[3dem] RE: electron diffraction

Mon Aug 26 06:08:18 PDT 2013

Dear Philip,

All IMAGIC CTF programs including "transfer", "ctf2d-operations" and 
"ctf2d-find" ask you for the focal distance and the objective aperture 
and they do show you the cut-off effects on the CTF by this aperture.  
In fact, when you have partial coherence in the illumination, the CTF 
cutoff is more complicated, as it is determined by the convolution of 
the source image in the back focal plane with the coherent transfer 
function multiplied by the aperture function. Almost all EM CTF programs 
use the (incorrect) envelope approximation for dealing with partial 
coherent illumination.  People often ask me why the IMAGIC progams ask 
you for the focal distance of the objective lens: you do need it for a 
correct transfer function calculation. (See: Marin van Heel, *On the 
imaging of relatively strong objects in partially coherent illumination 
in optics and electron optics**,* /Optik/ *47* (1978) 389-408).

Cheers

Marin

On 26-Aug-13 9:28 AM, Philip Köck wrote:
> Thank you all very much for the answers you sent. I just picked one out to reply to.
> Thank you , Nestor, for the tables.
>
> The reason I asked is that I want to know what spatial frequencies are removed by an objective aperture
> when recording high resolution (phase contrast) images.
> I wasn't sure whether the objective lens settings change when one switches between imaging and diffraction.
> Therefore the strange way of asking the question.
> Secondly I wasn't sure whether one can use the simple formulas given that the lens is not a thin lens.
> I don't know the position of the specimen with respect to the focal planes or the principal planes either.
>
> In any case everybody seems to point me to a simple calculation.
> For example for 200 kV and 1 Angstrom resolution cutoff I can take twice the angle in Nestor's table,
> resulting in angle= 25 mrad.
> I can also get that from Lamda = d sin(angle), if I regard the specimen as a two dimensional grating.
>
> The next step is to use the focal length (not the distance between specimen and focal plane) as camera length,
> giving a distance of the spot from the optical axis R = 72.5 micrometers for 2.9 mm focal length (f).
> The formula is f * tan(angle) = R.
> Most answers seem to agree about using f.
>
> Please tell me if I got anything wrong.
>
> Philip
>
>
> -----Original Message-----
> From: Wim Hagen [mailto:wim.hagen at embl.de]
> Sent: 24 August 2013 14:05
> To: Philip Köck
> Cc: microscopy at microscopy.com; 3dem at ncmir.ucsd.edu
> Subject: Re: [3dem] electron diffraction
>
> Hi Philip,
>
> A simple estimation:
>
> Angular distance in back focal plane [rad] = 2 * Bragg angle  [rad] =  Lambda (relativistic wavelength)  [m] / d (sample spacing) [m] = R (distance) [m] / F (focal length) [m]
>
> All CM/Tecnai Twin systems have a focal length of ~2.9 mm. For 200KV, a 0.1 nm spacing gives ~25 mrad so ~72.5 micrometers distance from optical axis in back focal plane.
>
> Put in the radius of your objective apertures for R and you can calculate where your objective apertures cut off resolution for each KV.
>
> Best,
>
> Wim
>
>
> On Aug 23, 2013, at 4:18 PM, Philip Köck wrote:
>
>> Hi everybody,
>>
>> I'm looking for a simple estimation that I can't find in any textbook I've looked in, nor on the internet.
>> I wonder if anybody can help me.
>>
>> If I put a diffraction grating with spacing 1 Angstrom into the specimen holder and record an image of it.
>> At what distance from the optical axis will the corresponding
>> diffraction spot (for 1 Angstrom spacing) appear in the back focal plane of the objective lens.
>>
>> Assume a TEM with 200 kV and a twin lens, one that's typically used for protein structure determination.
>>
>> Thanks,
>>
>> Philip
>> _______________________________________________
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> -------------------------------------------------------------------
>    Wim Hagen
>    Senior Engineer Electron Microscopy

>    European Molecular Biology Laboratory (EMBL)
>    Heidelberg, Germany
> --------------------------------------------------------------------
>
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> 3dem at ncmir.ucsd.edu
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-- 
================================================================

     Marin van Heel

     Professor of Cryo-EM Data Processing

     Leiden University
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     and:

     Professor of Structural Biology

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     email:  m.vanheel(A_T)ic.ac.uk

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