Source code for punchbowl.level1.alignment

import os
import copy
import warnings
from collections.abc import Callable

import astrometry
import astropy.units as u
import numpy as np
import pandas as pd
import scipy
import sep
from astropy.coordinates import SkyCoord
from astropy.io import fits
from astropy.wcs import WCS, DistortionLookupTable, NoConvergence, utils
from lmfit import Parameters, minimize
from ndcube import NDCube
from regularizepsf import ArrayPSFTransform
from skimage.transform import resize

from punchbowl.data.wcs import calculate_celestial_wcs_from_helio, calculate_helio_wcs_from_celestial
from punchbowl.prefect import punch_task

_ROOT = os.path.abspath(os.path.dirname(__file__))
HIPPARCOS_URL = "https://cdsarc.cds.unistra.fr/ftp/cats/I/239/hip_main.dat"

[docs] def filter_distortion_table(data: np.ndarray, blur_sigma: float = 4, med_filter_size: float = 3) -> np.ndarray: """ Filter a copy of the distortion lookup table. Any rows/columns at the edges that are all NaNs will be removed and replaced with a copy of the closest non-removed edge at the end of processing. Any NaN values that don't form a complete edge row/column will be replaced with the median of all surrounding non-NaN pixels. Then median filtering is performed across the whole map to remove outliers, and Gaussian filtering is applied to accept only slowly-varying distortions. Parameters ---------- data The distortion map to be filtered blur_sigma : float The number of pixels constituting one standard deviation of the Gaussian kernel. Set to 0 to disable Gaussian blurring. med_filter_size : int The size of the local neighborhood to consider for median filtering. Set to 0 to disable median filtering. Notes ----- Modified from https://github.com/svank/wispr_analysis/blob/main/wispr_analysis/image_alignment.py """ data = data.copy() # Trim empty (all-nan) rows and columns trimmed = [] i = 0 while np.all(np.isnan(data[0])): i += 1 data = data[1:] trimmed.append(i) i = 0 while np.all(np.isnan(data[-1])): i += 1 data = data[:-1] trimmed.append(i) i = 0 while np.all(np.isnan(data[:, 0])): i += 1 data = data[:, 1:] trimmed.append(i) i = 0 while np.all(np.isnan(data[:, -1])): i += 1 data = data[:, :-1] trimmed.append(i) # Replace interior nan values with the median of the surrounding values. # We're filling in from neighboring pixels, so if there are any nan pixels # fully surrounded by nan pixels, we need to iterate a few times. while np.any(np.isnan(data)): nans = np.nonzero(np.isnan(data)) replacements = np.zeros_like(data) with warnings.catch_warnings(): warnings.filterwarnings(action="ignore", message="All-NaN slice") for r, c in zip(*nans, strict=False): r1, r2 = r - 1, r + 2 c1, c2 = c - 1, c + 2 r1, r2 = max(r1, 0), min(r2, data.shape[0]) c1, c2 = max(c1, 0), min(c2, data.shape[1]) replacements[r, c] = np.nanmedian(data[r1:r2, c1:c2]) data[nans] = replacements[nans] # Median-filter the whole image if med_filter_size: data = scipy.ndimage.median_filter(data, size=med_filter_size, mode="reflect") # Gaussian-blur the whole image if blur_sigma > 0: data = scipy.ndimage.gaussian_filter(data, sigma=blur_sigma) # Replicate the edge rows/columns to replace those we trimmed earlier return np.pad(data, [trimmed[0:2], trimmed[2:]], mode="edge")
[docs] def get_data_path(path: str) -> str: """Get the path to the local data directory.""" return os.path.join(_ROOT, "data", path)
[docs] def load_hipparcos_catalog(catalog_path: str = get_data_path("reduced_hip.csv")) -> pd.DataFrame: """ Load the Hipparcos catalog from the local, reduced version. This version only keeps necessary columns. Parameters ---------- catalog_path : str path to the catalog, defaults to a provided version Returns ------- pd.DataFrame loaded catalog with selected columns """ return pd.read_csv(catalog_path)
[docs] def load_raw_hipparcos_catalog(catalog_path: str = HIPPARCOS_URL) -> pd.DataFrame: """ Download hipparcos catalog from the website. Not recommended for routine use. Parameters ---------- catalog_path : str path to the Hipparcos catalog Returns ------- pd.DataFrame loaded catalog with selected columns """ column_names = ( "Catalog", "HIP", "Proxy", "RAhms", "DEdms", "Vmag", "VarFlag", "r_Vmag", "RAdeg", "DEdeg", "AstroRef", "Plx", "pmRA", "pmDE", "e_RAdeg", "e_DEdeg", "e_Plx", "e_pmRA", "e_pmDE", "DE:RA", "Plx:RA", "Plx:DE", "pmRA:RA", "pmRA:DE", "pmRA:Plx", "pmDE:RA", "pmDE:DE", "pmDE:Plx", "pmDE:pmRA", "F1", "F2", "---", "BTmag", "e_BTmag", "VTmag", "e_VTmag", "m_BTmag", "B-V", "e_B-V", "r_B-V", "V-I", "e_V-I", "r_V-I", "CombMag", "Hpmag", "e_Hpmag", "Hpscat", "o_Hpmag", "m_Hpmag", "Hpmax", "HPmin", "Period", "HvarType", "moreVar", "morePhoto", "CCDM", "n_CCDM", "Nsys", "Ncomp", "MultFlag", "Source", "Qual", "m_HIP", "theta", "rho", "e_rho", "dHp", "e_dHp", "Survey", "Chart", "Notes", "HD", "BD", "CoD", "CPD", "(V-I)red", "SpType", "r_SpType", ) df = pd.read_csv( catalog_path, sep="|", names=column_names, usecols=["HIP", "Vmag", "RAdeg", "DEdeg", "Plx"], na_values=[" ", " ", " ", " "], ) df["distance"] = 1000 / df["Plx"] df = df[df["distance"] > 0] return df.iloc[np.argsort(df["Vmag"])]
[docs] def filter_for_visible_stars(catalog: pd.DataFrame, dimmest_magnitude: float = 6) -> pd.DataFrame: """ Filter to only include stars brighter than a given magnitude. Parameters ---------- catalog : pd.DataFrame a catalog loaded from `~load_hipparcos_catalog` or `~load_raw_hipparcos_catalog` dimmest_magnitude : float the dimmest magnitude to keep Returns ------- pd.DataFrame` a catalog with stars dimmer than the `dimmest_magnitude` removed """ return catalog[catalog["Vmag"] < dimmest_magnitude]
[docs] def find_catalog_in_image( catalog: pd.DataFrame, wcs: WCS, image_shape: tuple[int, int], mask: Callable | None = None, mode: str = "all", ) -> pd.DataFrame: """ Convert the RA/DEC catalog into pixel coordinates using the provided WCS. Parameters ---------- catalog : pd.DataFrame a catalog loaded from `~thuban.catalog.load_hipparcos_catalog` or `~thuban.catalog.load_raw_hipparcos_catalog` wcs : WCS the world coordinate system of a given image image_shape: (int, int) the shape of the image array associated with the WCS, used to only consider stars with coordinates in image mask: Callable a function that indicates whether a given coordinate is included mode : str either "all" or "wcs", see <https://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html#astropy.coordinates.SkyCoord.to_pixel> Returns ------- pd.DataFrame pixel coordinates of stars in catalog that are present in the image """ try: xs, ys = SkyCoord( ra=np.array(catalog["RAdeg"]) * u.degree, dec=np.array(catalog["DEdeg"]) * u.degree, distance=np.array(catalog["distance"]) * u.parsec, ).to_pixel(wcs, mode=mode) except NoConvergence as e: xs, ys = e.best_solution[:, 0], e.best_solution[:, 1] bounds_mask = (xs >= 0) * (xs < image_shape[0]) * (ys >= 0) * (ys < image_shape[1]) if mask is not None: bounds_mask *= mask(xs, ys) reduced_catalog = catalog[bounds_mask].copy() reduced_catalog["x_pix"] = xs[bounds_mask] reduced_catalog["y_pix"] = ys[bounds_mask] return reduced_catalog
[docs] def find_star_coordinates(image_data: np.ndarray, saturation_limit: float = np.inf, max_distance_from_center: float = 700, background_size: int = 16, detection_threshold: float = 5.0) -> np.ndarray: """ Extract the coordinates of observed stars in an image using sep. Parameters ---------- image_data : np.ndarray an array of an image saturation_limit : float stars brighter than this are ignored max_distance_from_center: float only returns stars at most this distance from the center of th eimage background_size: int pixel size used by sep when building background model detection_threshold : float number of sigma brighter than noise level a star must be for detection Returns ------- np.ndarray pixel coordinates of stars that are present in the image """ image_copy = image_data.copy() image_copy[image_copy > saturation_limit] = 0 background = sep.Background(image_data, bw=background_size, bh=background_size) image_sub = image_data - background objects = sep.extract(image_sub, detection_threshold, err=background.globalrms) objects = pd.DataFrame(objects).sort_values("flux") observed_coords = np.stack([objects["x"], objects["y"]], axis=-1) center = image_data.shape[0]//2, image_data.shape[1]//2 distance = np.sqrt(np.square(observed_coords[:, 0] - center[0]) + np.square(observed_coords[:, 1] - center[1])) return observed_coords[distance < max_distance_from_center, :]
[docs] def astrometry_net_initial_solve(observed_coords: np.ndarray, image_wcs: WCS, search_scales: tuple[int] = (14, 15, 16), num_stars: int = 150, lower_arcsec_per_pixel: float = 80.0, upper_arcsec_per_pixel: float = 100.0) -> WCS | None: """ Solve for the WCS of an image using Astrometry.net. Parameters ---------- observed_coords : np.ndarray pixel coordinates of stars in image, returned by `find_star_coordinates` image_wcs : WCS best guess WCS search_scales: tuple[int] scales to use for search, see https://github.com/neuromorphicsystems/astrometry?tab=readme-ov-file#choosing-series num_stars: int number of stars in the observed_coords to use for search lower_arcsec_per_pixel: float lower guess on the platescale upper_arcsec_per_pixel: float upper guess on the platescale Returns ------- WCS | None the best WCS if search successful, otherwise None """ with astrometry.Solver( astrometry.series_4100.index_files( cache_directory="astrometry_cache", scales=search_scales, ), ) as solver: solution = solver.solve( stars=observed_coords[-num_stars:], size_hint=astrometry.SizeHint( lower_arcsec_per_pixel=lower_arcsec_per_pixel, upper_arcsec_per_pixel=upper_arcsec_per_pixel, ), position_hint=astrometry.PositionHint( ra_deg=image_wcs.wcs.crval[0], dec_deg=image_wcs.wcs.crval[1], radius_deg=15, ), solution_parameters=astrometry.SolutionParameters( sip_order=0, tune_up_logodds_threshold=None, ), ) if solution.has_match(): return solution.best_match().astropy_wcs() return None
[docs] def _residual(params: Parameters, subcatalog: pd.DataFrame, observed_coords: np.ndarray, guess_wcs: WCS, max_error: float = 30) -> float: """ Residual used when optimizing the pointing. Parameters ---------- params : Parameters optimization parameters from lmfit observed_coords : np.ndarray pixel coordinates of stars observed in the image, i.e. the coordinates found by sep of the actual star location subcatalog : pd.DataFrame image catalog of stars to match against guess_wcs : WCS initial guess of the world coordinate system, must overlap with the true WCS max_error: float stars more distant than this are complete misses, and their error is zeroed out Returns ------- np.ndarray residual """ refined_wcs = guess_wcs.deepcopy() refined_wcs.wcs.cdelt = (-params["platescale"].value, params["platescale"].value) refined_wcs.wcs.crval = (params["crval1"].value, params["crval2"].value) refined_wcs.wcs.pc = np.array( [ [np.cos(params["crota"]), -np.sin(params["crota"])], [np.sin(params["crota"]), np.cos(params["crota"])], ], ) refined_wcs.cpdis1 = guess_wcs.cpdis1 refined_wcs.cpdis2 = guess_wcs.cpdis2 try: xs, ys = SkyCoord( ra=np.array(subcatalog["RAdeg"]) * u.degree, dec=np.array(subcatalog["DEdeg"]) * u.degree, distance=np.array(subcatalog["distance"]) * u.parsec, ).to_pixel(refined_wcs, mode="all") except NoConvergence as e: xs, ys = e.best_solution[:, 0], e.best_solution[:, 1] refined_coords = np.stack([xs, ys], axis=-1) out = np.array([np.min(np.linalg.norm(observed_coords - coord, axis=-1)) for coord in refined_coords]) out[out > max_error] = 0 return np.nansum(out)
[docs] def extract_crota_from_wcs(wcs: WCS) -> tuple[float, float]: """Extract CROTA from a WCS.""" delta_ratio = abs(wcs.wcs.cdelt[1]) / abs(wcs.wcs.cdelt[0]) return (np.arctan2(wcs.wcs.pc[1, 0]/delta_ratio, wcs.wcs.pc[0, 0])) * u.rad
[docs] def convert_cd_matrix_to_pc_matrix(wcs: WCS) -> WCS: """Convert a WCS with a CD matrix to one with a PC matrix.""" if not hasattr(wcs.wcs, "cd"): return wcs cdelt1, cdelt2 = utils.proj_plane_pixel_scales(wcs) crota = np.arctan2(abs(cdelt1) * wcs.wcs.cd[0, 1], abs(cdelt2) * wcs.wcs.cd[0, 0]) new_wcs = WCS(naxis=2) new_wcs.wcs.ctype = wcs.wcs.ctype new_wcs.wcs.crval = wcs.wcs.crval new_wcs.wcs.crpix = wcs.wcs.crpix new_wcs.wcs.pc = np.array( [ [-np.cos(crota), -np.sin(crota) * (cdelt1 / cdelt2)], [np.sin(crota) * (cdelt2 / cdelt1), -np.cos(crota)], ]) new_wcs.wcs.cdelt = (-cdelt1, cdelt2) new_wcs.wcs.cunit = "deg", "deg" return new_wcs
[docs] def refine_pointing_single_step( guess_wcs: WCS, observed_coords: np.ndarray, subcatalog: pd.DataFrame, method: str = "least_squares", ra_tolerance: float = 10, dec_tolerance: float = 5, fix_crval: bool = False, fix_crota: bool = False, fix_pv: bool = True) -> WCS: """Perform a single step of pointing refinement.""" # set up the optimization params = Parameters() initial_crota = extract_crota_from_wcs(guess_wcs) params.add("crota", value=initial_crota.to(u.rad).value, min=-np.pi, max=np.pi, vary=not fix_crota) params.add("crval1", value=guess_wcs.wcs.crval[0], min=guess_wcs.wcs.crval[0]-ra_tolerance, max=guess_wcs.wcs.crval[0]+ra_tolerance, vary=not fix_crval) params.add("crval2", value=guess_wcs.wcs.crval[1], min=guess_wcs.wcs.crval[1]-dec_tolerance, max=guess_wcs.wcs.crval[1]+dec_tolerance, vary=not fix_crval) params.add("platescale", value=abs(guess_wcs.wcs.cdelt[0]), min=0, max=1, vary=False) pv = guess_wcs.wcs.get_pv()[0][-1] if guess_wcs.wcs.get_pv() else 0.0 params.add("pv", value=pv, min=0.0, max=1.0, vary=not fix_pv) out = minimize(_residual, params, method=method, args=(subcatalog, observed_coords, guess_wcs), max_nfev=100, calc_covar=False) result_wcs = guess_wcs.deepcopy() result_wcs.wcs.cdelt = (-out.params["platescale"].value, out.params["platescale"].value) result_wcs.wcs.crval = (out.params["crval1"].value, out.params["crval2"].value) result_wcs.wcs.pc = np.array( [ [np.cos(out.params["crota"].value), -np.sin(out.params["crota"].value)], [np.sin(out.params["crota"].value), np.cos(out.params["crota"].value)], ], ) result_wcs.cpdis1 = guess_wcs.cpdis1 result_wcs.cpdis2 = guess_wcs.cpdis2 result_wcs.wcs.set_pv([(2, 1, out.params["pv"].value)]) return result_wcs
[docs] def solve_pointing( image_data: np.ndarray, image_wcs: WCS, distortion: WCS | None = None, saturation_limit: float = np.inf) -> WCS: """Carefully refine the pointing of an image based on a guess WCS.""" observed = find_star_coordinates(image_data, saturation_limit=saturation_limit) astrometry_net = astrometry_net_initial_solve(observed, image_wcs.deepcopy()) if astrometry_net is None: msg = "Astrometry.net initial solution failed." raise RuntimeError(msg) astrometry_net = convert_cd_matrix_to_pc_matrix(astrometry_net) image_center = (image_data.shape[0]//2 + 0.5, image_data.shape[1]//2 + 0.5) center = astrometry_net.all_pix2world( np.array([image_center]), 0) guess_wcs = astrometry_net.deepcopy() guess_wcs.wcs.ctype = "RA---AZP", "DEC--AZP" guess_wcs.wcs.crval = center[0] guess_wcs.wcs.crpix = image_center guess_wcs.wcs.cdelt = image_wcs.wcs.cdelt guess_wcs.sip = None if distortion is not None: guess_wcs.cpdis1 = distortion.cpdis1 guess_wcs.cpdis2 = distortion.cpdis2 if distortion.wcs.get_pv(): pv = distortion.wcs.get_pv()[0][-1] guess_wcs.wcs.set_pv([(2, 1, pv)]) catalog = filter_for_visible_stars(load_hipparcos_catalog(), dimmest_magnitude=8.0) stars_in_image = find_catalog_in_image(catalog, guess_wcs, (2048, 2048)) candidate_wcs = [] for _ in range(50): sample = stars_in_image.sample(n=15) candidate_wcs.append(refine_pointing_single_step(guess_wcs, observed, sample, fix_pv=True)) ras = [w.wcs.crval[0] for w in candidate_wcs] decs = [w.wcs.crval[1] for w in candidate_wcs] crotas = [extract_crota_from_wcs(w) for w in candidate_wcs] solved_wcs = image_wcs.deepcopy() solved_wcs.wcs.crval = (np.median(ras), np.median(decs)) mean_crota = np.median([c.value for c in crotas]) cdelt1, cdelt2 = image_wcs.wcs.cdelt solved_wcs.wcs.pc = np.array( [ [np.cos(mean_crota), np.sin(mean_crota) * (cdelt1 / cdelt2)], [-np.sin(mean_crota) * (cdelt2 / cdelt1), np.cos(mean_crota)], ], ) if distortion is not None: solved_wcs.cpdis1 = distortion.cpdis1 solved_wcs.cpdis2 = distortion.cpdis2 return solved_wcs
[docs] def measure_wcs_error( image_data: np.ndarray, w: WCS, dimmest_magnitude: float = 6.0, max_error: float = 15.0) -> float: """Estimate the error in the WCS based on an image.""" catalog = filter_for_visible_stars(load_hipparcos_catalog(), dimmest_magnitude=dimmest_magnitude) stars_in_image = find_catalog_in_image(catalog, w, image_data.shape) try: xs, ys = SkyCoord( ra=np.array(stars_in_image["RAdeg"]) * u.degree, dec=np.array(stars_in_image["DEdeg"]) * u.degree, distance=np.array(stars_in_image["distance"]) * u.parsec, ).to_pixel(w, mode="all") except NoConvergence as e: xs, ys = e.best_solution[:, 0], e.best_solution[:, 1] refined_coords = np.stack([xs, ys], axis=-1) observed_coords = find_star_coordinates( image_data, detection_threshold = 15.0, max_distance_from_center=800, saturation_limit=1000) out = np.array([np.min(np.linalg.norm(observed_coords - coord, axis=-1)) for coord in refined_coords]) out[out > max_error] = np.nan return np.sqrt(np.nanmean(np.square(out)))
[docs] def build_distortion_model( l0_paths: list[str], dimmest_magnitude: float = 6.5, num_bins: int = 60, psf_transform: ArrayPSFTransform | None = None) -> WCS: """Create a distortion model from a set of PUNCH L0 images.""" refined_wcses = [] image_cube = [] for path in l0_paths: with fits.open(path) as hdul: image_head = hdul[1].header image_data = hdul[1].data.astype(float) image_data = image_data ** 2 / image_head["SCALE"] if psf_transform is not None: saturation_threshold = image_head["DSATVAL"]**2/image_head["SCALE"]*0.9 image_data = psf_transform.apply(image_data, saturation_threshold=saturation_threshold).copy() img_shape = image_data.shape image_wcs = WCS(hdul[1].header, hdul, key="A") mask = image_data != 0 solved_wcs = solve_pointing(image_data, image_wcs) image_cube.append(image_data) refined_wcses.append(solved_wcs) catalog = filter_for_visible_stars(load_hipparcos_catalog(), dimmest_magnitude=dimmest_magnitude) all_distortions = [] for image_data, new_wcs in zip(image_cube, refined_wcses, strict=False): stars_in_image = find_catalog_in_image(catalog, new_wcs, image_data.shape) subcoords = np.column_stack([[stars_in_image["RAdeg"], stars_in_image["DEdeg"]]]).T refined_coords = new_wcs.all_world2pix(subcoords, 0) refined_coords = refined_coords[ image_data[refined_coords[:, 1].astype(int), refined_coords[:, 0].astype(int)] > 10] observed_coords = find_star_coordinates(image_data, max_distance_from_center=1100, detection_threshold=25.0, saturation_limit=1000) closest_star = np.array([np.argmin(np.linalg.norm(observed_coords - coord, axis=-1)) for coord in refined_coords]) distance = np.array([np.min(np.linalg.norm(observed_coords - coord, axis=-1)) for coord in refined_coords]) for i in range(len(closest_star)): all_distortions.append({"distance": distance[i], "ox": observed_coords[closest_star[i]][0], "oy": observed_coords[closest_star[i]][1], "nx": refined_coords[i][0], "ny": refined_coords[i][1]}) df = pd.DataFrame(all_distortions) xbins, r, c, _ = scipy.stats.binned_statistic_2d( df["oy"], df["ox"], df["ox"] - df["nx"], "median", (num_bins, num_bins), expand_binnumbers=True, range=((0, img_shape[1]), (0, img_shape[0])), ) ybins, _, _, _ = scipy.stats.binned_statistic_2d( df["oy"], df["ox"], df["oy"] - df["ny"], "median", (num_bins, num_bins), expand_binnumbers=True, range=((0, img_shape[1]), (0, img_shape[0])), ) mask = resize(mask, (num_bins, num_bins)) xbins *= mask ybins *= mask xbins = filter_distortion_table(xbins, 1.1, 1) * mask ybins = filter_distortion_table(ybins, 1.1, 1) * mask r = np.linspace(0, 2048, num_bins + 1) c = np.linspace(0, 2048, num_bins + 1) r = (r[1:] + r[:-1]) / 2 c = (c[1:] + c[:-1]) / 2 err_px, err_py = r, c cpdis1 = DistortionLookupTable( -xbins.astype(np.float32), (0, 0), (err_px[0], err_py[0]), ((err_px[1] - err_px[0]), (err_py[1] - err_py[0])), ) cpdis2 = DistortionLookupTable( -ybins.astype(np.float32), (0, 0), (err_px[0], err_py[0]), ((err_px[1] - err_px[0]), (err_py[1] - err_py[0])), ) out_wcs = solved_wcs.copy() out_wcs.cpdis1 = cpdis1 out_wcs.cpdis2 = cpdis2 return out_wcs
[docs] @punch_task def align_task(data_object: NDCube, distortion_path: str | None) -> NDCube: """ Determine the pointing of the image and updates the metadata appropriately. Parameters ---------- data_object : NDCube data object to align distortion_path: str | None path to a distortion model Returns ------- NDCube a modified version of the input with the WCS more accurately determined """ celestial_input = calculate_celestial_wcs_from_helio(copy.deepcopy(data_object.wcs), data_object.meta.astropy_time, data_object.data.shape) refining_data = data_object.data.copy() refining_data[np.isinf(refining_data)] = 0 refining_data[np.isnan(refining_data)] = 0 if distortion_path: with fits.open(distortion_path) as distortion_hdul: distortion = WCS(distortion_hdul[0].header, distortion_hdul) else: distortion = None celestial_output = solve_pointing(refining_data, celestial_input, distortion) recovered_wcs, _ = calculate_helio_wcs_from_celestial(celestial_output, data_object.meta.astropy_time, data_object.data.shape) if distortion_path: with fits.open(distortion_path) as distortion_hdul: distortion_wcs = WCS(distortion_hdul[0].header, distortion_hdul) recovered_wcs.cpdis1 = distortion_wcs.cpdis1 recovered_wcs.cpdis2 = distortion_wcs.cpdis2 output = NDCube(data=data_object.data, wcs=recovered_wcs, uncertainty=data_object.uncertainty, unit=data_object.unit, meta=data_object.meta) output.meta.history.add_now("LEVEL1-Align", "alignment done") return output