diff --git a/src/mrpro/operators/_FourierOp.py b/src/mrpro/operators/_FourierOp.py
index de3a2f73e..05e72a9a3 100644
--- a/src/mrpro/operators/_FourierOp.py
+++ b/src/mrpro/operators/_FourierOp.py
@@ -34,9 +34,9 @@ def __init__(
         recon_shape: SpatialDimension[int],
         encoding_shape: SpatialDimension[int],
         traj: KTrajectory,
-        oversampling: float | SpatialDimension[float] = 2.0,  # only used for nuFFT
-        numpoints: int = 6,
-        kbwidth: float = 2.34,
+        nufft_oversampling: float = 2.0,  
+        nufft_numpoints: int = 6,
+        nufft_kbwidth: float = 2.34,
     ) -> None:
         """Fourier Operator class.
 
@@ -48,19 +48,15 @@ def __init__(
             dimension of the encoded k-space
         traj
             the k-space trajectories where the frequencies are sampled
-        oversampling
-            oversampling for (potential) nuFFT directions
-        numpoints
-            number of neighbors for interpolation for nuFFTs
-        kbwidth
-            size of the Kaiser-Bessel kernel for the nuFFT
+        nufft_oversampling
+            oversampling used for interpolation in non-uniform FFTs 
+        nufft_numpoints
+            number of neighbors for interpolation in non-uniform FFTs
+        nufft_kbwidth
+            size of the Kaiser-Bessel kernel interpolation in non-uniform FFTs
         """
         super().__init__()
 
-        # convert oversampling to SpatialDimension if float
-        if isinstance(oversampling, float):
-            oversampling = SpatialDimension(oversampling, oversampling, oversampling)
-
         def get_spatial_dims(spatial_dims: SpatialDimension, dims: Sequence[int]):
             return [
                 s
@@ -103,10 +99,7 @@ def get_traj(traj: KTrajectory, dims: Sequence[int]):
                 )
 
             self._nufft_im_size = get_spatial_dims(recon_shape, self._nufft_dims)
-            grid_size = [
-                int(s * os)
-                for s, os in zip(self._nufft_im_size, get_spatial_dims(oversampling, self._nufft_dims), strict=True)
-            ]
+            grid_size = [int(size * nufft_oversampling) for size in self._nufft_im_size]
             omega = [
                 k * 2 * torch.pi / ks
                 for k, ks in zip(
@@ -116,21 +109,21 @@ def get_traj(traj: KTrajectory, dims: Sequence[int]):
                 )
             ]
 
-            # Broadcast shapes (not always needed but also does not hurt)
+            # Broadcast shapes not always needed but also does not hurt
             omega = [k.expand(*np.broadcast_shapes(*[k.shape for k in omega])) for k in omega]
-            self._omega = torch.stack(omega, dim=-4)  # use the 'coil' dim for the direction
+            self.register_buffer('_omega', torch.stack(omega, dim=-4)) # use the 'coil' dim for the direction
 
             self._fwd_nufft_op = KbNufft(
                 im_size=self._nufft_im_size,
                 grid_size=grid_size,
-                numpoints=numpoints,
-                kbwidth=kbwidth,
+                numpoints=nufft_numpoints,
+                kbwidth=nufft_kbwidth,
             )
             self._adj_nufft_op = KbNufftAdjoint(
                 im_size=self._nufft_im_size,
                 grid_size=grid_size,
-                numpoints=numpoints,
-                kbwidth=kbwidth,
+                numpoints=nufft_numpoints,
+                kbwidth=nufft_kbwidth,
             )
 
             self._kshape = traj.broadcasted_shape