def reflection(xvals, p):
#position=p[0]; intensity=p[1]; slit=p[2]; stth=p[3]; background=p[4]; thickness=p[5]; absorption=p[6]
x0 = p[0]
i0 = p[1]
w = p[2]
theta = p[3]
ib = p[4]
thick = p[5]
u = p[6]
th = np.deg2rad(theta)
p0 = w * np.sin(th) / np.sin(2 * th)
out = []
for x in xvals:
if x < (x0 - p0):
val = ib
elif ((x >= (x0 - p0)) and (x < x0)):
val = i0 * ((x - x0 + p0) / u) - i0 * (np.sin(th) /
(2 * u * u)) * (1 - np.exp(
(-2 * u / np.sin(th)) *
(x - x0 + p0))) + ib
elif ((x >= x0) and (x < (x0 + p0))):
val = i0 * (np.sin(th) / (2 * u * u)) * (np.exp(
(-2 * u / np.sin(th)) * (x - x0 + p0)) - 2 * np.exp(
(-2 * u / np.sin(th)) *
(x - x0)) + 1) + i0 * ((x0 + p0 - x) / u) + ib
elif (x >= (x0 + p0)):
val = i0 * np.sin(th) / (
2 * u * u) * (np.exp(-2 * u * (x - x0 + p0) / np.sin(th)) -
2 * np.exp(-2 * u * (x - x0) / np.sin(th)) +
np.exp(-2 * u * (x - x0 - p0) / np.sin(th))) + ib
out = out + [val]
return np.array(out)
def wall(xvals, parms):
#position=p[0]; intensity=p[1]; slit=p[2]; stth=p[3]; background=p[4]; thickness=p[5]; absorption=p[6]
midpoint = parms[0]
i0 = parms[1]
w = parms[2]
theta = parms[3]
ib = parms[4]
thick = parms[5]
u = parms[6]
midpoint = parms[0]
x0 = midpoint - thick / 2.0
th = np.deg2rad(theta)
p = w * np.cos(th)
Atot = w * w / np.sin(2.0 * th)
out = []
for x in xvals:
if (x <= (x0 - p)):
val = ib
#elif ((x0-p) >= (x-thick)) and ((x0+p) >= x): #Gauge volume is smaller than thickness
if ((x > (x0 - p)) and (x0 - p > (x - thick)) and (x <= x0)):
val = ib + i0 * ((x - (x0 - p)) * ((x -
(x0 - p)) * np.tan(th))) / Atot
elif ((x > x0) and (x <= x0 + p) and (x0 - p > (x - thick))):
val = ib + i0 * (Atot - (x0 + p - x) *
(x0 + p - x) * np.tan(th)) / Atot
elif (x0 - p > (x - thick)
and (x0 + p < x)): #Gauge volume is smaller than thickness
val = ib + i0
elif (x0 - p < (x - thick)
and (x0 + p > x)): #Gauge volume is larger than thickness
A2 = (x0 + p - x) * (x0 + p - x) * np.tan(th)
A3 = ((x - thick) - (x0 - p)) * (((x - thick) -
(x0 - p)) * np.tan(th))
val = ib + i0 * (Atot - A2 - A3) / Atot
elif ((x0 - p) < (x - thick)) and ((x0 + p) < x) and (x0 >=
(x - thick)):
A3 = ((x - thick) - (x0 - p)) * (((x - thick) -
(x0 - p)) * np.tan(th))
val = ib + i0 * (Atot - A3) / Atot
elif (x0 < (x - thick) and ((x0 + p >= (x - thick)))):
A2 = (x0 + p - (x - thick)) * ((x0 + p) - (x - thick)) * np.tan(th)
val = ib + i0 * (A2 / Atot)
elif (x0 + p < (x - thick)):
val = ib
#elif ((x0-p) < (x-thick)) and ((x0+p) >= x): #Gauge volume is larger than thickness
# A2 = (x0+p-x)*(x0+p-x)*np.tan(th)
# A3 = ((x-thick)-(x0-p))*(((x-thick)-(x0-p))*np.tan(th))
# val = ib + i0*(Atot-A2-A3)/Atot
out = out + [val]
return np.array(out)
def transmission(xvals, parms):
#position=p[0]; intensity=p[1]; slit=p[2]; stth=p[3]; background=p[4]; thickness=p[5]; absorption=p[6]
#x0=p[0]; i0=p[1]; w=p[2]; theta=p[3]; ib=p[4]; thick=p[5]; u=p[6];
#th = np.deg2rad(theta)
#p0 = w * np.cos(th)/np.cos(2*th)
#out = []
#for x in xvals:
# if x < (x0 - p0):
# val = ib
# elif ((x>=x0-p0) and (x < x0)):
# val = i0*(x-x0+p0)*(x-x0+p0)+ib
# elif ((x>=x0) and (x<(x0+p0))):
# val = i0*(2.0*p0*p0-(x0+p0-x)*(x0+p0-x))+ib
# elif (x>=x0+p0):
# val=2*i0*p0*p0 +ib
# out = out + [val]
x0 = parms[0]
i0 = parms[1]
w = parms[2]
theta = parms[3]
ib = parms[4]
thick = parms[5]
u = parms[6]
th = np.deg2rad(theta)
p = w * np.cos(th)
Atot = w * w / np.sin(2.0 * th)
out = []
for x in xvals:
if (x <= (x0 - p)):
val = ib
elif ((x > (x0 - p)) and (x <= x0)):
val = ib + i0 * ((x - (x0 - p)) * ((x -
(x0 - p)) * np.tan(th))) / Atot
elif ((x > x0) and (x <= x0 + p)):
val = ib + i0 * (Atot - (x0 + p - x) *
(x0 + p - x) * np.tan(th)) / Atot
elif (x > x0 + p):
val = ib + i0
out = out + [val]
return np.array(out)
def reflection1(xvals, parms):
#position=p[0]; intensity=p[1]; slit=p[2]; stth=p[3]; background=p[4]; thickness=p[5]; absorption=p[6]
x0 = parms[0]
i0 = parms[1]
w = parms[2]
theta = parms[3]
ib = parms[4]
thick = parms[5]
u = parms[6]
th = np.deg2rad(theta)
p = w * np.sin(th)
Atot = w * w / np.sin(2.0 * th)
out = []
ni = 5
irng = np.array(range(1, ni + 1))
for x in xvals:
if x < (x0 - p):
val = ib
elif ((x0 - p) < x and x0 > x):
l1 = x - (x0 - p)
nrleft = int(np.ceil(l1 / (2 * p) * ni))
if nrleft < 1: nrleft = 1
irngleft = np.array(range(1, nrleft + 1))
dl1 = l1 / float(nrleft)
dl = irngleft * dl1
triA = dl * dl / np.tan(th) #triangle areas
secA = [triA[0]
] + [triA[i] - triA[i - 1]
for i in range(1, nrleft)] #section areas
secA = np.array(secA)
m1 = np.linspace(
x0 - p + dl1 / 2.0, x - dl1 / 2.0, nrleft
) #section midpoint position - path length calculated from this
plen = np.abs(2 * m1 / np.sin(th))
val = ib + np.sum(i0 * secA * np.exp(-u * plen))
elif (x0 <= x) and (x0 + p >= x):
l1 = p
nrleft = int(np.ceil(l1 / (2 * p) * ni))
if nrleft < 1: nrleft = 1
irngleft = np.array(range(1, nrleft + 1))
dl1left = l1 / float(nrleft)
dlleft = irngleft * dl1left
triAleft = dlleft * dlleft / np.tan(th) #triangle areas
secAleft = [triAleft[0]] + [
triAleft[i] - triAleft[i - 1] for i in range(1, nrleft)
] #section areas
secAleft = np.array(secAleft)
m1left = np.linspace(x0 - p + dl1left / 2.0, x0 - dl1left / 2.0,
nrleft) + (x - x0)
plenleft = np.abs(2 * m1left / np.sin(th))
valleft = np.sum(i0 * secAleft * np.exp(-u * plenleft))
l2 = x - x0
nrright = int(np.ceil(x - x0 / (2 * p) * ni))
if nrright < 1: nrright = 1
irngright = np.array(range(1, nrright + 1))
dl1right = l2 / float(nrright)
dlright = p - np.append(0.0, dl1right * irngright)
triAright = dlright * dlright / np.tan(th)
secAright = [
triAright[i] - triAright[i + 1] for i in range(nrright)
]
secAright = np.array(secAright)
m1right = np.linspace(x - x0 - dl1right / 2.0, dl1right / 2.0,
nrright)
plenright = np.abs(2 * m1right / np.sin(th))
valright = np.sum(i0 * secAright * np.exp(-u * plenright))
val = ib + valleft + valright
elif (x > x0 + p):
l1 = p
#nrleft = int(np.ceil(l1/(x-(x0-p))*ni));
nrleft = int(np.ceil(l1 / (2 * p) * ni))
if nrleft < 1: nrleft = 1
irngleft = np.array(range(1, nrleft + 1))
dl1left = l1 / float(nrleft)
dlleft = irngleft * dl1left
triAleft = dlleft * dlleft / np.tan(th) #triangle areas
secAleft = [triAleft[0]] + [
triAleft[i] - triAleft[i - 1] for i in range(1, nrleft)
] #section areas
secAleft = np.array(secAleft)
m1left = np.linspace(x0 - p + dl1left / 2.0, x0 - dl1left / 2.0,
nrleft) + (x - x0)
plenleft = np.abs(2 * m1left / np.sin(th))
valleft = np.sum(i0 * secAleft * np.exp(-u * plenleft))
l2 = p
nrright = int(np.ceil(l2 / (2 * p) * ni))
if nrright < 1: nrright = 1
irngright = np.array(range(1, nrright + 1))
dl1right = l2 / float(nrright)
dlright = p - np.append(0.0, dl1right * irngright)
triAright = dlright * dlright / np.tan(th)
secAright = [
triAright[i] - triAright[i + 1] for i in range(nrright)
]
secAright = np.array(secAright)
m1right = np.linspace(dlright[0] - dl1right / 2.0, dlright[-1] +
dl1right / 2.0, nrright) + (x - (x0 + p))
plenright = np.abs(2 * m1right / np.sin(th))
valright = np.sum(i0 * secAright * np.exp(-u * plenright))
val = ib + valleft + valright
out = out + [val]
return np.array(out)
def walltransmission(xvals, parms):
#position=p[0]; intensity=p[1]; slit=p[2]; stth=p[3]; background=p[4]; thickness=p[5]; absorption=p[6]
midpoint = parms[0]
i0 = parms[1]
w = parms[2]
theta = parms[3]
ib = parms[4]
thick = parms[5]
u = parms[6]
midpoint = parms[0]
x0 = midpoint - thick / 2.0
th = np.deg2rad(theta)
p = w * np.cos(th)
t = thick
Atot1 = w * w / np.sin(2.0 * th)
Atot = 2 * w * np.sin(th) * w * np.cos(th)
out = []
baselength = 2 * p
Gvol_area = 2 * w * w * np.sin(th) * np.cos(th)
if baselength > thick:
Ar = 0.5 * (p - thick / 2.0) * (p - thick / 2.0) * np.tan(th)
maxbeam = Gvol_area - 4.0 * Ar
else:
maxbeam = Gvol_area
for x in xvals:
x1 = x
x2 = x - thick
if (x1 <= (x0 - p)) and (x2 <= x0 - p):
val = ib
elif (x0 - p) >= x2 and (x0 - p <= x1) and (x0 > x1):
A = (x1 - (x0 - p))
val = ib + A * A * np.tan(th) / maxbeam * i0
elif (x0 - p <= x2) and (x0 >= x1):
C = (x1 - (x0 - p))
B = (x2 - (x0 - p))
val = ib + (C * C * np.tan(th) - B * B * np.tan(th)) / maxbeam * i0
elif (x2 <= (x0 - p)) and (x0 >= x2) and (x0 <= x1) and (x1 <=
(x0 + p)):
A = (x1 - (x0 + p))
val = ib + (Gvol_area - A * A * np.tan(th)) / maxbeam * i0
elif (x2 <= (x0 - p)) and (x0 >= x2) and (x0 <= x1) and (x1 >=
(x0 + p)):
val = ib + i0
elif (x2 >= (x0 - p)) and (x0 >= x2) and (x0 <= x1) and (x1 <=
(x0 + p)):
A = (x1 - (x0 + p))
B = (x2 - (x0 - p))
val = ib + (Gvol_area - A * A * np.tan(th) -
B * B * np.tan(th)) / maxbeam * i0
elif (x2 >= (x0 - p)) and (x0 >= x2) and (x0 <= x1) and (x1 >=
(x0 + p)):
B = (x2 - (x0 - p))
val = ib + (Gvol_area - B * B * np.tan(th)) / maxbeam * i0
elif (x0 + p >= x1) and (x0 <= x2):
A = (x1 - (x0 + p))
C = (x2 - (x0 + p))
val = ib + (C * C * np.tan(th) - A * A * np.tan(th)) / maxbeam * i0
elif (x2 >= (x0 - p)) and (x0 <= x2) and (x0 <= x1) and (
x1 >= (x0 + p)) and (x2 <= (x0 + p)):
A = (x0 + p - x2)
val = ib + A * A * np.tan(th) / maxbeam * i0
elif (x0 - p) >= x2 and (x0 + p) <= x2:
val = ib
out = out + [val]
return np.array(out)