def convertToMultiFit(i3data, x_size, y_size, frame, nm_per_pixel, inverted=False): """ Create a 3D-DAOSTORM, sCMOS or Spliner analysis compatible peak array from I3 data. Notes: (1) This uses the non-drift corrected positions. (2) This sets the initial fitting error to zero and the status to RUNNING. """ i3data = maskData(i3data, (i3data['fr'] == frame)) peaks = numpy.zeros((i3data.size, utilC.getNPeakPar())) peaks[:,utilC.getBackgroundIndex()] = i3data['bg'] peaks[:,utilC.getHeightIndex()] = i3data['h'] peaks[:,utilC.getZCenterIndex()] = i3data['z'] * 0.001 if inverted: peaks[:,utilC.getXCenterIndex()] = y_size - i3data['x'] peaks[:,utilC.getYCenterIndex()] = x_size - i3data['y'] ax = i3data['ax'] ww = i3data['w'] peaks[:,utilC.getYWidthIndex()] = 0.5*numpy.sqrt(ww*ww/ax)/nm_per_pixel peaks[:,utilC.getXWidthIndex()] = 0.5*numpy.sqrt(ww*ww*ax)/nm_per_pixel else: peaks[:,utilC.getYCenterIndex()] = i3data['x'] - 1 peaks[:,utilC.getXCenterIndex()] = i3data['y'] - 1 ax = i3data['ax'] ww = i3data['w'] peaks[:,utilC.getXWidthIndex()] = 0.5*numpy.sqrt(ww*ww/ax)/nm_per_pixel peaks[:,utilC.getYWidthIndex()] = 0.5*numpy.sqrt(ww*ww*ax)/nm_per_pixel return peaks
def __init__(self, parameters): # Initialized from parameters. self.find_max_radius = parameters.getAttr("find_max_radius", 5) # Radius (in pixels) over which the maxima is maximal. self.iterations = parameters.getAttr("iterations") # Maximum number of cycles of peak finding, fitting and subtraction to perform. self.sigma = parameters.getAttr("sigma") # Peak sigma (in pixels). self.threshold = parameters.getAttr("threshold") # Peak minimum threshold (height, in camera units). self.z_value = parameters.getAttr("z_value", 0.0) # The starting z value to use for peak fitting. # Other member variables. self.background = None # Current estimate of the image background. self.image = None # The original image. self.margin = PeakFinderFitter.margin # Size of the unanalyzed "edge" around the image. self.neighborhood = PeakFinder.unconverged_dist * self.sigma # Radius for marking neighbors as unconverged. self.new_peak_radius = PeakFinder.new_peak_dist # Minimum allowed distance between new peaks and current peaks. self.parameters = parameters # Keep access to the parameters object. self.peak_locations = None # Initial peak locations, as explained below. self.peak_mask = None # Mask for limiting peak identification to a particular AOI. self.taken = None # Spots in the image where a peak has already been added. # # This is for is you already know where your want fitting to happen, as # for example in a bead calibration movie and you just want to use the # approximate locations as inputs for fitting. # # peak_locations is a text file with the peak x, y, height and background # values as white spaced columns (x and y positions are in pixels as # determined using visualizer). # # 1.0 2.0 1000.0 100.0 # 10.0 5.0 2000.0 200.0 # ... # if parameters.hasAttr("peak_locations"): print("Using peak starting locations specified in", parameters.getAttr("peak_locations")) # Only do one cycle of peak finding as we'll always return the same locations. if (self.iterations != 1): print("WARNING: setting number of iterations to 1!") self.iterations = 1 # Load peak x,y locations. peak_locs = numpy.loadtxt(parameters.getAttr("peak_locations"), ndmin = 2) print(peak_locs.shape) # Create peak array. self.peak_locations = numpy.zeros((peak_locs.shape[0], utilC.getNPeakPar())) self.peak_locations[:,utilC.getXCenterIndex()] = peak_locs[:,1] + self.margin self.peak_locations[:,utilC.getYCenterIndex()] = peak_locs[:,0] + self.margin self.peak_locations[:,utilC.getHeightIndex()] = peak_locs[:,2] self.peak_locations[:,utilC.getBackgroundIndex()] = peak_locs[:,3] self.peak_locations[:,utilC.getXWidthIndex()] = numpy.ones(peak_locs.shape[0]) * self.sigma self.peak_locations[:,utilC.getYWidthIndex()] = numpy.ones(peak_locs.shape[0]) * self.sigma
def getPeaks(self, threshold, margin): """ Extract peaks from the deconvolved image and create an array that can be used by a peak fitter. FIXME: Need to compensate for up-sampling parameter in x,y. """ fx = self.getXVector() # Get area, position, height. fd_peaks = fdUtil.getPeaks(fx, threshold, margin) num_peaks = fd_peaks.shape[0] peaks = numpy.zeros((num_peaks, utilC.getNPeakPar())) peaks[:, utilC.getXWidthIndex()] = numpy.ones(num_peaks) peaks[:, utilC.getYWidthIndex()] = numpy.ones(num_peaks) peaks[:, utilC.getXCenterIndex()] = fd_peaks[:, 2] peaks[:, utilC.getYCenterIndex()] = fd_peaks[:, 1] # Calculate height. # # FIXME: Typically the starting value for the peak height will be # under-estimated unless a large enough number of FISTA # iterations is performed to completely de-convolve the image. # h_index = utilC.getHeightIndex() #peaks[:,h_index] = fd_peaks[:,0] for i in range(num_peaks): peaks[i, h_index] = fd_peaks[i, 0] * self.psf_heights[int( round(fd_peaks[i, 3]))] # Calculate z (0.0 - 1.0). if (fx.shape[2] > 1): peaks[:, utilC.getZCenterIndex()] = fd_peaks[:, 3] / ( float(fx.shape[2]) - 1.0) # Background term calculation. bg_index = utilC.getBackgroundIndex() for i in range(num_peaks): ix = int(round(fd_peaks[i, 1])) iy = int(round(fd_peaks[i, 2])) peaks[i, bg_index] = self.background[ix, iy] return peaks
def convertToMultiFit(i3data, x_size, y_size, frame, nm_per_pixel, inverted=False): """ Create a 3D-DAOSTORM, sCMOS or Spliner analysis compatible peak array from I3 data. Notes: (1) This uses the non-drift corrected positions. (2) This sets the initial fitting error to zero and the status to RUNNING. """ i3data = maskData(i3data, (i3data['fr'] == frame)) peaks = numpy.zeros((i3data.size, utilC.getNPeakPar())) peaks[:, utilC.getBackgroundIndex()] = i3data['bg'] peaks[:, utilC.getHeightIndex()] = i3data['h'] peaks[:, utilC.getZCenterIndex()] = i3data['z'] * 0.001 if inverted: peaks[:, utilC.getXCenterIndex()] = y_size - i3data['x'] peaks[:, utilC.getYCenterIndex()] = x_size - i3data['y'] ax = i3data['ax'] ww = i3data['w'] peaks[:, utilC.getYWidthIndex()] = 0.5 * numpy.sqrt( ww * ww / ax) / nm_per_pixel peaks[:, utilC.getXWidthIndex()] = 0.5 * numpy.sqrt( ww * ww * ax) / nm_per_pixel else: peaks[:, utilC.getYCenterIndex()] = i3data['x'] - 1 peaks[:, utilC.getXCenterIndex()] = i3data['y'] - 1 ax = i3data['ax'] ww = i3data['w'] peaks[:, utilC.getXWidthIndex()] = 0.5 * numpy.sqrt( ww * ww / ax) / nm_per_pixel peaks[:, utilC.getYWidthIndex()] = 0.5 * numpy.sqrt( ww * ww * ax) / nm_per_pixel return peaks
def psfLocalizations(i3_filename, mapping_filename, frame = 1, aoi_size = 8, movie_filename = None): # Load localizations. i3_reader = readinsight3.I3Reader(i3_filename) # Load mapping. mappings = {} if os.path.exists(mapping_filename): with open(mapping_filename, 'rb') as fp: mappings = pickle.load(fp) else: print("Mapping file not found, single channel data?") # Try and determine movie frame size. i3_metadata = readinsight3.loadI3Metadata(i3_filename) if i3_metadata is None: if movie_filename is None: raise Exception("I3 metadata not found and movie filename is not specified.") else: movie_fp = datareader.inferReader(movie_filename) [movie_y, movie_x] = movie_fp.filmSize()[:2] else: movie_data = i3_metadata.find("movie") # FIXME: These may be transposed? movie_x = int(movie_data.find("movie_x").text) movie_y = int(movie_data.find("movie_y").text) # Load localizations in the requested frame. locs = i3_reader.getMoleculesInFrame(frame) print("Loaded", locs.size, "localizations.") # Remove localizations that are too close to each other. in_locs = numpy.zeros((locs["x"].size, util_c.getNPeakPar())) in_locs[:,util_c.getXCenterIndex()] = locs["x"] in_locs[:,util_c.getYCenterIndex()] = locs["y"] out_locs = util_c.removeNeighbors(in_locs, 2 * aoi_size) xf = out_locs[:,util_c.getXCenterIndex()] yf = out_locs[:,util_c.getYCenterIndex()] # # Remove localizations that are too close to the edge or # outside of the image in any of the channels. # is_good = numpy.ones(xf.size, dtype = numpy.bool) for i in range(xf.size): # Check in Channel 0. if (xf[i] < aoi_size) or (xf[i] + aoi_size >= movie_x): is_good[i] = False continue if (yf[i] < aoi_size) or (yf[i] + aoi_size >= movie_y): is_good[i] = False continue # Check other channels. for key in mappings: if not is_good[i]: break coeffs = mappings[key] [ch1, ch2, axis] = key.split("_") if (ch1 == "0"): if (axis == "x"): xm = coeffs[0] + coeffs[1]*xf[i] + coeffs[2]*yf[i] if (xm < aoi_size) or (xm + aoi_size >= movie_x): is_good[i] = False break elif (axis == "y"): ym = coeffs[0] + coeffs[1]*xf[i] + coeffs[2]*yf[i] if (ym < aoi_size) or (ym + aoi_size >= movie_y): is_good[i] = False break # # Save localizations for each channel. # gx = xf[is_good] gy = yf[is_good] basename = os.path.splitext(i3_filename)[0] with writeinsight3.I3Writer(basename + "_c1_psf.bin") as w3: w3.addMoleculesWithXY(gx, gy) index = 1 while ("0_" + str(index) + "_x" in mappings): cx = mappings["0_" + str(index) + "_x"] cy = mappings["0_" + str(index) + "_y"] #cx = mappings[str(index) + "_0" + "_x"] #cy = mappings[str(index) + "_0" + "_y"] xm = cx[0] + cx[1] * gx + cx[2] * gy ym = cy[0] + cy[1] * gx + cy[2] * gy with writeinsight3.I3Writer(basename + "_c" + str(index+1) + "_psf.bin") as w3: w3.addMoleculesWithXY(xm, ym) index += 1 # # Print localizations that were kept. # print(gx.size, "localizations were kept:") for i in range(gx.size): print("ch0: {0:.2f} {1:.2f}".format(gx[i], gy[i])) index = 1 while ("0_" + str(index) + "_x" in mappings): cx = mappings["0_" + str(index) + "_x"] cy = mappings["0_" + str(index) + "_y"] xm = cx[0] + cx[1] * gx[i] + cx[2] * gy[i] ym = cy[0] + cy[1] * gx[i] + cy[2] * gy[i] print("ch" + str(index) + ": {0:.2f} {1:.2f}".format(xm, ym)) index += 1 print("") print("")
def __init__(self, parameters): """ This is called once at the start of analysis to initialize the parameters that will be used for peak fitting. parameters - A parameters object. """ # Initialized from parameters. self.find_max_radius = parameters.getAttr( "find_max_radius", 5) # Radius (in pixels) over which the maxima is maximal. self.iterations = parameters.getAttr( "iterations" ) # Maximum number of cycles of peak finding, fitting and subtraction to perform. self.sigma = parameters.getAttr("sigma") # Peak sigma (in pixels). self.threshold = parameters.getAttr( "threshold") # Peak minimum threshold (height, in camera units). self.z_value = parameters.getAttr( "z_value", 0.0) # The starting z value to use for peak fitting. # Other member variables. self.background = None # Current estimate of the image background. self.image = None # The original image. self.margin = PeakFinderFitter.margin # Size of the unanalyzed "edge" around the image. self.neighborhood = PeakFinder.unconverged_dist * self.sigma # Radius for marking neighbors as unconverged. self.new_peak_radius = PeakFinder.new_peak_dist # Minimum allowed distance between new peaks and current peaks. self.parameters = parameters # Keep access to the parameters object. self.peak_locations = None # Initial peak locations, as explained below. self.peak_mask = None # Mask for limiting peak identification to a particular AOI. self.taken = None # Spots in the image where a peak has already been added. # # This is for is you already know where your want fitting to happen, as # for example in a bead calibration movie and you just want to use the # approximate locations as inputs for fitting. # # peak_locations is a text file with the peak x, y, height and background # values as white spaced columns (x and y positions are in pixels as # determined using visualizer). # # 1.0 2.0 1000.0 100.0 # 10.0 5.0 2000.0 200.0 # ... # if parameters.hasAttr("peak_locations"): print("Using peak starting locations specified in", parameters.getAttr("peak_locations")) # Only do one cycle of peak finding as we'll always return the same locations. if (self.iterations != 1): print("WARNING: setting number of iterations to 1!") self.iterations = 1 # Load peak x,y locations. peak_locs = numpy.loadtxt(parameters.getAttr("peak_locations"), ndmin=2) print(peak_locs.shape) # Create peak array. self.peak_locations = numpy.zeros( (peak_locs.shape[0], utilC.getNPeakPar())) self.peak_locations[:, utilC.getXCenterIndex( )] = peak_locs[:, 1] + self.margin self.peak_locations[:, utilC.getYCenterIndex( )] = peak_locs[:, 0] + self.margin self.peak_locations[:, utilC.getHeightIndex()] = peak_locs[:, 2] self.peak_locations[:, utilC.getBackgroundIndex()] = peak_locs[:, 3] self.peak_locations[:, utilC.getXWidthIndex()] = numpy.ones( peak_locs.shape[0]) * self.sigma self.peak_locations[:, utilC.getYWidthIndex()] = numpy.ones( peak_locs.shape[0]) * self.sigma
ndpointer(dtype=numpy.float64), ndpointer(dtype=numpy.float64), c_double, c_int, c_int, c_int, c_int] multi.initializeZParameters.argtypes = [ndpointer(dtype=numpy.float64), ndpointer(dtype=numpy.float64), c_double, c_double] # Globals default_tol = 1.0e-6 peakpar_size = util_c.getNPeakPar() resultspar_size = util_c.getNResultsPar() ## # Helper functions. ## def calcSxSy(wx_params, wy_params, z): zx = (z - wx_params[1])/wx_params[2] sx = 0.5 * wx_params[0] * math.sqrt(1.0 + zx*zx + wx_params[3]*zx*zx*zx + wx_params[4]*zx*zx*zx*zx) zy = (z - wy_params[1])/wy_params[2] sy = 0.5 * wy_params[0] * math.sqrt(1.0 + zy*zy + wy_params[3]*zy*zy*zy + wy_params[4]*zy*zy*zy*zy) return [sx, sy] def fitStats(results): total = results.shape[0]
def measurePSF(movie_name, zfile_name, movie_mlist, psf_name, want2d=False, aoi_size=12, z_range=750.0, z_step=50.0): """ The actual z range is 2x z_range (i.e. from -z_range to z_range). """ # Load dax file, z offset file and molecule list file. dax_data = datareader.inferReader(movie_name) z_offsets = None if os.path.exists(zfile_name): try: z_offsets = numpy.loadtxt(zfile_name, ndmin=2)[:, 1] except IndexError: z_offsets = None print("z offsets were not loaded.") i3_data = readinsight3.loadI3File(movie_mlist) if want2d: print("Measuring 2D PSF") else: print("Measuring 3D PSF") # # Go through the frames identifying good peaks and adding them # to the average psf. For 3D molecule z positions are rounded to # the nearest 50nm. # z_mid = int(z_range / z_step) max_z = 2 * z_mid + 1 average_psf = numpy.zeros((max_z, 4 * aoi_size, 4 * aoi_size)) peaks_used = 0 totals = numpy.zeros(max_z) [dax_x, dax_y, dax_l] = dax_data.filmSize() for curf in range(dax_l): # Select localizations in current frame & not near the edges. mask = (i3_data['fr'] == curf + 1) & (i3_data['x'] > aoi_size) & ( i3_data['x'] < (dax_x - aoi_size - 1)) & (i3_data['y'] > aoi_size) & (i3_data['y'] < (dax_y - aoi_size - 1)) xr = i3_data['x'][mask] yr = i3_data['y'][mask] # Use the z offset file if it was specified, otherwise use localization z positions. if z_offsets is None: if (curf == 0): print("Using fit z locations.") zr = i3_data['z'][mask] else: if (curf == 0): print("Using z offset file.") zr = numpy.ones(xr.size) * z_offsets[curf] ht = i3_data['h'][mask] # Remove localizations that are too close to each other. in_peaks = numpy.zeros((xr.size, util_c.getNPeakPar())) in_peaks[:, util_c.getXCenterIndex()] = xr in_peaks[:, util_c.getYCenterIndex()] = yr in_peaks[:, util_c.getZCenterIndex()] = zr in_peaks[:, util_c.getHeightIndex()] = ht out_peaks = util_c.removeNeighbors(in_peaks, 2 * aoi_size) #out_peaks = util_c.removeNeighbors(in_peaks, aoi_size) print(curf, "peaks in", in_peaks.shape[0], ", peaks out", out_peaks.shape[0]) # Use remaining localizations to calculate spline. image = dax_data.loadAFrame(curf).astype(numpy.float64) xr = out_peaks[:, util_c.getXCenterIndex()] yr = out_peaks[:, util_c.getYCenterIndex()] zr = out_peaks[:, util_c.getZCenterIndex()] ht = out_peaks[:, util_c.getHeightIndex()] for i in range(xr.size): xf = xr[i] yf = yr[i] zf = zr[i] xi = int(xf) yi = int(yf) if want2d: zi = 0 else: zi = int(round(zf / z_step) + z_mid) # check the z is in range if (zi > -1) and (zi < max_z): # get localization image mat = image[xi - aoi_size:xi + aoi_size, yi - aoi_size:yi + aoi_size] # zoom in by 2x psf = scipy.ndimage.interpolation.zoom(mat, 2.0) # re-center image psf = scipy.ndimage.interpolation.shift( psf, (-2.0 * (xf - xi), -2.0 * (yf - yi)), mode='nearest') # add to average psf accumulator average_psf[zi, :, :] += psf totals[zi] += 1 # Force PSF to be zero (on average) at the boundaries. for i in range(max_z): edge = numpy.concatenate((average_psf[i, 0, :], average_psf[i, -1, :], average_psf[i, :, 0], average_psf[i, :, -1])) average_psf[i, :, :] -= numpy.mean(edge) # Normalize the PSF. if want2d: max_z = 1 for i in range(max_z): print(i, totals[i]) if (totals[i] > 0.0): average_psf[i, :, :] = average_psf[i, :, :] / numpy.sum( numpy.abs(average_psf[i, :, :])) average_psf = average_psf / numpy.max(average_psf) # Save PSF (in image form). if True: import storm_analysis.sa_library.daxwriter as daxwriter dxw = daxwriter.DaxWriter( os.path.join(os.path.dirname(psf_name), "psf.dax"), average_psf.shape[1], average_psf.shape[2]) for i in range(max_z): dxw.addFrame(1000.0 * average_psf[i, :, :] + 100) dxw.close() # Save PSF. if want2d: psf_dict = {"psf": average_psf[0, :, :], "type": "2D"} else: cur_z = -z_range z_vals = [] for i in range(max_z): z_vals.append(cur_z) cur_z += z_step psf_dict = { "psf": average_psf, "pixel_size": 0.080, # 1/2 the camera pixel size in nm. "type": "3D", "zmin": -z_range, "zmax": z_range, "zvals": z_vals } with open(psf_name, 'wb') as fp: pickle.dump(psf_dict, fp)
def measurePSF(movie_name, zfile_name, movie_mlist, psf_name, want2d = False, aoi_size = 12, z_range = 750.0, z_step = 50.0): """ The actual z range is 2x z_range (i.e. from -z_range to z_range). """ # Load dax file, z offset file and molecule list file. dax_data = datareader.inferReader(movie_name) z_offsets = None if os.path.exists(zfile_name): try: z_offsets = numpy.loadtxt(zfile_name, ndmin = 2)[:,1] except IndexError: z_offsets = None print("z offsets were not loaded.") i3_data = readinsight3.loadI3File(movie_mlist) if want2d: print("Measuring 2D PSF") else: print("Measuring 3D PSF") # # Go through the frames identifying good peaks and adding them # to the average psf. For 3D molecule z positions are rounded to # the nearest 50nm. # z_mid = int(z_range/z_step) max_z = 2 * z_mid + 1 average_psf = numpy.zeros((max_z,4*aoi_size,4*aoi_size)) peaks_used = 0 totals = numpy.zeros(max_z) [dax_x, dax_y, dax_l] = dax_data.filmSize() for curf in range(dax_l): # Select localizations in current frame & not near the edges. mask = (i3_data['fr'] == curf+1) & (i3_data['x'] > aoi_size) & (i3_data['x'] < (dax_x - aoi_size - 1)) & (i3_data['y'] > aoi_size) & (i3_data['y'] < (dax_y - aoi_size - 1)) xr = i3_data['x'][mask] yr = i3_data['y'][mask] # Use the z offset file if it was specified, otherwise use localization z positions. if z_offsets is None: if (curf == 0): print("Using fit z locations.") zr = i3_data['z'][mask] else: if (curf == 0): print("Using z offset file.") zr = numpy.ones(xr.size) * z_offsets[curf] ht = i3_data['h'][mask] # Remove localizations that are too close to each other. in_peaks = numpy.zeros((xr.size,util_c.getNPeakPar())) in_peaks[:,util_c.getXCenterIndex()] = xr in_peaks[:,util_c.getYCenterIndex()] = yr in_peaks[:,util_c.getZCenterIndex()] = zr in_peaks[:,util_c.getHeightIndex()] = ht out_peaks = util_c.removeNeighbors(in_peaks, 2*aoi_size) #out_peaks = util_c.removeNeighbors(in_peaks, aoi_size) print(curf, "peaks in", in_peaks.shape[0], ", peaks out", out_peaks.shape[0]) # Use remaining localizations to calculate spline. image = dax_data.loadAFrame(curf).astype(numpy.float64) xr = out_peaks[:,util_c.getXCenterIndex()] yr = out_peaks[:,util_c.getYCenterIndex()] zr = out_peaks[:,util_c.getZCenterIndex()] ht = out_peaks[:,util_c.getHeightIndex()] for i in range(xr.size): xf = xr[i] yf = yr[i] zf = zr[i] xi = int(xf) yi = int(yf) if want2d: zi = 0 else: zi = int(round(zf/z_step) + z_mid) # check the z is in range if (zi > -1) and (zi < max_z): # get localization image mat = image[xi-aoi_size:xi+aoi_size, yi-aoi_size:yi+aoi_size] # zoom in by 2x psf = scipy.ndimage.interpolation.zoom(mat, 2.0) # re-center image psf = scipy.ndimage.interpolation.shift(psf, (-2.0*(xf-xi), -2.0*(yf-yi)), mode='nearest') # add to average psf accumulator average_psf[zi,:,:] += psf totals[zi] += 1 # Force PSF to be zero (on average) at the boundaries. for i in range(max_z): edge = numpy.concatenate((average_psf[i,0,:], average_psf[i,-1,:], average_psf[i,:,0], average_psf[i,:,-1])) average_psf[i,:,:] -= numpy.mean(edge) # Normalize the PSF. if want2d: max_z = 1 for i in range(max_z): print(i, totals[i]) if (totals[i] > 0.0): average_psf[i,:,:] = average_psf[i,:,:]/numpy.sum(numpy.abs(average_psf[i,:,:])) average_psf = average_psf/numpy.max(average_psf) # Save PSF (in image form). if True: import storm_analysis.sa_library.daxwriter as daxwriter dxw = daxwriter.DaxWriter(os.path.join(os.path.dirname(psf_name), "psf.dax"), average_psf.shape[1], average_psf.shape[2]) for i in range(max_z): dxw.addFrame(1000.0 * average_psf[i,:,:] + 100) dxw.close() # Save PSF. if want2d: psf_dict = {"psf" : average_psf[0,:,:], "type" : "2D"} else: cur_z = -z_range z_vals = [] for i in range(max_z): z_vals.append(cur_z) cur_z += z_step psf_dict = {"psf" : average_psf, "pixel_size" : 0.080, # 1/2 the camera pixel size in nm. "type" : "3D", "zmin" : -z_range, "zmax" : z_range, "zvals" : z_vals} pickle.dump(psf_dict, open(psf_name, 'wb'))