft.ifft2(np.fft.ifftshift(img2_rand2_comb)))
shift8 = rand2amp_img2phase + np.min(rand2amp_img2phase)
shift8[shift8 > 255] = 255
rand2amp_img2phase[rand2amp_img2phase > 255] = 255
rand2amp_img2phase[rand2amp_img2phase < 0] = 0
# plot reconstructions
rows = 2
columns = 2
fig = plt.figure(figsize=(10, 10))
plt.tight_layout()
fig.add_subplot(rows, columns, 1)
plt.imshow(img1amp_rand1phase, cmap='gray')
plt.axis('off')
plt.title(r"Image 1's amplitudes + random phases")
fig.add_subplot(rows, columns, 2)
plt.imshow(rand1amp_img1phase, cmap='gray')
plt.axis('off')
plt.title(r"Random amplitudes + image 1's phases")
fig.add_subplot(rows, columns, 3)
plt.imshow(img2amp_rand2phase, cmap='gray')
plt.axis('off')
plt.title(r"Image 2's amplitudes + random phases")
fig.add_subplot(rows, columns, 4)
plt.imshow(rand2amp_img2phase, cmap='gray')
plt.axis('off')
plt.title(r"Random amplitudes + image 2's phases")
plt.show()
