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BP GW - Back Projection - weighted, arbitrary geometry

(9/17/94)

PURPOSE

This is the first step of the weighted back projection with arbitrary geometry.

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 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 GW

.CRITICAL VALUE FOR W: 0.6
[Give upper limit for inverse of weighting function to avoid noise enhancement. (remark: this parameter will be changed. A value smaller than 1 allows a weighting function larger than 1 A value of 0.6 seems to be adequate) ]

.3D VOLUME DIAMETER: 32
[Enter diameter of reconstruction volume]

.GENER.ANGLES IN (L)ABEL,(D)OCF,(E)XTERNAL: L
[Enter if angles of the projections, which are used to generate the weighting function are contained in the label of the files, in a document file or if they will be entered externally]

.WGT. ANGLES IN (L)ABEL,(D)OCF,(E)XTERNAL: L
[Enter if angles of the projections which will be weighted are contained in label, document file, or externally given]

.TEMPLATE OF INPUT FILE SERIES: PRO***
[Enter prefix of input files]

.TEMPLATE OF OUTPUT FILE SERIES: PRW***
[Enter prefix of output files]

.FILE NUMBERS OF GENERATING FILES: 1,5,6-36
[Enter file numbers of the projections, which generate the weighting function]

.FILE NUMBERS OF FILES TO BE WEIGHTED: 1,5, 7-36
[Enter file numbers of files which will be weighted]

If angles of generating projections are given externally:
.PHI: 10.

.THETA: 45.

[Enter phi and theta for each generating projection]

If angles of generating projections are contained in document file:
.DOC1: DOC001
[Enter name of document file which contains the angles of the generating projections. see also note 2!!!]

.BOTH IMAGE SETS IDENTICAL (Y/N): N
[If the set of projections which generate the weighting function and the set which is to be weighted are identical answer Y. Note: Answer yes only, if both sets are really the same images, correponding to each other image by image including the file numbers.]

If they are not identical and the angles of the projections which are to be weighted are given externally:

.INPUT DATA OF THE PROJECTION SET TO BE WEIGHTED:

.PHI: 10

.THETA: 50

[Enter the angles of these projections]

If they are not identical and the angles of the projections which are to be weighted are contained in document file:

.DOC2: DOC002
[Enter document file that contains the angle of the projections that are to be weighted. It can be the same file as DOC1. see also note 2.!!!]

NOTES

  1. The projections must have power-of-2 dimensions. 'BP GW' also does an in-core Fourier transform. Maximum size of projections is currently 128x128.

  2. The document files have to have the format: KEY=file #, THETA (cone angle), PHI (azimuth), FLAG (1 if used,0 if skipped)

  3. Gaps in keys are not allowed, instead enter a line that has a 0 flag. Document file keys must be in sequential order !!!

  4. The program calculates the weighting function along a section in Fourier space corresponding to a projection. The weighting function is the invers of the sum of the sinc-functions along the z-directions in the coordinate systems of each generating projection.

  5. Let PW be the projection to be weighted and PG the projection generating the sinc-function. Let RW(w) be a vector in the coordinate system belonging to PW and RW(g) the same vector represented in the coordinate system of PG. The argument of the sinc-function is the plane RW(g) with ZW=0 (ZW z-coordinate in PW).

  6. Let R be a vector in the space fixed coordinate system. [DW] the rotation matrix from R to RW (R(w)=[DW]*R). analogous let [DG] be the rotation matrix from R to RG (R(g)=[DG]*R). The argument of the sinc function then is: projection onto Zg of
           
                                    -1 
              RW(g)=[D]*RW(w)=[DG]*[DW]  *RW(w) 
                  :=[DGthe]*[DGphi]*[DWphi]*[DWthe]*RW(w). 
    
    The matrices used are (consistent with MIRQBXS used in the simple backprojection called in spider by 'BP XY'):
           
                    |cos(theta(g)) 0 -sin(theta(g))| | cos(phi(g)) sin(phi(g) 0| 
              [DG]= |       0       1       0      |*|-sin(phi(g)) cos(phi(g) 0| 
                    |sin(theta(g)) 0  cos(theta(g))| |      0          0      1| 
                  -1 |cos(phi(w)) -sin(phi(w)) 0| | cos(theta(w)) 0 sin(theta(w))| 
              [DW]  =|sin(phi(w))  cos(phi(w)) 0|*|       0       1       0      | 
                     |     0            0      1| |-sin(theta(w)) 0 cos(theta(w))| 
    

SUBROUTINES

GENW, FOUR2

CALLER

VTIL2

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