def beam_size(tmpkat, f):
kat = copy.deepcopy(tmpkat)
# 1. run finesse with input laser mode matched to cavity (no thermal lens)
out = kat.run()
# beam at laser when matched to cold cavity
# (note the sign flip of the real part to change direction of gauss param)
q0 = -1.0 * out['w0'].conjugate()
beam0 = beam_param(q=q0)
kat.psl.npsl.node.setGauss(kat.psl, beam0)
kat.parseKatCode("startnode npsl")
# add thermal lens and propagate input beam to ITM
kat.ITM_TL.f = f
if "ITM_TL_r" in kat._kat__components:
kat.ITM_TL_r.f = f
out = kat.run()
# computing beam size at ITM
# and then we reflect of ITM, an set it as new startnode
q_in = out['w1']
from pykat.optics.ABCD import apply, mirror_refl
abcd = mirror_refl(1, -2500)
q_out = apply(abcd, q_in, 1, 1)
beam1 = beam_param(q=q_out)
kat.removeLine("startnode")
kat.psl.npsl.node.removeGauss()
if "ITM_TL_r" in kat._kat__components:
kat.ITM.nITM1r.node.setGauss(kat.ITM, beam1)
kat.parseKatCode("startnode nITM1r")
else:
kat.ITM.nITM1.node.setGauss(kat.ITM, beam1)
kat.parseKatCode("startnode nITM1")
out = kat.run()
# computing beam size at WFS1 and WFS2
q2 = out['w2']
beam2 = beam_param(q=q2)
q3 = out['w3']
beam3 = beam_param(q=q3)
print(
" Sideband (input mode) beam size with thermal lens f={0}".format(
f))
print(" - WFS1 w={0:.6}cm".format(100.0 * beam2.w))
print(" (w0={0}, z={1})".format(beam2.w0, beam2.z))
print(" - WFS2 w={0:.6}cm".format(100.0 * beam3.w))
print(" (w0={0}, z={1})".format(beam3.w0, beam3.z))
input("Press enter to continue")
return (beam1, beam2, beam3)
def beam_size(tmpkat, f, beam0):
kat = copy.deepcopy(tmpkat)
kat.psl.npsl.node.setGauss(kat.psl, beam0)
# add thermal lens and propagate input beam to ITM
kat = set_thermal_lens(kat, f)
out = kat.run()
# computing beam size at ITM
# and then we reflect of ITM, an set it as new startnode
q_in = out['w1']
#import pykat.optics.ABCD as ABCD
#abcd = ABCD.mirror_refl(1,2500)
#q_out = ABCD.apply(abcd,q_in,1,1)
beam1 = beam_param(q=q_in)
kat.removeLine("startnode")
kat.psl.npsl.node.removeGauss()
if "ITM_TL_r" in kat._kat__components:
kat.ITM.nITM1r.node.setGauss(kat.ITM, beam1)
kat.parseKatCode("startnode nITM1r")
else:
kat.ITM.nITM1.node.setGauss(kat.ITM, beam1)
kat.parseKatCode("startnode nITM1")
out = kat.run()
# computing beam size at WFS1 and WFS2
q2 = out['w2']
beam2 = beam_param(q=q2)
q3 = out['w3']
beam3 = beam_param(q=q3)
# computing beam size at pick off
q4 = out['w4']
beam4 = beam_param(q=q4)
print(" Input mode beam size with thermal lens f={0}".format(f))
print(" - ITM w={0:.6}cm (w0={1}, z={2})".format(100.0*beam1.w,beam1.w0, beam1.z))
print(" - WFS1 w={0:.6}cm (w0={1}, z={2})".format(100.0*beam2.w,beam2.w0, beam2.z))
print(" - WFS2 w={0:.6}cm (w0={1}, z={2})".format(100.0*beam3.w,beam3.w0, beam3.z))
print(" - npo2 w={0:.6}cm (w0={1}, z={2})".format(100.0*beam4.w,beam4.w0, beam4.z))
#raw_input("Press enter to continue")
return [beam1, beam2, beam3, beam4]
def main():
print("""
--------------------------------------------------------------
Example file for using PyKat for an FFT-based simulation
of an Advanced LIGO arm cavity
PyKat: http://www.gwoptics.org/pykat
Advanced LIGO: http://www.advancedligo.mit.edu/
Requires surface map file: etm08_virtual.txt
Andreas Freise 20.12.2014
--------------------------------------------------------------
""")
# defining variables as global for debugging
tmpresultfile = 'myshelf1.dat'
result={}
#Advanced LIGO parameters
# length [m] 3994.5
# FSR [kHz] 37.5
# T1 1.4%
# T2 5ppm
# finesse 445
# FWHM [Hz] 84
# mirror diameter: 0.32 m
# ITM RC [m] 1934
# ETM RC [m] 2245
# w0 [cm] 1.2
# w1 [cm] 5.3
# w2 [cm] 6.2
# z1 [m] -1834
# loading kat file to get parameters and to compute input beam parameters
global kat, out
kat = pykat.finesse.kat()
kat.verbose = False
kat.loadKatFile('aligo_Xarm.kat')
# setting ITM T to larger value for better plots
kat.itmX.T=0.1
kat.itmX.R=0.9
Lambda = kat.lambda0
LX=kat.LX.L.value
kat.maxtem=0
out = kat.run()
w0=out.y[0][0]
z0=-out.y[0][1]
# load and create mirror maps
global itm, etm
surface=read_map('etm08_virtual.txt')
itm=curvedmap('itm_Rc',surface.size,surface.step_size, -1.0*abs(kat.itmX.Rc.value))
etm=curvedmap('etm_Rc',surface.size,surface.step_size, -1.0*abs(kat.etmX.Rc.value))
#itm.plot()
#etm.plot()
# apply measured map to etm, using 20 times larger distortions
etm.data = etm.data + surface.data*surface.scaling/etm.scaling*20
# setup grid for FFT propagation
[xpoints,ypoints] = surface.size
xsize = xpoints * surface.step_size[0]
ysize = ypoints * surface.step_size[1]
xoffset = 0.0
yoffset = 0.0
global shape
shape = grid(xpoints, ypoints, xsize, ysize, xoffset, yoffset)
x = shape.xaxis
y = shape.yaxis
result['shape']=shape
# generate roughly mode-matched input beam
global laser
gx = beam_param(w0=w0, z=z0)
beam = HG_mode(gx,gx,0,0)
laser = beam.Unm(x,y)
# some debugging plots
"""
plot_field(laser)
Lrange= np.linspace(0,4000,200)
plot_propagation(laser, shape, Lambda, 0, 1, Lrange, 1)
laser1=FFT_propagate(laser,shape,Lambda,LX,1)
laser2=np.sqrt(kat.etmX.R.value)*FFT_apply_map(laser1, etm, Lambda)
laser3=FFT_propagate(laser2,shape,Lambda,LX,1)
Lrange= np.linspace(0,4000,200)
plot_propagation(laser2, shape, Lambda, 0, 1, Lrange, 1)
plot_field(laser3)
"""
precompute_roundtrips(shape, laser, kat)
# now save any `result' variables:
tmpfile = shelve.open(tmpresultfile)
tmpfile['result']=result
tmpfile.close()
def main():
print("""
--------------------------------------------------------------
Example file for using PyKat http://www.gwoptics.org/pykat
Simple spatial filter to measure the mode content in a
Hermite Gauss beam
Andreas Freise, 18.10.2016
--------------------------------------------------------------
""")
plt.close('all')
# wavelength
Lambda = 1064.0E-9
# distance to propagate/focal length of lens
D = 10
# mix coefficients
c1 = 0.7
c2 = 0.3
# mode indices
n1 = 2
m1 = 3
n2 = 1
m2 = 0
######## Generate Grid stucture required for FFT propagation ####
xpoints = 512
ypoints = 512
xsize = 0.05
ysize = 0.05
# Apply offset such that the center of the beam lies in the
# center of a grid tile
xoffset = -0.5 * xsize / xpoints
yoffset = -0.5 * ysize / ypoints
global shape
shape = grid(xpoints, ypoints, xsize, ysize, xoffset, yoffset)
x = shape.xaxis
y = shape.yaxis
######## Generates a mixture of fields ################
gx = beam_param(w0=2e-3, z=0)
gy = beam_param(w0=2e-3, z=0)
beam = HG_mode(gx, gy, n1, m1)
field1 = beam.Unm(x, y)
beam2 = HG_mode(gx, gy, n2, m2)
field2 = beam2.Unm(x, y)
global field, laser1, laser2
field = np.sqrt(c1) * field1 + np.sqrt(c2) * field2
####### Apply phase plate #######################################
laser1 = field * (np.conjugate(field1))
laser2 = field * (np.conjugate(field2))
####### Propagates the field by FFT ##############################
laser1 = FFT_propagate(laser1, shape, Lambda, D, 1)
laser2 = FFT_propagate(laser2, shape, Lambda, D, 1)
f = D
#laser1 = apply_lens(laser1, shape, Lambda, f)
#laser2 = apply_lens(laser2, shape, Lambda, f)
laser1 = apply_thin_lens(laser1, shape, Lambda, f)
laser2 = apply_thin_lens(laser2, shape, Lambda, f)
laser1 = FFT_propagate(laser1, shape, Lambda, D, 1)
laser2 = FFT_propagate(laser2, shape, Lambda, D, 1)
# midpoint computation for even number of points only!
midx = (xpoints) // 2
midy = (ypoints) // 2
coef1 = np.abs(laser1[midx, midy])
coef2 = np.abs(laser2[midx, midy])
ratio = (coef1 / coef2)**2
pc2 = 1 / (1 + ratio)
pc1 = pc2 * ratio
print("c1 {0}, coef1 {1}, error {3} (raw output {2})".format(
c1, pc1, coef1, np.abs(c1 - pc1)))
print("c2 {0}, coef2 {1}, error {3} (raw output {2})".format(
c2, pc2, coef2, np.abs(c2 - pc2)))
# plot hand tuned for certain ranges and sizes, not automtically scaled
fig = plt.figure(110)
fig.clear()
off1 = xpoints / 10
off2 = xpoints / 6
plt.subplot(1, 3, 1)
plt.imshow(abs(field))
plt.xlim(midx - off1, midx + off1)
plt.ylim(midy - off1, midy + off1)
plt.draw()
plt.subplot(1, 3, 2)
plt.imshow(abs(laser1))
plt.xlim(midx - off2, midx + off2)
plt.ylim(midy - off2, midy + off2)
plt.draw()
plt.subplot(1, 3, 3)
plt.imshow(abs(laser2))
plt.xlim(midx - off2, midx + off2)
plt.ylim(midy - off2, midy + off2)
plt.draw()
if in_ipython():
plt.show(block=0)
else:
plt.show(block=1)
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
from pykat.optics.ABCD import apply, mirror_trans
from pykat.optics.gaussian_beams import beam_param
nr1 = 1
nr2 = 1.44963098985906
q1 = beam_param(q=5.96343 + 3.04713j)
abcd = mirror_trans(nr1, nr2, float("inf"))
# into material
q2 = apply(abcd, q1.q, nr1, nr2)
# and out again
q3 = apply(abcd, q2.q, nr2, nr1)
print("q1 =", q1, " w0 =", q1.w0, " w =", q1.w, " z =", q1.z)
print("q2 =", q2, " w0 =", q2.w0, " w =", q2.w, " z =", q2.z)
print("q3 =", q3, " w0 =", q3.w0, " w =", q3.w, " z =", q3.z)
def main():
print("""
--------------------------------------------------------------
Example file for using PyKat http://www.gwoptics.org/pykat
Generate a HG11 mode from a HG00 mode with a simple
phase plate.
Andreas Freise, 18.10.2016
--------------------------------------------------------------
""")
plt.close('all')
# wavelength
Lambda = 1064.0E-9
# distance to propagate/focal length of lens
D = 4
######## Generate Grid stucture required for FFT propagation ####
xpoints = 512
ypoints = 512
xsize = 0.05
ysize = 0.05
# Apply offset such that the center of the beam lies in the
# center of a grid tile
xoffset = -0.5 * xsize / xpoints
yoffset = -0.5 * ysize / ypoints
shape = grid(xpoints, ypoints, xsize, ysize, xoffset, yoffset)
x = shape.xaxis
y = shape.yaxis
######## Generates input beam ################
gx = beam_param(w0=2e-3, z=0)
gy = beam_param(w0=2e-3, z=0)
beam = HG_mode(gx, gy, 0, 0)
global field, laser
field = beam.Unm(x, y)
####### Apply phase plate #######################################
plate = np.ones([xpoints, ypoints])
plate[0:xpoints // 2, 0:ypoints // 2] = -1.0
plate[xpoints // 2:xpoints, ypoints // 2:ypoints] = -1.0
field2 = field * plate
####### Propagates the field by FFT ##############################
field2 = FFT_propagate(field2, shape, Lambda, D, 1)
# maybe apply a thin lens
f = D
field2 = apply_thin_lens(field2, shape, Lambda, f)
field2 = FFT_propagate(field2, shape, Lambda, D, 1)
midx = (xpoints) // 2
midy = (ypoints) // 2
off1 = 50
off2 = 50
# plot hand tuned for certain ranges and sizes, not automtically scaled
fig = plt.figure(110)
fig.clear()
plt.subplot(1, 3, 1)
plt.imshow(abs(field))
plt.xlim(midx - off1, midx + off1)
plt.ylim(midy - off1, midy + off1)
plt.draw()
plt.subplot(1, 3, 2)
plt.imshow(plate)
#pl.xlim(midx-off2,midx+off2)
#pl.ylim(midy-off2,midy+off2)
plt.draw()
plt.subplot(1, 3, 3)
plt.imshow(abs(field2))
plt.xlim(midx - off2, midx + off2)
plt.ylim(midy - off2, midy + off2)
plt.draw()
if in_ipython():
plt.show(block=0)
else:
plt.show(block=1)
def main():
print("""
--------------------------------------------------------------
Example file for using PyKat to automate Finesse simulations
Finesse: http://www.gwoptics.org/finesse
PyKat: https://pypi.python.org/pypi/PyKat/
The file runs through the various Finesse simulations
to generate the Finesse results reported in the document:
`Comparing Finesse simulations, analytical solutions and OSCAR
simulations of Fabry-Perot alignment signals', LIGO-T1300345,
freely available online: http://arxiv.org/abs/1401.5727
Run this file after master2.py to create data which can be
plotted using master4_plot.py. Results are saved after
each step and plots can be created at any time.
Andreas Freise 16.01.2014
--------------------------------------------------------------
""")
# shall we clear the workspace?
# %reset -f
# making these global during testing and debugging
#global kat, out
kat = finesse.kat(tempdir=".",tempname="test")
kat.verbose = False
tmpresultfile = 'myshelf2.dat'
# loading data saved by master.py
kat.loadKatFile('asc_base3.kat')
try:
with open(tmpresultfile, 'rb') as handle:
result = pickle.load(handle)
except: raise Exception("Could not open temprary results file {0}".format(tmpresultfile))
# this does not work yet due to the scale command
kat.PDrefl_p.enabled = False
kat.PDrefl_q.enabled = False
kat.WFS1_I.enabled = False
kat.WFS1_Q.enabled = False
kat.WFS2_I.enabled = False
kat.WFS2_Q.enabled = False
kat.ETM.phi=result['phi_tuned']
print("--------------------------------------------------------")
print(" 11. Do beam tracing to measure beam parameters")
# get beam parameters at nodes: "npsl", "nITM1", "nWFS1", "nWFS2", "npo2"
global beam1, beam2, beam3
beam1 = get_qs(kat,1e13)
beam2 = get_qs(kat,50e3)
beam3 = get_qs(kat,5e3)
# starting with cold beam at npsl
kat.psl.npsl.node.setGauss(kat.psl, beam1[0])
kat.parseKatCode("startnode npsl")
# if we use bs-based cavity we try to set good beam
# parameter for reflected beam, first by
# computing 'average' beam from cold and hot beams
x1=0.70
x2=0.30
if "ITM_TL_r" in kat._kat__components:
beam50 = beam_param(z=(x1*beam1[1].z+x2*beam2[1].z), w0=(x1*beam1[1].w0+x2*beam2[1].w0))
beam5 = beam_param(z=(x1*beam1[1].z+x2*beam3[1].z), w0=(x1*beam1[1].w0+x2*beam3[1].w0))
node_text = "at ITM->nITM1r"
t_comp=kat.ITM
t_node=kat.ITM.nITM1r
else:
beam50 = beam_param(z=(x1*beam1[4].z+x2*beam2[4].z), w0=(x1*beam1[4].w0+x2*beam2[4].w0))
beam5 = beam_param(z=(x1*beam1[4].z+x2*beam3[4].z), w0=(x1*beam1[4].w0+x2*beam3[4].w0))
node_text = "at s2->npo2"
t_comp=kat.s2
t_node=kat.s2.npo2
kat = set_thermal_lens(kat,50.0e3)
print("--------------------------------------------------------")
print(" 12. computing beam tilt with thermal lens (f={0})".format(kat.ITM_TL.f))
print(" Setting compromise beam parameter {0}:\n w0={1}, z={2}".format(node_text, beam50.w0, beam50.z))
t_node.node.setGauss(t_comp, beam50)
kat.maxtem=8
print(" Calculating maxtem = %d " % kat.maxtem)
tmp = gravity_tilt(kat)
kat = set_thermal_lens(kat,5e3)
print("--------------------------------------------------------")
print(" 13. computing beam tilt with thermal lens (f={0})".format(kat.ITM_TL.f))
print(" Setting compromise beam parameter {0}:\n w0={1}, z={2}".format(node_text, beam5.w0, beam5.z))
t_node.node.setGauss(t_comp, beam5)
#maxtems = [1, 3, 5, 9, 11, 13, 15, 19, 23, 25, 27, 29]
#maxtems = [1, 3, 5, 9, 11, 13, 15]
maxtems = [1, 3, 5, 7]
converge_tilt(kat, maxtems)
kat.PDrefl_p.enabled = True
kat.WFS1_I.enabled = True
kat.WFS2_I.enabled = True
kat = set_thermal_lens(kat,50e3)
print("--------------------------------------------------------")
print(" 12. computing alignment signal with thermal lens (f={0})".format(kat.ITM_TL.f))
t_node.node.setGauss(t_comp, beam50)
#maxtems = [1, 3, 5, 9, 11, 13, 15, 17, 19]
#maxtems = [1, 3, 5, 9, 11, 13, 15]
maxtems = [1, 3, 5, 7]
converge_asc(kat, maxtems, 'asc_signals_50.txt')
kat = set_thermal_lens(kat,5e3)
print("--------------------------------------------------------")
print(" 13. computing alignment signal with thermal lens (f={0})".format(kat.ITM_TL.f))
t_node.node.setGauss(t_comp, beam5)
#maxtems = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]
#maxtems = [1, 3, 5, 9, 11, 13, 15]
maxtems = [1, 3, 5, 7]
converge_asc(kat, maxtems, 'asc_signals_5.txt')
def get_qs(tmpkat,f):
global kat, out
kat = copy.deepcopy(tmpkat)
# measure beam parameter for the 'cold beam' i.e. the laser beam
# matched to the cavity without any thermal lens
nodenames=["npsl", "nITM1", "nWFS1", "nWFS2", "npo2"]
for idx, nname in enumerate(nodenames):
kat.parseKatCode('bp w{0} y q {1}'.format(idx, nname))
kat.parseKatCode('yaxis re:im')
kat.noxaxis = True
kat.maxtem=0
def beam_size(tmpkat, f, beam0):
kat = copy.deepcopy(tmpkat)
kat.psl.npsl.node.setGauss(kat.psl, beam0)
# add thermal lens and propagate input beam to ITM
kat = set_thermal_lens(kat, f)
out = kat.run()
# computing beam size at ITM
# and then we reflect of ITM, an set it as new startnode
q_in = out['w1']
#import pykat.optics.ABCD as ABCD
#abcd = ABCD.mirror_refl(1,2500)
#q_out = ABCD.apply(abcd,q_in,1,1)
beam1 = beam_param(q=q_in)
kat.removeLine("startnode")
kat.psl.npsl.node.removeGauss()
if "ITM_TL_r" in kat._kat__components:
kat.ITM.nITM1r.node.setGauss(kat.ITM, beam1)
kat.parseKatCode("startnode nITM1r")
else:
kat.ITM.nITM1.node.setGauss(kat.ITM, beam1)
kat.parseKatCode("startnode nITM1")
out = kat.run()
# computing beam size at WFS1 and WFS2
q2 = out['w2']
beam2 = beam_param(q=q2)
q3 = out['w3']
beam3 = beam_param(q=q3)
# computing beam size at pick off
q4 = out['w4']
beam4 = beam_param(q=q4)
print(" Input mode beam size with thermal lens f={0}".format(f))
print(" - ITM w={0:.6}cm (w0={1}, z={2})".format(100.0*beam1.w,beam1.w0, beam1.z))
print(" - WFS1 w={0:.6}cm (w0={1}, z={2})".format(100.0*beam2.w,beam2.w0, beam2.z))
print(" - WFS2 w={0:.6}cm (w0={1}, z={2})".format(100.0*beam3.w,beam3.w0, beam3.z))
print(" - npo2 w={0:.6}cm (w0={1}, z={2})".format(100.0*beam4.w,beam4.w0, beam4.z))
#raw_input("Press enter to continue")
return [beam1, beam2, beam3, beam4]
#global out
# run finesse with input laser mode matched to cavity (no thermal lens)
out = kat.run()
# beam at laser when matched to cold cavity
# (note the sign flip of the real part to change direction of gauss param)
q0 = -1.0*out['w0'].conjugate()
beam0 = beam_param(q=q0)
# compute beam sizes when tracing this beam back through the system
(beam1,beam2,beam3, beam4)=beam_size(kat,f,beam0)
return (beam0, beam1, beam2,beam3, beam4)
