Name

prgs - calculate 2-D projection of a 3-D volume using three Eulerian angles and two shifts using the gridding technique. The volume has to be prepared and the interpolants have to be provided. This is a version of prg command that is suitable for generating a set of projections: the time of calculation is reduced by using the input volume that is prepared for interpolation

Usage

For square volumes:

• volft,kb = prep_vol( vol )
  
  proj = prgs(volft, kb, params)
  
  

For rectangular volumes:

• volft, kbx, kby, kb = prep_vol( vol )
  
  proj = prgs(volft, kb, params, kbx, kby)
  
  

Input

volft

input volume prepared using prep_vol.The volume can be either cubic or rectangular

kb

interpolants generated using prep_vol (tabulated Kaiser-Bessel function). If the volume is cubic, kb is the only interpolant. Otherwise, kb is used for caculating weigthing along z direction.

kbx,kby

interpolants generated using prep_vol and are used to calculae weighting along x and y direction. Default is None when the volume is cubic. If the volume is rectangular, kbx and kby must be given.

params

input paramters given as a list [phi, theta, psi, s2x, s2y], projection in calculated using the three Eulerian angles and then shifted by s2x,s2y

Output

proj

generated a square 2-D projection

Method

gridding.

Reference

Penczek, P.A., Renka, R. and Schomberg, H.: Gridding-based direct Fourier inversion of the three-dimensional ray transform. J. Opt. Soc. Am. A. 21:499-509, 2004.

Author / Maintainer

Pawel A. Penczek

Keywords

category 1

TRANSFORMS

category 2

FOURIER

Files

projection.py

See also

prep_vol, prg

Maturity

stable

works for most people, has been tested; test cases/examples available.

Bugs

None. It is perfect.