amplitude contrast (inelastic scattering) in multislice

[geoffwoollard]

In Kirkland’s TEMSIM, he uses an imaginary potential to account for inelastic scattering (amplitude contrast).
https://www.ccp4.ac.uk/ccp4-ed/projects/multislice/

[geoffwoollard]

This is happening on the fly...

https://github.com/mjo22/cryojax/blob/main/src/cryojax/simulator/_common_functions.py#L47-L65

def apply_amplitude_contrast_ratio(
    integrated_potential: Float[Array, "y_dim x_dim"] | Complex[Array, "y_dim x_dim"],
    amplitude_contrast_ratio: Float[Array, ""] | float,
) -> Complex[Array, "y_dim x_dim"]:
    """Apply the amplitude contrast ratio to compute a complex scattering potential,
    given the integrated potential computed just with a weak-phase calculation.

    !!! info
        Given a projected electrostatic potential $\\u(x, y)$, the complex potential
        $\\phi(x, y)$ for amplitude contrast ratio $\\alpha$ is

        $$\\phi(x, y) = \\sqrt{1 - \\alpha^2} \\ u(x, y) + i \\alpha \\ u(x, y)$$
    """
    ac = amplitude_contrast_ratio
    if jnp.iscomplexobj(integrated_potential):
        return jnp.sqrt(1.0 - ac**2) * integrated_potential.real + 1.0j * (
            integrated_potential.imag + ac * integrated_potential.real
        )
    else:
        return (jnp.sqrt(1.0 - ac**2) + 1.0j * ac) * integrated_potential

[geoffwoollard]

I can't find where the amplitude contrast or complex potential is incorporated. It seems to only support real spaced potential... https://github.com/jhgorse/kirkland/blob/master/temsim/mulslice.cpp

[mjo22]

Nice! This is what we do too. However I’m not sure I’ve computed the imaginary part correctly… whatever it is it must be consistent with how it’s defined in the usual linear theory.

We do this on the 2D integrated potential, or the 3D potential. In the 2D case, I especially don’t know how to do this in the “thick phase grating appoximation” because this involves ewald sphere extraction. In this case the “2D potential” itself is also complex object!

The function apply_amplitude_contrast_ratio is applied here and also here in the code.

Its source code is here. I think I have the non-ewald sphere case correct, but we should be sure.

[geoffwoollard]

In Kirkland’s TEMSIM, he uses an imaginary potential to account for inelastic scattering (amplitude contrast). https://www.ccp4.ac.uk/ccp4-ed/projects/multislice/

Actually Kirkland told me "The two URL's you list are not from me, and are pirating an old obsolete version of my programs and plagiarizing figures from my book. Please do not quote me for what is on these sites." He pointed me to this code:
https://sourceforge.net/projects/computem/?source=directory
https://github.com/ejkirkland/computem

He also said that " An imaginary potential is not even close to correct for inelastic scattering in multislice which is a much harder problem (see for example C. Dwyer, Ultramic. 104, 2005, p. 141). You have to continue propagating the inelast. scattered electrons at many different energies."

Dwyer, C. (2005). Multislice theory of fast electron scattering incorporating atomic inner-shell ionization. Ultramicroscopy, 104(2), 141–151. http://doi.org/10.1016/j.ultramic.2005.03.005

[geoffwoollard]

I read up more on Peng et al and how they use fit the absorbtive atomic scattering factor with a complex potential.

Chapter 14 "The atomic scattering factor and the optical potential" in the 2004 textbook "High Energy Electron Diffraction and Microscopy" (Peng, Dudarev and Wheelan; 2004) has FORTRAN code in the appendix D.2 for fitting the "absorptive atomic scattering factor". The complex parts of as and bs can be evaluated on the fly for a given atomic number, acceleration voltage and Debye-Waller factor. (I suppose all this is familiar to you...). This seems very feasible to incorporate, but let's see if it's worth the effort by getting more input from multislice developers.

[geoffwoollard]

I asked Toma Susi about what they do in abtem and he replied: Unfortunately we do not support the standard way of using an imaginary absorptive potential, so I cannot advise you on that, sorry. As far as I know, it is as simple as adding an imaginary term to the potential, but how that is correctly implemented with slicing etc, I cannot say.

[mjo22]

This makes sense. I think for us, I guess the immediate question is “is there a simple implementation that gives multislice added value beyond cryo-EM’s usual approximations”?

If there is no such simple implementation, multislice may not match real cryo-EM images. What do you think? I think if the current method reduces to usual cryo-EM approximations it is ok; my tests by eye seem to suggest it does. What do you think?

EDIT:
Elaborating on this, forgetting about multislice for a second the way of doing this for the ewald sphere + high energy (eikonal) approximation case is the following: what implementation of the real vs imaginary potential reduces to the implementation here?

[mjo22]

More thoughts: one path forward could be to match parakeet’s implementation!