ENH: add analysis of chi sensativity

TLDR; 7mdeg / .5mdeg is enough

Author: tacaswell

design_scripts/FDR/chi_sensativity.py

@@ -0,0 +1,115 @@
+# %% [markdown]
+# # Sensitivity to χ missalignment on 2ϴ to 2θ correction
+
+
+# %%
+import dataclasses
+
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+import numpy as np
+from multihead.config import AnalyzerConfig
+from multihead.corrections import tth_from_z
+from scipy import optimize
+
+from hrd_tools.xrt import CrystalProperties
+
+# %%
+mpl.rcParams["savefig.dpi"] = 300
+
+# %% [markdown]
+#
+# The error gets large with both the displacment across the detector
+# and the detector arm angle
+
+# %%
+
+props = CrystalProperties.create(E=40)
+
+# Configure analyzer with realistic parameters
+cfg = AnalyzerConfig(
+    910,  # R: sample to crystal distance (mm)
+    120,  # Rd: crystal to detector distance (mm)
+    props.bragg_angle,
+    2 * props.bragg_angle,
+    detector_roll=0,
+)
+
+z = 15
+
+
+fig, (ax1, ax2) = plt.subplots(1, 2, layout="constrained", sharey=True)
+
+
+def one_z(z, ax):
+    arm_angle = np.linspace(2, 88)
+    baseline, _ = tth_from_z(z, arm_angle, cfg)
+    for chi in [0.0001, 0.001, 0.01]:
+        corrected_tths, _ = tth_from_z(
+            z, arm_angle, dataclasses.replace(cfg, crystal_roll=chi)
+        )
+        (ln,) = ax.plot(
+            arm_angle, (baseline - corrected_tths) * 1000, label=rf"$\chi$={chi}"
+        )
+        corrected_tths, _ = tth_from_z(
+            -z, arm_angle, dataclasses.replace(cfg, crystal_roll=chi)
+        )
+        ax.plot(arm_angle, (baseline - corrected_tths) * 1000, color=ln.get_color())
+
+    ax.axhline(1e-1, color=".5", ls="--")
+    ax.axhline(-1e-1, color=".5", ls="--")
+
+    ax.legend(loc="best")
+    ax.set_title(rf"$z_d$={z}mm")
+    ax.set_xlabel(r"arm $2\Theta$ (deg)")
+
+
+def one_angle(arm_angle, ax):
+    z = np.linspace(-20, 20, 256)
+    baseline, _ = tth_from_z(z, arm_angle, cfg)
+    for chi in [0.0001, 0.001, 0.01]:
+        corrected_tths, _ = tth_from_z(
+            z, arm_angle, dataclasses.replace(cfg, crystal_roll=chi)
+        )
+        ax.plot(z, (baseline - corrected_tths) * 1000, label=rf"$\chi$={chi}")
+
+    ax.axhline(1e-1, color=".5", ls="--")
+    ax.axhline(-1e-1, color=".5", ls="--")
+
+    ax.legend()
+    ax.set_title(rf"$2\Theta$={arm_angle}deg")
+    ax.set_xlabel(r"arm $2\Theta$ (deg)")
+
+
+ax1.set_ylabel(r"scatter $\Delta 2\theta$ (mdeg)")
+
+one_z(z, ax2)
+one_angle(45, ax1)
+
+
+plt.show()
+
+# %%
+
+zd = 15
+arm_angle = 88
+delta_tth = 1e-5
+
+baseline_tth, _ = tth_from_z(zd, arm_angle, cfg)
+
+
+def f(chi, delta):
+    corrected_tth, _ = tth_from_z(
+        zd, arm_angle, dataclasses.replace(cfg, crystal_roll=chi)
+    )
+
+    return delta - (-corrected_tth + baseline_tth)
+
+
+chi_limit = optimize.root_scalar(f, args=(delta_tth,), bracket=[0, 0.01])
+
+print(
+    f"at z_d={zd}mm and 2ϴ={arm_angle}deg the maximum χ "
+    f"to stay under Δ2θ ≤ {delta_tth * 1000:.2g}mdeg "
+    f"is {1000 * chi_limit.root:.2g}mdeg"
+)