maps.py 18.1 KB
 Andreas Freise committed Dec 20, 2014 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 """ ------------------------------------------------------ Utility functions for handling mirror surface maps. Some functions based on earlier version in Matlab (http://www.gwoptics.org/simtools/) Work in progress, currently these functions are untested! http://www.gwoptics.org/pykat/ ------------------------------------------------------ """ from __future__ import absolute_import from __future__ import division from __future__ import print_function  Daniel Brown committed Apr 10, 2015 16 17 18 19 from pykat.optics.romhom import makeReducedBasis, makeEmpiricalInterpolant, makeWeights, makeWeightsNew from scipy.interpolate import interp2d, interp1d from pykat.maths.zernike import *  Daniel Brown committed Jul 31, 2014 20 import numpy as np  Daniel Brown committed Jul 25, 2014 21 import math  Daniel Brown committed Apr 10, 2015 22 import pickle  Daniel Brown committed Dec 01, 2014 23   Daniel Brown committed Jul 31, 2014 24 class surfacemap(object):  Daniel Brown committed Mar 30, 2014 25 26 27 28 29 30 31  def __init__(self, name, maptype, size, center, step_size, scaling, data=None): self.name = name self.type = maptype self.center = center self.step_size = step_size self.scaling = scaling  Daniel Brown committed Sep 04, 2014 32 33  self.__interp = None  Andreas Freise committed Dec 21, 2014 34  if data is None:  Daniel Brown committed Jul 31, 2014 35 36 37 38  self.data = np.zeros(size) else: self.data = data  Daniel Brown committed Jul 22, 2014 39  self._rom_weights = None  Daniel Brown committed Mar 30, 2014 40 41 42 43 44 45 46  def write_map(self, filename): with open(filename,'w') as mapfile: mapfile.write("% Surface map\n") mapfile.write("% Name: {0}\n".format(self.name)) mapfile.write("% Type: {0}\n".format(self.type))  Daniel Brown committed Jul 25, 2014 47  mapfile.write("% Size: {0} {1}\n".format(self.data.shape[0], self.data.shape[1]))  Daniel Brown committed Mar 30, 2014 48 49 50 51 52 53 54 55 56 57  mapfile.write("% Optical center (x,y): {0} {1}\n".format(self.center[0], self.center[1])) mapfile.write("% Step size (x,y): {0} {1}\n".format(self.step_size[0], self.step_size[1])) mapfile.write("% Scaling: {0}\n".format(float(self.scaling))) mapfile.write("\n\n") for i in range(0, self.data.shape[0]): for j in range(0, self.data.shape[1]): mapfile.write("%.15g " % self.data[i,j]) mapfile.write("\n")  Daniel Brown committed Sep 04, 2014 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93  @property def data(self): return self.__data @data.setter def data(self, value): self.__data = value self.__interp = None @property def center(self): return self.__center @center.setter def center(self, value): self.__center = value self.__interp = None @property def step_size(self): return self.__step_size @step_size.setter def step_size(self, value): self.__step_size = value self.__interp = None @property def scaling(self): return self.__scaling @scaling.setter def scaling(self, value): self.__scaling = value self.__interp = None  Daniel Brown committed Jun 27, 2014 94 95  @property def x(self):  Daniel Brown committed Jul 31, 2014 96  return self.step_size[0] * (np.array(range(1, self.data.shape[0]+1)) - self.center[0])  Daniel Brown committed Jun 27, 2014 97 98 99  @property def y(self):  Daniel Brown committed Jul 31, 2014 100  return self.step_size[1] * (np.array(range(1, self.data.shape[1]+1))- self.center[1])  Daniel Brown committed Jul 25, 2014 101 102 103 104 105  @property def size(self): return self.data.shape  Daniel Brown committed Jul 22, 2014 106 107  @property def offset(self):  Daniel Brown committed Aug 29, 2014 108  return np.array(self.step_size)*(np.array(self.center) - 1/2. - np.array(self.size)/2.0)  Daniel Brown committed Jul 22, 2014 109 110 111 112  @property def ROMWeights(self): return self._rom_weights  Daniel Brown committed Jul 25, 2014 113   Daniel Brown committed May 27, 2015 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132  def z_xy(self, x=None, y=None, wavelength=1064e-9, direction="11", nr1=1.0, nr2=1.0): """ For this given map the field perturbation is computed. This data is used in computing the coupling coefficient. It returns a grid of complex values representing the change in amplitude or phase of the field. x, y : Points to interpolate at, 'None' for no interpolation. wavelength: Wavelength of light in vacuum [m] direction : 11 (reflection front) 12 (transmission front to back) 21 (transmission back to front) 22 (reflection back) nr1 : refractive index on front side nr2 : refractive index on back side """ assert(nr1 >= 1) assert(nr2 >= 1)  Daniel Brown committed Sep 02, 2014 133   Andreas Freise committed Dec 21, 2014 134  if x is None and y is None:  Daniel Brown committed Sep 04, 2014 135 136  data = self.scaling * self.data else:  Andreas Freise committed Dec 21, 2014 137  if self.__interp is None:  Daniel Brown committed Sep 04, 2014 138 139 140 141  self.__interp = interp2d(self.x, self.y, self.data * self.scaling) data = self.__interp(x, y)  Daniel Brown committed May 27, 2015 142  if direction == "11" or direction == "22":  Daniel Brown committed Sep 02, 2014 143  if "phase" in self.type:  Daniel Brown committed May 27, 2015 144 145 146 147 148 149  k = math.pi * nr1 * 2 / wavelength if direction == "11": return np.exp(-2j * k * data) else: return np.exp(2j * k * data[:, ::-1])  Daniel Brown committed Sep 04, 2014 150   Daniel Brown committed Sep 02, 2014 151  elif "absorption" in self.type:  Daniel Brown committed May 27, 2015 152 153 154 155  if direction == "11": return np.sqrt(1.0 - data) else: return np.sqrt(1.0 - data[:, ::-1])  Daniel Brown committed Sep 02, 2014 156 157  else: raise BasePyKatException("Map type needs handling")  Daniel Brown committed Apr 16, 2015 158   Daniel Brown committed May 27, 2015 159  elif direction == "12" or direction == "21":  Daniel Brown committed Sep 02, 2014 160 161  if "phase" in self.type: k = math.pi * 2 / wavelength  Daniel Brown committed Sep 04, 2014 162   Daniel Brown committed May 27, 2015 163 164 165 166  if direction == "12": return np.exp((nr1-nr2)*k * data) else: return np.exp((nr1-nr2)*k * data[:, ::-1])  Daniel Brown committed Sep 04, 2014 167   Daniel Brown committed May 27, 2015 168 169 170 171 172  elif "absorption" in self.type: if direction == "12": return np.sqrt(1.0 - data) else: return np.sqrt(1.0 - data[:, ::-1])  Daniel Brown committed Sep 02, 2014 173 174  else: raise BasePyKatException("Map type needs handling")  Daniel Brown committed May 27, 2015 175   Daniel Brown committed Jul 25, 2014 176  else:  Daniel Brown committed May 27, 2015 177  raise ValueError("Direction not valid")  Daniel Brown committed Jul 25, 2014 178   Daniel Brown committed Jul 30, 2014 179   Daniel Brown committed Apr 10, 2015 180   Daniel Brown committed May 14, 2015 181  def generateROMWeights(self, EIxFilename, EIyFilename=None, verbose=False, interpolate=False, newtonCotesOrder=8):  Daniel Brown committed Apr 10, 2015 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202  if interpolate == True: # Use EI nodes to interpolate if we with open(EIxFilename, 'rb') as f: EIx = pickle.load(f) if EIyFilename is None: EIy = EIx else: with open(EIyFilename, 'rb') as f: EIy = pickle.load(f) x = EIx.x x.sort() nx = np.unique(np.hstack((x, -x[::-1]))) y = EIy.x y.sort() ny = np.unique(np.hstack((y, -y[::-1]))) self.interpolate(nx, ny)  Daniel Brown committed May 14, 2015 203  self._rom_weights = makeWeightsNew(self, EIxFilename, EIyFilename, verbose=verbose, newtonCotesOrderMapWeight=newtonCotesOrder)  Daniel Brown committed Apr 10, 2015 204 205 206 207 208  return self.ROMWeights def interpolate(self, nx, ny, **kwargs): """ Interpolates the map for some new x and y values.  Daniel Brown committed Jul 22, 2014 209   Daniel Brown committed Apr 10, 2015 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228  Uses scipy.interpolate.interp2d and any keywords arguments are passed on to it, thus settings like interpolation type and fill values can be set. The range of nx and ny must contain the value zero so that the center point of the map can be set. """ D = interp2d(self.x, self.y, self.data, **kwargs) data = D(nx-self.offset[0], ny-self.offset[0]) Dx = interp1d(nx, np.arange(1,len(nx)+1)) Dy = interp1d(ny, np.arange(1,len(ny)+1)) self.center = (Dx(0), Dy(0)) self.step_size = (nx[1]-nx[0], ny[1]-ny[0]) self.data = data  Daniel Brown committed Oct 11, 2014 229  def plot(self, show=True, clabel=None, xlim=None, ylim=None):  Daniel Brown committed Mar 30, 2014 230 231 232  import pylab  Andreas Freise committed Dec 21, 2014 233  if xlim is not None:  Daniel Brown committed Oct 11, 2014 234 235 236 237 238 239 240 241  _x = np.logical_and(self.x<=max(xlim)/100.0, self.x>=min(xlim)/100.0) xmin = np.min(np.where(_x == True)) xmax = np.max(np.where(_x == True)) else: xmin = 0 xmax = len(self.x)-1 xlim = [self.x.min()*100, self.x.max()*100]  Andreas Freise committed Dec 21, 2014 242  if ylim is not None:  Daniel Brown committed Oct 11, 2014 243 244 245 246 247 248 249 250 251 252 253  _y = np.logical_and(self.y<=max(ylim)/100.0, self.y>=min(ylim)/100.0) ymin = np.min(np.where(_y == True)) ymax = np.max(np.where(_y == True)) else: ymin = 0 ymax = len(self.y)-1 ylim = [self.y.min()*100, self.y.max()*100] zmin = self.data[xmin:xmax,ymin:ymax].min() zmax = self.data[xmin:xmax,ymin:ymax].max()  Daniel Brown committed Jul 22, 2014 254  # 100 factor for scaling to cm  Daniel Brown committed Jun 27, 2014 255 256  xrange = 100*self.x yrange = 100*self.y  Daniel Brown committed Oct 11, 2014 257   Daniel Brown committed Mar 30, 2014 258  fig = pylab.figure()  Daniel Brown committed Oct 11, 2014 259  axes = pylab.pcolormesh(xrange, yrange, self.data, vmin=zmin, vmax=zmax)  Daniel Brown committed Mar 30, 2014 260 261  pylab.xlabel('x [cm]') pylab.ylabel('y [cm]')  Daniel Brown committed May 13, 2014 262   Andreas Freise committed Dec 21, 2014 263 264  if xlim is not None: pylab.xlim(xlim) if ylim is not None: pylab.ylim(ylim)  Daniel Brown committed Oct 11, 2014 265   Daniel Brown committed Mar 30, 2014 266  pylab.title('Surface map {0}, type {1}'.format(self.name, self.type))  Daniel Brown committed Oct 11, 2014 267   Daniel Brown committed Mar 30, 2014 268  cbar = fig.colorbar(axes)  Daniel Brown committed Oct 11, 2014 269  cbar.set_clim(zmin, zmax)  Daniel Brown committed May 13, 2014 270   Andreas Freise committed Dec 21, 2014 271  if clabel is not None:  Daniel Brown committed May 13, 2014 272  cbar.set_label(clabel)  Daniel Brown committed Oct 11, 2014 273   Daniel Brown committed May 13, 2014 274 275  if show: pylab.show()  Daniel Brown committed Oct 11, 2014 276   Daniel Brown committed May 13, 2014 277  return fig  278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295  class mergedmap: """ A merged map combines multiple surfaces map to form one. Such a map can be used for computations of coupling coefficients but it cannot be written to a file to be used with Finesse. For this you must output each map separately. """ def __init__(self, name, size, center, step_size, scaling): self.name = name self.center = center self.step_size = step_size self.scaling = scaling self.__interp = None self._rom_weights = None self.__maps = []  Daniel Brown committed May 11, 2015 296 297  self.weighting = None  298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354  def addMap(self, m): self.__maps.append(m) @property def center(self): return self.__center @center.setter def center(self, value): self.__center = value self.__interp = None @property def step_size(self): return self.__step_size @step_size.setter def step_size(self, value): self.__step_size = value self.__interp = None @property def scaling(self): return self.__scaling @scaling.setter def scaling(self, value): self.__scaling = value self.__interp = None @property def x(self): return self.step_size[0] * (np.array(range(1, self.size[0]+1)) - self.center[0]) @property def y(self): return self.step_size[1] * (np.array(range(1, self.size[1]+1))- self.center[1]) @property def size(self): return self.__maps[0].data.shape @property def offset(self): return np.array(self.step_size)*(np.array(self.center) - 1/2. - np.array(self.size)/2.0) @property def ROMWeights(self): return self._rom_weights def z_xy(self, wavelength=1064e-9, direction="reflection", nr1=1.0, nr2=1.0): z_xy = np.ones(self.size, dtype=np.complex128) for m in self.__maps: z_xy *= m.z_xy(wavelength=wavelength, direction=direction, nr1=nr1, nr2=nr2)  Daniel Brown committed May 11, 2015 355 356 357 358  if self.weighting is None: return z_xy else: return z_xy * self.weighting  359   Daniel Brown committed May 11, 2015 360  def generateROMWeights(self, EIxFilename, EIyFilename=None, verbose=False, interpolate=False, newtonCotesOrder=8):  361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381  if interpolate == True: # Use EI nodes to interpolate if we with open(EIxFilename, 'rb') as f: EIx = pickle.load(f) if EIyFilename is None: EIy = EIx else: with open(EIyFilename, 'rb') as f: EIy = pickle.load(f) x = EIx.x x.sort() nx = np.unique(np.hstack((x, -x[::-1]))) y = EIy.x y.sort() ny = np.unique(np.hstack((y, -y[::-1]))) self.interpolate(nx, ny)  Daniel Brown committed May 11, 2015 382  self._rom_weights = makeWeightsNew(self, EIxFilename, EIyFilename, verbose=verbose, newtonCotesOrderMapWeight=newtonCotesOrder)  Daniel Brown committed May 11, 2015 383   384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449  return self.ROMWeights def interpolate(self, nx, ny, **kwargs): """ Interpolates all the maps that are used to fc Uses scipy.interpolate.interp2d and any keywords arguments are passed on to it, thus settings like interpolation type and fill values can be set. The range of nx and ny must contain the value zero so that the center point of the map can be set. """ for m in self.__maps: m.interpolate(nx, ny) def plot(self, mode="absorption", show=True, clabel=None, xlim=None, ylim=None, wavelength=1064e-9): import pylab if xlim is not None: _x = np.logical_and(self.x<=max(xlim)/100.0, self.x>=min(xlim)/100.0) xmin = np.min(np.where(_x == True)) xmax = np.max(np.where(_x == True)) else: xmin = 0 xmax = len(self.x)-1 xlim = [self.x.min()*100, self.x.max()*100] if ylim is not None: _y = np.logical_and(self.y<=max(ylim)/100.0, self.y>=min(ylim)/100.0) ymin = np.min(np.where(_y == True)) ymax = np.max(np.where(_y == True)) else: ymin = 0 ymax = len(self.y)-1 ylim = [self.y.min()*100, self.y.max()*100] if mode == "absorption": # plots how much of field is absorbed data = 1-np.abs(self.z_xy()) elif mode == "meter": # plot the phase in terms of meters of displacement k = 2*np.pi/wavelength data = np.angle(self.z_xy()) / (2*k) zmin = data[xmin:xmax,ymin:ymax].min() zmax = data[xmin:xmax,ymin:ymax].max() # 100 factor for scaling to cm xrange = 100*self.x yrange = 100*self.y fig = pylab.figure() axes = pylab.pcolormesh(xrange, yrange, data, vmin=zmin, vmax=zmax) pylab.xlabel('x [cm]') pylab.ylabel('y [cm]') if xlim is not None: pylab.xlim(xlim) if ylim is not None: pylab.ylim(ylim) pylab.title('Merged map {0}, mode {1}'.format(self.name, mode)) cbar = fig.colorbar(axes) cbar.set_clim(zmin, zmax)  Daniel Brown committed Sep 02, 2014 450   451 452 453 454 455 456 457 458  if clabel is not None: cbar.set_label(clabel) if show: pylab.show() return fig  Daniel Brown committed Sep 02, 2014 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 class aperturemap(surfacemap): def __init__(self, name, size, step_size, R): surfacemap.__init__(self, name, "absorption both", size, (np.array(size)+1)/2.0, step_size, 1) self.R = R @property def R(self): return self.__R @R.setter def R(self, value): self.__R = value xx, yy = np.meshgrid(self.x, self.y) radius = np.sqrt(xx**2 + yy**2) self.data = np.zeros(self.size) self.data[radius > self.R] = 1.0 class curvedmap(surfacemap): def __init__(self, name, size, step_size, Rc): surfacemap.__init__(self, name, "phase reflection", size, (np.array(size)+1)/2.0, step_size, 1e-6) self.Rc = Rc @property def Rc(self): return self.__Rc @Rc.setter def Rc(self, value): self.__Rc = value xx, yy = np.meshgrid(self.x, self.y) Rsq = xx**2 + yy**2 self.data = (self.Rc - math.copysign(1.0, self.Rc) * np.sqrt(self.Rc**2 - Rsq))/ self.scaling  Daniel Brown committed Jul 31, 2014 499 500  class tiltmap(surfacemap):  Daniel Brown committed May 27, 2015 501 502 503 504 505 506 507 508 509 510 511 512  """ To create a tiltmap, plot it and write it to a file to use with Finesse: tilts = (1e-6, 1e-8) # tilt in (x, y) radians\ dx = 1e-4 L = 0.2 N = L/dx tmap = tiltmap("tilt", (N, N), (dx,dx), tilts) tmap.plot() tmap.write_map("mytilt.map") """  Daniel Brown committed Jul 31, 2014 513 514  def __init__(self, name, size, step_size, tilt):  Daniel Brown committed Feb 03, 2015 515  surfacemap.__init__(self, name, "phase reflection", size, (np.array(size)+1)/2.0, step_size, 1e-9)  Daniel Brown committed Jul 31, 2014 516 517 518 519 520 521 522 523 524 525 526 527  self.tilt = tilt @property def tilt(self): return self.__tilt @tilt.setter def tilt(self, value): self.__tilt = value xx, yy = np.meshgrid(self.x, self.y)  528  self.data = (yy * self.tilt[1] + xx * self.tilt[0])/self.scaling  Daniel Brown committed Jul 31, 2014 529   Daniel Brown committed Dec 01, 2014 530 531 532  class zernikemap(surfacemap): def __init__(self, name, size, step_size, radius, scaling=1e-9):  Daniel Brown committed Feb 03, 2015 533  surfacemap.__init__(self, name, "phase reflection", size, (np.array(size)+1)/2.0, step_size, scaling)  Daniel Brown committed Dec 01, 2014 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562  self.__zernikes = {} self.radius = radius @property def radius(self): return self.__radius @radius.setter def radius(self, value, update=True): self.__radius = float(value) if update: self.update_data() def setZernike(self, m, n, amplitude, update=True): self.__zernikes["%i%i" % (m, n)] = (m,n,amplitude) if update: self.update_data() def update_data(self): X,Y = np.meshgrid(self.x, self.y) R = np.sqrt(X**2 + Y**2) PHI = np.arctan2(Y, X) data = np.zeros(np.shape(R)) for i in self.__zernikes.items(): data += i[1][2] * zernike(i[1][0], i[1][1], R/self.radius, PHI) self.data = data  Daniel Brown committed Mar 30, 2014 563 564 565 566 567 568 def read_map(filename): with open(filename, 'r') as f: f.readline() name = f.readline().split(':')[1].strip() maptype = f.readline().split(':')[1].strip()  Daniel Brown committed May 07, 2015 569  size = tuple(map(lambda x: float(x), f.readline().split(':')[1].strip().split()))  Daniel Brown committed Mar 30, 2014 570 571 572 573 574 575  center = tuple(map(lambda x: float(x), f.readline().split(':')[1].strip().split())) step = tuple(map(lambda x: float(x), f.readline().split(':')[1].strip().split())) scaling = float(f.readline().split(':')[1].strip())  Daniel Brown committed Jul 31, 2014 576  data = np.loadtxt(filename, dtype=np.float64,ndmin=2,comments='%')  Daniel Brown committed Mar 30, 2014 577 578 579 580  return surfacemap(name,maptype,size,center,step,scaling,data)  Andreas Freise committed May 22, 2015 581 582 583 584 585 586 587 # TODO: Recreate functions from Simtools:, List taken from: ligo_maps/FT_convert_ligo_map_for_finesse.m # map=FT_recenter_mirror_map(map); # [map2,A2,Rc_out]=FT_remove_zernike_curvatures_from_map(map,Rc_in); # [map2,Rc_out]=FT_remove_curvature_from_mirror_map(map,Rc_in,w, display_style); # [map2,offset]=FT_remove_offset_from_mirror_map(map2,1e-2); # [map3,x_tilt,y_tilt,offset2]=FT_remove_piston_from_mirror_map(map2,w, display_style); # map3=FT_invert_mirror_map(map3, invert);