def test_image_GSM():
z_0 = sympy.Symbol("z_0", real=True, positive=True)
z_1 = sympy.Symbol("z_1", real=True, positive=True)
gs = GSM()
g = GaussBeam()
z0m = free_space(z_0, force_positive=True)
z1m = free_space(z_1, force_positive=True)
F = lens("F", force_positive=True)
# z1 = free_space('z1')
M = z1m * F * z0m
gs1 = gs.apply_matrix(M)
g1 = g.apply_matrix(M)
# magnification
m_gs = gs1.rms_size / gs.rms_size
m_g = g1.rms_size / g.rms_size
m_gs = m_gs.simplify()
m_g = m_g.simplify()
print("Gauss magnification", m_g)
print("GSM magnification", m_gs)
print("Limit of GSM for ξ→0", m_gs.limit(gs.rms_cl, 0))
print("Limit of GSM for ξ→inf", m_gs.limit(gs.rms_cl, sympy.oo))
return m_gs, m_g
def test_collimate_GSM():
print("Defining default Gaussian and Gaussian-Schell beams")
gs = GSM()
g = GaussBeam()
z0m = free_space("z_0")
z0 = z0m.B
# F = lens(z_0.B)
F = lens("F", force_positive=True)
# z1 = free_space('z1')
print("Create ABCD matrix z_0 translation + lens F")
M = F * z0m
print("Applying matrix to both beams")
gs1 = gs.apply_matrix(M)
g1 = g.apply_matrix(M)
print("Find best z_0 to minimize divergence of resulting Gaussian Beam")
d1 = find_roots(g1.divergence, z0, use_derivative=True)
print("Best z0 = ", str(d1[0]), "(divergence ", str(d1[1]), ")")
print(
"Find best z_0 to minimize divergence of resulting Gaussian-Schell Beam"
)
ds1 = find_roots(gs1.divergence, z0, use_derivative=True)
print("Best z0 = ", str(d1[0]), "(divergence ", str(d1[1]), ")")
return gs1, g1
def collimate_undulator():
gsh = GSM(wavelen=1.6e-10, rms_size=30e-6, rms_cl=3.1e-6)
gsv = GSM(wavelen=1.6e-10, rms_size=5.4e-6, rms_cl=3.8e-6)
z0 = free_space("z0")
F = lens("F")
z1 = free_space("z1")
# gsbh = Gauss-Schell Before Horizontal
gsbh = gsh.apply_matrix(z0)
gsbv = gsv.apply_matrix(z0)
gsah = gsh.apply_matrix(z1 * F * z0)
gsav = gsv.apply_matrix(z1 * F * z0)
beams = dict(h=gsh, v=gsv)
attrs = dict(size="rms_size", cl="rms_cl")
funcs = dict()
for bname, beam in beams.items():
funcs[bname] = dict()
for name, attr in attrs.items():
funcs[bname][name] = dict()
expr_b = getattr(beam.apply_matrix(z0), attr)
expr_b = sympy.lambdify(expr_b.free_symbols, expr_b)
expr_a = getattr(beam.apply_matrix(z1 * F * z0), attr)
print(expr_a.free_symbols)
symbols = (
get_symbol(expr_a, "z0"),
get_symbol(expr_a, "F"),
get_symbol(expr_a, "z1"),
)
expr_a = sympy.lambdify(symbols, expr_a)
funcs[bname][name]["before"] = expr_b
funcs[bname][name]["after"] = expr_a
def f(z, z0=30, F=30):
if isinstance(z, (float, int)):
z = np.asarray([z])
res = dict()
for bname in beams.keys():
res[bname] = dict()
for name in attrs.keys():
res[bname][name] = dict()
y = np.zeros_like(z)
idx = z < z0
y[idx] = funcs[bname][name]["before"](z[idx]) * 1e6
y[~idx] = funcs[bname][name]["after"](z0, F,
z[~idx] - z0) * 1e6
res[bname][name] = y
return ds(res)
return f, funcs
def test_image_GSM_numeric():
gs = GSM(wavelen=1e-10, rms_waist_size=3e-6, rms_waist_cl=2e-6)
z0m = free_space(60)
F = lens(15)
# z1 = free_space('z1')
M = F * z0m
gs1 = apply_matrix_GSM(M, gs)
return gs1
def test_collimate_gauss():
g1 = GaussBeam(wavelen="λ", rms_size="σ_0")
z0m = free_space("z_0")
z0 = z0m.B
print("Defining generic Gaussin beam", str(g1))
l = lens("F", force_positive=True)
print("Putting lens of focal length F")
g2 = gs.apply_matrix(l * z0m)
print("Divergence of gauss beam after lens (F) @ dist z_0",
g2.divergence.simplify())
sol = find_roots(g2.divergence, z0, use_derivative=True)
print("Distance z_0 that minimizes divergence z_0=", sol[0])
print("New divergence is", sol[1].simplify())
def test_image_gauss():
g1 = GaussBeam(wavelen="λ", rms_size="σ_0")
z0m = free_space("z_0")
z0 = z0m.B
l = lens("f")
z1m = free_space("z_1")
z1 = z1m.B
g2 = gs.apply_matrix(z1m * l * z0m)
magnification = (g2.rms_size / g1.rms_size).simplify()
print("Magnification:", magnification.simplify())
# find best focus
sol = find_roots(magnification, z1, use_derivative=True)
dist_to_focus = sol[0]
print("Position of image", str(dist_to_focus.simplify()))
print("1-z1/F=", (1 - dist_to_focus / l.C).simplify())
return g1, g2, magnification, dist_to_focus
def test_collimate_undulator():
LPOS = 30
DZ = 1
gsh = GSM(wavelen=1.6e-10, rms_size=30e-6, rms_cl=3.1e-6)
gsv = GSM(wavelen=1.6e-10, rms_size=5.4e-6, rms_cl=3.8e-6)
clh = []
sh = []
clv = []
sv = []
z = []
for zi in np.arange(0, LPOS, DZ):
z.append(zi)
d = free_space(zi)
# cl.append(gs.rms_cl(zi).evalf()*1e6)
gh = gsh.apply_matrix(d)
sh.append(gh.rms_size.evalf() * 1e6)
clh.append(gh.rms_cl.evalf() * 1e6)
gv = gsv.apply_matrix(d)
sv.append(gv.rms_size.evalf() * 1e6)
clv.append(gv.rms_cl.evalf() * 1e6)
z0m = free_space(LPOS)
F = lens(LPOS)
for zi in np.arange(LPOS, 200, DZ):
z1m = free_space(zi - LPOS)
M = z1m * F * z0m
gh = gsh.apply_matrix(M)
sh.append(gh.rms_size.evalf() * 1e6)
clh.append(gh.rms_cl.evalf() * 1e6)
gv = gsv.apply_matrix(M)
sv.append(gv.rms_size.evalf() * 1e6)
clv.append(gv.rms_cl.evalf() * 1e6)
return z, sh, clh, sv, clv