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 or detector instability. 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 . Therefore, I/sigma(I) = I/sqrt(v(I)) will be lower than 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 lower than 20 for good crystals at bad beamlines. 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.