Ensure correct rotation of backfacing retarders (#947)

src/bsdfs/retarder.cpp

@@ -111,13 +111,15 @@ class LinearRetarder final : public BSDF<Float, Spectrum> {
             UnpolarizedSpectrum delta = dr::deg_to_rad(m_delta->eval(si, active));
 
             // Approximate angle-of-incidence behaviour with a cosine falloff
-            delta *= dr::abs(Frame3f::cos_theta(si.wi));
+            Float cos_theta = Frame3f::cos_theta(si.wi);
+            delta *= dr::abs(cos_theta);
 
             // Get standard Mueller matrix for a linear polarizer.
             Spectrum M = mueller::linear_retarder(delta);
 
-            // Rotate optical element by specified angle
-            M = mueller::rotated_element(theta, M);
+            /* Rotate optical element by specified angle. The angle is flipped if
+               the element is intersected from the backside. */
+            M = mueller::rotated_element(dr::sign(cos_theta) * theta, M);
 
             /* The `forward` direction here is always along the direction that
                light travels. This is needed for the coordinate system rotation
@@ -161,13 +163,15 @@ class LinearRetarder final : public BSDF<Float, Spectrum> {
             UnpolarizedSpectrum delta = dr::deg_to_rad(m_delta->eval(si, active));
 
             // Approximate angle-of-incidence behaviour with a cosine falloff
-            delta *= dr::abs(Frame3f::cos_theta(si.wi));
+            Float cos_theta = Frame3f::cos_theta(si.wi);
+            delta *= dr::abs(cos_theta);
 
             // Get standard Mueller matrix for a linear polarizer.
             Spectrum M = mueller::linear_retarder(delta);
 
-            // Rotate optical element by specified angle
-            M = mueller::rotated_element(theta, M);
+            /* Rotate optical element by specified angle. The angle is flipped if
+               the element is intersected from the backside. */
+            M = mueller::rotated_element(dr::sign(cos_theta) * theta, M);
 
             /* The `forward` direction here is always along the direction that
                light travels. This is needed for the coordinate system rotation

src/bsdfs/tests/test_retarder.py

@@ -497,3 +497,53 @@ def spectrum_from_stokes(v):
     # Make sure observations match expectations
     for k in range(len(expected)):
         assert dr.allclose(observed[k], expected[k], atol=1e-3)
+
+
+def test08_rotated_quarter_wave(variant_scalar_mono_polarized):
+
+    def spectrum_from_stokes(v):
+        res = mi.Spectrum(0.0)
+        for i in range(4):
+            res[i,0] = v[i]
+        return res
+
+    linear_horizontal = spectrum_from_stokes([1, +1, 0, 0])
+    linear_vertical   = spectrum_from_stokes([1, -1, 0, 0])
+    circular_right    = spectrum_from_stokes([1, 0, 0, +1])
+    circular_left     = spectrum_from_stokes([1, 0, 0, -1])
+
+    bsdf = mi.load_dict({
+        'type': 'retarder',
+        'theta': 45.0,
+        'delta': 90.0,
+    })
+
+    ctx = mi.BSDFContext()
+    ctx.mode = mi.TransportMode.Importance
+    si = mi.SurfaceInteraction3f()
+    si.p = [0, 0, 0]
+    si.wi = [0, 0, 1]
+    n = [0, 0, 1]
+    si.n = n
+    si.sh_frame = mi.Frame3f(si.n)
+
+    _, M = bsdf.sample(ctx, si, 0.0, [0.0, 0.0])
+    M_null = bsdf.eval_null_transmission(si)
+    assert dr.allclose(M, M_null, atol=1e-3)
+
+    assert dr.allclose(M @ linear_horizontal, circular_right, atol=1e-3)
+    assert dr.allclose(M @ linear_vertical, circular_left, atol=1e-3)
+    assert dr.allclose(M @ circular_right, linear_vertical, atol=1e-3)
+    assert dr.allclose(M @ circular_left, linear_horizontal, atol=1e-3)
+
+    # Reverse incident direction.
+    si.wi = [0, 0, -1]
+
+    _, M = bsdf.sample(ctx, si, 0.0, [0.0, 0.0])
+    M_null = bsdf.eval_null_transmission(si)
+    assert dr.allclose(M, M_null, atol=1e-3)
+
+    assert dr.allclose(M @ linear_horizontal, circular_left, atol=1e-3)
+    assert dr.allclose(M @ linear_vertical, circular_right, atol=1e-3)
+    assert dr.allclose(M @ circular_right, linear_horizontal, atol=1e-3)
+    assert dr.allclose(M @ circular_left, linear_vertical, atol=1e-3)