**PURPOSE**- Calculates the Fourier Ring Correlation (FRC) curve between two images. Stores the FRC curve in a document file and determines the resolution at which FRC falls below requested value (default is 0.5). Takes real or Fourier input images. Can apply a soft mask to real input before FSC calculation. Example.

**SEE ALSO****FSC**[Fourier shell correlation and resolution determination ||] **RF**[Phase Residual & Fourier ring correlation, 2D ||] **FT**[Fourier Transform ||] **MO**[Create Model image]

**USAGE**- .OPERATION: FRC [half],[sf],[resol]

- [This operation can return threee optional register variables:
Variable Example Receives First [half] Interpolated pixel where the FRC falls below requested value Second [sf] Approximate resolution (in spatial frequency units) at this level Third [resol] Resolution (in Angstroms) at this level If there are multiple downward crossings of the FSC cutoff line then the values are reported for the

**last**crossing. If there is no such crossing the**minimal**values from the FSC curve are reported.].FIRST INPUT IMAGE: IMG001

[Enter the name of the first input image. File can be real or Fourier format. ].SECOND INPUT IMAGE: IMG002

[Enter the name of the second input image. File must be of same type and dimensions as first input file.] - If both input files are real format then SPIDER asks:

.RING WIDTH (RECIPROCAL SPACE UNITS) & MASKING RADIUS (PIXELS) : 0.5, 66

[Enter the shell width in reciprocal space sampling units i.e. (1/number of pixels). Enter radius for second order super-Gaussian masking. See MO for details. If radius is zero or missing then masking is skipped.]- Instead, if both input files not real format then SPIDER asks:

.RING WIDTH (RECIPROCAL SPACE UNITS): 0.5

[Enter the shell width in reciprocal space sampling units.].PIXEL SIZE (A) & RESOLUTION CUTOFF: 0.42, .5

[Enter the pixel size in Angstroms for images. If unknown, enter 1.0 and resolution column will be reported in pixel units. Enter resolution cutoff (if missing the default is 0.5).].FRC OUTPUT DOCUMENT FILE: FRC001

[Enter name of document file in which results are to be saved.].GNUPLOT FILE: res-plot.gn

[Enter name for a file which will contain Gnuplot commands which can be used to plot the FRC curve. Enter '*' if you do not want this plotting file.]

**NOTES**

- The following measures are reported for each ring:

a) Normalized Frequency. |NORM-FREQ| ---Doc. file register: #1

a) Resolution in Angstroms. |Resolution| ---Doc. file register: #2

c) Fourier Ring Correlation |FRC| ---Doc. file register: #3

[SUM(F1 * CONJ(F2))] / [SQRT{SUM(ABS(F1)**2) * SUM(ABS(F2)**2)}]

where 'CONJ' denotes complex conjugate.

- If you do not want a results file listing of the FRC curve use
'MD' operation with option
'VERBOSE OFF' first.
- References:

Saxton and Baumeister,*J. of Microscopy*, 127,(1982) 127-138.

M. van Heel,*Ultramicroscopy*, 21, (1987) 95-100.

Unser, et. al.,*Ultramicroscopy*, 23, (1987) 39-52.

- Pawel Penczek has notes on interpreting FRC/FSC curves.

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

**CALLER**- FOUR1

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