diff --git a/pyproject.toml b/pyproject.toml
index 39cb1c0..4ea8135 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -39,6 +39,7 @@ dependencies = [
     "torch-cubic-spline-grids",
     "torch-fourier-shift",
     "torch-image-lerp",
+    "torch-fourier-slice >= 0.0.5",
     "cryotypes == 0.2",
     "einops",
     "numpy",
diff --git a/src/tttsa/optimizers.py b/src/tttsa/optimizers.py
index f76d96f..6045c8d 100644
--- a/src/tttsa/optimizers.py
+++ b/src/tttsa/optimizers.py
@@ -3,10 +3,10 @@
 import einops
 import torch
 from torch_cubic_spline_grids import CubicBSplineGrid1d
+from torch_fourier_slice import project_2d_to_1d
 
 from .affine import affine_transform_2d
-from .projection import common_lines_projection
-from .transformations import T_2d, stretch_matrix
+from .transformations import R_2d, T_2d, stretch_matrix
 
 
 def stretch_loss(
@@ -69,10 +69,10 @@ def optimize_tilt_axis_angle(
     coarse_aligned_masked = aligned_ts * coarse_alignment_mask
 
     # generate a weighting for the common line ROI by projecting the mask
-    mask_weights = common_lines_projection(
-        einops.rearrange(coarse_alignment_mask, "h w -> 1 h w"),
-        0.0,  # angle does not matter
-    )
+    mask_weights = project_2d_to_1d(
+        coarse_alignment_mask,
+        torch.eye(2).to(coarse_alignment_mask.device),  # angle does not matter
+    ).squeeze()  # remove starting empty dimension
     mask_weights /= mask_weights.max()  # normalise to 0 and 1
 
     # optimize tilt axis angle
@@ -94,8 +94,19 @@ def optimize_tilt_axis_angle(
     )
 
     def closure() -> torch.Tensor:
-        tilt_axis_angles = tilt_axis_grid(interpolation_points)
-        projections = common_lines_projection(coarse_aligned_masked, tilt_axis_angles)
+        # The common line is the projection perpendicular to the aligned tilt-axis (
+        # aligned with the y-axis), hence add 90 degrees to project along the x-axis.
+        M = R_2d(tilt_axis_grid(interpolation_points) + 90, yx=False)[:, :2, :2]
+        projections = einops.rearrange(
+            [
+                project_2d_to_1d(
+                    coarse_aligned_masked[(i,)],
+                    M[(i,)].to(coarse_aligned_masked.device),
+                ).squeeze()  # squeeze as we only calculate one projection
+                for i in range(len(coarse_aligned_masked))
+            ],
+            "n w -> n w",
+        )
         projections = projections - einops.reduce(
             projections, "tilt w -> tilt 1", reduction="mean"
         )
diff --git a/src/tttsa/projection/__init__.py b/src/tttsa/projection/__init__.py
index d054365..e7aef33 100644
--- a/src/tttsa/projection/__init__.py
+++ b/src/tttsa/projection/__init__.py
@@ -1,8 +1,7 @@
 """Projection of images and volumes."""
 
-from .project_real import common_lines_projection, tomogram_reprojection
+from .project_real import tomogram_reprojection
 
 __all__ = [
-    "common_lines_projection",
     "tomogram_reprojection",
 ]
diff --git a/src/tttsa/projection/project_real.py b/src/tttsa/projection/project_real.py
index b1608c0..349336b 100644
--- a/src/tttsa/projection/project_real.py
+++ b/src/tttsa/projection/project_real.py
@@ -9,50 +9,15 @@
 from torch_grid_utils import coordinate_grid
 from torch_image_lerp import insert_into_image_2d
 
-from tttsa.affine import affine_transform_2d
 from tttsa.transformations import (
-    R_2d,
-    T_2d,
     projection_model_to_projection_matrix,
 )
-from tttsa.utils import dft_center, homogenise_coordinates
+from tttsa.utils import homogenise_coordinates
 
 # update shift
 PMDL.SHIFT = [PMDL.SHIFT_Y, PMDL.SHIFT_X]
 
 
-def common_lines_projection(
-    images: torch.Tensor,
-    tilt_axis_angles: torch.Tensor,
-    # this might as well takes shifts
-) -> torch.Tensor:
-    """Predict a projection from an intermediate reconstruction.
-
-    For now only assumes to project with a single matrix, but should also work for
-    sets of matrices.
-    """
-    device = images.device
-    image_dimensions = images.shape[-2:]
-
-    # TODO pad image if not square
-
-    image_center = dft_center(image_dimensions, rfft=False, fftshifted=True)
-
-    # time for real space projection
-    s0 = T_2d(-image_center)
-    r0 = R_2d(tilt_axis_angles, yx=True)
-    s1 = T_2d(image_center)
-    # invert because the tilt axis angle is forward in the sample projection model
-    M = torch.linalg.inv(s1 @ r0 @ s0).to(device)
-
-    rotated = affine_transform_2d(
-        images,
-        M,
-    )
-    projections = rotated.mean(axis=-1).squeeze()
-    return projections
-
-
 def tomogram_reprojection(
     tomogram: torch.Tensor,
     tilt_image_dimensions: Tuple[int, int],
@@ -77,6 +42,7 @@ def tomogram_reprojection(
     grid = einops.rearrange(grid, "d h w coords -> d h w coords 1")
     grid = Mproj @ grid
     grid = einops.rearrange(grid, "... d h w coords 1 -> ... d h w coords")
+
     projection, weights = insert_into_image_2d(
         tomogram.view(-1),  # flatten
         grid.view(-1, 2),
diff --git a/src/tttsa/tttsa.py b/src/tttsa/tttsa.py
index 00cd94f..4526683 100644
--- a/src/tttsa/tttsa.py
+++ b/src/tttsa/tttsa.py
@@ -64,7 +64,7 @@ def tilt_series_alignment(
     ).numpy()
 
     start_taa_grid_points = 1  # taa = tilt-axis angle
-    pm_taa_grid_points = 3  # pm = projection matching
+    pm_taa_grid_points = 1  # pm = projection matching
 
     console.print(
         f"=== Optimizing tilt-axis angle with {start_taa_grid_points} grid point."