NRAMM Discussion Forum

Anchi Cheng measured the Krios at TSRI with a Cs=2.7.

Apparently Cs value is determined by the distance between optics. Therefore, it should not change once the scope is built.

We use 2.7, but I remember Hong Zhou made a statement a few years ago that the Cs needed to be optimized. I haven't pursued it further, but it has always been in the back of my mind.

As far as the CTF is concerned the Cs, defocus and pixel size are all linked. If the pixel size is wrong, then you can correct it by adjusting your Cs. Which do you feel you have a better estimate of the Cs or the pixel size?

Hmmm...that doesn't sound right to me. When I look at the equation for CTF, I see that the Cs term is multiplied by s^4 while defocus is multiplied by s^2. These seem like different effects to me. I will give you that it doesn't matter until really high spatial frequencies. Regarding your question, I'm moving to optimizing pixel size based on reconstructing known structures and fitting crystal structures to them, then optimizing the reconstruction pixel size to match the xtal.

You can match them, because the defocus is unknown.

CTF = sin(-pi/2 Cs lambda^3 s^4/p^4 + pi lambda defocus s^2/p^2 + phi)
which is basically:
CTF = sin(A Cs s^4/p^4 + B def s^2/p^2 + phi)

old values
Cs = 2
p = 1.5
defocus = 1 and 2

A Cs s^4/p^4 + B def s^2/p^2 = A Cs' s^4/p'^4 + B def' s^2/p'^2
for all s

So s^4 terms must be the same:
A Cs'/p'^4 = A Cs/p^4
=> p'^4 = Cs'/Cs * p^4
=> p' = (Cs'/Cs)^(1/4) * p
=> p' = 1.51840835

And s^2 terms must be the same:
B def/p^2 = B def'/p'^2
def' = def * (p'/p)^2
def' = 1.02469460 and 2.0493892

new values
Cs = 2.1
p = 1.51840835
defocus = 1.02469460 and 2.0493892

[At least I think I did the calculation right]

Neail,

This can not be right.

The quad term has one order of Cs and 3 orders of s. They don't cancel out. The thing is that lambda is determined by the electron gun high tension, not any camera parameter. Therefore it has no contribution from pixel size.

Oops, I meant 4 orders of s.

The pixel size is built into the spatial frequency. Do you see anything wrong with my math? I think Craig originally pointed this out to me.

Using one of Anke's 30S images, I get high resolution CTF estimates at both Cs = 2.0 and Cs = 2.3:

12jun06h52a_09oct22c_00004sq_v01_00032hl_v01_00004en_1.mrc

best run from ACE2:

pixelsize: 1.63 A
def: 2.12 um
amp con: 0.20
cs: 2.0
V: 120 kV

Plug into ctfEval:
Resolution limit is 7.10 at 0.8 and 6.04 at 0.5

let's use a bad Cs = 2.3

new pixelsize = (Cs'/Cs)^(1/4) * p = (2.3/2.0)^0.25 * 1.63 = 1.687960 A

new def = def * (p'/p)^2 = 2.12 * (1.687960/1.63)^2 = 2.273447 um

Plug into ctfEval:
Resolution limit is 7.36 at 0.8 and 6.25 at 0.5

https://github.com/vossman/ctfeval

Neil,

After thinking about it more, I think you are right that it is possible to match a set of Cs, pixel size, and defocus to get the same CTF function. Furthermore, it does not matter how many terms of wave aberration function is included at higher resolution, it can be mapped to the unitless space of pixels if we DONOT have any coefficient in the equation known with physical space accuracy.

Cs value measurement I did from comparing the gold diffraction and the node of extended Scherzer defocus (the point resolution: see http://www.maxsidorov.com/ctfexplorer/science/point_resolution.htm) is still subject to this normalization so it is only good if one of them is known well. The other method for measuring
Cs I know of relies on defocus series, and therefore relies on a different calibration on the scope which we don't know how that is done.

That being said, arbitrarily picking a pair of Cs and pixel size is not an option in physical space. They are not always used together. Pixel size will be used, not Cs value, nor defocus, when scaling the size of the particle, for example. The values need to be mapped to something with physical sense, such as the crystal structure scale (from some x-ray absorbance edge, that is) of known structure, and/or in the case of the Cs, assumes that the optics in the microscope is placed with good accuracy. Percentage-wise, your calculation says that 1% change in pixel size coupled with 5 % change in Cs causes defocus to go from 1 to 2. Therefore I would say that using published Cs value as the starting point is better.

Hi Anchi,

I agree. I like Scott's idea of getting the pixel size from the reconstruction. I just wanted to point out that if you think you Cs is wrong, maybe you should check your pixel size first. I never really trusted the CCD pixel size measurements, because of that one time where we went from 1.63 to 1.55 and then back to 1.63 again on the Tietz at 50k mag.