diff --git a/bin/test_square_knm.py b/bin/test_square_knm.py
new file mode 100644
index 0000000000000000000000000000000000000000..c1950c9807926489c0e05d185961065033c0baaf
--- /dev/null
+++ b/bin/test_square_knm.py
@@ -0,0 +1,20 @@
+import pykat
+import numpy as np
+from pykat.optics.knm import square_aperture_HG_knm, riemann_HG_knm
+import math
+
+R = 0.15
+q = pykat.beam_param(w0=6e-3, z=2000)
+N = 1201
+
+mode_i = (0,0)
+mode_o = (0,0)
+
+k = square_aperture_HG_knm(mode_i, mode_o, q, R)
+
+x = y = np.linspace(-R, R, N)
+Axy = np.ones((N,N))
+k_ = riemann_HG_knm(x, y, mode_i, mode_o, q, q, Axy=Axy, newtonCotesOrder=2)
+
+print "%15.15f + %15.15fi" % (k.real, k.imag)
+print "%15.15f + %15.15fi" % (k_.real, k_.imag), abs(k-k_)/1e-6, "ppm"
\ No newline at end of file
diff --git a/pykat/optics/gaussian_beams.py b/pykat/optics/gaussian_beams.py
index b7e524fee880b38e4ce03ebb0e124fadee9a5adb..6d8c0ed4f2879343ea251c0b929d80493b652f41 100644
--- a/pykat/optics/gaussian_beams.py
+++ b/pykat/optics/gaussian_beams.py
@@ -318,7 +318,15 @@ class HG_beam(object):
self._qy = copy.deepcopy(value)
else:
self._qy = beam_param(q=complex(value))
-
+
+ @property
+ def constant_x(self):
+ return self.__xpre_const
+
+ @property
+ def constant_y(self):
+ return self.__ypre_const
+
def _calc_constants(self):
self.__xpre_const = math.pow(2.0/math.pi, 0.25)
self.__xpre_const *= np.sqrt(1.0/(self._qx.w0 * 2**(self._n) * np.math.factorial(self._n)))
@@ -338,7 +346,7 @@ class HG_beam(object):
self.__invqx = 1/ self._qx.q
self.__invqy = 1/ self._qy.q
-
+
def Un(self, x):
return self.__xpre_const * self._hn(self.__sqrt2_wxz * x) * np.exp(-0.5j * self.__kx * x*x * self.__invqx)
diff --git a/pykat/optics/knm.py b/pykat/optics/knm.py
index 69435a818e210b90265c0394217e6da92db132f6..881efc4fad864c47603083e44b65e534929c8320 100644
--- a/pykat/optics/knm.py
+++ b/pykat/optics/knm.py
@@ -6,6 +6,10 @@ from pykat.external.progressbar import ProgressBar, ETA, Percentage, Bar
from scipy.interpolate import interp2d
from scipy.integrate import dblquad
from pykat.optics.romhom import ROMWeights
+from math import factorial
+from pykat.maths.hermite import hermite
+from scipy.misc import comb
+from scipy.integrate import newton_cotes
import time
import pykat.optics.maps
@@ -144,15 +148,16 @@ def adaptive_knm(mode_in, mode_out, q1, q2, q1y=None, q2y=None, smap=None, delta
return R + 1j * I
-def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None, cache=None, delta=(0,0), params={}):
+def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None,
+ Axy=None, cache=None, delta=(0,0), params={}, newtonCotesOrder=0):
- if Axy == None:
+ if Axy is None:
Axy == np.ones((len(x), len(y)))
- if q1y == None:
+ if q1y is None:
q1y = q1
- if q2y == None:
+ if q2y is None:
q2y = q2
if len(mode_in) != 2 or len(mode_out) != 2:
@@ -164,11 +169,35 @@ def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None
if cache == None:
Hg_in = HG_beam(qx=q1, qy=q1y, n=mode_in[0], m=mode_in[1])
Hg_out = HG_beam(qx=q2, qy=q2y, n=mode_out[0], m=mode_out[1])
-
+
U1 = Hg_in.Unm(x+delta[0], y+delta[1])
U2 = Hg_out.Unm(x,y).conjugate()
-
- return dx * dy * np.einsum('ij,ij', Axy, U1*U2)
+
+ if newtonCotesOrder > 0:
+
+ W = newton_cotes(newtonCotesOrder, 1)[0]
+
+ if newtonCotesOrder > 1:
+ if (len(x) - len(W)) % newtonCotesOrder != 0:
+ raise ValueError("To use Newton-Cotes order {0} the number of data points in x must ensure: (N_x - ({0}+1)) mod {0} == 0".format(newtonCotesOrder) )
+
+ if (len(y) - len(W)) % newtonCotesOrder != 0:
+ raise ValueError("To use Newton-Cotes order {0} the number of data points in y must ensure: (N_y - ({0}+1)) mod {0} == 0".format(newtonCotesOrder) )
+
+ wx = np.zeros(x.shape, dtype=np.float64)
+ wy = np.zeros(y.shape, dtype=np.float64)
+
+ N = len(W)
+
+ for i in range(0, (len(wx)-1)/newtonCotesOrder): wx[(i*(N-1)):(i*(N-1)+N)] += W
+ for i in range(0, (len(wy)-1)/newtonCotesOrder): wy[(i*(N-1)):(i*(N-1)+N)] += W
+
+ Wxy = np.outer(wx, wy)
+
+ if newtonCotesOrder == 0:
+ return dx * dy * np.einsum('ij,ij', Axy, U1*U2)
+ else:
+ return dx * dy * np.einsum('ij,ij', Axy, U1*U2*Wxy)
else:
strx = "u1[%i,%i]" % (mode_in[0], mode_out[0])
@@ -438,6 +467,63 @@ def bayerhelms_HG_knm(mode_in, mode_out, q1, q2, q1y=None, q2y=None, gamma=(0,0)
return __bayerhelms_kn(n,_n, q1, q2, 2*gamma[0]) * __bayerhelms_kn(m, _m, q1y, q2y, 2*gamma[1])
+def __sqaure_knm_int(n, _n, R):
+ # This uses the H_n(x) * H_m(x) product identity to reduce the overlap into
+ # a sum of factorial and an integral of a single Hermite with a gaussian function
+ # thus making it easier to solve
+ expR = math.exp(-(R**2))
+ S = 0
+
+ for j in range(0, min(n, _n)+1):
+ _j1 = _n + n - 2*j - 1
+
+ if _j1+1 == 0:
+ # for the zeroth order we just have the gaussian integral to solve
+ L = math.sqrt(math.pi) * math.erf(R)
+ elif (_j1+1) % 2 == 1:
+ # if the Hermite is odd then the integral is always 0 as its anti-symmetric
+ L = 0
+ else:
+ L = 2 * hermite(_j1, 0) - expR * (hermite(_j1, R) - hermite(_j1, -R))
+
+ I = 2**j * factorial(j) * comb(n, j) * comb(_n, j)
+
+ S += I * L
+
+ return S
+
+
+def square_aperture_HG_knm(mode_in, mode_out, q, R):
+ """
+ Computes the coupling coefficients for a square aperture.
+ """
+ # x modes
+ n = mode_in[0]
+ _n = mode_out[0]
+
+ # y modes
+ m = mode_in[1]
+ _m = mode_out[1]
+
+ hg1 = HG_beam(q, n=n, m=m)
+ hg2 = HG_beam(q, n=_n, m=_m)
+
+ kx = hg1.constant_x * hg2.constant_x.conjugate()
+ ky = hg1.constant_y * hg2.constant_y.conjugate()
+
+ print hg1.constant_x, hg2.constant_x, hg1.constant_y, hg2.constant_y
+
+ f = q.w / math.sqrt(2)
+ R = R / (q.w / math.sqrt(2))
+
+ kx *= f
+ kx *= __sqaure_knm_int(n, _n, R)
+
+ ky *= f
+ ky *= __sqaure_knm_int(m, _m, R)
+
+ return kx * ky
+
def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riemann", verbose=False, profile=False, gamma=(0,0), delta=(0,0), params={}):
@@ -547,6 +633,9 @@ def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riema
return K.reshape(couplings.shape[:-1])
+
+
+
def plot_knm_matrix(couplings, knm):
import pylab as plt
diff --git a/pykat/optics/romhom.py b/pykat/optics/romhom.py
index b0b75f18f156300ae55aa661aa734bedf83000e7..1938d249f8e088c5de92cbd9e6933b9f259b418e 100644
--- a/pykat/optics/romhom.py
+++ b/pykat/optics/romhom.py
@@ -177,7 +177,11 @@ def makeReducedBasis(x, isModeMatched=True, tolerance = 1e-12, sigma = 1, greedy
greedyfile = os.path.join(pykat.__path__[0],'optics','greedypoints',greedypts)
- limits = np.loadtxt(greedyfile, usecols=(1,))[:5]
+ # Two potential different formats
+ try:
+ limits = np.loadtxt(greedyfile, usecols=(3,))[:5]
+ except IndexError:
+ limits = np.loadtxt(greedyfile, usecols=(1,))[:5]
romlimits = ROMLimits(w0min=limits[0], w0max=limits[1], zmin=limits[2], zmax=limits[3], max_order=limits[4])