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Quantum Wavefront Shaping with a 48-element Programmable Phase Plate for Electrons

by Chu-Ping Yu, Francisco Vega Ibañez, Armand Béché, Johan Verbeeck

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Submission summary

Authors (as registered SciPost users): Francisco Vega
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-11-20
Date submitted: 2023-09-29 13:36
Submitted by: Vega, Francisco
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
Approaches: Theoretical, Experimental


We present a 48-element programmable phase plate for coherent electron waves consisting of chip-based microscopic electrostatic elements. This brings the highly successful concept of wavefront shaping from light optics into the realm of electron optics and provides an important new degree of freedom to prepare the quantum state of electron waves. The phase plate is produced by a combination of photolithography and focused ion beam post-processing. It consists of an array of 48 electrostatic Einzel lenses distributed along a polar grid with 12-fold rotational symmetry. The phase plate chip is controlled by a series of 16-bit digital-to-analog converters and is mounted on an aperture rod placed in the C2 plane of a state-of-the-art transmission electron microscope operating in the 100-300 keV range. The experimental phase plate behavior is characterized by a Gerchberg-Saxton phase reconstruction algorithm, showing a phase sensitivity of 0.075 rad/mV at 300 keV, with a phase resolution of approximately 3$\cdot$10$^{-3}~\pi$. The performance of the phase plate is demonstrated by preparing a series of orthogonal quantum states with specific intensity profiles. We discuss a range of attractive applications in electron microscopy and show an experimental proof of concept of a self-tuning electron microscope setup, demonstrating the potential of adaptive electron optics.

Published as SciPost Phys. 15, 223 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-11-8 (Invited Report)


The authors present their latest enormous progress in development and application of a 48-element programmable phase-plate. Their device is comparable with a spatial light modulator, but using it for electrons by changing locally the applied phase shift by means of appropriate electrostatic potentials (an old dream in electron microscopy). First experimental evidence of the working device as well as extensive simulated examples of possible applications are presented in the manuscript. It shows original work, worth to be published in SciPost Physics, where it perfectly fits into the scope of the journal. I can strongly recommend the publication of the manuscript as it is only with a tiny error correction of referencing figure 6 (naming a) and b) ).

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2023-10-31 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2308.16304v2, delivered 2023-10-31, doi: 10.21468/SciPost.Report.8025


1) The authors present an interesting study on a novel phase plate for electron beams, with superior performance with respect to previously developed phase plates, including those developed by the authors themselves.
2) The phase sensitivity and phase resolution of the novel phase plate are investigated and reported. The advance with existing phase plate approaches is detailed in the introduction; notably that the phase plate can be altered with voltages in the mV range is a major advantage.
3) They also convincingly demonstrate the capabilities of the phase plate. In particular the experimental result on the ramped phase setting (Fig. 3(f)) for creating a vortex beam is impressive, but also the resolution improvement obtained by phase modification as described in section 3.3 is a straightforward proof of a useful application.
4) Future avenues are highlighted and the study is well connected to existing literature.


None. It is a very strong and straightforward paper.


The manuscript is of outstanding scientific quality and sufficiently novel. The manuscript is somewhat technological in nature, but based on advanced physical concepts. It also fits well into the scope of SciPost Physics, and can be accepted for publication as is.

Requested changes

I have only a few TYPO-level comments for the authors to consider:

p. 1, Abstract, line 7: microscopes are typically operated at a voltage, which implies kV, not keV. It is best to use keV only when it refers to the kinetic energy of the accelerated electrons. Please correct or rephrase.
p. 9, Figure 5, caption: “…for better presentation. and that the …”
p. 10, line 6: common aberration -> common aberrations
p. 10, line 12: Titan operation at 300 keV -> kV
p. 10, line -4: khz -> kHz

  • validity: high
  • significance: high
  • originality: top
  • clarity: good
  • formatting: good
  • grammar: good

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