BP 3E - Back Projection - in XY planes

PURPOSE

The second step of the weighted back projection method. The input projections are back projected into a given volume. This volume may already exist; in this case the pro- jections are added on. If the volume does not exist, it will create a volume containing 0 density, if the question ".IS THIS A NEW 3D (Y/N):" is answered Y. The program works for both single axis and conical tilting series. The angles of the projections have to be written into the title of the image using the command 'ST'. In contrast to BP XY BP 3E uses all three Euler angles.

SEE ALSO

BP 3 [(ART Back Projection - 3D)]
BP 3D [(3D Reconstruction - using three Eulerian angles]
BP GW [3D reconstruction with general weighting]
BP LOCAL [Back projection calculated to a specific local area]
BP MEM2 [2D reconstruction by Max. Entropy Method]
BP RP [Iterative Reconstruction With Constraints]
BP R2 [R**2 weighting for 2D]
BP S2 [2D Single-tilt Iterative Recon. With Constraints]
BP W2 [2D filtered, weighted back projection]
BP WX [Weighted Back Projection]
BP WY [Weighted Back Projection]
BP XY [Back Projection in X-Y planes]

USAGE

.OPERATION: BP 3E

.THREED FILE: REC100
[Enter the name of the reconstruction volume.]

.IS THIS A NEW 3D (Y/N): Y

If the last answer was "Y" it asks:

.X,Y DIMENSIONS: 64,64

.Z DIMENSION: 64
[Define the dimensions of the reconstruction volume. These 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: 10,50
[Self-explanatory.]

.STEP: 1
[Enter the steps between the slices to be calculated. This allows for the reconstruction, for example, of every second slice. However, the slices not calculated are still part of the reconstructed volume, and contain 0 density.]

.ENLARGEMENT FACTOR: 1
[Since the dimensions of the volume are independent of those of the projections, different grids for the reconstruction volume and the projections may be defined by the enlargement factor. The default=1.]

.FIRST FILE: PRO001

.LAST FILE: PRO020
[Enter the names of the first and last projections.]

NOTES

1. The reconstructed volume has to be filtered to the correct resolution, which is determined by the number of projecttions. This can be done either after the reconstruction, by filtering the volume, or by filtering the input projections before the reconstruction the the correct resolu- tion. For the formulas to calculate the resolution, see:

2. Single-Axis Tilting: Crowther R.A., DeRosier D.J., Klug A., Proc. Roy. Soc. Lond. A. 317,319-340 (1970) (specifically, page 332).

3. Conical Tilting: Radermacher M., Hoppe W., Proc. 7th Europ. Congr. El. Micr. den Haag, 1980 Vol.1 132-133.

4. Arbitrary tilting: The resollution can be estimated from a histogram of the angular distribution or a comparison of two or more independent reconstructions. Exact formulas are not available.

SUBROUTINES

BAPI, MIRQBXS

CALLER

VTIL2