ISa

CORRECT is the scaling step of XDS.

An estimate for the overall quality of an experimental setup

A useful Unix command that prints a single number that depends on the overall quality of an experimental setup (beam, crystal, spindle, detector, cryo, software, ...) is

awk '/a          b/{getline;print 1/($1*$2)^0.5}' CORRECT.LP

This will give you the upper limit of I/sigma(I) for any reflection in your dataset - even if your crystal is great, all reflections are bound to be worse than that.

Why does the command give you such a useful value? It just finds the line " a b " in CORRECT.LP, grabs the values of "a" and "b" from the next line, and prints out 1/sqrt(a*b). The values a and b appear in the formula v(I)=a*(v0(I)+b*I^2) which is used by CORRECT to adjust the variances of the intensities, to match their experimental spread. For strong and well-measured reflections, the variance is dominated by the systematic error that is introduced by any beam /spindle / detector /cryo or other instability or malfunction. For weak reflections, v0(I), the variance from counting statistics, dominates. The value for v(I) that the formula gives, will be higher than v'(I)=a*b*I^2 by an amount a*v0(I). Therefore, I/sigma(I) = I/sqrt(v(I)) will be lower than I/sqrt(v'(I)) = 1/sqrt(a*b) which is what the Unix command prints out.

What might go wrong with this simple measure? Sometimes, e.g. if too few strong reflections exist in the dataset, b might come out negative. In that case the Unix command prints out "nan" which means "not a number" and indicates that it could not calculate the square root of a negative number.

As you can see from the formula, low values of a and b are good in the sense that a high upper limit of I/sigma(I) results. If e.g. the crystal is badly split or broken, or reflections are too close on the detector, or the data reduction is not good (wrong parameters), then the values of a and b are elevated.

If your crystal is good (and no matter how good your crystal is!), then a and b will reflect the quality of the other components of the experimental setup (e.g. beamline stability). I have seen values around 20 for good crystals that still allowed my to solve a MAD structure, but that required high multiplicity of observations. On the bright side, I have also seen a value of 87.6 for Z. Dauter's 0.98A Proteinase K (2ID8) sulfur-SAD data from J. Holton's APS/22-ID beamline.