Yes, bigger is okay, and perhaps a little better if you consider the
effects of beam/crystal vibration and two sharp-edged boundaries dancing
over each other. But bigger is better only to a point. That point is
when the illuminated area of non-good-stuff is about equal to the area
of the good stuff. This is because the total background noise is equal
to the square root of the number of photons and equal volumes of any
given "stuff" (good or non-good) yield about the same number of
background-scattered photons. So, since you're taking the square root,
completely eliminating the non-good-stuff only buys you a gain of 40% in
total noise. Given that other sources of noise come into play when the
beam and crystal are exactly matched (flicker), 40% is a reasonable
compromise. This is why I recommend loop sizes that are about 40%
bigger than the crystal itself. Much less risk of surface-tension
injury, and the air around the loop scatters 1000x less than the
non-crystal stuff in the loop: effectively defining the "beam size".
As for what beam profiles look like at different beamlines, there are
some sobering mug-shots in this paper:
http://dx.doi.org/10.1107/S0909049511008235
Some interesting quirks in a few of them, but in general optimally
focused beams are Gaussian. Almost by definition! (central limit
theorem and all that). It is when you "de-focus" that things get really
embarrassing. X-ray mirrors all have a "fingerprint" in the de-focused
region that leads to striations and other distortions. The technology
is improving, but good solutions for "de focusing" are still not widely
available. Perhaps because they are hard to fund.
Genuine top-hat beams are rare, but there are a few of them. Petra-III
is particularly proud of theirs. But top-hats are usually defined by
collimation of a Gaussian and the more x-rays you have hitting the back
of the aperture the more difficult it is to control the background
generated by the collimator. If you can see the shadow of your pin on
the detector, then you know there is a significant amount of
"background" that is coming from upstream of your crystal! My solution
is to collimate at roughly the FWHM. This chops off the tails and gives
you a tolerably "flat" beam in the middle.
How much more intense is the peak than the tails? Well, at the FWHM,
the intensity is, well, half of that at the center. At twice that
distance from the center, you are down to 6.2%. The equation is
exp(-log(16)*(x/hwhm)**2) where "hwhm" is 1/2 of the FHWM.
HTH!
-James Holton
MAD Scientist
On 12/30/2014 12:10 PM, Keller, Jacob wrote:
Yes, it gets complicated, doesn't it? This is why I generally recommend
trying to use a beam that matches your crystal size.
...or is bigger, right? Diffuse scattering, yes, but more even illumination
might be worth it?
Generally, James, I have a question: what is the nature of the intensity
cross-sections at most beamlines--are they usually Gaussian, or are some
flatter? Or I guess, if Gaussian, how much more intense is the peak than the
tails?
JPK
