**PURPOSE**- Computes phase residual and Fourier ring correlation measures of proximity between two images. Calculates the differential phase residual over a ring with of specified ring width and the Fourier ring correlation between rings of the specified widths and stores the values in a document file. Takes real or Fourier input images. Example.

**SEE ALSO****FRC**[Fourier ring correlation and resolution determination ||] **RF 3**[Phase Residual & Fourier shell correlation, 3D ||] **RF SN**[Spectral SNR of images, resolution determination & integral SNR ||] **FT**[Fourier Transform ||]

**USAGE**- .OPERATION: RF

- .FIRST INPUT IMAGE: FIL001

[Enter the name of the first input file. File can be real or Fourier.].SECOND INPUT IMAGE: FIL002

[Enter the name of the second input file. File must be of dimensions as first input file].RING WIDTH (RECIPROCAL SPACE SAMPLING UNITS): 1.

[Enter the ring thickness in reciprocal space sampling units.].SCALE FACTORS (LOWER, UPPER): 0.8, 1.2

[Give the range of scale factors by which the second Fourier must be multiplied for the comparison. This range is divided into 20 steps for a scale search.].OUTPUT DOCUMENT FILE: DOC001

[Enter name of document file in which results are saved.

**NOTES**

- The following measures are reported for each ring:

a) Normalized Frequency.

|NORM-FREQ| -- Doc. file register: #1

b) Phase Residual.

|DPH| -- Doc. file register: #2

c) Fourier Ring Correlation, which should be larger than the Critical Fourier Ring Correlation (FRCCRIT) provided for comparison.

|FRC| -- Doc. file register: #3

d) Critical Fourier Ring Correlation

|FRCCRIT| -- Doc. file register: #4

e) Number of pixels in ring.

|PIXELS| -- Doc. file register: #5 - If you do not want a results file listing use
'MD' operation with option
'VERBOSE OFF'.
- Scale search is done separately for each ring in Fourier
space. 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 searched for
the lowest value, and the actual scaling factor used is printed.
- If the scale range specified contains no maximum, then an error message is printed: "NO MAXIMUM IN CFACT CURVE FOUND FOR RING XX" where XX is the ring number where the error occurred. This is only relevant for phase residual calculation.

**SUBROUTINES**- RFACTSDO, PR3DB, RFACTSD2, FMRS_2

**CALLER**- FOUR1

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