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BP GW3 - Back Projection - weighted, arbitrary geometry, 3 angles

(1/26/94)

PURPOSE

This is the first step of the weighted back projection with arbitrary geometry and three Euler angles.

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 GW [Back Projection - weighted, arbitrary geometry]
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 GW3

.(S)INC-FCT.,(G)AUSS-FCT.,(M)IXED : M
[Enter if weighting function should be constructed by a summation of sinc-functions, Gaussian functions or a mixture of both. Sinc function weighting implies that the reprojection rays are limited by a multiplication with a box-function, i.e., a sharp cutoff, Gaussian, that the (infinite) reprojection rays are limited by multiplication with a Gaussian function, Mixed, that the rays are limited by an apodized box function, the falloff of this box function is determined by the half width of the Gaussian. The weighting function then is calculated from the sum of sinc-functions multiplied with Gaussians]

If either G of M was answered:

.SIGMA (absolute units): .1
[Enter the sigma of the Gaussian in Fourier space, use absolute units. If in real space the box-function is apodized by multiplication of the box function with a Gaussian function with halfwidth s (in pixels) then sigma should be 1/s.]

.(T)RANSFER OR (W)EIGHTING-FCT.: w
[Enter if you want the Transfer function or the Weighting function (= 1./(Transfer function)). The calculation of the transfer function may be desirable for test purposes]

.CRITICAL VALUE FOR W: 0.6
[Give upper limit for inverse of weighting function (=transfer 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: 80
[Enter diameter of reconstructed volume in real space]

.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. It is strongly recommended to provide these angle in the file label. This is the most used mode and thus the best tested.]

.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. s. remark above.]

.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
[Answer "N"!. Only if the set of projections which generate the weighting function and the set which is to be weighted are identical you may answer Y. Warning: Answer yes only, if both sets are really the same images, corresponding to each other image by image including the file numbers. N always works! ]

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 #, PHI (azimuth), THETA (cone angle), PSI (rotation within the plane of the projection), FLAG (1 if image 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) 
                                           -1        -1        -1 
                  :=[DGthe]*[DGphi]*[DWphi]  *[DWthe]  *[DWPSI]  *RW(w). 
    

  7. The matrices used are consistent with BAPI3A used in the simple backprojection called in SPIDER by 'BP 3E'.

SUBROUTINES

GENW3E, FOUR2

CALLER

VTIL2

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