Angular search

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The basic idea in a cross-correlation method is that the template is rotated several times, and each rotated copy is compared with the particle.

Parametrization of an angular grid

In Dynamo, an angular grid (i.e., a set of Euler triplets to be scanned) is defined by five parameters:

  • cone_range,
  • cone_sampling
  • inplane_range
  • inplane_sampling
  • old _angles

The first four are project parameters that can be chosen by the user and will be applied for the analysis of all particles. The last one, old_angles is obviously different for each particle, and in runtime is read from the table (provided by the user or generated by Dynamo during the iteration procedure). The cone_ parameters define a set of orientations that will be sampled around a previously determined old orientation. Here we speak of orientations of the vertical axis of the template, not full unconstrained rotations. Allowing this axis to move inside a cone involves only two Euler angles (tdrot and tilt). ‘cone_range’, is the extent of this cone in degrees (360 being the full possible range of axis orientations). cone_sampling is the step inside this cone, also in degrees. The orientations are generated so as to provide an uniform coverage. The inplane_ parameters complete the set of scanned Euler triplets. After each of the axis reorentations defined by the cone_ parameters, the template will be rotated about the new orientation of its axis. This is frequently referred to as azymuthal rotation. This involves only the narot angle. The project parameter inplane_range defines the angular interval to be scanned around the old value of narot, and ‘inplane_sampling’ defines the interval. By convention, passing value 0 to inplane_range generates ‘inplane’ rotations: only axis orientations of the axis will be scanned.

Multilevel refinement of an angular grid

Two further project parameters control the refinement of the grid: when Dynamo finds the triplet [tdrot,tilt,narot] that maximizes the similarity between rotated template and particle, a new grid is generated around this angles. The project parameter refine defines how many times this process will be repeated for each particle. refine_factor defines the range of the new set of angles. A value of 2, for instance, means that the range of the new grid should twice as large as the step of the old grid.