diff --git a/tests/test_qlsi.py b/tests/test_qlsi.py
index a8f507d..48b5e06 100644
--- a/tests/test_qlsi.py
+++ b/tests/test_qlsi.py
@@ -127,6 +127,11 @@ def test_qlsi_unwrap_phase_2d_3d():
 
 
 def test_qlsi_rotate_2d_3d(hologram):
+    """
+    Ensure the old 2d and new 3d rotation is identical.
+    Note that the hologram is used only as an example input image,
+    and it is not the correct data type for QLSI.
+    """
     data_2d = hologram
     data_3d, _ = qpretrieve.data_array_layout._convert_2d_to_3d(data_2d)
 
@@ -155,6 +160,11 @@ def test_qlsi_rotate_2d_3d(hologram):
 
 
 def test_qlsi_pad_2d_3d(hologram):
+    """
+    Ensure the old 2d and new 3d padding is identical.
+    Note that the hologram is used only as an example input image,
+    and it is not the correct data type for QLSI.
+    """
     data_2d = hologram
     data_3d, _ = qpretrieve.data_array_layout._convert_2d_to_3d(data_2d)
 
@@ -171,22 +181,31 @@ def test_qlsi_pad_2d_3d(hologram):
 
 
 def test_fxy_complex_mul(hologram):
+    """
+    Ensure the old 2d and new 3d complex multiplication is identical.
+    Note that the hologram is used only as an example input image,
+    and it is not the correct data type for QLSI.
+    """
     data_2d = hologram
     data_3d, _ = qpretrieve.data_array_layout._convert_2d_to_3d(data_2d)
 
     assert np.array_equal(data_2d, data_3d[0])
 
     # 2d
-    fx_2d = data_2d.reshape(-1, 1)
-    fy_2d = data_2d.reshape(1, -1)
+    fx_2d = np.fft.fftfreq(data_2d.shape[0]).reshape(-1, 1)
+    fy_2d = np.fft.fftfreq(data_2d.shape[1]).reshape(1, -1)
     fxy_2d = -2 * np.pi * 1j * (fx_2d + 1j * fy_2d)
+    assert fxy_2d.shape == (64, 64)
     fxy_2d[0, 0] = 1
 
     # 3d
-    fx_3d = data_3d.reshape(data_3d.shape[0], -1, 1)
-    fy_3d = data_3d.reshape(data_3d.shape[0], 1, -1)
+    fx_3d = np.fft.fftfreq(data_3d.shape[-2]).reshape(-1, 1)
+    fy_3d = np.fft.fftfreq(data_3d.shape[-1]).reshape(1, -1)
     fxy_3d = -2 * np.pi * 1j * (fx_3d + 1j * fy_3d)
+    fxy_3d = np.repeat(fxy_3d[np.newaxis, :, :],
+                       repeats=data_3d.shape[0], axis=0)
+    assert fxy_3d.shape == (1, 64, 64)
     fxy_3d[:, 0, 0] = 1
 
-    assert np.array_equal(fx_2d, fx_3d[0])
+    assert np.array_equal(fx_2d, fx_3d)
     assert np.array_equal(fxy_2d, fxy_3d[0])