**PURPOSE**- Calculates a 3D reconstruction by back-projecting the input projections using interpolation in Fourier space. See: Comparison of 'BP' operations. Example.

**SEE ALSO****BP 32F**[Back Projection - 3D, Sampled, Interpolated in Fourier space ||*] **BP CG**[Back Projection - 3D, Iterative, Conjugate Gradients ||*] **BP R2**[Back Projection - Weight image series ||] **BP RP**[Back Projection - 3D, iterative, Richardson, constrained ||*] **BP S2**[Back Projection - 2D, single tilt, iterative, constrained ||] **RB 3F**[Rotate, Shift, Back Projection in Fourier space |] **BP 3F MERGE**[Back Projection - 3D, Interpolated in Fourier space, Merge ||]

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

- .TEMPLATE FOR IMAGE FILES (E.G. STK@****): PROJ***

[Enter a template for input image files to be back projected. This template can alternatively refer to a series of single images (e.g. img***), or to a series of stacked images (e.g stack3@***), or to a whole stack of images ending in '@' (e.g. stk@). Templates containing an asterisk will have the astericks substituted with a number for the file. (The MPI version can not use a selection file for image numbers).] - If the template contains an asterisk SPIDER will ask:

.FILE NUMBERS OR SELECTION DOC FILE NAME: IMAGE_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, the rotation angle in column 6, and the X and Y shifts in columns 7-8.].SYMMETRIES DOC FILE: symmetries

[If there are no symmetries, enter symbol "*".

Otherwise, enter the name of the document file containing Eulerian angles defining symmetries (psi, theta, phi). The angles should be such that when used in operation 'RT 3D' transform the volume into itself. The identity operation (angles 0,0,0) MUST be included.

The symmetries are enforced in two steps: projections related by the symmetry operations are added in Fourier space to the volume; in order to reduce the residual artifacts, additional real-space symmetrization is applied.].RECONSTRUCTED VOLUME FILE: VOL001

[Name for the output volume calculated using all input projections specified in the selection document file.]

**NOTES**

- 5x5x5 Kaiser-Bessel interpolation scheme is used.
- Operation parallelized for use with MPI.
- Implemented by Paul Penczek and ArDean Leith.

**SUBROUTINES**- BP3F, BUILDM, BUILDS, ONELINE, SYMVOL, FILLBESSI0, FMRS

**CALLER**- VTIL2

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