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RF 3 - Phase Residual & Fourier shell correlation, 3D

(5/1/96)

PURPOSE

Calculate the differential 3-D phase residual and the Fourier Shell Correlation between two 3-D volumes. The Differential Phase Residual over a shell with thickness given by shell width and the Fourier Shell Correlation between shells of specified widths are computed and stored in the document file. Does not need powers of two dimensions (for exclusions see 'FT' operation) and needs REAL input images. NSAM, NROW and NSLICE need to be equal.

SEE ALSO

RF [R Factor]
RF SN [Spectral signal to noise ratio]
FT [Fourier transform]

USAGE

.OPERATION: RF 3

.FIRST INPUT FILE: SUB001
[Enter name of first real 3-D volume.]

.SECOND INPUT FILE: SUB002
[Enter name of second real 3-D volume.]

.RING WIDTH:1.
[Enter the shell thickness in reciprocal space sampling units.]

.SCALE FACTOR (LOWER,UPPER): 0.6,1.2
[Give the range of scale factors by which the second Fourier must be multiplied for the comparison.]

.MISSING CONE/WEDGE ANGLE(C/W):c
[Use 'C' if you have a missing cone and w if you have a missing wedge.

.MAXIMUM TILT ANGLE:30
[Give the angle of maximum tilt angle in degrees. (When the missing cone is covered angle=90.0)]

.FACTOR FOR NOISE COMPARISON: 3.0
[The factor given here determines the FSCCRIT. Here 3.0 corresponds to the 3 sigma criterion i.e., 3/SQRT(N), where N is number of voxels for a given shell. You could use 2, 1,4 or anything.]

.DOCUMENT FILE: DOC001
[Enter name of doc file in which results are to be saved.]

NOTES

  1. The inclination angle theta starts from the Z*=0 plane.

  2. Scale search is done separately for each shell. This will NOT lead to sensible results if one of the transforms falls off rapidly in a frequency range where the other transform is strong. The range specified by the user is divided into 20 steps and searched for the lowest value The value:
    R(McPherson) = 2*SUM(ABS(F1)-ABS(F2))/SUM(ABS(F1)+ABS(F2))
    is calculated at each step within a ring and its minimum is used to determine the correct scale factor for the second Fourier transform. 3. The following measures are computed and tabulated:
     
                a) PHASE RESIDUAL =   
                      SQRT(SUM[(ABS(F1)+ABS(F2))*DPHI**2]/ SUM(ABS(F1)+ABS(F2)))  
                   where DPHI = The phase difference between corresponding Fourier, 
                   coefficients which should be < 45 DEG.  
                b) SHELL CORRELATION =  
                      [SUM(F1*CONJ(F2))]/ [SQRT{SUM(ABS(F1)**2)*SUM(ABS(F2)**2)}]  
                  where CONJ implies complex conjugate. 
    

  3. Contents of DOC file:
     
                COLUMN:     #1         #2    #3    #4         #5     #6                                                    
    |NUMBER| |NORMALIZED |DPH| |FSC| |FSCCRIT| |VOXELS| |FREQUENCY|

  4. COMMENTS and REFERENCES with regard to FSC Ref: Saxton and Baumeister, J.of.Micr., 127,(1982) 127-138. M. van Heel, Ultramicroscopy., 21, (1987) 95-100. Unser,et.al., Ultramicroscopy, 23, (1987) 39-52. A correlation coefficient "r" implies a SNR=2*r/(1-r). (factor 2 comes from the fact that for the purpose of comparison whole data set is divided into halves). SNR=4.0 implies r=0.67 SNR=2.0 implies r=0.5 WHY these two special cases of SNR? According to Unser FSC=0.67 should correspond to DPH=45.

SUBROUTINES

PR3D, PR3DB

CALLER

FOUR1

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