**PURPOSE**- Calculates 3D reconstruction using non-uniform Fourier interpolation (gridding). See: Comparison of 'BP' operations.

**SEE ALSO****BP 3F**[Back Projection - 3D, 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 ||] **BP W2**[Back Projection - 2D, filtered, weighted ||]

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

- .TEMPLATE FOR 2-D IMAGE FILE: PROJ***

[Enter template for input projections.].FILE NUMBERS OR SELECTION DOC. FILE NAME: 1-700

[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.].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 3-D FILE: VOLUME1001

[Name of the output file.]

**NOTES**

- Implemented by Paul Penczek & ArDean Leith.
- Using the same 250x250 pixel, low quality set of aligned projections
various SPIDER back projection operations gave
the following resolutions:

'BP 3F' -------- Res: 22.03

'BPD 3F' -------- Res: 22.03

'BPD 32F' -------- Res: 22.05

'BP CG' -------- Res: 21.80

'BP 3G' -------- Res: 23.53

However on phantom data the back projection from 'BP 3G' appeared to be sharper to the eye. al

**SUBROUTINES**- WIW3G

**CALLER**- VTIL2

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