487 lines
22 KiB
Python
Executable File
487 lines
22 KiB
Python
Executable File
"""
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Library function for background estimation steps of the reduction pipeline.
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prototypes :
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- display_bkg(data, background, std_bkg, headers, histograms, binning, rectangle, savename, plots_folder)
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Display and save how the background noise is computed.
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- bkg_hist(data, error, mask, headers, sub_shape, display, savename, plots_folder) -> n_data_array, n_error_array, headers, background)
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Compute the error (noise) of the input array by computing the base mode of each image.
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- bkg_mini(data, error, mask, headers, sub_shape, display, savename, plots_folder) -> n_data_array, n_error_array, headers, background)
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Compute the error (noise) of the input array by looking at the sub-region of minimal flux in every image and of shape sub_shape.
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"""
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from copy import deepcopy
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from datetime import datetime, timedelta
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from os.path import join as path_join
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import matplotlib.dates as mdates
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import matplotlib.pyplot as plt
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import numpy as np
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from astropy.time import Time
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from lib.plots import plot_obs
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from matplotlib.colors import LogNorm
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from matplotlib.patches import Rectangle
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from scipy.optimize import curve_fit
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def gauss(x, *p):
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N, mu, sigma = p
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return N * np.exp(-((x - mu) ** 2) / (2.0 * sigma**2))
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def gausspol(x, *p):
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N, mu, sigma, a, b, c, d = p
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return N * np.exp(-((x - mu) ** 2) / (2.0 * sigma**2)) + a * np.log(x) + b / x + c * x + d
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def bin_centers(edges):
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return (edges[1:] + edges[:-1]) / 2.0
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def display_bkg(data, background, std_bkg, headers, histograms=None, binning=None, coeff=None, rectangle=None, savename=None, plots_folder="./"):
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plt.rcParams.update({"font.size": 15})
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convert_flux = np.array([head["photflam"] for head in headers])
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date_time = np.array([Time((headers[i]["expstart"] + headers[i]["expend"]) / 2.0, format="mjd", precision=0).iso for i in range(len(headers))])
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date_time = np.array([datetime.strptime(d, "%Y-%m-%d %H:%M:%S") for d in date_time])
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date_err = np.array([timedelta(seconds=headers[i]["exptime"] / 2.0) for i in range(len(headers))])
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filt = np.array([headers[i]["filtnam1"] for i in range(len(headers))])
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dict_filt = {"POL0": "yo", "POL60": "bv", "POL120": "rs"}
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c_filt = np.array([dict_filt[f][0] for f in filt])
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fig, ax = plt.subplots(figsize=(10, 4), constrained_layout=True)
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ax.errorbar(date_time, background * convert_flux, xerr=date_err, yerr=std_bkg * convert_flux, fmt="+k", markersize=0, ecolor=c_filt)
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for f in np.unique(filt):
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mask = [fil == f for fil in filt]
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ax.scatter(date_time[mask], background[mask] * convert_flux[mask], color=dict_filt[f][0], marker=dict_filt[f][1], label="{0:s}".format(f))
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# Date handling
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locator = mdates.AutoDateLocator()
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formatter = mdates.ConciseDateFormatter(locator)
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ax.xaxis.set_major_locator(locator)
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ax.xaxis.set_major_formatter(formatter)
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# ax.set_ylim(bottom=0.)
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ax.set_yscale("log")
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ax.set_xlabel("Observation date and time")
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ax.set_ylabel(r"Flux [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]")
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plt.legend()
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if savename is not None:
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this_savename = deepcopy(savename)
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if savename[-4:] not in [".png", ".jpg", ".pdf"]:
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this_savename += "_background_flux.pdf"
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else:
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this_savename = savename[:-4] + "_background_flux" + savename[-4:]
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fig.savefig(path_join(plots_folder, this_savename), bbox_inches="tight", facecolor="None", edgecolor="None")
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if histograms is not None:
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filt_obs = {"POL0": 0, "POL60": 0, "POL120": 0}
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fig_h, ax_h = plt.subplots(figsize=(10, 8), constrained_layout=True)
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for i, (hist, bins) in enumerate(zip(histograms, binning)):
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filt_obs[headers[i]["filtnam1"]] += 1
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ax_h.plot(
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bins * convert_flux[i],
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hist,
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"+",
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color="C{0:d}".format(i),
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alpha=0.8,
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label=headers[i]["filtnam1"] + " (Obs " + str(filt_obs[headers[i]["filtnam1"]]) + ")",
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)
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ax_h.plot([background[i] * convert_flux[i], background[i] * convert_flux[i]], [hist.min(), hist.max()], "x--", color="C{0:d}".format(i), alpha=0.8)
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if i == 0:
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xmin, xmax = np.min(np.array(bins)[np.array(hist) > 5e1]) * convert_flux[0], np.max(np.array(bins)[np.array(hist) > 5e1]) * convert_flux[0]
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else:
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xmin, xmax = (
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min(xmin, np.min(np.array(bins)[np.array(hist) > 5e1]) * convert_flux[0]),
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max(xmax, np.max(np.array(bins)[np.array(hist) > 5e1]) * convert_flux[0]),
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)
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if coeff is not None:
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if len(coeff[i]) == 7:
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ax_h.plot(bins * convert_flux[i], gausspol(bins, *coeff[i]), "--", color="C{0:d}".format(i), alpha=0.8)
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elif len(coeff[i]) == 3:
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ax_h.plot(bins * convert_flux[i], gauss(bins, *coeff[i]), "--", color="C{0:d}".format(i), alpha=0.8)
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ax_h.set_xscale("log")
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ax_h.set_yscale("log")
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ax_h.set_ylim([5e1, np.max([hist.max() for hist in histograms])])
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ax_h.set_xlim([max(xmin, np.min(background * convert_flux) * 1e-2), min(xmax, np.max(background * convert_flux) * 1e2)])
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ax_h.set_xlabel(r"Flux [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]")
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ax_h.set_ylabel(r"Number of pixels in bin")
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ax_h.set_title("Histogram for each observation")
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plt.legend()
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if savename is not None:
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this_savename = deepcopy(savename)
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if savename[-4:] not in [".png", ".jpg", ".pdf"]:
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this_savename += "_histograms.pdf"
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else:
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this_savename = savename[:-4] + "_histograms" + savename[-4:]
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fig_h.savefig(path_join(plots_folder, this_savename), bbox_inches="tight", facecolor="None", edgecolor="None")
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fig2, ax2 = plt.subplots(figsize=(10, 10))
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data0 = data[0] * convert_flux[0]
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bkg_data0 = data0 <= background[0] * convert_flux[0]
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instr = headers[0]["instrume"]
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rootname = headers[0]["rootname"]
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exptime = headers[0]["exptime"]
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filt = headers[0]["filtnam1"]
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# plots
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im2 = ax2.imshow(data0, norm=LogNorm(data0[data0 > 0.0].mean() / 10.0, data0.max()), origin="lower", cmap="gray")
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ax2.imshow(bkg_data0, origin="lower", cmap="Reds", alpha=0.5)
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if rectangle is not None:
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x, y, width, height, angle, color = rectangle[0]
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ax2.add_patch(Rectangle((x, y), width, height, edgecolor=color, fill=False, lw=2))
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ax2.annotate(
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instr + ":" + rootname, color="white", fontsize=10, xy=(0.01, 1.00), xycoords="axes fraction", verticalalignment="top", horizontalalignment="left"
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)
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ax2.annotate(filt, color="white", fontsize=14, xy=(0.01, 0.01), xycoords="axes fraction", verticalalignment="bottom", horizontalalignment="left")
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ax2.annotate(
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str(exptime) + " s", color="white", fontsize=10, xy=(1.00, 0.01), xycoords="axes fraction", verticalalignment="bottom", horizontalalignment="right"
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)
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ax2.set(xlabel="pixel offset", ylabel="pixel offset", aspect="equal")
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fig2.subplots_adjust(hspace=0, wspace=0, right=1.0)
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fig2.colorbar(im2, ax=ax2, location="right", shrink=0.60, aspect=50, pad=0.025, label=r"Flux [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]")
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if savename is not None:
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this_savename = deepcopy(savename)
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if savename[-4:] not in [".png", ".jpg", ".pdf"]:
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this_savename += "_" + filt + "_background_location.pdf"
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else:
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this_savename = savename[:-4] + "_" + filt + "_background_location" + savename[-4:]
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fig2.savefig(path_join(plots_folder, this_savename), bbox_inches="tight", facecolor="None", edgecolor="None")
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if rectangle is not None:
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plot_obs(
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data,
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headers,
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vmin=data[data > 0.0].min() * convert_flux.mean(),
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vmax=data[data > 0.0].max() * convert_flux.mean(),
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rectangle=rectangle,
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savename=savename + "_background_location",
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plots_folder=plots_folder,
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)
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elif rectangle is not None:
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plot_obs(data, headers, vmin=data[data > 0.0].min(), vmax=data[data > 0.0].max(), rectangle=rectangle)
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plt.show()
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def sky_part(img):
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rand_ind = np.unique((np.random.rand(np.floor(img.size / 4).astype(int)) * 2 * img.size).astype(int) % img.size)
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rand_pix = img.flatten()[rand_ind]
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# Intensity range
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sky_med = np.median(rand_pix)
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sig = np.min([img[img < sky_med].std(), img[img > sky_med].std()])
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sky_range = [sky_med - 2.0 * sig, np.max([sky_med + sig, 7e-4])] # Detector background average FOC Data Handbook Sec. 7.6
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sky = img[np.logical_and(img >= sky_range[0], img <= sky_range[1])]
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return sky, sky_range
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def bkg_estimate(img, bins=None, chi2=None, coeff=None):
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if bins is None or chi2 is None or coeff is None:
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bins, chi2, coeff = [8], [], []
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else:
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try:
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bins.append(int(3.0 / 2.0 * bins[-1]))
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except IndexError:
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bins, chi2, coeff = [8], [], []
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hist, bin_edges = np.histogram(img[img > 0], bins=bins[-1])
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binning = bin_centers(bin_edges)
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peak = binning[np.argmax(hist)]
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bins_stdev = binning[hist > hist.max() / 2.0]
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stdev = bins_stdev[-1] - bins_stdev[0]
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# p0 = [hist.max(), peak, stdev, 1e-3, 1e-3, 1e-3, 1e-3]
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p0 = [hist.max(), peak, stdev]
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try:
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# popt, pcov = curve_fit(gausspol, binning, hist, p0=p0)
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popt, pcov = curve_fit(gauss, binning, hist, p0=p0)
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except RuntimeError:
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popt = p0
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# chi2.append(np.sum((hist - gausspol(binning, *popt))**2)/hist.size)
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chi2.append(np.sum((hist - gauss(binning, *popt)) ** 2) / hist.size)
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coeff.append(popt)
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return bins, chi2, coeff
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def bkg_fit(data, error, mask, headers, subtract_error=True, display=False, savename=None, plots_folder=""):
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"""
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----------
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Inputs:
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data : numpy.ndarray
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Array containing the data to study (2D float arrays).
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error : numpy.ndarray
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Array of images (2D floats, aligned and of the same shape) containing
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the error in each pixel of the observation images in data_array.
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mask : numpy.ndarray
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2D boolean array delimiting the data to work on.
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headers : header list
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Headers associated with the images in data_array.
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subtract_error : float or bool, optional
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If float, factor to which the estimated background should be multiplied
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If False the background is not subtracted.
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Defaults to True (factor = 1.).
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display : boolean, optional
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If True, data_array will be displayed with a rectangle around the
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sub-image selected for background computation.
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Defaults to False.
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savename : str, optional
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Name of the figure the map should be saved to. If None, the map won't
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be saved (only displayed). Only used if display is True.
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Defaults to None.CNRS-Unistra Labo ObsAstroS
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plots_folder : str, optional
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Relative (or absolute) filepath to the folder in wich the map will
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be saved. Not used if savename is None.
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Defaults to current folder.
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----------
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Returns:
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data_array : numpy.ndarray
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Array containing the data to study minus the background.
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headers : header list
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Updated headers associated with the images in data_array.
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error_array : numpy.ndarray
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Array containing the background values associated to the images in
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data_array.
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background : numpy.ndarray
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Array containing the pixel background value for each image in
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data_array.
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"""
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n_data_array, n_error_array = deepcopy(data), deepcopy(error)
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error_bkg = np.ones(n_data_array.shape)
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std_bkg = np.zeros((data.shape[0]))
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background = np.zeros((data.shape[0]))
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histograms, binning = [], []
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for i, image in enumerate(data):
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# Compute the Count-rate histogram for the image
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sky, sky_range = sky_part(image[image > 0.0])
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bins, chi2, coeff = bkg_estimate(sky)
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while bins[-1] < 256:
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bins, chi2, coeff = bkg_estimate(sky, bins, chi2, coeff)
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hist, bin_edges = np.histogram(sky, bins=bins[-1])
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histograms.append(hist)
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binning.append(bin_centers(bin_edges))
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chi2, coeff = np.array(chi2), np.array(coeff)
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weights = 1 / chi2**2
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weights /= weights.sum()
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bkg = np.sum(weights * (coeff[:, 1] + np.abs(coeff[:, 2]) * subtract_error))
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error_bkg[i] *= bkg
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n_error_array[i] = np.sqrt(n_error_array[i] ** 2 + error_bkg[i] ** 2)
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# Substract background
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if np.abs(subtract_error) > 0:
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n_data_array[i][mask] = n_data_array[i][mask] - bkg
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n_data_array[i][np.logical_and(mask, n_data_array[i] <= 1e-3 * bkg)] = 1e-3 * bkg
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std_bkg[i] = image[np.abs(image - bkg) / bkg < 1.0].std()
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background[i] = bkg
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if display:
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display_bkg(data, background, std_bkg, headers, histograms=histograms, binning=binning, coeff=coeff, savename=savename, plots_folder=plots_folder)
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return n_data_array, n_error_array, headers, background
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def bkg_hist(data, error, mask, headers, sub_type=None, subtract_error=True, display=False, savename=None, plots_folder=""):
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"""
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----------
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Inputs:
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data : numpy.ndarray
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Array containing the data to study (2D float arrays).
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error : numpy.ndarray
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Array of images (2D floats, aligned and of the same shape) containing
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the error in each pixel of the observation images in data_array.
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mask : numpy.ndarray
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2D boolean array delimiting the data to work on.
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headers : header list
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Headers associated with the images in data_array.
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sub_type : str or int, optional
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If str, statistic rule to be used for the number of bins in counts/s.
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If int, number of bins for the counts/s histogram.
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Defaults to "Scott".
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subtract_error : float or bool, optional
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If float, factor to which the estimated background should be multiplied
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If False the background is not subtracted.
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Defaults to True (factor = 1.).
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display : boolean, optional
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If True, data_array will be displayed with a rectangle around the
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sub-image selected for background computation.
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Defaults to False.
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savename : str, optional
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Name of the figure the map should be saved to. If None, the map won't
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be saved (only displayed). Only used if display is True.
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Defaults to None.
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plots_folder : str, optional
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Relative (or absolute) filepath to the folder in wich the map will
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be saved. Not used if savename is None.
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Defaults to current folder.
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----------
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Returns:
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data_array : numpy.ndarray
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Array containing the data to study minus the background.
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headers : header list
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Updated headers associated with the images in data_array.
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error_array : numpy.ndarray
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Array containing the background values associated to the images in
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data_array.
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background : numpy.ndarray
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Array containing the pixel background value for each image in
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data_array.
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"""
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n_data_array, n_error_array = deepcopy(data), deepcopy(error)
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error_bkg = np.ones(n_data_array.shape)
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std_bkg = np.zeros((data.shape[0]))
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background = np.zeros((data.shape[0]))
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histograms, binning, coeff = [], [], []
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for i, image in enumerate(data):
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# Compute the Count-rate histogram for the image
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n_mask = np.logical_and(mask, image > 0.0)
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if sub_type is not None:
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if isinstance(sub_type, int):
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n_bins = sub_type
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elif sub_type.lower() in ["square-root", "squareroot", "sqrt"]:
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n_bins = np.fix(np.sqrt(image[n_mask].size)).astype(int) # Square-root
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elif sub_type.lower() in ["sturges"]:
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n_bins = np.ceil(np.log2(image[n_mask].size)).astype(int) + 1 # Sturges
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elif sub_type.lower() in ["rice"]:
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n_bins = 2 * np.fix(np.power(image[n_mask].size, 1 / 3)).astype(int) # Rice
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elif sub_type.lower() in ["freedman-diaconis", "freedmandiaconis", "freedman", "diaconis"]:
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n_bins = np.fix(
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(image[n_mask].max() - image[n_mask].min())
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/ (2 * np.subtract(*np.percentile(image[n_mask], [75, 25])) / np.power(image[n_mask].size, 1 / 3))
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).astype(int) # Freedman-Diaconis
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else: # Fallback
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n_bins = np.fix((image[n_mask].max() - image[n_mask].min()) / (3.5 * image[n_mask].std() / np.power(image[n_mask].size, 1 / 3))).astype(
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int
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) # Scott
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else: # Default statistic
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n_bins = np.fix((image[n_mask].max() - image[n_mask].min()) / (3.5 * image[n_mask].std() / np.power(image[n_mask].size, 1 / 3))).astype(
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int
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) # Scott
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hist, bin_edges = np.histogram(np.log(image[n_mask]), bins=n_bins)
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histograms.append(hist)
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binning.append(np.exp(bin_centers(bin_edges)))
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# Fit a gaussian to the log-intensity histogram
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bins_stdev = binning[-1][hist > hist.max() / 2.0]
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stdev = bins_stdev[-1] - bins_stdev[0]
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# p0 = [hist.max(), binning[-1][np.argmax(hist)], stdev, 1e-3, 1e-3, 1e-3, 1e-3]
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# popt, pcov = curve_fit(gausspol, binning[-1], hist, p0=p0)
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p0 = [hist.max(), binning[-1][np.argmax(hist)], stdev]
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popt, pcov = curve_fit(gauss, binning[-1], hist, p0=p0)
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coeff.append(popt)
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bkg = popt[1] + np.abs(popt[2]) * subtract_error
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error_bkg[i] *= bkg
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|
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n_error_array[i] = np.sqrt(n_error_array[i] ** 2 + error_bkg[i] ** 2)
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|
|
|
# Substract background
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if np.abs(subtract_error) > 0:
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n_data_array[i][mask] = n_data_array[i][mask] - bkg
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n_data_array[i][np.logical_and(mask, n_data_array[i] <= 1e-3 * bkg)] = 1e-3 * bkg
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|
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std_bkg[i] = image[np.abs(image - bkg) / bkg < 1.0].std()
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background[i] = bkg
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|
|
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if display:
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|
display_bkg(data, background, std_bkg, headers, histograms=histograms, binning=binning, coeff=coeff, savename=savename, plots_folder=plots_folder)
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return n_data_array, n_error_array, headers, background
|
|
|
|
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def bkg_mini(data, error, mask, headers, sub_shape=(15, 15), subtract_error=True, display=False, savename=None, plots_folder=""):
|
|
"""
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|
Look for sub-image of shape sub_shape that have the smallest integrated
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|
flux (no source assumption) and define the background on the image by the
|
|
standard deviation on this sub-image.
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|
----------
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|
Inputs:
|
|
data : numpy.ndarray
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|
Array containing the data to study (2D float arrays).
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|
error : numpy.ndarray
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|
Array of images (2D floats, aligned and of the same shape) containing
|
|
the error in each pixel of the observation images in data_array.
|
|
mask : numpy.ndarray
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|
2D boolean array delimiting the data to work on.
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|
headers : header list
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|
Headers associated with the images in data_array.
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|
sub_shape : tuple, optional
|
|
Shape of the sub-image to look for. Must be odd.
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|
Defaults to 10% of input array.
|
|
subtract_error : float or bool, optional
|
|
If float, factor to which the estimated background should be multiplied
|
|
If False the background is not subtracted.
|
|
Defaults to True (factor = 1.).
|
|
display : boolean, optional
|
|
If True, data_array will be displayed with a rectangle around the
|
|
sub-image selected for background computation.
|
|
Defaults to False.
|
|
savename : str, optional
|
|
Name of the figure the map should be saved to. If None, the map won't
|
|
be saved (only displayed). Only used if display is True.
|
|
Defaults to None.
|
|
plots_folder : str, optional
|
|
Relative (or absolute) filepath to the folder in wich the map will
|
|
be saved. Not used if savename is None.
|
|
Defaults to current folder.
|
|
----------
|
|
Returns:
|
|
data_array : numpy.ndarray
|
|
Array containing the data to study minus the background.
|
|
headers : header list
|
|
Updated headers associated with the images in data_array.
|
|
error_array : numpy.ndarray
|
|
Array containing the background values associated to the images in
|
|
data_array.
|
|
background : numpy.ndarray
|
|
Array containing the pixel background value for each image in
|
|
data_array.
|
|
"""
|
|
sub_shape = np.array(sub_shape)
|
|
# Make sub_shape of odd values
|
|
if not (np.all(sub_shape % 2)):
|
|
sub_shape += 1 - sub_shape % 2
|
|
shape = np.array(data.shape)
|
|
diff = (sub_shape - 1).astype(int)
|
|
temp = np.zeros((shape[0], shape[1] - diff[0], shape[2] - diff[1]))
|
|
|
|
n_data_array, n_error_array = deepcopy(data), deepcopy(error)
|
|
error_bkg = np.ones(n_data_array.shape)
|
|
std_bkg = np.zeros((data.shape[0]))
|
|
background = np.zeros((data.shape[0]))
|
|
rectangle = []
|
|
|
|
for i, image in enumerate(data):
|
|
# Find the sub-image of smallest integrated flux (suppose no source)
|
|
# sub-image dominated by background
|
|
fmax = np.finfo(np.double).max
|
|
img = deepcopy(image)
|
|
img[1 - mask] = fmax / (diff[0] * diff[1])
|
|
for r in range(temp.shape[1]):
|
|
for c in range(temp.shape[2]):
|
|
temp[i][r, c] = np.where(mask[r, c], img[r : r + diff[0], c : c + diff[1]].sum(), fmax / (diff[0] * diff[1]))
|
|
|
|
minima = np.unravel_index(np.argmin(temp.sum(axis=0)), temp.shape[1:])
|
|
|
|
for i, image in enumerate(data):
|
|
rectangle.append([minima[1], minima[0], sub_shape[1], sub_shape[0], 0.0, "r"])
|
|
# Compute error : root mean square of the background
|
|
sub_image = image[minima[0] : minima[0] + sub_shape[0], minima[1] : minima[1] + sub_shape[1]]
|
|
# bkg = np.std(sub_image) # Previously computed using standard deviation over the background
|
|
bkg = np.sqrt(np.sum(sub_image**2) / sub_image.size) * subtract_error if subtract_error > 0 else np.sqrt(np.sum(sub_image**2) / sub_image.size)
|
|
error_bkg[i] *= bkg
|
|
|
|
n_error_array[i] = np.sqrt(n_error_array[i] ** 2 + error_bkg[i] ** 2)
|
|
|
|
# Substract background
|
|
if np.abs(subtract_error) > 0:
|
|
n_data_array[i][mask] = n_data_array[i][mask] - bkg
|
|
n_data_array[i][np.logical_and(mask, n_data_array[i] <= 1e-3 * bkg)] = 1e-3 * bkg
|
|
|
|
std_bkg[i] = image[np.abs(image - bkg) / bkg < 1.0].std()
|
|
background[i] = bkg
|
|
|
|
if display:
|
|
display_bkg(data, background, std_bkg, headers, rectangle=rectangle, savename=savename, plots_folder=plots_folder)
|
|
return n_data_array, n_error_array, headers, background
|