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BP XY - Back Projection - simple for single axis & conical tilting

(9/17/94)

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 projections 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 geometrical relation between the object and the projections is described by the rotation matrix:
COS(THETA)COS(PHI) COS(THETA)SIN(PHI) -SIN(THETA)
-SIN(PHI) COS(PHI) 1
If, for example, you have a single-axis tilting series with Y as the tilt axis, use 'BP WX' to weight the projections perpendicular to the tilt axis and define only THETA in the back projection step.

SEE ALSO

BP 3 [Back Projection - 3D, iterative]
BP 3D [Back Projection - 3D, using Euler angles, ||]
BP 3E [Back Projection - 3D, using Euler angles]
BP CTF [Back Projection - 3D, CTF correction, ||]
BP GW [Back Projection - weighted, arbitrary geometry]
BP GW3 [Back Projection - weighted, arbitrary geometry, 3 angles]
BP MEM2 [Back Projection - 2D maximum entropy method]
BP R2 [Back Projection - 2D, R**2 weighting of the image series]
BP RP [Back Projection - 3D, iterative, with constraints, ||]
BP S2 [Back Projection - 2D, single tilt iterative, with constraints]
BP W2 [Back Projection - 2D, filtered weighted]
BP WX [Back Projection - weighted, X]
BP WY [Back Projection - weighted, Y]

USAGE

.OPERATION: BP XY

.3D 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.]

.SLICE INTERVAL: 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=1.0]

.FIRST PROJECTION FILE: PRO001

.LAST PROJECTION 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 resolution. For the formulas to calculate the resolution, see:
    Single-Axis Tilting:
    Crowther R.A., DeRosier D.J., Klug A., Proc. Roy. Soc. Lond. A. 317,319-340 (1970) (specifically, page 332). Conical Tilting:
    Radermacher M., Hoppe W., Proc. 7th Europ. Congr. El. Micr. den Haag, 1980 Vol.1 132-133. Arbitrary tilting:
    The resolution 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

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