James and other enthusiasts
First of all, to help James with his identity crisis, he is not a biologist or
a physicist. He is a biophysicist. A noble pursuit. It also has the advantage
that you can impress your biology friends with your knowledge of physics and
impress your physics friends with your knowledge of biology. I agree that the
idea is to solve problems relevant to biology (rather than physics) and the
ones James describes are relevant in this regard.
So James 4 cases.
Case 1 - I agree.
Case 2 - I don't think an even smaller beam will work. It will not be possible
to avoid twin domains along the path length of the beam. As pointed out it
merges in to case 3 anyway.
Case 3 . Now the idea is to try to limit the coherence and only see
interference effects for one domain at a time. For the direction along the beam
path, the problem is that the path length which the coherent beam probes is
dependent on the scattering angle. There is no one solution.
Case 4 I agree.
However, there might be a way (or several ways) of covering all these cases
but probably with a practical problem.
By illuminating the entire crystal with a coherent beam one will find each
diffraction spot has a structure in the form of a speckle pattern. The speckle
pattern corresponds to the transform of the crystal as a whole when viewed in
the direction corresponding to the hkl value for the spot. The speckle patterns
can in principle be used to reconstruct the whole crystal and see the
individual domains or even each individual unit cell. This is called coherent
diffraction imaging. There is a variation on it called ptychography in which a
smaller coherent beam is moved across the specimen, with translation
increments for each scattering pattern somewhat less than the size of the spot.
The overlapping sampling helps to reconstruct the image.
If you can reconstruct a 3D image of the crystal, showing the individual
domains, some information about each domain must be in the speckle pattern. The
question then is how to extract it directly and whether it would give the
information about the contribution of each domain to the composite measured
intensity. I don't know but I will solicit the views of people pursuing the
technique.
The problem might be radiation damage. Can one observe the speckle pattern for
the weaker spots to give the required information about the domains making up
the spots.
All this is speculation. Even if it doesnt work for James case, these methods
are being pursued for real biological problems for example to image chromatin
in the nucleus of mammalian cells at a resolution of better than 10nm (so one
can see nucleosomes for example). Have to end on a biological problem!
Regards
Colin
-----Original Message-----
From: CCP4 bulletin board on behalf of James Holton
Sent: Tue 03/02/2009 09:28
To: CCP4BB@JISCMAIL.AC.UK
Subject: [ccp4bb] correlation length - reloaded
Thanks Colin,
Yours is one of several lessons I have received on coherence and optics
in the past few days. I do appreciate all effort and the input.
However, as I mentioned before I am a biologist and I don't so much care
about the fundamental nature of the universe as I do about how it
relates to helping people solve protein structures. So, I think I would
like to perhaps re-phrase Bernhard's question, but primarily ask a
question of my own:
______________________________________________________________________________________________________
Is there a way to use a fancy x-ray beam to overcome lattice pathologies
... such as, shall we say: turn a nightmare like a lattice translocation
defect into a "simple" merohedral twin?
______________________________________________________________________________________________________
That is, I think this whole discussion started with those streaky spots
Margriet Ovaere posted last week. We have all seen streaky spots and
wondered what they mean, but far more important than that we wanted to
get rid of them. So, let me pose the following 4 situations:
1) The easiest kind of merohedral twin to think about is when you have
two "good" crystals stuck together. They are both in the beam and
oriented so that their lattices line up and there is no practical
detector distance that will resolve the spots produced from crystal A vs
crystal B. This is not a problem so long as the overlapping spots
correspond to symmetry-equivalent HKL indicies, but if you have one of
those annoying space groups (like P4, P3, and others) where the "a" and
"b" axes are the same length, but non-equivalent, then the "a" axis of
"A" can be aligned with the "b" axis of "B", and then you have a
merohedral twin. You then feel like you are a bad crystallographer for
wanting to go and grow new crystals.
However, you can be saved from 1) if you have a fancy x-ray beam.
That is, shoot just one of the two crystals that are stuck together
(either with a small beam, or simply by translating crystal B out of the
beam) and voila! De-twinning! I love this beamline and the beamline
scientist should get a really really big raise for showing me how to do
that! This leads us to:
2) The "crystal" you have in the beam contains a large number of very
small "twin domains". Half of them are oriented as "A" above and the
other half as "B". This is annoying because you really don't want to
learn about twinning and the x-ray beam is not small enough to just
shoot one of the "A" crystals at a time. So, you write a big grant to
build a beamline with a smaller x-ray beam. Hooray! Problem solved by
physics again. However, there must be a limit to how far you can push
this "strategy":
3) The twin domains are so small that you cannot go more than a few
unit cells in the crystal without stumbling across an "A" to "B"
boundary. With so few unit cells in each "twin domain" the scattering
from "A" actually starts to scatter "coherently" with "B" inasmuch as
the amplitudes and phases are adding instead of simply adding the
intensities contributed by each type of twin domain together into each
spot. To add to the headache, every other spot in the diffraction
pattern is smeary and your beamline scientist tells you that you have
something called a "lattice translocation defect" (then he goes off to
"lunch" and never comes back). This is very annoying because noone
seems to distribute a program for removing this problem from your data,
and you wonder how much money it will take to build a beamline that will
"solve" this problem for you. Perhaps if you could somehow reduce the
"coherence length" you could graduate from having a "lattice
translocation defect" into merely having a merohedral twin? On the
other hand, what if you unit cell gets really big and starts to get
comparable to the "coherence length"? Will that somehow mess up your
data? What the heck is a "coherence length" anyway?
4) The "twin domains" are only one unit cell each and for every "A"
unit cell there is a "B" unit cell right next to it and always in the
same direction. This is actually a "regular" crystal (with NCS and
twice the unit cell size of 1). It is deviations from the "A always
next to B" rule that I think leads to the streakiness in Margriet's
spots (the description I posted last week). That is, I think she is in
the twilight zone between 3) and 4). This will perhaps have a
"pseudotranslation" which is another scary word to hear at the beamline,
but I don't think there will ever be a fancy x-ray beam that can solve
this problem.
So, it appears that somewhere between 2) and 3) there is a dark place in
x-ray physics? Is there a fancy type of x-ray beam that will let us do
some new science here?
Perhaps the most relevant definition of "correlation length" for protein
crystallography is:
______________________________________________________________________________________________________
How far apart can two unit cells be before the integrated spot
intensities are given by |F_A|^2+|F_B|^2 instead of 0.5*|F_A+F_B|^2?
______________________________________________________________________________________________________
I am going to insist that the answer to this question has everything to
do with the structure of the crystal and nothing to do with the
"coherence" of the x-ray beam until someone can describe to me and
experiment to MEASURE the real answer.
-James Holton
MAD Scientist
Nave, C (Colin) wrote:
> Bernard, James
> Well, we are struggling to find a simple description of coherence length
>
> One thing I would advise is not to mix up wave and photon descriptions at the
> same time. You end up trying to solve the same problem as how a single photon
> goes through 2 slits and interfers. Richard Feynman (no less) said he could
> not understand this. Things have advanced since then but there is still no
> rational description of it which is accepted. The spooky descriptions do not
> count. There may be some more fundamental underlying theory (hopefully not
> Strings) which rationalises all this but it remains a fundamental problem of
> physics (along with 4 others I think).
>
> If wanting a photon description, one concept is how many photons there are in
> the coherence volume. This photon redundancy is 10^6 or more for visible
> lasers, less than 1 for most synchrotron beamlines and more than 1 for short
> pulse width FELs. However, one does not need to have a high photon redundancy
> to get coherence effects.
>
> A distant star twinkles due to the fact the light is coherent and one gets
> interference effects through the atmosphere. The atmospheric turbulence
> produces the variation of intensity seen by eye. Venus (a fine sight at the
> moment) does not produce this effect because it is too near. Similar affects
> are used in dynamic light scattering to measure particle size. Also in x-ray
> photon correlation spectroscopy (but I mentioned the word photon when I
> wanted a wave description!).
>
> I will dig out a reference (from a group at Cornell) giving a photon based
> description of coherence.
>
> Cheers
> Colin
>
>
>
>
> -----Original Message-----
> From: Bernhard Rupp [mailto:bernhardr...@sbcglobal.net]
> Sent: Mon 02/02/2009 19:38
> To: Nave, C (Colin)
> Subject: RE: [ccp4bb] X-ray photon correlation length
>
> Thanks - but I think I made a fundamental thinking flaw: also the coherence
> length
> seems only relevant/defined according to you reference for a
> two photon process - is that in fact true?
>
> what I am looking for in diffraction is the
> length of coherence for the single photon scattering -
> or how many electrons it rings in a 'single photon coherence volume'
> or whatever that term would be.....
>
> I thought the dimension of the wave packet might be a limiting factor
> for single photon coherent scattering. But the photon particle is
> nondispersive
> and apparently of no dimension....
>
> James Holton and I are now trying to find a particle/scattering physicist...
>
>
> Cheers, BR
>
> -----Original Message-----
> From: Nave, C (Colin) [mailto:colin.n...@diamond.ac.uk]
> Sent: Monday, February 02, 2009 2:15 AM
> To: Bernhard Rupp
> Subject: RE: [ccp4bb] X-ray photon correlation length
>
> Bernard
> Yes it depends on a combination of both the intrinsic bandwidth of the mono
> (approx 1.2 x 10^-4 for Si 111) and the range of angles on it (which the
> beamline designer will try and minimise).
> Bending magnet beamlines might approach the intrinsic bandwidth of the mono.
> It is easier to get there with low divergence undulator radiation. 1.5 x
> 10^-4 to 10^-3 are ballpark figures but will change depending on how the
> beamline is set up.
>
> However, you should consider both the transverse and longitudinal coherence
> when working out the volume of the specimen which is coherently illuminated.
> This volume also changes with scattering angle as the path differences
> increase at higher angle. This can be understood simply by considering that
> a variation in wavelength of 1% say will smear the 100th diffraction order
> in to the 101st order.
>
> If considering just the forward direction, for the longitudinal coherence
> alone (i.e. assuming beam is as parallel as it can be within the diffraction
> limit), one has to consider the variation in the optical path length
> (allowing for refractive index changes) through the specimen when working
> out the path length over which the specimen is coherently illuminated. The
> forward beam is retarded due to this variation in refractive index. This
> effect is used for phase contrast imaging.
>
> Cheers
> Colin
>
>
>
>
>
>
> -----Original Message-----
> From: Bernhard Rupp [mailto:bernhardr...@sbcglobal.net]
> Sent: Sat 31/01/2009 21:24
> To: Nave, C (Colin)
> Subject: RE: [ccp4bb] X-ray photon correlation length
>
> OK thx - very useful update indeed. then I need to find the source bandwidth
> for each beam line -I take it that the
> monochromator bandwidth etc is secondary and NOT the delLambda to be used
> for longitudinal
> coherence, but enters a prefactor or so.
>
> Do you perhaps have a ball park for what a source bandwidth is for certain
> SR devices?
>
> Thx, BR
> -----Original Message-----
> From: Nave, C (Colin) [mailto:colin.n...@diamond.ac.uk]
> Sent: Saturday, January 31, 2009 3:15 AM
> To: Bernhard Rupp
> Subject: RE: [ccp4bb] X-ray photon correlation length
>
>
> Bernard
> If talking strictly about longitudinal coherence, there is probably not much
> difference between the two. A copper Kalpha line width is approximately 2.4
> eV (http://wwwastro.msfc.nasa.gov/xraycal/linewidths.html ) or about
> 3X10^-4. This is not too different from many beamlines at synchrotrons.
>
> Colin
>
> -----Original Message-----
> From: Bernhard Rupp [mailto:bernhardr...@sbcglobal.net]
> Sent: Fri 30/01/2009 18:49
> To: Nave, C (Colin)
> Subject: RE: [ccp4bb] X-ray photon correlation length
>
> I think the major contribution is in fact from the
> fundamental lambda**/delLambda longitudinal coherence.
>
> As a qualitative statement, the range of A few 1000 A
> for anodes to several microns for synchrotrons seems
> reasonable and in agreement with prior knowledge.
>
> What would you say?
>
> BR
>
> -----Original Message-----
> From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Nave,
> C (Colin)
> Sent: Friday, January 30, 2009 1:20 AM
> To: CCP4BB@JISCMAIL.AC.UK
> Subject: Re: [ccp4bb] X-ray photon correlation length
>
> Hi
> Both transverse and longitudinal coherence length need to be considered in
> this. These parameters are detemined by monochromators, focusing optics and
> the position of the specimen along the path not just the undulator (or x-ray
> generator).
>
> Matching to the specimen is not necessarily as simple as the dimensions of
> the mosaic blocks in the specimen. It is the optical path length which is
> important. One would have to consider the variation in refractive index
> between mosaic blocks and the surroundings.
> Cheers
> Colin
>
> -----Original Message-----
> From: CCP4 bulletin board on behalf of Ethan Merritt
> Sent: Thu 29/01/2009 19:24
> To: CCP4BB@JISCMAIL.AC.UK
> Subject: Re: [ccp4bb] X-ray photon correlation length
>
> On Thursday 29 January 2009 10:59:23 Bernhard Rupp wrote:
>
>> Ok, following seems to be correct:
>>
>>
>>
>> a) interaction length = mean free path : relevant for absorption
>>
>> b) correlation length = time correlation between photons : relevant
>>
> for
>
>> multi-photon scattering
>>
>> c) coherence length = longitudinal coherence length : relevant for
>> single photon scattering.
>>
>>
>>
>> It follows from Heisenberg for a Lorentzian source (anode) with natural
>> emisson line width per
>>
>> formula on p 5007 of Colin's ref
>>
>>
>>
>> Lc=(2/pi)lambda**2/delLambda
>>
>>
>>
>> Using 8084 eV and 2.1 eV respectively for Cu, I obtain ~3800 A coherence
>> length for a Cu (anode) X-ray photon
>>
>>
>>
>> The pre-factor is different for other source types like synchrotron.
>>
>
> The coherence length for an undulator source is the relativistically
> contracted length of the undulator.
> Ref:
> http://xdb.lbl.gov/Section2/Sec_2-1.html
>
>
>
>> In any case I would accept the vague term of 'a few 1000 A' or 'several
>> 1000 A' as a general statement for
>>
>> coherence length in materials where the interaction length is larger
>> (practically always).
>>
>>
>>
>> Does this sound reasonable?
>>
>
> My impression is that the coherence length from synchrotron sources
> is generally larger than the x-ray path through a protein crystal.
> But I have not gone through the exercise of plugging in specific
> storage ring energies and undulator parameters to confirm this
> impression. Perhaps James Holton will chime in again?
>
>
> Ethan
>
>
>>
>>
>> From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of
>>
> Nave,
>
>> C (Colin)
>> Sent: Thursday, January 29, 2009 10:14 AM
>> To: CCP4BB@JISCMAIL.AC.UK
>> Subject: Re: [ccp4bb] X-ray photon correlation length
>>
>>
>>
>> Bernard
>>
>> I guess this came from
>>
>> "Aren't detwinning methods appropriate only in the case of true twin
>>
> domains
>
>> which are larger than the X-ray photon correlation length in order for the
>> assumption to be valid that |F|^2 from each domain can be summed? This
>> wouldn't give rise to the apparent 'diffuse scatter' phenomenon."
>>
>>
>>
>> I think this is normally called coherence length. Probably best not to
>>
> think
>
>> of photons at all but waves (though there is an equivalent quantum
>> mechanical treatment based, as V Nagarajan says, on the uncertainty
>> principle). I don't think the domains have to be larger then the
>>
> correlation
>
>> (sorry coherence) length of the incident x-rays in any case. They have to
>>
> be
>
>> large enough to give an intensity which can be integrated. If smaller
>> domains are present, the intensity just spread out a bit more.When the
>> domains are very large, the size of the spots would be determined by the
>> incident beam properties.
>>
>>
>>
>> The article cited some years ago on CCP4BB gives a primer on all this
>>
>> J. Phys.: Condens. Matter 16 (2004) 5003-5030 PII: S0953-8984(04)75896-8.
>> Coherent x-ray scattering Friso van der Veen1,2 and Franz Pfeiffer1
>>
>>
>>
> http://www.iop.org/EJ/article/0953-8984/16/28/020/cm4_28_020.pdf?request-id=
>
>> 8848d3f0-5a4b-4ffe-8ea4-c1eabfaf1657
>>
>>
>>
>> Cheers
>>
>> Colin
>>
>>
>>
>> _____
>>
>> From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of
>> Bernhard Rupp
>> Sent: 29 January 2009 17:51
>> To: CCP4BB@JISCMAIL.AC.UK
>> Subject: [ccp4bb] X-ray photon correlation length
>>
>> I always wondered - how is the X-ray photon correlation length defined
>>
>> and where do I find it? This is not the interaction length, I assume.
>>
>>
>>
>> So, to the physicists: How large is the 'X-ray photon correlation length'
>>
>> for a given wavelength in a given material?
>>
>>
>>
>> I had the impression that the term photon correlation refers
>>
>> to the time correlation of the scattering such as in photon correlation
>> spectroscopy.
>>
>>
>>
>> Best regards, BR
>>
>>
>>
>>
>>
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