At the risk of creating another runaway thread, I have spent some time 
trying to reconcile what Ian was talking about and what I was talking 
about.  The discussion actually is still relevant to the original posted 
question about refining against images, so I am continuing it here.

Ian made a good criticism of one of my statements, which I should take 
back: diffuse scatter does contain information about the disorder in the 
structure, and this can be measured under favorable conditions.  The 
point I was trying to make, however, is that one is still at the mercy 
of the lattice transform when looking at diffuse scatter, and the total 
scattering is the product of the molecular transform and the lattice 
transform.  There is generally no a-priori way to deconvolute the two!  
And this will make refinement against images difficult.

However, Colin makes a good point that the differences are largely 
semantic.  Unlike crystallographers, crystals, atoms, electrons and 
photons don't really care what names we call them.  They just do 
whatever it is they do, and the photons make little pops when they hit 
the detector.  That's all we really know.

So, in an effort to clear things up (both in my head and on this 
thread), I have assembled some simulated diffraction patterns from my 
nearBragg program here:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/

I have included some limited discussion about how the images were made, 
but the point here is that all these images are generated by simply 
computing the general scattering equation for a constellation of atoms.  
I found in an instructive exercise and perhaps other interested parties 
will as well.

-James Holton
MAD Scientist


Colin Nave wrote:
>  Nice overview from Ian - though I think James did make some good points
> too.
>
> I thought it might be helpful to categorise the various contributions to
> an imperfect diffraction pattern. Categorising things seems to be one of
> the English (as distinct from Scottish, Irish or Welsh!) diseases. 
>
> 1. Those that contribute to the structure of a Bragg reflection
> i) Mosaic structure - limited size and mosaic spread
> ii) Dislocations, shift and stacking disorders
> iii) More macroscopic defects giving "split" spots
> iv) Unit cell variations (e.g. due to strain on cooling)
> v) Twinning (?)
>
> 2. Diffuse scatter
> i) Uncorrelated disorder - broad diffuse scatter distributed over image
> ii) Disorder correlated between cells - sharper diffuse scatter centred
> on Bragg peaks 
> iii) Related to above inelastic scattering - Brillouin scattering,
> acoustic scattering, scattering from phonons
> iv) Compton scattering (essentially elastic but incoherent)
> v) Fluorescence
> vi) Disordered material between crystalline "blocks" but within whole
> crystal
> vii) Scatter from mother liquor
> viii) Scatter from sample mount
>
> 3. Instrument effects
> i) Air scatter
> ii)Scatter from apertures, poorly mounted beamstop
> iii) Smearing of spot shapes due to badly matched incident beams, poor
> detector resolution, too large a rotation range, 
> iv) Detector noise
>
>
> The trouble with categorisation is that one can (Oh no) 
> i) Have multiple categories for the same thing
> ii) Miss out something important
> iii) Give impression that categories are distinct when they might merge
> in to each other. Categorising seagulls (or any species) is an example,
> perhaps categorising protein folds is too. Not sure about categorising
> in to English, Scottish etc.
>
> All of these flaws will be in the categories above. Despite this, I
> believe it would help structure determination to have an accurate as
> possible model of the crystal. This should be coupled with the ability
> to determine the parameters of the model from the best possible
> recording instrument. Such a set up would enable better estimates of the
> intensity of weak Bragg spots in the presence of a high "background".
> There may be an additional gain by exploiting information from the
> diffuse scatter of the protein.
>
> At present, the normal procedure is to treat the background components
> as the same, have some parameter called "mosaicity" and use learned
> profiles derived from nearby stronger spots (ignoring the fact that the
> intrinsic profiles of a hkl and a 6h 6k 6l reflection will be closely
> related). The normal procedure is obviously very good but we don't know
> what we are missing!
>
> Any corrections additions to the categories plus other comments welcome
>
> Regards
>    Colin
>
>
>   
>> -----Original Message-----
>> From: CCP4 bulletin board [mailto:[log in to unmask]] On 
>> Behalf Of Ian Tickle
>> Sent: 22 January 2010 10:54
>> To: [log in to unmask]
>> Subject: Re: [ccp4bb] Refining against images instead of only 
>> reflections
>>
>>
>>  > -----Original Message-----
>>     
>>> From: [log in to unmask]
>>> [mailto:[log in to unmask]] On Behalf Of James Holton
>>> Sent: 21 January 2010 08:39
>>> To: [log in to unmask]
>>> Subject: Re: [ccp4bb] Refining against images instead of only 
>>> reflections
>>>
>>> It is interesting and relevant here I think that if you measure 
>>> background-subtracted spot intensities you actually are 
>>>       
>> measuring the 
>>     
>>> AVERAGE electron density.  Yes, the arithmetic average of 
>>>       
>> all the unit 
>>     
>>> cells in the crystal.  It does not matter how any of the vibrations 
>>> are "correlated", it is still just the average (as long as you 
>>> subtract the background).  The diffuse scatter does NOT 
>>>       
>> tell you about 
>>     
>>> the deviations from this average; it tells you how the 
>>>       
>> deviations are 
>>     
>>> correlated from unit cell to unit cell.
>>>       
>> James, as I've pointed out before this is completely 
>> inconsistent with both established DS theory and many 
>> experiments performed over the years.  If you're simulation 
>> is producing this result, then the obvious conclusion is that 
>> you're not simulating what you claim to be.  I don't know of 
>> a single experimental result that supports your claim.  In 
>> order for it to be true the total background (i.e. the sum of 
>> the detector noise, air scatter, scattering from the 
>> cryobuffer, Compton scattering from the crystal and of course 
>> the diffuse scattering itself) would have to be a linear 
>> function (or more precisely planar since the detector co-ords 
>> are obviously 2-D) of the detector co-ordinates in the region 
>> of the Bragg spots, since that is the background model that 
>> is used for background subtraction.  Whilst it may be true 
>> that detector noise and non-crystalline scattering can be 
>> accurately modeled by a linear background model (at least in 
>> the local region of each Bragg spot), this cannot possibly be 
>> generally true of the DS component, and since getting at the 
>> DS component is the whole purpose of the experiment, it is 
>> crucial that this be modeled accurately.  Of course your 
>> claim may well be true if there's no DS, but we're talking 
>> specifically about cases where there is observable DS 
>> (otherwise what's the point of your simulation?).  The reason 
>> it can't be true that the DS is a linear function is that 
>> there's a wealth of simulation work and experimental data 
>> that demonstrate that it's not true (not to mention simple 
>> manual observation of the images!).  The simulations cannot 
>> easily be dismissed as unrealistic because in many cases they 
>> give an accurate fit to the experimental data.
>>
>> As an example see here:
>> http://journals.iucr.org/a/issues/2008/01/00/sc5007/sc5007.pdf .
>>
>> Looking at the various simulations here (Figs 3 & 5) it's 
>> obvious that the DS is very non-linear at the Bragg positions 
>> (and more importantly it's also non-linear between the Bragg 
>> positions).  Note that the simulated calculated patterns here 
>> contain no Bragg peaks since as noted in the Figure legends, 
>> the average structure (or the average density) has been 
>> subtracted in the calculation, i.e. the simulations are 
>> showing only the DS component.  I fail to see how any kind of 
>> background subtraction model could cope with the DS and give 
>> the right answer for the Bragg intensity in these kind of 
>> cases.  Even from the observed patterns it's plain that the 
>> DS is non-linear, and therefore a linear background 
>> correction couldn't possibly correct the raw integrated 
>> intensity for the DS component.
>>
>> Well-established theory says that the total coherent 
>> scattered intensity is proportional to (~=) the time-average 
>> of the squared modulus of the structure factor of the crystal:
>>
>> 	I(coherent) ~= <|Fc|^2>
>>
>> If we make the assumption that the deviations of the 
>> contributions to the structure factor from different unit 
>> cells are uncorrelated, we can show that the Bragg intensity 
>> is the squared modulus of the time and lattice-averaged SF 
>> sampled at the reciprocal lattice points:
>>
>> 	I(Bragg) 	~= |<F>|^2
>>
>> The time/lattice-averaged SF is the FT of the average 
>> density, and therefore I(Bragg) indeed corresponds to the 
>> average density.
>>
>> The diffuse intensity is the difference between these:
>>
>> 	I(diffuse) 	= I(coherent) - I(Bragg)
>>
>> 			~= <|F|^2> - |<F>|^2
>>
>> The assumption above implies that we're assuming that there's 
>> no 'acoustic' component of the DS, since this arises from 
>> correlations between different unit cells.  However this 
>> doesn't mean that there *is* no acoustic component, it simply 
>> means that we are ignoring it: for one thing we have no 
>> alternative since the acoustic and Bragg scattering are 
>> practically inseparable; for another, correlations between 
>> different unit cells are purely an artifact of the 
>> crystallisation process, so have no biological significance, 
>> hence we're usually not interested in them anyway.
>>
>>     
>>> The diffuse scatter does NOT tell you about the deviations 
>>>       
>> from this 
>>     
>>> average; it tells you how the deviations are correlated 
>>>       
>> from unit cell 
>>     
>>> to unit cell.
>>>       
>> This is completely wrong, the previous equation can be rewritten as:
>>
>> 	I(diffuse)	= <|F - <F>|^2>
>>
>> clearly demonstrating that the DS does indeed tell you about 
>> the mean-squared deviation of the SF from the average (i.e. 
>> the variance of the SF), and therefore the density from its 
>> time/lattice average.  Note that I(diffuse) must necessarily 
>> be positive implying that the measured intensity always 
>> overestimates the Bragg intensity; it cannot average out to zero.
>>
>> If we further assume the usual harmonic model for the atomic 
>> displacements, we can show that the DS intensity is related 
>> to the covariance (or less correctly the correlation) of the 
>> displacements: I suspect this is what you meant.  This is all 
>> nicely explained in Michael Wall's doctorate thesis which is 
>> available online:
>>
>> http://lunus.sourceforge.net/Wall-Princeton-1996.pdf .
>>
>> This also has a nice historical survey of all PX DS results 
>> obtained up until 1996.
>>
>> Cheers
>>
>> -- Ian
>>
>>
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