diff --git a/README.md b/README.md
index 15f18ef6347b42419b551268a48d3f7ef1882be8..0fb8d7c5b287b6b6093cafd8dd9b8762fb053d56 100644
--- a/README.md
+++ b/README.md
@@ -10,4 +10,6 @@ The so far implemented features are:
* calculates beam sizes and position for 2 energies
* calculates sample position (membrane size and pitch) as well as etched facets
* calculates position of the DSSC module 15 as well as filter bar position
-* calculates focal length change due to the KBS
\ No newline at end of file
+* calculates focal length change due to the KBS
+* calculates beam focusing by KBS for the zone plate 0th order
+* calculates beam and sample shape for sample at non-normal incidence angle
diff --git a/TZPGcalc.py b/TZPGcalc.py
index 4e5129ba606d7b2d3e3ae0774172cffe2049aa3b..e934626a323deedacc5457224b61a1bfb138b627 100644
--- a/TZPGcalc.py
+++ b/TZPGcalc.py
@@ -9,7 +9,7 @@
import numpy as np
import matplotlib.pyplot as plt
-from matplotlib.patches import Rectangle
+from matplotlib.patches import Rectangle, Polygon
from matplotlib.colors import hsv_to_rgb
import ipywidgets as widgets
@@ -26,6 +26,7 @@ Z0 = 230*1e-3 # [m]
d = 3.3 - Z0 # distance between HFM and TZPG
f1 = 7.3 # HFM focus 2 m behind second interaction point
F = F*(d-f1)/(d-f1-F)
+KBS_F = f1 - d # KBS focus distance from TZPG
# number of membrane to show
SampleN = 7
@@ -63,50 +64,86 @@ class TZPGcalc():
c_gr = hsv_to_rgb([95/360, 60/100, 100/100])
c_gb = hsv_to_rgb([145/360, 60/100, 100/100])
- self.samBeamsL = {'F0G0': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G-1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F1G0': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_rr, alpha=0.7, lw=None)),
- 'F1G1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gr, alpha=0.7, lw=None)),
- 'F1G-1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gr, alpha=0.7, lw=None))
- }
-
- self.detBeamsL = {'F0G0': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G-1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F1G0': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_rr, alpha=0.7, lw=None)),
- 'F1G1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gr, alpha=0.7, lw=None)),
- 'F1G-1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gr, alpha=0.7, lw=None))
- }
-
- self.samBeamsH = {'F0G0': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G-1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F1G0': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_rb, alpha=0.7, lw=None)),
- 'F1G1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gb, alpha=0.7, lw=None)),
- 'F1G-1': self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gb, alpha=0.7, lw=None))
- }
-
- self.detBeamsH = {'F0G0': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F0G-1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="black", alpha=0.4, lw=None)),
- 'F1G0': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_rb, alpha=0.7, lw=None)),
- 'F1G1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gb, alpha=0.7, lw=None)),
- 'F1G-1': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor=c_gb, alpha=0.7, lw=None))
- }
-
- self.detLines = {'module': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, fill=False, facecolor='k')),
- 'Vfilter': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="blue", alpha=0.4)),
- 'Hfilter': self.ax_det.add_patch(Rectangle((0, 0), 1, 1, facecolor="blue", alpha=0.4)),
- 'diamond': self.ax_det.add_patch(Rectangle((-8, -8), 16, 16, facecolor="blue", alpha=0.4, angle=45))
+ self.samBeamsL = {
+ 'F0G0': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G-1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F1G0': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor=c_rr, alpha=0.7, lw=None)),
+ 'F1G1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor=c_gr, alpha=0.7, lw=None)),
+ 'F1G-1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor=c_gr, alpha=0.7, lw=None))
+ }
+
+ self.detBeamsL = {
+ 'F0G0': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G-1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F1G0': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor=c_rr, alpha=0.7, lw=None)),
+ 'F1G1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor=c_gr, alpha=0.7, lw=None)),
+ 'F1G-1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor=c_gr, alpha=0.7, lw=None))
+ }
+
+ self.samBeamsH = {
+ 'F0G0': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G-1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F1G0': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor=c_rb, alpha=0.7, lw=None)),
+ 'F1G1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor=c_gb, alpha=0.7, lw=None)),
+ 'F1G-1': self.ax_sam.add_patch(
+ Polygon([(0, 0)], facecolor=c_gb, alpha=0.7, lw=None))
+ }
+
+ self.detBeamsH = {
+ 'F0G0': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F0G-1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor="black", alpha=0.4, lw=None)),
+ 'F1G0': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor=c_rb, alpha=0.7, lw=None)),
+ 'F1G1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor=c_gb, alpha=0.7, lw=None)),
+ 'F1G-1': self.ax_det.add_patch(
+ Polygon([(0, 0)], facecolor=c_gb, alpha=0.7, lw=None))
+ }
+
+ self.detLines = {
+ 'module': self.ax_det.add_patch(
+ Rectangle((0, 0), 1, 1, fill=False, facecolor='k')),
+ 'Vfilter': self.ax_det.add_patch(
+ Rectangle((0, 0), 1, 1, facecolor="blue", alpha=0.4)),
+ 'Hfilter': self.ax_det.add_patch(
+ Rectangle((0, 0), 1, 1, facecolor="blue", alpha=0.4)),
+ 'diamond': self.ax_det.add_patch(
+ Rectangle((-8, -8), 16, 16, facecolor="blue", alpha=0.4, angle=45))
}
# 5x5 membranes
self.sampleLines = {}
self.etchLines = {}
for k in range(SampleN*SampleN):
- self.sampleLines[k] = self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, fill=False, facecolor='k'))
- self.etchLines[k] = self.ax_sam.add_patch(Rectangle((0, 0), 1, 1, fill=False, facecolor='k', alpha=0.4, ls='--'))
+ self.sampleLines[k] = self.ax_sam.add_patch(
+ Rectangle((0, 0), 1, 1, fill=False, facecolor='k'))
+ self.etchLines[k] = self.ax_sam.add_patch(
+ Rectangle((0, 0), 1, 1, fill=False, facecolor='k', alpha=0.4, ls='--'))
+
def RectUpdate(self, rect, xLeft, yBottom, xRight, yTop):
""" Updates the position and size of the given Rectangle.
@@ -126,13 +163,54 @@ class TZPGcalc():
rect.set_height(self.scale*yw)
rect.set_width(self.scale*xw)
- def UpdateBeams(self, Beams, Z, conf):
+ def PolyUpdate(self, poly, xLeft, yBottom, xRight, yTop):
+ """ Updates the corner position of a Polygon.
+
+ poly: regular Polygon to update
+ xLeft: x position of the left corner
+ yBottom: y position of the bottom corner
+ xRight: x position of the right corner
+ yTop: y position of the top corner
+ """
+
+ xy = self.scale*np.array([
+ [xLeft, yBottom],
+ [xLeft, yTop],
+ [xRight, yTop],
+ [xRight, yBottom]])
+
+ poly.set_xy(xy)
+
+ def LinePlaneIntersection(self, l1, l2, p0, n):
+ """ Calculate the intersection point in space between a line (beam)
+ passing through 2 points l1 and l2 and a (sample) plane passing by
+ p0 with normal n
+
+ l1: [x,y,z] point on line
+ l2: [x,y,z] point on line
+ p0: [x,y,z] point on plane
+ n: plane normal vector
+ """
+
+ # plane parametrized as (p - p0).n = 0
+ # line parametrized as p = l1 + l12*d with d Real
+ l12 = l2 - l1
+
+ if np.dot(l12,n) == 0:
+ return [0,0,0] # line is either in the plane or outside the plane
+ else:
+ d = np.dot((p0 - l1), n)/np.dot(l12,n)
+ return l1 + l12*d
+
+ def UpdateBeams(self, Beams, Z, incidence, conf):
""" Update the position and size of the beams.
- Beams: dictionary of f'F{f}G{g}' Rectangles for f = 0 and 1 zone plate order and
- g = +1, 0 and -1 grating order
+ Beams: dictionary of f'F{f}G{g}' Polygon for f = 0 and 1 zone
+ plate order and g = +1, 0 and -1 grating order
Z: distance Z between the zone plate and the current imaging plane
- conf: dictionnary of distance for calculation {'F', 'TZPGwH', 'TZPGwV', 'TZPGo', 'theta_grating'}
+ incidence: incidence angle of the imaging plane in rad
+ conf: dictionnary of distance for calculation {'F', 'TZPGwH',
+ 'TZPGwV', 'TZPGo', 'theta_grating'}
"""
F = conf['F']
wH = conf['TZPGwH']
@@ -140,36 +218,34 @@ class TZPGcalc():
o = conf['TZPGo']
offaxis = wV/2 + o
- # side view X
- Fx = F*np.arctan(conf['theta_grating'])
-
- Xdg0 = np.abs(Z - F)/F*wH/2
- Xdg1L = Z/F*(Fx - wH/2) + wH/2
- Xdg1 = Z*np.tan(conf['theta_grating'])
- Xdg1H = Z/F*(Fx + wH/2) - wH/2
-
- # top view Y
- YdfL = (o*(Z - F)/F + offaxis)
- Ydf = ((o + wV/2)*(Z - F)/F + offaxis)
- YdfH = ((o + wV)*(Z - F)/F + offaxis)
-
- if Z < F: # before zone plate focus, low and high beam edges are swapped
- Xdg1L, Xdg1H = (Xdg1H, Xdg1L)
- YdfL, YdfH = (YdfH, YdfL)
-
- self.RectUpdate(Beams['F0G0'],
- -wH/2, -wV/2, wH/2, wV/2)
- self.RectUpdate(Beams['F0G1'],
- Xdg1-wH/2, -wV/2, Xdg1+wH/2, wV/2)
- self.RectUpdate(Beams['F0G-1'],
- -Xdg1-wH/2, -wV/2, -Xdg1+wH/2, wV/2)
-
- self.RectUpdate(Beams['F1G0'],
- -Xdg0, YdfL, Xdg0, YdfH)
- self.RectUpdate(Beams['F1G1'],
- Xdg1L, YdfL, Xdg1H, YdfH)
- self.RectUpdate(Beams['F1G-1'],
- -Xdg1H, YdfL, -Xdg1L, YdfH)
+ # imaging plane
+ n = np.array([np.sin(incidence), 0, np.cos(incidence)])
+ p0 = np.array([0,0,Z])
+
+ # zone plate 4 corner points
+ l1_list = [
+ np.array([wH/2,wV/2,0]),
+ np.array([wH/2,-wV/2,0]),
+ np.array([-wH/2,-wV/2,0]),
+ np.array([-wH/2,wV/2,0])
+ ]
+
+ # 6 beam focus point
+ l2_list = {
+ 'F0G0': np.array([0,0,KBS_F]),
+ 'F0G1': np.array([KBS_F*np.arctan(conf['theta_grating']),0,KBS_F]),
+ 'F0G-1': np.array([-KBS_F*np.arctan(conf['theta_grating']),0,KBS_F]),
+ 'F1G0': np.array([0,offaxis,F]),
+ 'F1G1': np.array([F*np.arctan(conf['theta_grating']),offaxis,F]),
+ 'F1G-1': np.array([-F*np.arctan(conf['theta_grating']),offaxis,F])
+ }
+
+ for beam in l2_list.keys():
+ l2 = l2_list[beam]
+ corners = []
+ for l1 in l1_list:
+ corners.append(self.LinePlaneIntersection(l1, l2, p0, n)[:2])
+ Beams[beam].set_xy(self.scale*np.array(corners))
def DetectorUpdate(self, Xoff, Yoff):
""" Draw DSSC detector module with filter mask.
@@ -199,7 +275,8 @@ class TZPGcalc():
# moving rotated rectangles is a pain in matplotlib
self.detLines['diamond'].set_xy((self.scale*Xoff, self.scale*(Yoff - diamondW/2*np.sqrt(2))))
- def SampleUpdate(self, w, p, Xoff, Yoff, thickness=0.525):
+ def SampleUpdate(self, w, p, Xoff, Yoff, thickness=0.525,
+ incidence=0, etch_angle=54.74):
""" Draw the sample.
w: membrane width
@@ -207,15 +284,26 @@ class TZPGcalc():
Xoff: sample x offset
Yoff: sample y offset
thickness: sample thickness used to calculate the etched facets
+ incidence: incidence angle in rad
+ etch_angle: etching angle from surface in rad
"""
# Si etching angle
- wp = w +2*thickness/np.tan(np.deg2rad(54.74))
+ wp = w +2*thickness/np.tan(etch_angle)
+
+ # incidence angle squeezes sample and etch lines
+ # and induces an apparent shift off the etch lines
+ ci = np.cos(incidence)
+ thsi = thickness*np.sin(incidence)
j = 0
for k in range(-(SampleN-1)//2, (SampleN-1)//2+1):
for l in range(-(SampleN-1)//2, (SampleN-1)//2+1):
- self.RectUpdate(self.sampleLines[j], k*p - w/2 + Xoff, l*p - w/2 - Yoff, k*p + w/2 + Xoff, l*p + w/2 - Yoff)
- self.RectUpdate(self.etchLines[j], k*p - wp/2 + Xoff, l*p - wp/2 - Yoff, k*p + wp/2 + Xoff, l*p + wp/2 - Yoff)
+ self.RectUpdate(self.sampleLines[j],
+ ci*(k*p - w/2 + Xoff), l*p - w/2 - Yoff,
+ ci*(k*p + w/2 + Xoff), l*p + w/2 - Yoff)
+ self.RectUpdate(self.etchLines[j],
+ ci*(k*p - wp/2 + Xoff)+thsi, l*p - wp/2 - Yoff,
+ ci*(k*p + wp/2 + Xoff)+thsi, l*p + wp/2 - Yoff)
j+=1
def UpdateFig(self):
@@ -232,6 +320,7 @@ class TZPGcalc():
theta_grating = self.grating_slider.value*1e-3 # [rad]
sampleZ = self.samz_slider.value*1e-3 # [m]
+ samIncidence = np.deg2rad(self.samIncidence_slider.value) # [rad]
detectorZ = self.det_slider.value*1e-3 # [m]
TZPGwH = self.TZPGwH_slider.value*1e-3 #[m]
TZPGwV = self.TZPGwV_slider.value*1e-3 #[m]
@@ -253,10 +342,10 @@ class TZPGcalc():
'TZPGwH':TZPGwH, 'TZPGwV':TZPGwV, 'TZPGo':TZPGo}
# update the beams
- self.UpdateBeams(self.samBeamsL, Z0 + sampleZ, confL)
- self.UpdateBeams(self.detBeamsL, Z0 + detectorZ, confL)
- self.UpdateBeams(self.samBeamsH, Z0 + sampleZ, confH)
- self.UpdateBeams(self.detBeamsH, Z0 + detectorZ, confH)
+ self.UpdateBeams(self.samBeamsL, Z0 + sampleZ, samIncidence, confL)
+ self.UpdateBeams(self.detBeamsL, Z0 + detectorZ, 0, confL)
+ self.UpdateBeams(self.samBeamsH, Z0 + sampleZ, samIncidence, confH)
+ self.UpdateBeams(self.detBeamsH, Z0 + detectorZ, 0, confH)
# update the detector
detXoff = self.detX_slider.value*1e-3 #[m]
@@ -269,7 +358,9 @@ class TZPGcalc():
samXoff = self.samX_slider.value*1e-3 #[m]
samYoff = self.samY_slider.value*1e-3 #[m]
samthickness = self.samthickness_slider.value*1e-6 #[m]
- self.SampleUpdate(samw, samp, samXoff, samYoff, samthickness)
+ samEtchAngle = np.deg2rad(self.samEtchAngle_slider.value) #[rad]
+ self.SampleUpdate(samw, samp, samXoff, samYoff, samthickness,
+ samIncidence, samEtchAngle)
def initWidgets(self):
""" Creates the necessary interactive widget controls.
@@ -379,12 +470,28 @@ class TZPGcalc():
step=1,
readout_format='.0f',
)
+ self.samIncidence_slider = widgets.FloatSlider(
+ value=0,
+ min=0,
+ max=90,
+ step=1,
+ readout_format='.0f',
+ )
+ self.samEtchAngle_slider = widgets.FloatSlider(
+ value=54.74,
+ min=0,
+ max=90,
+ step=0.01,
+ readout_format='.2f',
+ )
samTab = VBox(children=[HBox([widgets.Label(value='Sample Z (mm):'), self.samz_slider]),
HBox(children=[HBox([widgets.Label(value='Membrane width (mm):'), self.samw_slider]),
HBox([widgets.Label(value='Membrane pitch (mm):'), self.samp_slider])]),
HBox(children=[HBox([widgets.Label(value='Sample X-Offset (mm):'), self.samX_slider]),
HBox([widgets.Label(value='Sample Y-Offset (mm):'), self.samY_slider])]),
- HBox([widgets.Label(value='Substrate thickness (um):'), self.samthickness_slider])
+ HBox([widgets.Label(value='Substrate thickness (um):'), self.samthickness_slider]),
+ HBox([HBox([widgets.Label(value='Normal incidence (deg):'), self.samIncidence_slider]),
+ HBox([widgets.Label(value='Etch angle from surface (deg):'), self.samEtchAngle_slider])])
])
#detector tab