from astropy.table import Table import astropy.constants as cons import collections from collections import OrderedDict from scipy import interpolate from astropy import units as u # from numpy import * import numpy as np from pylab import * import galsim import sys import os def rotate90(array_orig=None, xc=0, yc=0, isClockwise=0): if array_orig is None: return l1 = array_orig.shape[0] l2 = array_orig.shape[1] if xc < 0 or xc > l2 - 1 or yc < 0 or yc > l1 - 1: return n_xc = xc n_yc = yc array_final = np.zeros_like(array_orig.T) if isClockwise == 1: for i in np.arange(l2): array_final[i] = array_orig[:, l2 - i - 1] n_xc = yc n_yc = l2 - 1 - xc else: for i in np.arange(l2): array_final[i] = array_orig[::-1, i] n_xc = l1 - 1 - yc n_yc = xc return array_final, n_xc, n_yc class SpecDisperser(object): def __init__(self, orig_img=None, xcenter=0, ycenter=0, origin=[100, 100], tar_spec=None, band_start=6200, band_end=10000, isAlongY=0, conf='../param/CONF/csst.conf', gid=0): """ orig_img: normal image,galsim image xcenter, ycenter: the center of galaxy in orig_img origin : [int, int] `origin` defines the lower left pixel index (y,x) of the `direct` cutout from a larger detector-frame image tar_spec: galsim.SED """ # self.img_x = orig_img.shape[1] # self.img_y = orig_img.shape[0] self.thumb_img = np.abs(orig_img.array) self.thumb_x = orig_img.center.x self.thumb_y = orig_img.center.y self.img_sh = orig_img.array.shape self.id = gid self.xcenter = xcenter self.ycenter = ycenter self.isAlongY = isAlongY if self.isAlongY == 1: self.thumb_img, self.thumb_x, self.thumb_y = rotate90(array_orig=self.thumb_img, xc=orig_img.center.x, yc=orig_img.center.y, isClockwise=1) self.img_sh = orig_img.array.T.shape self.xcenter = ycenter self.ycenter = xcenter self.origin = origin self.band_start = band_start self.band_end = band_end self.spec = tar_spec self.beam_flux = OrderedDict() self.grating_conf = aXeConf(conf) self.grating_conf.get_beams() self.grating_conf_file = conf def compute_spec_orders(self): all_orders = OrderedDict() beam_names = self.grating_conf.beams for beam in beam_names: #for beam in ['A','B']: all_orders[beam] = self.compute_spec(beam) return all_orders def compute_spec(self, beam): from .disperse_c import interp from .disperse_c import disperse # from MockObject.disperse_c import disperse dx = self.grating_conf.dxlam[beam] xoff = 0 ytrace_beam, lam_beam = self.grating_conf.get_beam_trace(x=self.xcenter, y=self.ycenter, dx=(dx + xoff), beam=beam) ### Account for pixel centering of the trace yfrac_beam = ytrace_beam - floor(ytrace_beam) ysens = lam_beam * 0 lam_index = argsort(lam_beam) conf_sens = self.grating_conf.sens[beam] lam_intep = np.linspace(self.band_start, self.band_end, int((self.band_end - self.band_start) / 0.1)) thri = interpolate.interp1d(conf_sens['WAVELENGTH'], conf_sens['SENSITIVITY']) spci = interpolate.interp1d(self.spec['WAVELENGTH'], self.spec['FLUX']) beam_thr = thri(lam_intep) spec_sample = spci(lam_intep) bean_thr_spec = beam_thr * spec_sample ###generate sensitivity file for aXe # ysensitivity = lam_beam * 0 # # ysensitivity[lam_index] = interp.interp_conserve_c(lam_beam[lam_index], lam_intep, # beam_thr * math.pi * 100 * 100 * 1e-7 / ( # cons.h.value * cons.c.value / ( # lam_intep * 1e-10)), integrate=0, left=0, # right=0) # # self.writerSensitivityFile(conffile = self.grating_conf_file, beam = beam, w = lam_beam[lam_index], sens = ysensitivity[lam_index]) ysens[lam_index] = interp.interp_conserve_c(lam_beam[lam_index], lam_intep, bean_thr_spec, integrate=1, left=0, right=0) sensitivity_beam = ysens len_spec_x = len(dx) len_spec_y = int(ceil(yfrac_beam[-1]) - floor(yfrac_beam[0]) + 1) beam_sh = (self.img_sh[0] + len_spec_y, self.img_sh[1] + len_spec_x) modelf = zeros(product(beam_sh), dtype=float) model = modelf.reshape(beam_sh) idx = np.arange(modelf.size, dtype=int64).reshape(beam_sh) x0 = array((self.thumb_y, self.thumb_x), dtype=int64) dxpix = dx - dx[0] + x0[1] dyc = cast[int](ytrace_beam) dypix = dyc - dyc[0] + x0[0] flat_index = idx[dypix, dxpix] nonz = sensitivity_beam != 0 status = disperse.disperse_grism_object(self.thumb_img, flat_index[nonz], yfrac_beam[nonz], sensitivity_beam[nonz], modelf, x0, array(self.img_sh, dtype=int64), array(beam_sh, dtype=int64)) model = modelf.reshape(beam_sh) self.beam_flux[beam] = sum(modelf) origin_in = zeros_like(self.origin) dx0_in = dx[0] dy0_in = dyc[0] if self.isAlongY == 1: model, tmx, tmy = rotate90(array_orig=model, isClockwise=0) origin_in[0] = self.origin[0] origin_in[1] = self.origin[1] - len_spec_y dx0_in = -dyc[0] dy0_in = dx[0] else: origin_in[0] = self.origin[0] origin_in[1] = self.origin[1] dx0_in = dx[0] dy0_in = dyc[0] originOut_x = origin_in[1] + dx0_in - 1 originOut_y = origin_in[0] + dy0_in - 1 return model, originOut_x, originOut_y def writerSensitivityFile(self, conffile = '', beam = '', w = None, sens = None): orders={'A':'1st','B':'0st','C':'2st','D':'-1st','E':'-2st'} sens_file_name = conffile[0:-5]+'_sensitivity_'+ orders[beam] + '.fits' if not os.path.exists(sens_file_name) == True: senstivity_out = Table(array([w,sens]).T, names=('WAVELENGTH', 'SENSITIVITY')) senstivity_out.write(sens_file_name, format='fits') """ Demonstrate aXe trace polynomials. """ class aXeConf(): def __init__(self, conf_file='WFC3.IR.G141.V2.5.conf'): """Read an aXe-compatible configuration file Parameters ---------- conf_file: str Filename of the configuration file to read """ if conf_file is not None: self.conf = self.read_conf_file(conf_file) self.conf_file = conf_file self.count_beam_orders() ## Global XOFF/YOFF offsets if 'XOFF' in self.conf.keys(): self.xoff = np.float(self.conf['XOFF']) else: self.xoff = 0. if 'YOFF' in self.conf.keys(): self.yoff = np.float(self.conf['YOFF']) else: self.yoff = 0. def read_conf_file(self, conf_file='WFC3.IR.G141.V2.5.conf'): """Read an aXe config file, convert floats and arrays Parameters ---------- conf_file: str Filename of the configuration file to read. Parameters are stored in an OrderedDict in `self.conf`. """ from collections import OrderedDict conf = OrderedDict() lines = open(conf_file).readlines() for line in lines: ## empty / commented lines if (line.startswith('#')) | (line.strip() == '') | ('"' in line): continue ## split the line, taking out ; and # comments spl = line.split(';')[0].split('#')[0].split() param = spl[0] if len(spl) > 2: value = np.cast[float](spl[1:]) else: try: value = float(spl[1]) except: value = spl[1] conf[param] = value return conf def count_beam_orders(self): """Get the maximum polynomial order in DYDX or DLDP for each beam """ self.orders = {} for beam in ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J']: order = 0 while 'DYDX_{0:s}_{1:d}'.format(beam, order) in self.conf.keys(): order += 1 while 'DLDP_{0:s}_{1:d}'.format(beam, order) in self.conf.keys(): order += 1 self.orders[beam] = order - 1 def get_beams(self): """Get beam parameters and read sensitivity curves """ import os from collections import OrderedDict from astropy.table import Table, Column self.dxlam = OrderedDict() self.nx = OrderedDict() self.sens = OrderedDict() self.beams = [] for beam in self.orders: if self.orders[beam] > 0: self.beams.append(beam) self.dxlam[beam] = np.arange(self.conf['BEAM{0}'.format(beam)].min(), self.conf['BEAM{0}'.format(beam)].max(), dtype=int) self.nx[beam] = int(self.dxlam[beam].max() - self.dxlam[beam].min()) + 1 self.sens[beam] = Table.read( '{0}/{1}'.format(os.path.dirname(self.conf_file), self.conf['SENSITIVITY_{0}'.format(beam)])) # self.sens[beam].wave = np.cast[np.double](self.sens[beam]['WAVELENGTH']) # self.sens[beam].sens = np.cast[np.double](self.sens[beam]['SENSITIVITY']) ### Need doubles for interpolating functions for col in self.sens[beam].colnames: data = np.cast[np.double](self.sens[beam][col]) self.sens[beam].remove_column(col) self.sens[beam].add_column(Column(data=data, name=col)) self.beams.sort() def field_dependent(self, xi, yi, coeffs): """aXe field-dependent coefficients See the `aXe manual `_ for a description of how the field-dependent coefficients are specified. Parameters ---------- xi, yi : float or array-like Coordinate to evaluate the field dependent coefficients, where `xi = x-REFX` and `yi = y-REFY`. coeffs : array-like Field-dependency coefficients Returns ------- a : float or array-like Evaluated field-dependent coefficients """ ## number of coefficients for a given polynomial order ## 1:1, 2:3, 3:6, 4:10, order:order*(order+1)/2 if isinstance(coeffs, float): order = 1 else: order = int(-1 + np.sqrt(1 + 8 * len(coeffs))) // 2 ## Build polynomial terms array ## $a = a_0+a_1x_i+a_2y_i+a_3x_i^2+a_4x_iy_i+a_5yi^2+$ ... xy = [] for p in range(order): for px in range(p + 1): # print 'x**%d y**%d' %(p-px, px) xy.append(xi ** (p - px) * yi ** (px)) ## Evaluate the polynomial, allowing for N-dimensional inputs a = np.sum((np.array(xy).T * coeffs).T, axis=0) return a def evaluate_dp(self, dx, dydx): """Evalate arc length along the trace given trace polynomial coefficients Parameters ---------- dx : array-like x pixel to evaluate dydx : array-like Coefficients of the trace polynomial Returns ------- dp : array-like Arc length along the trace at position `dx`. For `dydx` polynomial orders 0, 1 or 2, integrate analytically. Higher orders must be integrated numerically. **Constant:** .. math:: dp = dx **Linear:** .. math:: dp = \sqrt{1+\mathrm{DYDX}[1]}\cdot dx **Quadratic:** .. math:: u = \mathrm{DYDX}[1] + 2\ \mathrm{DYDX}[2]\cdot dx .. math:: dp = (u \sqrt{1+u^2} + \mathrm{arcsinh}\ u) / (4\cdot \mathrm{DYDX}[2]) """ ## dp is the arc length along the trace ## $\lambda = dldp_0 + dldp_1 dp + dldp_2 dp^2$ ... poly_order = len(dydx) - 1 if (poly_order == 2): if np.abs(np.unique(dydx[2])).max() == 0: poly_order = 1 if poly_order == 0: ## dy=0 dp = dx elif poly_order == 1: ## constant dy/dx dp = np.sqrt(1 + dydx[1] ** 2) * (dx) elif poly_order == 2: ## quadratic trace u0 = dydx[1] + 2 * dydx[2] * (0) dp0 = (u0 * np.sqrt(1 + u0 ** 2) + np.arcsinh(u0)) / (4 * dydx[2]) u = dydx[1] + 2 * dydx[2] * (dx) dp = (u * np.sqrt(1 + u ** 2) + np.arcsinh(u)) / (4 * dydx[2]) - dp0 else: ## high order shape, numerical integration along trace ## (this can be slow) xmin = np.minimum((dx).min(), 0) xmax = np.maximum((dx).max(), 0) xfull = np.arange(xmin, xmax) dyfull = 0 for i in range(1, poly_order): dyfull += i * dydx[i] * (xfull - 0.5) ** (i - 1) ## Integrate from 0 to dx / -dx dpfull = xfull * 0. lt0 = xfull < 0 if lt0.sum() > 1: dpfull[lt0] = np.cumsum(np.sqrt(1 + dyfull[lt0][::-1] ** 2))[::-1] dpfull[lt0] *= -1 # gt0 = xfull > 0 if gt0.sum() > 0: dpfull[gt0] = np.cumsum(np.sqrt(1 + dyfull[gt0] ** 2)) dp = np.interp(dx, xfull, dpfull) if dp[-1] == dp[-2]: dp[-1] = dp[-2] + np.diff(dp)[-2] return dp def get_beam_trace(self, x=507, y=507, dx=0., beam='A'): """Get an aXe beam trace for an input reference pixel and list of output x pixels `dx` Parameters ---------- x, y : float or array-like Evaluate trace definition at detector coordinates `x` and `y`. dx : float or array-like Offset in x pixels from `(x,y)` where to compute trace offset and effective wavelength beam : str Beam name (i.e., spectral order) to compute. By aXe convention, `beam='A'` is the first order, 'B' is the zeroth order and additional beams are the higher positive and negative orders. Returns ------- dy : float or array-like Center of the trace in y pixels offset from `(x,y)` evaluated at `dx`. lam : float or array-like Effective wavelength along the trace evaluated at `dx`. """ NORDER = self.orders[beam] + 1 xi, yi = x - self.xoff, y - self.yoff xoff_beam = self.field_dependent(xi, yi, self.conf['XOFF_{0}'.format(beam)]) yoff_beam = self.field_dependent(xi, yi, self.conf['YOFF_{0}'.format(beam)]) ## y offset of trace (DYDX) dydx = np.zeros(NORDER) # 0 #+1.e-80 dydx = [0] * NORDER for i in range(NORDER): if 'DYDX_{0:s}_{1:d}'.format(beam, i) in self.conf.keys(): coeffs = self.conf['DYDX_{0:s}_{1:d}'.format(beam, i)] dydx[i] = self.field_dependent(xi, yi, coeffs) # $dy = dydx_0+dydx_1 dx+dydx_2 dx^2+$ ... dy = yoff_beam for i in range(NORDER): dy += dydx[i] * (dx - xoff_beam) ** i ## wavelength solution dldp = np.zeros(NORDER) dldp = [0] * NORDER for i in range(NORDER): if 'DLDP_{0:s}_{1:d}'.format(beam, i) in self.conf.keys(): coeffs = self.conf['DLDP_{0:s}_{1:d}'.format(beam, i)] dldp[i] = self.field_dependent(xi, yi, coeffs) self.eval_input = {'x': x, 'y': y, 'beam': beam, 'dx': dx} self.eval_output = {'xi': xi, 'yi': yi, 'dldp': dldp, 'dydx': dydx, 'xoff_beam': xoff_beam, 'yoff_beam': yoff_beam, 'dy': dy} dp = self.evaluate_dp(dx - xoff_beam, dydx) # ## dp is the arc length along the trace # ## $\lambda = dldp_0 + dldp_1 dp + dldp_2 dp^2$ ... # if self.conf['DYDX_ORDER_%s' %(beam)] == 0: ## dy=0 # dp = dx-xoff_beam # elif self.conf['DYDX_ORDER_%s' %(beam)] == 1: ## constant dy/dx # dp = np.sqrt(1+dydx[1]**2)*(dx-xoff_beam) # elif self.conf['DYDX_ORDER_%s' %(beam)] == 2: ## quadratic trace # u0 = dydx[1]+2*dydx[2]*(0) # dp0 = (u0*np.sqrt(1+u0**2)+np.arcsinh(u0))/(4*dydx[2]) # u = dydx[1]+2*dydx[2]*(dx-xoff_beam) # dp = (u*np.sqrt(1+u**2)+np.arcsinh(u))/(4*dydx[2])-dp0 # else: # ## high order shape, numerical integration along trace # ## (this can be slow) # xmin = np.minimum((dx-xoff_beam).min(), 0) # xmax = np.maximum((dx-xoff_beam).max(), 0) # xfull = np.arange(xmin, xmax) # dyfull = 0 # for i in range(1, NORDER): # dyfull += i*dydx[i]*(xfull-0.5)**(i-1) # # ## Integrate from 0 to dx / -dx # dpfull = xfull*0. # lt0 = xfull <= 0 # if lt0.sum() > 1: # dpfull[lt0] = np.cumsum(np.sqrt(1+dyfull[lt0][::-1]**2))[::-1] # dpfull[lt0] *= -1 # # # gt0 = xfull >= 0 # if gt0.sum() > 0: # dpfull[gt0] = np.cumsum(np.sqrt(1+dyfull[gt0]**2)) # # dp = np.interp(dx-xoff_beam, xfull, dpfull) ## Evaluate dldp lam = dp * 0. for i in range(NORDER): lam += dldp[i] * dp ** i return dy, lam def show_beams(self, beams=['E', 'D', 'C', 'B', 'A']): """ Make a demo plot of the beams of a given configuration file """ import matplotlib.pyplot as plt x0, x1 = 507, 507 dx = np.arange(-800, 1200) if 'WFC3.UV' in self.conf_file: x0, x1 = 2073, 250 dx = np.arange(-1200, 1200) if 'G800L' in self.conf_file: x0, x1 = 2124, 1024 dx = np.arange(-1200, 1200) s = 200 # marker size fig = plt.figure(figsize=[10, 3]) plt.scatter(0, 0, marker='s', s=s, color='black', edgecolor='0.8', label='Direct') for beam in beams: if 'XOFF_{0}'.format(beam) not in self.conf.keys(): continue xoff = self.field_dependent(x0, x1, self.conf['XOFF_{0}'.format(beam)]) dy, lam = self.get_beam_trace(x0, x1, dx=dx, beam=beam) xlim = self.conf['BEAM{0}'.format(beam)] ok = (dx >= xlim[0]) & (dx <= xlim[1]) plt.scatter(dx[ok] + xoff, dy[ok], c=lam[ok] / 1.e4, marker='s', s=s, alpha=0.5, edgecolor='None') plt.text(np.median(dx[ok]), np.median(dy[ok]) + 1, beam, ha='center', va='center', fontsize=14) print('Beam {0}, lambda=({1:.1f} - {2:.1f})'.format(beam, lam[ok].min(), lam[ok].max())) plt.grid() plt.xlabel(r'$\Delta x$') plt.ylabel(r'$\Delta y$') cb = plt.colorbar(pad=0.01, fraction=0.05) cb.set_label(r'$\lambda\,(\mu\mathrm{m})$') plt.title(self.conf_file) plt.tight_layout() plt.savefig('{0}.pdf'.format(self.conf_file)) # def load_grism_config(conf_file): # """Load parameters from an aXe configuration file # Parameters # ---------- # conf_file : str # Filename of the configuration file # Returns # ------- # conf : `~grizli.grismconf.aXeConf` # Configuration file object. Runs `conf.get_beams()` to read the # sensitivity curves. # """ # conf = aXeConf(conf_file) # conf.get_beams() # return conf