def ex7(energy=10, pinhole=0.5):
print("ex7 showing that with too small of a pinhole it properly focus")
print(
"The horizontal undulator beam is propagated for 150 m, then slitted")
print("down to 0.1,0.2,0.4,0.8 FWHM ξ")
print("For each lens set the beam value at 200 m is calculated and the")
print("best set is used")
beam = source(period=20, length=2.5, energy=energy)[0] # [0] is hor
# prepare beam to be focussed
beam = beam.propagate(150)
sizes = [0.1, 0.2, 0.4, 0.8, 1.6]
x = np.arange(0, 100, 0.1)
plt.figure("ex7")
for pinhole in sizes:
print(f"\n\n### Working on pinhole {pinhole} ###")
cl = beam.rms_cl * 2.35 * pinhole
beam1 = beam.hard_aperture(cl)
s_at_200 = [
beam1.apply(l).propagate(50).rms_size
for l in transfocator.all_sets
]
s_at_200 = np.asarray(s_at_200)
idx = np.argmin(s_at_200)
best_lens = transfocator.all_sets[idx]
print(f"Best size at 200m {min(s_at_200)*1e6:.2f}μm")
print("Best set to have smallest spot @ 200m", str(best_lens))
focus = best_lens.calc_focusing_GSM(beam1)
gsm = beam1.apply(best_lens)
plt.plot(150 + x, gsm.propagate(x).rms_size * 1e6, label=str(pinhole))
return focus
def ex2(energy=10, pinhole=0.5):
beam = source(period=20, length=2.5, energy=energy)[0]
return propagate(
beam=beam,
optics=[[100, f"x{pinhole}", None], [150, None, "focus@200"]],
z=np.arange(0, 230, 0.5),
use_transfocator=True,
transfocator=transfocator,
)
def ex5(energy=10, pinhole=0.5):
print(
"This examples shows that numerically and analytically (Vartanyans 2013)"
)
print("one gets the same result")
beam = source(period=20, length=2.5, energy=energy)[0] # [0] is hor
# prepare beam to be focussed
beam = beam.propagate(40).hard_aperture("x0.5").propagate(120)
# pick lenses
lenses = transfocator.find_best_set_for_focal_length(
focal_length=25, energy=energy).best_lens_set
# do analytical
beam_at_focus = lenses.calc_focusing_GSM(beam)
dist = beam_at_focus.focus_distance
beam_analytical = beam_at_focus.gsm_at_focus
dz = np.arange(-5, 5, 0.1)
# do numerical
beam_numerical = beam.apply(lenses)
fwhm_analytical = [
beam_analytical.propagate(dzi).rms_size * 2.35 * 1e6 for dzi in dz
]
fwhm_numerical = [
beam_numerical.propagate(dist + dzi).rms_size * 2.35 * 1e6
for dzi in dz
]
cl_fwhm_analytical = [
beam_analytical.propagate(dzi).rms_cl * 2.35 * 1e6 for dzi in dz
]
cl_fwhm_numerical = [
beam_numerical.propagate(dist + dzi).rms_cl * 2.35 * 1e6 for dzi in dz
]
fig, ax = plt.subplots(2, 1, sharex=True)
ax[0].plot(dz, fwhm_analytical, label="FWHM analytical")
ax[0].plot(dz, fwhm_numerical, ".", label="FWHM numerical")
ax[1].plot(dz, cl_fwhm_analytical, label="ξ FWHM analytical")
ax[1].plot(dz, cl_fwhm_numerical, ".", label="ξ FWHM numerical")
ax[1].set_xlabel("Distance from analytical focus")
ax[0].set_title(f"Focusing {dist:.3f}m from lens")
for a in ax:
a.grid()
ax[0].set_ylabel("FWHM size")
ax[1].set_ylabel("ξ FWHM")
return beam_analytical
def ex6(energy=10, pinhole=0.5):
print("ex6: showing that adding an aperture `outside` the CRL object")
print(" gives equivalent output than the Vartanyans 2013 paper")
beam = source(period=20, length=2.5, energy=energy)[0] # [0] is hor
# prepare beam to be focussed
beam = beam.propagate(150)
# pick lenses
lenses = transfocator.find_best_set_for_focal_length(
focal_length=35, energy=energy).best_lens_set
cl = beam.rms_cl * 2.35 * pinhole
beam1 = beam.hard_aperture(cl)
# focus apertured beam
beam_at_focus1 = lenses.calc_focusing_GSM(beam1)
print("\n\n")
print("\n\n")
# focus beam
lenses.pinhole = cl
beam_at_focus2 = lenses.calc_focusing_GSM(beam)
dist = beam_at_focus2.focus_distance
beam_at_focus1 = beam_at_focus1.gsm_at_focus
beam_at_focus2 = beam_at_focus2.gsm_at_focus
dz = np.arange(-5, 5, 0.1)
s1 = [beam_at_focus1.propagate(dzi).rms_size * 2.35 * 1e6 for dzi in dz]
s2 = [beam_at_focus2.propagate(dzi).rms_size * 2.35 * 1e6 for dzi in dz]
cl1 = [beam_at_focus1.propagate(dzi).rms_cl * 2.35 * 1e6 for dzi in dz]
cl2 = [beam_at_focus2.propagate(dzi).rms_cl * 2.35 * 1e6 for dzi in dz]
fig, ax = plt.subplots(2, 1, sharex=True)
ax[0].plot(dz, s1, label="FWHM aperturing outside CRL object")
ax[0].plot(dz, s2, label="FWHM aperturing in CRL object")
ax[1].plot(dz, cl1, label="ξ1")
ax[1].plot(dz, cl2, label="ξ2")
ax[1].set_xlabel(f"Distance from focus @ {dist:.2f}m from optics")
#ax[0].set_title(f"Focusing {dist:.3f}m from lens")
for a in ax:
a.grid()
ax[0].set_ylabel("FWHM size")
ax[1].set_ylabel("ξ FWHM")
return
def ex8(energy=10):
print("ex8 similar conclusions as ex7")
print(
"The horizontal undulator beam is propagated for 150 m, then slitted")
print("The beamsize at 200m is calculated as funciton of the focal length")
beam = source(period=20, length=2.5, energy=energy)[0] # [0] is hor
optics_dist = [0, 5, 10, 20, 40]
sizes = [0.1, 0.2, 0.4, 0.8, 1.6]
fig, ax = plt.subplots(len(optics_dist),
1,
num="ex8",
sharex=True,
sharey=True,
figsize=[8.27, 11.69])
#fig.clf()
f = np.arange(1, 50, 0.1)
for iplot, d in enumerate(optics_dist):
for pinhole in sizes:
# b1 is beam at lens
b1 = beam.propagate(150).hard_aperture(f"x{pinhole}").propagate(d)
aperture = beam.propagate(150).rms_cl * 2.35 * pinhole * 1e6
s = [
b1.lens(_f).propagate(50 - d).rms_size * 2.35 * 1e6 for _f in f
]
line, = ax[iplot].semilogy(
f, s, label=f"aperture {pinhole}xξ={aperture:.1f}μm")
dl_size = sr.coherent.diffraction_limited_spot_gaussian(
wavelength=beam.wavelen,
focal_length=50 - d,
fwhm=b1.rms_size * 2.35,
)
ax[iplot].axhline(dl_size * 1e6,
ls="--",
color=line.get_color(),
alpha=0.5)
ax[iplot].set_title(f"pinhole-optics distance {d}m")
ax[iplot].set_ylabel("FWHM beam size (μm)")
ax[iplot].grid()
ax[-1].legend()
ax[-1].set_xlabel("focal length (m)")
fig.tight_layout()