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

(02/16/95)

PURPOSE

Calculates Back-Projection step of 3D reconstruction using three Eulerian angles. Optionally one of two possible weighting functions is applied.

SEE ALSO

BP 3 [Back Projection - 3D, iterative]
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]
BP XY [Back Projection - simple for single axis & conical tilting]

USAGE

.OPERATION: BP 3D

.ENTER TEMPLATE FOR 2-D IMAGE FILE: PROJ001
[Enter the name of any projection from the set.]

.SELECTION DOC FILE: images127
[Enter 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).]

.3D VOLUME: X,Y DIMENSIONS: 75,77
[Enter X and Y (NSAM, NROW) dimensions of the volume to be reconstructed. 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).]

.3D VOLUME: Z DIMENSION: 35
[Enter Z (NSLICE) dimension of the volume to be reconstructed.]

.FIRST, LAST SLICE TO BE RECONSTRUCTED: 2,24
[Enter Z borders of the volume to be reconstructed.]

.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 FILE: VOLUME1001
    [Name of the output file.]

  • NOTES

    1. The projections do not have to have power-of-2 dimensions.

    2. 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.

    3. Weighting function used are applied in 2D and the type is decided by the sign of the parameter given in SNR/DIAMETER.
    4. For parameter equal zero no weighting is applied.
    5. 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.
    6. For parameter lower than zero type two weighting function is applied. Its 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.

    7. Implemented by Paul Penczek.

    SUBROUTINES

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

    CALLER

    VTIL2

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