Repository: pyxem/kikuchipy (language: python)

Issue:
Ensure PC in EMsoft convention behaves as expected when initializing an EBSDDetector
We need to make sure that the projection/pattern center (PC) in EMsoft convention is as expected when passing `px_size` and `binning` to `kikuchipy.detectors.EBSDDetector`. After discussing with @friedkitteh, this isn't always the case. It was concluded that when creating a dictionary of simulated EBSD patterns from a master pattern in the Lambert projection, the ratios between xpc, ypc and L is important, while the absolute values are unimportant.

Todo:
- [ ] A test ensuring that the ratios between xpc, ypc, and L are as expected when passing `px_size` and `binning` to `EBSDDetector.__init__()`
- [ ] Clarify in the docstring whether `px_size` always is the unbinned detector pixel size


Discussion / hints:
@friedkitteh, could you quickly remind me with which parameters to `EBSDDetector` you got an unexpected EMsoft PC from `pc_emsoft()`?
Hmm, I don't recall exactly which... But I think it is just when you specify binning and a PC that is not in the EMsoft convention that everything gets a bit wonky

Fix patch:
diff --git a/doc/_static/image/reference_frames/detector_sample_geometry.png b/doc/_static/image/reference_frames/detector_sample_geometry.png
index 98761051..a5a581f3 100644
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+    <text
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+    <text
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diff --git a/doc/changelog.rst b/doc/changelog.rst
index cb1c54e8..f048bffb 100644
--- a/doc/changelog.rst
+++ b/doc/changelog.rst
@@ -21,9 +21,12 @@ Contributors
 
 Added
 -----
+- Sample tilt about RD can be passed as part of an EBSDDetector. This can be used when
+  projecting parts of master patterns onto a detector.
+  (`#381 <https://github.com/pyxem/kikuchipy/pull/381>`_)
 - Reader for EBSD patterns stored in Oxford Instrument's binary .ebsp file
   format, uncompressed and with intensities as 8-bit unsigned integers.
-  (`#? <https://github.com/pyxem/kikuchipy/pull/?>`_)
+  (`#371 <https://github.com/pyxem/kikuchipy/pull/371>`_)
 - Unit testing of docstring examples.
   (`#350 <https://github.com/pyxem/kikuchipy/pull/350>`_)
 - Support for Python 3.9.
diff --git a/doc/reference_frames.ipynb b/doc/reference_frames.ipynb
index a3eb20c4..b6671ca9 100644
--- a/doc/reference_frames.ipynb
+++ b/doc/reference_frames.ipynb
@@ -18,11 +18,10 @@
     "\n",
     "## Sample-detector geometry\n",
     "\n",
-    "The figures below show the\n",
-    "[sample reference frame](#detector-sample-geometry) and the\n",
-    "[detector reference frame](#detector-coordinates) used in kikuchipy, all of\n",
-    "which are right handed. In short, the sample reference frame is the one used by\n",
-    "EDAX TSL, RD-TD-ND, while the pattern center is defined as in the Bruker\n",
+    "The figure below shows the [sample reference frame](#detector-sample-geometry)\n",
+    "and the [detector reference frame](#detector-coordinates) used in kikuchipy, all\n",
+    "of which are right handed. In short, the sample reference frame is the one used\n",
+    "by EDAX TSL, RD-TD-ND, while the pattern center is defined as in the Bruker\n",
     "software."
    ]
   },
@@ -37,18 +36,20 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In **(a)**, a schematic of the microscope chamber shows the orientation of the\n",
-    "crystal reference frame, RD-TD-ND, attached to the sample. The\n",
-    "$x_{euler}-y_{euler}-z_{euler}$ crystal reference frame used by Bruker\n",
-    "Nano EDAX TSL is shown for reference. An EBSD pattern on the detector screen is\n",
-    "viewed from behind the screen towards the sample. **(b)** shows how the EBSD map\n",
-    "appears within the data collection software, with the crystal reference frame\n",
-    "and the scanning reference frame, $x_{scan}-y_{scan}-z_{scan}$, attached.\n",
-    "**(c)** shows the relationship between the crystal reference frame and the\n",
-    "detector reference frame, $x_{detector}-y_{detector}-z_{detector}$, with\n",
-    "the projection center highlighted. The detector tilt $\\theta$ and sample tilt\n",
-    "$\\sigma$, in this case $10^{\\circ}$ and $70^{\\circ}$, respectively, are also\n",
-    "shown."
+    "In **(a)** (lower left), a schematic of the microscope chamber shows the\n",
+    "definition of the sample reference frame, RD-TD-ND. The\n",
+    "$x_{euler}-y_{euler}-z_{euler}$ crystal reference frame used by Bruker is shown\n",
+    "for reference. An EBSD pattern on the detector screen is viewed from *behind*\n",
+    "the screen *towards* the sample. The inset **(b)** shows the detector and sample\n",
+    "normals viewed from above, and the azimuthal angle $\\omega$ which is defined as\n",
+    "the sample tilt angle round the RD axis. **(c)** shows how the EBSD map appears\n",
+    "within the data collection software, with the sample reference frame and the\n",
+    "scanning reference frame, $x_{scan}-y_{scan}-z_{scan}$, attached. Note the\n",
+    "$180^{\\circ}$ rotation of the map about ND. **(d)** shows the relationship\n",
+    "between the sample reference frame and the detector reference frame,\n",
+    "$x_{detector}-y_{detector}-z_{detector}$, with the projection center\n",
+    "highlighted. The detector tilt $\\theta$ and sample tilt $\\sigma$, in this case\n",
+    "$10^{\\circ}$ and $70^{\\circ}$, respectively, are also shown."
    ]
   },
   {
@@ -63,13 +64,13 @@
    "metadata": {},
    "source": [
     "The above figure shows the EBSD pattern in the\n",
-    "[sample reference frame figure](#detector-sample-geometry) **(a)** as viewed\n",
-    "from behind the screen towards the sample (left), with the detector reference\n",
-    "frame the same as in **(c)** with its origin (0, 0) in the upper left pixel. The\n",
-    "detector pixels' gnomonic coordinates can be described with a calibrated\n",
-    "projection center (PC) (right), with the gnomonic reference frame origin (0, 0)\n",
-    "in ($PC_x, PC_y$). The circles indicate the angular distance from the PC in\n",
-    "steps of $10^{\\circ}$."
+    "[sample reference frame figure](#detector-sample-geometry) (a) as viewed from\n",
+    "behind the screen towards the sample (left), with the detector reference frame\n",
+    "the same as in (d) with its origin (0, 0) in the upper left pixel. The detector\n",
+    "pixels' gnomonic coordinates can be described with a calibrated projection\n",
+    "center (PC) (right), with the gnomonic reference frame origin (0, 0) in ($PC_x,\n",
+    "PC_y$). The circles indicate the angular distance from the PC in steps of\n",
+    "$10^{\\circ}$."
    ]
   },
   {
@@ -327,7 +328,7 @@
     "estimated by the \"moving-screen\" technique\n",
     "<cite data-cite=\"hjelen1991electron\">Hjelen et al.</cite>. The technique relies\n",
     "on the assumption that the beam normal, shown in the\n",
-    "[top figure (c)](#detector-sample-geometry) above, is normal to the detector\n",
+    "[top figure (d)](#detector-sample-geometry) above, is normal to the detector\n",
     "screen as well as the incoming electron beam, and will therefore intersect the\n",
     "screen at a position independent of the detector distance (DD). To find this\n",
     "position, we need two EBSD patterns acquired with a stationary beam but with a\n",
diff --git a/kikuchipy/detectors/ebsd_detector.py b/kikuchipy/detectors/ebsd_detector.py
index b1a24d05..e4847c6f 100644
--- a/kikuchipy/detectors/ebsd_detector.py
+++ b/kikuchipy/detectors/ebsd_detector.py
@@ -45,6 +45,7 @@ def __init__(
         px_size: float = 1,
         binning: int = 1,
         tilt: float = 0,
+        azimuthal: float = 0,
         sample_tilt: float = 70,
         pc: Union[np.ndarray, list, tuple] = (0.5, 0.5, 0.5),
         convention: Optional[str] = None,
@@ -68,6 +69,10 @@ def __init__(
             Default is 1, i.e. no binning.
         tilt
             Detector tilt from horizontal in degrees. Default is 0.
+        azimuthal
+            Sample tilt about the sample RD (downwards) axis. A positive
+            angle means the sample normal moves towards the right
+            looking from the sample to the detector. Default is 0.
         sample_tilt
             Sample tilt from horizontal in degrees. Default is 70.
         pc
@@ -99,7 +104,7 @@ def __init__(
         ...     sample_tilt=70,
         ... )
         >>> det
-        EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 5, pc (0.421, 0.221, 0.505)
+        EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 5, azimuthal 0, pc (0.421, 0.221, 0.505)
         >>> det.navigation_shape  # (nrows, ncols)
         (149, 200)
         >>> det.bounds
@@ -112,6 +117,7 @@ def __init__(
         self.px_size = px_size
         self.binning = binning
         self.tilt = tilt
+        self.azimuthal = azimuthal
         self.sample_tilt = sample_tilt
         self.pc = pc
         self._set_pc_convention(convention)
@@ -353,7 +359,7 @@ def __repr__(self) -> str:
         return (
             f"{self.__class__.__name__} {self.shape}, "
             f"px_size {self.px_size} um, binning {self.binning}, "
-            f"tilt {self.tilt}, pc {tuple(self.pc_average)}"
+            f"tilt {self.tilt}, azimuthal {self.azimuthal}, pc {tuple(self.pc_average)}"
         )
 
     def _set_pc_convention(self, convention: Optional[str] = None):
diff --git a/kikuchipy/generators/ebsd_simulation_generator.py b/kikuchipy/generators/ebsd_simulation_generator.py
index c57bc2bd..b8d24be4 100644
--- a/kikuchipy/generators/ebsd_simulation_generator.py
+++ b/kikuchipy/generators/ebsd_simulation_generator.py
@@ -67,11 +67,11 @@ def __init__(self, detector: EBSDDetector, phase: Phase, rotations: Rotation):
         >>> simgen = kp.generators.EBSDSimulationGenerator(
         ...     detector=det,
         ...     phase=p,
-        ...     rotations=Rotation.from_euler([90, 45, 90])
+        ...     rotations=Rotation.from_euler([1.57, 0, 1.57])
         ... )
         >>> simgen
         EBSDSimulationGenerator (1,)
-        EBSDDetector (60, 60), px_size 1 um, binning 1, tilt 0, pc (0.5, 0.5, 0.5)
+        EBSDDetector (60, 60), px_size 1 um, binning 1, tilt 0, azimuthal 0, pc (0.5, 0.5, 0.5)
         <name: ni. space group: Fm-3m. point group: m-3m. proper point group: 432. color: tab:blue>
         Rotation (1,)
         """
diff --git a/kikuchipy/signals/ebsd_master_pattern.py b/kikuchipy/signals/ebsd_master_pattern.py
index c1b0f6b4..b189a928 100644
--- a/kikuchipy/signals/ebsd_master_pattern.py
+++ b/kikuchipy/signals/ebsd_master_pattern.py
@@ -297,19 +297,19 @@ def _get_direction_cosines(detector: EBSDDetector) -> Vector3d:
     Vector3d
         Direction cosines for each detector pixel.
     """
-    pc = detector.pc_emsoft()
-    xpc = pc[..., 0]
-    ypc = pc[..., 1]
-    L = pc[..., 2]
+    nrows, ncols = detector.shape
+
+    pcx, pcy, pcz = detector.pc[0]
+    xpc = ncols * (0.5 - pcx)
+    ypc = nrows * (0.5 - pcy)
+    L = nrows * pcz
+
+    ncols_array = np.arange(ncols)
+    nrows_array = np.arange(nrows)
 
     # Detector coordinates in microns
-    det_x = (
-        -((-xpc - (1.0 - detector.ncols) * 0.5) - np.arange(0, detector.ncols))
-        * detector.px_size
-    )
-    det_y = (
-        (ypc - (1.0 - detector.nrows) * 0.5) - np.arange(0, detector.nrows)
-    ) * detector.px_size
+    det_x = -((-xpc - (1.0 - ncols) * 0.5) - ncols_array)
+    det_y = (ypc - (1.0 - nrows) * 0.5) - nrows_array
 
     # Auxilliary angle to rotate between reference frames
     theta_c = np.radians(detector.tilt)
@@ -319,19 +319,19 @@ def _get_direction_cosines(detector: EBSDDetector) -> Vector3d:
     ca = np.cos(alpha)
     sa = np.sin(alpha)
 
-    # TODO: Enable detector azimuthal angle
-    omega = np.radians(0)  # angle between normal of sample and detector
+    # Angle between normal of sample and detector. A positive angle
+    # means the detector normal moves towards the right looking from the
+    # detector to the sample
+    omega = np.radians(detector.azimuthal)
     cw = np.cos(omega)
     sw = np.sin(omega)
 
-    r_g_array = np.zeros((detector.nrows, detector.ncols, 3))
+    r_g_array = np.zeros((nrows, ncols, 3))
 
     Ls = -sw * det_x + L * cw
     Lc = cw * det_x + L * sw
 
-    i, j = np.meshgrid(
-        np.arange(detector.nrows - 1, -1, -1), np.arange(detector.ncols), indexing="ij"
-    )
+    i, j = np.meshgrid(nrows_array[::-1], ncols_array, indexing="ij")
 
     r_g_array[..., 0] = det_y[i] * ca + sa * Ls[j]
     r_g_array[..., 1] = Lc[j]


Test patch:
diff --git a/kikuchipy/detectors/tests/test_ebsd_detector.py b/kikuchipy/detectors/tests/test_ebsd_detector.py
index ebebc7d6..191b4964 100644
--- a/kikuchipy/detectors/tests/test_ebsd_detector.py
+++ b/kikuchipy/detectors/tests/test_ebsd_detector.py
@@ -104,10 +104,11 @@ def test_detector_dimensions(
 
     def test_repr(self, pc1):
         """Expected string representation."""
-        assert repr(
-            EBSDDetector(shape=(1, 2), px_size=3, binning=4, tilt=5, pc=pc1)
-        ) == (
-            "EBSDDetector (1, 2), px_size 3 um, binning 4, tilt 5, pc "
+        det = EBSDDetector(
+            shape=(1, 2), px_size=3, binning=4, tilt=5, azimuthal=2, pc=pc1
+        )
+        assert repr(det) == (
+            "EBSDDetector (1, 2), px_size 3 um, binning 4, tilt 5, azimuthal 2, pc "
             "(0.421, 0.779, 0.505)"
         )
 
diff --git a/kikuchipy/generators/tests/test_ebsd_simulation_generator.py b/kikuchipy/generators/tests/test_ebsd_simulation_generator.py
index 58ee55d1..655f1524 100644
--- a/kikuchipy/generators/tests/test_ebsd_simulation_generator.py
+++ b/kikuchipy/generators/tests/test_ebsd_simulation_generator.py
@@ -114,7 +114,7 @@ def test_repr(self, nickel_ebsd_simulation_generator):
         """Desired string representation."""
         desired_repr = (
             "EBSDSimulationGenerator (25,)\n"
-            "EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 0, "
+            "EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 0, azimuthal 0, "
             "pc (0.421, 0.221, 0.505)\n"
             "<name: ni. space group: Fm-3m. point group: m-3m. "
             "proper point group: 432. color: tab:blue>\n"
diff --git a/kikuchipy/signals/tests/test_ebsd_masterpattern.py b/kikuchipy/signals/tests/test_ebsd_masterpattern.py
index 951b9d9b..454b0366 100644
--- a/kikuchipy/signals/tests/test_ebsd_masterpattern.py
+++ b/kikuchipy/signals/tests/test_ebsd_masterpattern.py
@@ -157,7 +157,6 @@ def test_properties(self, projection, hemisphere):
 
 
 class TestSimulatedPatternDictionary:
-    # Create detector model
     detector = kp.detectors.EBSDDetector(
         shape=(480, 640),
         px_size=50,
@@ -333,3 +332,31 @@ def test_get_patterns_navigation_shape_raises(self):
         detector = kp.detectors.EBSDDetector(shape=(60, 60))
         with pytest.raises(ValueError, match="The rotations object can only"):
             _ = mp.get_patterns(rotations=r, detector=detector, energy=20)
+
+    def test_detector_azimuthal(self):
+        """Test that setting an azimuthal angle of a detector results in
+        different patterns.
+        """
+        det1 = self.detector
+
+        # Looking from the detector toward the sample, the left part of
+        # the detector is closer to the sample than the right part
+        det2 = det1.deepcopy()
+        det2.azimuthal = 10
+
+        # Looking from the detector toward the sample, the right part of
+        # the detector is closer to the sample than the left part
+        det3 = det1.deepcopy()
+        det3.azimuthal = -10
+
+        mp = nickel_ebsd_master_pattern_small(projection="lambert")
+        r = Rotation.identity()
+
+        kwargs = dict(rotations=r, energy=20, compute=True)
+        sim1 = mp.get_patterns(detector=det1, **kwargs)
+        sim2 = mp.get_patterns(detector=det2, **kwargs)
+        sim3 = mp.get_patterns(detector=det3, **kwargs)
+
+        assert not np.allclose(sim1.data, sim2.data)
+        assert np.allclose(sim2.data.mean(), 44.06, atol=1e-2)
+        assert np.allclose(sim3.data.mean(), 43.88, atol=1e-2)
diff --git a/kikuchipy/simulations/tests/test_geometrical_ebsd_simulation.py b/kikuchipy/simulations/tests/test_geometrical_ebsd_simulation.py
index f52f62e8..ff5e4c5f 100644
--- a/kikuchipy/simulations/tests/test_geometrical_ebsd_simulation.py
+++ b/kikuchipy/simulations/tests/test_geometrical_ebsd_simulation.py
@@ -272,10 +272,10 @@ def test_repr(self, nickel_ebsd_simulation_generator, nickel_rlp, nav_shape):
 
         assert repr(sim) == (
             f"GeometricalEBSDSimulation {nav_shape}\n"
-            "EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 0, pc "
+            "EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 0, azimuthal 0, pc "
             "(0.421, 0.221, 0.505)\n"
-            "<name: ni. space group: Fm-3m. point group: m-3m. proper point "
-            "group: 432. color: tab:blue>\n"
+            "<name: ni. space group: Fm-3m. point group: m-3m. proper point group: 432."
+            " color: tab:blue>\n"
             f"KikuchiBand {str(nav_shape)[:-1]}|3)\n"
             f"Rotation {nav_shape}"
         )