BP 3D - Back Projection - 3D, using Euler angles ||

PURPOSE

Calculates Back-Projection step of 3D reconstruction using three Eulerian angles. Can optionally apply two different weighting functions. Used at Albany for double-tilt electron tomography.

SEE ALSO

BP 3F	[Back Projection - 3D, Interpolated in Fourier space ||*]
BP 32F	[Back Projection - 3D, Sampled, Interpolated in Fourier space ||*]
BP CG	[Back Projection - 3D, Conjugate gradients ||*]
BP R2	[Back Projection - 2D, weighting of image series ||]
BP RP	[Back Projection - 3D, iterative, with constraints, ||*]
BP S2	[Back Projection - 2D, single tilt iterative, constrained ||]
BP W2	[Back Projection - 2D, filtered, weighted ||]

USAGE

.OPERATION: BP 3D

<or>
BP 3DP

.ENTER TEMPLATE FOR 2-D INPUT IMAGES: PROJ***
[Enter tfile name template for the set of input projections.]

.ENTER FILE NUMBERS OR SELECTION DOC. FILE NAME: 1-700
[Enter projection file numbers or the name of the document file containing projection file numbers in the first column.]

.ANGLES DOC FILE: ANGLES27
[Enter the name of the document file containing Eulerian angles for the projections used (psi, theta, phi).]

.OUTPUT VOLUME: X, Y & Z DIMENSIONS: 75,77,35
[Enter X, Y, & Z (NSAM, NROW, & NSLICE) dimensions of the volume to be reconstructed. These dimensions are independent of the dimensions of the projections. The center is assumed to be at point (NSAM/2+1, NROW/2+1,NSLICE/2+1).]

.FIRST, LAST SLICE TO BE RECONSTRUCTED: 2,24
[Enter Z borders of the volume to be reconstructed. Must be no larger than Z dimension entered above. In case the volume is too large for your computer's memory this can be used to reconstruct slabs which can then be merged into a single larger reconstruction.]

.SNR / DIAMETER: 1.0E+4
[Depending on the value:
0 - Weighting will be ommited and only back projection will be done.
>0 - Signal-to-Noise-Ratio for the Wiener filtration of type one weighting function.
<0 - Diameter of the structure for the weighting in type two weighting function.]

.RECONSTRUCTED 3-D OUTPUT: VOLUME001
[Name of the output file.]

If using 'BP 3DP' the following question appears:

.FILE NUMBERS OR SELECTION DOC. FILE FOR THIS PARTITION: 1-30
[Give the list of projections used in this partition. Allows one to split the an overall back-projection operation into several partitions which could be run in parallel and then summed. Does not overcome lack of memory for large sized reconstructions however.]

NOTES

1. The output volume has dimensions defined by X and Y dimensions entered and has Z dimension defined by first and last slice entered. According to the numbers used above the volume would be 75x77x23.

2. Weighting function is applied in 2D and the type is decided by the sign of the parameter given in SNR/DIAMETER.
   For parameter equal zero no weighting is applied.
   For parameter larger than zero, type one weighting function is applied. The smaller the parameter the stronger the lowpass filtration effect. This weighting function is a Gaussian function as described in: M. Radermacher, Weighted Back-Projection Methods. (p.102) In: Electron Tomography. Ed.: J. Frank, 1992.
   

   For SNR / DIAMETER parameter lower than zero, type two weighting function is applied. It's absolute value defines the diameter of the reconstructed volume. Normally DIAMETER = NSAM. The smaller the parameter the stronger the lowpass filtration effect. This weighting function is a "triangular overlap function" as defined in: G. Harauz and M. van Heel, Exact filters for general geometry three dimensional reconstruction.Optik 73 (1986) 146-156.

3. For use in electron tomography of stained sections we have found a a negative filter value of one quarter of the image size works well. For electron tomography of cryo sections try a filter value of 1300-10000.

4. See bp3d_slab_pub.spi in the SPIDER PROCEDURE DIRECTORY for a procedure that can be used for large scale reconstructions on a cluster.

5. Implemented by Paul Penczek.

SUBROUTINES

BCQ, BUILDM, CANG, BPCQP, BPCMP, BPCQ, BPCM, WTF, WTM

CALLER

VTIL2