maps.py 18.2 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 Sep 04, 2014 114  def z_xy(self, x=None, y=None, wavelength=1064e-9, direction="reflection", nr1=1.0, nr2=1.0):  Daniel Brown committed Sep 02, 2014 115   Andreas Freise committed Dec 21, 2014 116  if x is None and y is None:  Daniel Brown committed Sep 04, 2014 117 118  data = self.scaling * self.data else:  Andreas Freise committed Dec 21, 2014 119  if self.__interp is None:  Daniel Brown committed Sep 04, 2014 120 121 122 123  self.__interp = interp2d(self.x, self.y, self.data * self.scaling) data = self.__interp(x, y)  Daniel Brown committed Sep 02, 2014 124 125 126  if direction == "reflection": if "phase" in self.type: k = math.pi * 2 / wavelength  Daniel Brown committed Sep 04, 2014 127 128  return np.exp(2j * k * data)  Daniel Brown committed Sep 02, 2014 129  elif "absorption" in self.type:  Daniel Brown committed Sep 04, 2014 130  return np.sqrt(1.0 - data)  Daniel Brown committed Sep 02, 2014 131 132  else: raise BasePyKatException("Map type needs handling")  Daniel Brown committed Apr 16, 2015 133   Daniel Brown committed Sep 02, 2014 134 135 136  elif direction == "transmission": if "phase" in self.type: k = math.pi * 2 / wavelength  Daniel Brown committed Sep 04, 2014 137 138  return np.exp((nr1-nr2)*k * data)  Daniel Brown committed Sep 02, 2014 139  elif "absorption" in self.type:  Daniel Brown committed Sep 04, 2014 140 141  return np.sqrt(1.0 - data)  Daniel Brown committed Sep 02, 2014 142 143  else: raise BasePyKatException("Map type needs handling")  Daniel Brown committed Jul 25, 2014 144 145 146  else: raise BasePyKatException("Map type needs handling")  Daniel Brown committed Jul 30, 2014 147   148  def generateROMWeights(self, isModeMatched=True, verbose=False, interpolate=False, interpolate_N=None, tolerance = 1e-12, sigma = 1, sort=False, greedyfile=None, useSymmetry=True):  Daniel Brown committed Aug 29, 2014 149 150 151 152 153 154  if interpolate: from scipy.interpolate import interp2d import numpy as np D = interp2d(self.x, self.y, self.data, fill_value=0)  Daniel Brown committed Jan 23, 2015 155 156 157  if interpolate_N is None: interpolate_N = (self.size[0], self.size[1])  Daniel Brown committed Aug 29, 2014 158 159  # only want even number of data points spread equally # about the axes  Daniel Brown committed Jan 23, 2015 160 161  if interpolate_N[0] % 2 == 0: Nx = interpolate_N[0]  Daniel Brown committed Aug 29, 2014 162  else:  Daniel Brown committed Jan 23, 2015 163  Nx = interpolate_N[0]-1  Daniel Brown committed Aug 29, 2014 164   Daniel Brown committed Jan 23, 2015 165 166  if interpolate_N[1] % 2 == 0: Ny = interpolate_N[1]  Daniel Brown committed Aug 29, 2014 167  else:  Daniel Brown committed Jan 23, 2015 168  Ny = interpolate_N[1]-1  Daniel Brown committed Aug 29, 2014 169   Daniel Brown committed Jan 23, 2015 170 171  nx = np.linspace(min(self.x), max(self.x), interpolate_N[0]) ny = np.linspace(min(self.y), max(self.y), interpolate_N[1])  Daniel Brown committed Aug 29, 2014 172 173 174  data = D(nx-self.offset[0], ny-self.offset[0])  Daniel Brown committed Feb 17, 2015 175  self.name += "[ROMHOM_Interpolated]"  Daniel Brown committed Aug 29, 2014 176 177 178 179  self.center = (np.array(data.shape)+1)/2.0 self.data = data  180 181 182 183 184 185 186  if useSymmetry: xm = self.x[self.x<0] ym = self.y[self.y<0] else: xm = self.x ym = self.y  Daniel Brown committed Aug 29, 2014 187 188 189  if min(xm) == min(ym) and max(xm) == max(ym) and len(xm) == len(ym): symm = True  190 191 192  else: symm = False  Daniel Brown committed Jul 30, 2014 193 194  EI = {}  195  EI["x"] = makeEmpiricalInterpolant(makeReducedBasis(xm, isModeMatched=isModeMatched, tolerance = tolerance, sigma = sigma, greedyfile=greedyfile), sort=sort)  Daniel Brown committed Aug 29, 2014 196 197  if symm:  198  EI["y"] = EI["x"]  Daniel Brown committed Aug 29, 2014 199  else:  200  EI["y"] = makeEmpiricalInterpolant(makeReducedBasis(ym, isModeMatched=isModeMatched, tolerance = tolerance, sigma = sigma, greedyfile=greedyfile), sort=sort)  Daniel Brown committed Jul 30, 2014 201   202  EI["limits"] = EI["x"].limits  Daniel Brown committed Jul 30, 2014 203   204  self._rom_weights = makeWeights(self, EI, verbose=verbose, useSymmetry=useSymmetry)  Daniel Brown committed Jul 22, 2014 205   Daniel Brown committed Jul 25, 2014 206  return self.ROMWeights, EI  Daniel Brown committed Apr 10, 2015 207 208   Daniel Brown committed May 11, 2015 209  def generateROMWeightsNew(self, EIxFilename, EIyFilename=None, verbose=False, interpolate=False, newtonCotesOrder=8):  Daniel Brown committed Apr 10, 2015 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230  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 231  self._rom_weights = makeWeightsNew(self, EIxFilename, EIyFilename, verbose=verbose, newtonCotesOrder=newtonCotesOrder)  Daniel Brown committed Apr 10, 2015 232 233 234 235 236  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 237   Daniel Brown committed Apr 10, 2015 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256  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 257  def plot(self, show=True, clabel=None, xlim=None, ylim=None):  Daniel Brown committed Mar 30, 2014 258 259 260  import pylab  Andreas Freise committed Dec 21, 2014 261  if xlim is not None:  Daniel Brown committed Oct 11, 2014 262 263 264 265 266 267 268 269  _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 270  if ylim is not None:  Daniel Brown committed Oct 11, 2014 271 272 273 274 275 276 277 278 279 280 281  _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 282  # 100 factor for scaling to cm  Daniel Brown committed Jun 27, 2014 283 284  xrange = 100*self.x yrange = 100*self.y  Daniel Brown committed Oct 11, 2014 285   Daniel Brown committed Mar 30, 2014 286  fig = pylab.figure()  Daniel Brown committed Oct 11, 2014 287  axes = pylab.pcolormesh(xrange, yrange, self.data, vmin=zmin, vmax=zmax)  Daniel Brown committed Mar 30, 2014 288 289  pylab.xlabel('x [cm]') pylab.ylabel('y [cm]')  Daniel Brown committed May 13, 2014 290   Andreas Freise committed Dec 21, 2014 291 292  if xlim is not None: pylab.xlim(xlim) if ylim is not None: pylab.ylim(ylim)  Daniel Brown committed Oct 11, 2014 293   Daniel Brown committed Mar 30, 2014 294  pylab.title('Surface map {0}, type {1}'.format(self.name, self.type))  Daniel Brown committed Oct 11, 2014 295   Daniel Brown committed Mar 30, 2014 296  cbar = fig.colorbar(axes)  Daniel Brown committed Oct 11, 2014 297  cbar.set_clim(zmin, zmax)  Daniel Brown committed May 13, 2014 298   Andreas Freise committed Dec 21, 2014 299  if clabel is not None:  Daniel Brown committed May 13, 2014 300  cbar.set_label(clabel)  Daniel Brown committed Oct 11, 2014 301   Daniel Brown committed May 13, 2014 302 303  if show: pylab.show()  Daniel Brown committed Oct 11, 2014 304   Daniel Brown committed May 13, 2014 305  return fig  306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323  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 324 325  self.weighting = None  326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382  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 383 384 385 386  if self.weighting is None: return z_xy else: return z_xy * self.weighting  387   Daniel Brown committed May 11, 2015 388  def generateROMWeights(self, EIxFilename, EIyFilename=None, verbose=False, interpolate=False, newtonCotesOrder=8):  389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409  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 410  self._rom_weights = makeWeightsNew(self, EIxFilename, EIyFilename, verbose=verbose, newtonCotesOrderMapWeight=newtonCotesOrder)  Daniel Brown committed May 11, 2015 411   412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477  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 478   479 480 481 482 483 484 485 486  if clabel is not None: cbar.set_label(clabel) if show: pylab.show() return fig  Daniel Brown committed Sep 02, 2014 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 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 527 528 529 530  class tiltmap(surfacemap): def __init__(self, name, size, step_size, tilt):  Daniel Brown committed Feb 03, 2015 531  surfacemap.__init__(self, name, "phase reflection", size, (np.array(size)+1)/2.0, step_size, 1e-9)  Daniel Brown committed Jul 31, 2014 532 533 534 535 536 537 538 539 540 541 542 543  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)  544  self.data = (yy * self.tilt[1] + xx * self.tilt[0])/self.scaling  Daniel Brown committed Jul 31, 2014 545   Daniel Brown committed Dec 01, 2014 546 547 548  class zernikemap(surfacemap): def __init__(self, name, size, step_size, radius, scaling=1e-9):  Daniel Brown committed Feb 03, 2015 549  surfacemap.__init__(self, name, "phase reflection", size, (np.array(size)+1)/2.0, step_size, scaling)  Daniel Brown committed Dec 01, 2014 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578  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 579 580 581 582 583 584 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 585  size = tuple(map(lambda x: float(x), f.readline().split(':')[1].strip().split()))  Daniel Brown committed Mar 30, 2014 586 587 588 589 590 591  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 592  data = np.loadtxt(filename, dtype=np.float64,ndmin=2,comments='%')  Daniel Brown committed Mar 30, 2014 593 594 595 596 597  return surfacemap(name,maptype,size,center,step,scaling,data)  Andreas Freise committed Dec 20, 2014 598