**PURPOSE**- Calculates Back-Projection step of 3D reconstruction using three Eulerian angles. Can optionally apply two different weighting functions. ART reconstruction. Used at Albany for double-tilt electron tomography. See: Comparison of 'BP' operations. Example.

**SEE ALSO****BP 3F**[Back Projection - 3D, Interpolated in Fourier space ||*] **BP CG**[Back Projection - 3D, Iterative, Conjugate Gradients ||*] **BP RP**[Back Projection - 3D, iterative, Richardson, constrained ||*] **BP S2**[Back Projection - 2D, single tilt, iterative, constrained ||] **BP W2**[Back Projection - 2D, filtered, weighted ||] **BP R2**[Back Projection - Weight image series ||]

**USAGE**- .OPERATION: BP 3D

- <or>

BP 3DP.TEMPLATE FOR 2-D INPUT IMAGES: PROJ***

[Enter file name template for the set of input projections.].FILE NUMBERS OR SELECTION DOC. FILE NAME: REFPROJ_SEL

[Enter projection file numbers or the name of the document file which contains the projection file numbers in its first register column.].ANGLES DOC FILE: ANGLES27

[Enter name of the document file which contains Eulerian angles: psi, theta, and phi in the first three registers columns.].OUTPUT VOLUME: X, Y & Z DIMENSIONS: 75, 77, 35

[Enter X, Y, & Z (NX, NY, & NZ) 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 (NX/2+1, NY/2+1,NZ/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 omitted, only back projection is done.

>0 - Signal-to-Noise-Ratio for Wiener filtration (type one weighting function).

<0 - Diameter of structure (type two weighting function).].RECONSTRUCTED 3-D OUTPUT: VOLUME001

[Name of the output file.] - If using 'BP 3DP' SPIDER asks:

.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**

- 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.
- 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, a 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, a type two weighting function is applied. It's absolute value defines the diameter of the reconstructed volume. Normally DIAMETER = NX. 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. - 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 electron microscopy
sections, try a filter value of 1300-10000.
- See bp3d_slab_pub.spi
for a procedure that can be used
for large scale reconstructions on a cluster.
- Implemented by Paul Penczek.

**SUBROUTINES**- BCQ, BUILDM, CANG, BPCQP, BPCMP, BPCQ, BPCM, WTF, WTM

**CALLER**- VTIL2

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