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Added off-axis propagation, SPIE scripts
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import numpy as np
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import os
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import sys
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sys.path.insert(0, '/Users/joost/Dropbox/Werk/PhD/Analyses/Python/Analytical/Fourier Optics')
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from fourierOptics import *
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'''
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Author: Joost van den Born, PhD student at University of Groningen
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Contact: born@astro.rug.nl
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Description: Script to analyse the shift of the PSF centroid as a
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function of the RMS value of the WFE.
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Script made for the SPIE manuscript.
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'''
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if __name__ == '__main__':
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plt.rc('font', family='serif')
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plt.rc('axes', labelsize='large')
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# Pick a wavelength
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l = 1.49e-3
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input_field_location = './data/ADC_input_field_1001x1001_1.49_onaxis_circular.pkl'
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# Initializing MICADO paraxial model
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mcd = ParaxialMICADO(n=1001, m=1001, dpix=160, entrance_pupil='open')
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# Propagation of the unperturbed system.
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Exyz_og, xp, yp = mcd.propagate(l=l,surface=-1, zoom=False, show=False,
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print_progress=False, hx=0, hy=0,
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load_up_to_adc=input_field_location)
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# Generate the wavefront error that will be used.
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wfe = WavefrontError(mcd.n,mcd.m)
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wfe.generate_height_map(5e-5, 2, 1) # 50 nm RMS for standard, power slope 2, cut-off 1
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h_data = wfe.data
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# Plotting the WFE, PSD and image planes
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oC = [np.min(xp), np.max(xp), np.min(yp), np.max(yp)]
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# Mask out areas where the ADC prism isn't
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_, xadc, yadc = mcd.propagate(l=l,surface=3, zoom=False, show=False,
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print_progress=True, hx=0, hy=0)
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mask = np.sqrt(xadc**2 + yadc**2) > 62.5
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# Setting up empty lists for fitting process
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popt_airy_list, popt_cust_list = [], []
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pcov_airy_list, custom_var_list = [], []
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Exyzlist, PSDlist, surfacelist = [], [], []
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central_frequencies = []
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# Bins in LogSpace
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x = mcd.x
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flist = np.asarray([0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 25,
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30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 120, 140, 160, 180, 200,
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220, 250, 280, 310, 340, 370, 400, 450, 500])
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plt.imshow(wfe.data*1e6, cmap='jet');plt.colorbar();plt.show()
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###############################
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### Lowpass filter analysis ###
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###############################
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# Do the analysis for each frequency in flist
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for fmax in flist:
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print('Lowpass filter - Freq.: {} - Sample {:02d}/{:02d}'.format(fmax, flist.tolist().index(fmax) + 1, len(flist) ) )
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if fmax == flist[0]:
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wfe.set_lowpass_filter(fmax)
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else:
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i = flist.tolist().index(fmax) - 1
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wfe.set_lowpass_filter(flist[i])
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scal = wfe.filteredData
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# Adding the wavefront error
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mcd.ELT_ADC.p1.add_wavefront_error(scal)
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# Performing the propagation using Fresnel approximation to the focal plane.
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Exyz_psd,xp,yp = mcd.propagate(l=l,surface=-1, zoom=False, show=False,
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print_progress=False, hx=0, hy=0,
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load_up_to_adc=input_field_location)
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# Set up fitting object
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psfFit_psd = PSFFitter(xp.real,yp.real,np.abs(Exyz_psd)**2)
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# Fit airy pattern and coupling integral
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amplitude_guess = np.max(np.abs(Exyz_psd))**2
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airyFitted, popt_airy, pcov_airy = psfFit_psd.fit_airy_PSF(initialGuess=(amplitude_guess, 0.0, 0.0, 0.0, 0.03))
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popt_airy_list.append(popt_airy)
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pcov_airy_list.append([ np.sqrt(pcov_airy[i][i]) for i in range(len(pcov_airy)) ])
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# Other properties
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original_PSD_curve = wfe.PSD2D[int((mcd.n-1)/2),int((mcd.n-1)/2):]
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wfe.calculate_1D_PSD(filteredDataFlag=True)
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PSDlist.append(wfe.filteredPSD2D[int((mcd.n-1)/2),int((mcd.n-1)/2):])
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surfacelist.append(wfe.filteredData)
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# Plot of the surface profile
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fig2 = plt.figure(figsize=(12,3))
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axi1 = fig2.add_subplot(1, 3, 1)
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wavefrontmap = wfe.filteredData.copy()*1e6
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wavefrontmap[mask] = np.nan
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imi1 = axi1.imshow(wavefrontmap, cmap='jet', origin='lower', extent=[xadc.min(), xadc.max(), yadc.min(), yadc.max()])
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axi1.set_xlabel('x (mm)')
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axi1.set_ylabel('y (mm)')
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axi1.set_xlim([-65,65])
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axi1.set_ylim([-65,65])
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fig2.colorbar(imi1, ax=axi1, label='Surface height (nm)')
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# Plot of the PSD
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axi2 = fig2.add_subplot(1, 3, 2)
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axi2.loglog(original_PSD_curve, 'k-')
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axi2.loglog(PSDlist[-1], 'y-')
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axi2.grid(which='major', alpha=0.3)
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axi2.grid(which='minor', alpha=0.1)
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axi2.set_xlabel('Normalized Radial Frequency ($\\rho/\\rho_c$)')
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axi2.set_ylabel('PSD (mm$^4$)')
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# Plot of the PSF
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axi3 = fig2.add_subplot(1, 3, 3)
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differential_amplitude = np.abs(Exyz_og) - np.abs(Exyz_psd)
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if (differential_amplitude == 0).all():
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norm_par = None
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else:
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norm_par = LogNorm()
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imi3 = axi3.imshow(differential_amplitude, extent=oC, cmap='gray', origin='lower', norm=norm_par)
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fig2.colorbar(imi3, ax=axi3, label='Differential amplitude')
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axi3.set_xlim([-1,1])
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axi3.set_ylim([-1,1])
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axi3.set_xlabel('x (mm)')
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axi3.set_ylabel('y (mm)')
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plt.tight_layout()
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plt.savefig('./figures/wfe_frequency_analysis/lowpass_spatial_freq_{:.0f}.png'.format(flist.tolist().index(fmax) + 1), bbox_inches='tight', transparent=True)
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plt.close()
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# Optimum fit parameters for all scaled surface errors
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amplitude_airy, x0_airy, y0_airy, R_airy, offset_airy = np.asarray(popt_airy_list).T
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amplitude_airy_err, x0_airy_err, y0_airy_err, R_airy_err, offset_airy_err = np.asarray(pcov_airy_list).T
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# Distance from original centroid at (0,0)
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r_airy = np.sqrt(x0_airy**2+y0_airy**2)
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r_err_airy = np.sqrt( (x0_airy**2*x0_airy_err**2+y0_airy**2*y0_airy_err**2) / (x0_airy**2+y0_airy**2))
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r_airy_mas = r_airy * mcd.platescale * 1000
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r_err_airy_mas = r_err_airy * mcd.platescale * 1000
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save_variable('./data/lowpass_frequency_filter_airy_distance.pkl', (r_airy, r_err_airy))
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save_variable('./data/lowpass_frequency_filter_airy_locations.pkl', (x0_airy, y0_airy, x0_airy_err, y0_airy_err))
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print('Platescale in mas/mm: ', mcd.platescale * 1000)
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################################
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### Bandpass filter analysis ###
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################################
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# Setting up empty lists for fitting process
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popt_airy_list, popt_cust_list = [], []
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pcov_airy_list, custom_var_list = [], []
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Exyzlist, PSDlist, surfacelist = [], [], []
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central_frequencies = []
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# Do the analysis for each frequency in flist
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for fmax in flist:
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print('Bandpass - Freq.: {} - Sample {:02d}/{:02d}'.format(fmax, flist.tolist().index(fmax) + 1, len(flist) ) )
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if fmax == flist[0]:
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# Use a lowpass filter only for the very first element in flist
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wfe.set_lowpass_filter(fmax)
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central_frequencies.append(fmax)
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else:
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# Set a bandpass between the current and previous frequency element
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i = flist.tolist().index(fmax) - 1
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wfe.set_bandpass_filter(flist[i], fmax)
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central_frequencies.append(np.mean([flist[i],fmax]))
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# Adding the wavefront error
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scal = wfe.filteredData
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mcd.ELT_ADC.p1.add_wavefront_error(scal)
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# Performing the propagation using Fresnel approximation to the focal plane.
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Exyz_psd,xp,yp = mcd.propagate(l=l,surface=-1, zoom=False, show=False,
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print_progress=False, hx=0, hy=0,
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load_up_to_adc=input_field_location)
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# Set up fitting object
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psfFit_psd = PSFFitter(xp.real,yp.real,np.abs(Exyz_psd)**2)
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# Fit airy pattern and coupling integral
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amplitude_guess = np.max(np.abs(Exyz_psd))**2
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airyFitted, popt_airy, pcov_airy = psfFit_psd.fit_airy_PSF(initialGuess=(amplitude_guess, 0.0, 0.0, 0.0, 0.03))
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popt_airy_list.append(popt_airy)
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pcov_airy_list.append([ np.sqrt(pcov_airy[i][i]) for i in range(len(pcov_airy)) ])
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# Other properties
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original_PSD_curve = wfe.PSD2D[int((mcd.n-1)/2),int((mcd.n-1)/2):]
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wfe.calculate_1D_PSD(filteredDataFlag=True)
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PSDlist.append(wfe.filteredPSD2D[int((mcd.n-1)/2),int((mcd.n-1)/2):])
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surfacelist.append(wfe.filteredData)
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# Plot of the surface profile
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fig2 = plt.figure(figsize=(12,3))
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axi1 = fig2.add_subplot(1, 3, 1)
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wavefrontmap = wfe.filteredData.copy()*1e6
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wavefrontmap[mask] = np.nan
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imi1 = axi1.imshow(wavefrontmap, cmap='jet', origin='lower', extent=[xadc.min(), xadc.max(), yadc.min(), yadc.max()])
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axi1.set_xlabel('x (mm)')
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axi1.set_ylabel('y (mm)')
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axi1.set_xlim([-65,65])
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axi1.set_ylim([-65,65])
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fig2.colorbar(imi1, ax=axi1, label='Surface height (nm)')
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# Plot of the PSD
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axi2 = fig2.add_subplot(1, 3, 2)
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axi2.loglog(original_PSD_curve, 'k-')
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axi2.loglog(PSDlist[-1], 'y-')
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axi2.grid(which='major', alpha=0.3)
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axi2.grid(which='minor', alpha=0.1)
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axi2.set_xlabel('Normalized Radial Frequency ($\\rho/\\rho_c$)')
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axi2.set_ylabel('PSD (mm$^4$)')
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# Plot of the PSF
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axi3 = fig2.add_subplot(1, 3, 3)
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differential_amplitude = np.abs(Exyz_og) - np.abs(Exyz_psd)
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if (differential_amplitude == 0).all():
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norm_par = None
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else:
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norm_par = LogNorm()
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imi3 = axi3.imshow(differential_amplitude, extent=oC, cmap='gray', origin='lower', norm=norm_par)
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fig2.colorbar(imi3, ax=axi3, label='Differential amplitude')
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axi3.set_xlim([-1,1])
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axi3.set_ylim([-1,1])
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axi3.set_xlabel('x (mm)')
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axi3.set_ylabel('y (mm)')
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plt.tight_layout()
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plt.savefig('./figures/wfe_frequency_analysis/bandpass_spatial_freq_{:.0f}.png'.format(flist.tolist().index(fmax) + 1), bbox_inches='tight', transparent=True)
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plt.close()
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# Optimum fit parameters for all scaled surface errors
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amplitude_airy, x0_airy, y0_airy, R_airy, offset_airy = np.asarray(popt_airy_list).T
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amplitude_airy_err, x0_airy_err, y0_airy_err, R_airy_err, offset_airy_err = np.asarray(pcov_airy_list).T
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# Distance from original centroid at (0,0)
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r_airy = np.sqrt(x0_airy**2+y0_airy**2)
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r_err_airy = np.sqrt( (x0_airy**2*x0_airy_err**2+y0_airy**2*y0_airy_err**2) / (x0_airy**2+y0_airy**2))
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r_airy_mas = r_airy * mcd.platescale * 1000
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r_err_airy_mas = r_err_airy * mcd.platescale * 1000
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save_variable('./data/bandpass_frequency_filter_airy_distance.pkl', (r_airy, r_err_airy))
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save_variable('./data/bandpass_frequency_filter_airy_locations.pkl', (x0_airy, y0_airy, x0_airy_err, y0_airy_err))
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save_variable('./data/bandpass_frequency_filter_central_frequencies.pkl', central_frequencies)
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print('Platescale in mas/mm: ', mcd.platescale * 1000)
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