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arXiv:1901.09702 · Physical Review A

Reduced damage in electron microscopy by using interaction-free measurement and conditional reillumination

Akshay Agarwal, Karl K. Berggren, Yuri J. van Staaden, Vivek K Goyal

Published Jun 5, 2019• 12 citations
arXivHTMLPDF

Abstract

Interaction-free measurement (IFM) has been proposed as a means of high-resolution, low-damage imaging of radiation-sensitive samples, such as biomolecules and proteins. The basic setup for IFM is a Mach-Zehnder interferometer, and recent progress in nanofabricated electron-diffraction gratings has made it possible to incorporate a Mach-Zehnder interferometer in a transmission electron microscope (TEM). Therefore, the limits of performance of IFM with such an interferometer and a shot-noise limited electron source (such as that in a TEM) are of interest. In this paper, we compare the error probability and sample damage for ideal IFM and classical imaging schemes, through theoretical analysis and numerical simulation. We consider a sample that is either completely transparent or completely opaque at each pixel. In our analysis, we also evaluate the impact of an additional detector for scattered electrons. Inclusion of the scattering detector results in reduction of error by up to an order of magnitude, for both IFM and classical schemes. We also investigate a sample reillumination scheme based on updating priors after each round of illumination and find that this scheme further reduces error. Implementation of these methods is likely achievable with existing instrumentation and would result in improved resolution in low-dose electron microscopy.

DOI
10.1103/physreva.99.063809

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Interaction-free measurement (IFM) has been proposed as a means of high-resolution, low-damage imaging of radiation-sensitive samples, such as biomolecules and proteins. The basic setup for IFM is a Mach-Zehnder interferometer, and recent progress in nanofabricated electron-diffraction gratings has made it possible to incorporate a Mach-Zehnder interferometer in a transmission electron microscope (TEM). Therefore, the limits of performance of IFM with such an interferometer and a shot-noise limited electron source (such as that in a TEM) are of interest. In this paper, we compare the error probability and sample damage for ideal IFM and classical imaging schemes, through theoretical analysis and numerical simulation. We consider a sample that is either completely transparent or completely opaque at each pixel. In our analysis, we also evaluate the impact of an additional detector for scattered electrons. Inclusion of the scattering detector results in reduction of error by up to an order of magnitude, for both IFM and classical schemes. We also investigate a sample reillumination scheme based on updating priors after each round of illumination and find that this scheme further reduces error. Implementation of these methods is likely achievable with existing instrumentation and would result in improved resolution in low-dose electron microscopy.
High energy electrons enable atomic resolution, but also engender radiolysis or ionization damage to beam-sensitive materials, hampering the atomic imaging of medically and technologically relevant materials/processes such as cellular dynamics and proteomics. The dose required to resolve beam-sensitive materials usually far exceeds its critical dose, requiring dose dispersion across identically prepared samples that incur extensive computational processing and precise sample preparation. Numerous techniques are proposed and employed to minimize ionization damage while maximizing information acquired. The Elitzur and Vaidman quantum bomb detector is one such method [1], involving interaction-free measurements (IFM) [2-3]. In the thought experiment of Elitzur and Vaidman, single particles that are spacelike separated pass through an aligned Mach–Zehnder interferometer such that the particles self-interfere resulting in detections only at the bright port (Fig. 1(a)). Inserting an opaque object into the interferometer, disrupts the self-interference of the particles such that detections occur at the dark port (Fig. 1(b)). These dark port detections (IFMs) inform on the presence of the opaque object without the particles directly interacting with it. This phenomena extends to phase objects enabling quantitative phase imaging using interaction free measurements. A two-grating Mach–Zehnder interferometer (2GMZI) was constructed in a Titan TEM to realize IFM with electrons [4]. Now we construct the 2GMZI in a Spectra TEM similarly as before and is schematically shown in Figure 1(c). There are numerous new features from the previous generation Titan TEM pertinent to 2GMZI—such as a cold FEG and a Dectris ELA (direct electron) detector—improving electron coherence and signal-to-noise of the dark port. In the interim between the 2GMZI setups, analyses and simulations were performed to optimize the two nanofabricated gratings in mill pattern and configuration. Here we discuss such grating optimizations with an objective to maximize the Fisher information per unit radiation damage in beam-sensitive materials. The Fisher information (FIM) of interest quantifies the expected information in the detected electrons about phase differences imparted by the specimen (see Figure 2). The FIM is tunable by varying the proportion of electrons propagating via each path determined by the gratings. For instance, the pump probe configuration—where the pump carries most electrons through vacuum and the probe passes through the sample—minimizes radiation damage to the sample, but reduces the Fisher information and increases background noise via longer imaging sessions to acquire the necessary signal. The output grating may also be tuned to create multiple dark ports, increasing the overall signal. The interplay between minimizing radiation damage while maximizing the Fisher information leads to many local solutions where the global solution status depends on the critical dose of samples and the background shot noise. Utilizing these global solution configurations of 2GMZI for IFM imaging will improve low-dose phase imaging of beam-sensitive materials, decreasing the dose for high resolution imaging [5]. Sub figures (a) and (b) illustrate an electron, Mach–Zehnder interferometer in which traditional optical components—such as beam splitters and mirrors—are interchanged for gratings and magnetic lenses. Inserting an opaque object (b), prevents deconstructive interference at the dark port (DP), enabling interaction free measurements. Sub figure (c) further details the implementation of a Mach–Zehnder interferometer in an electron microscope. These two sub figures were simulated using two incident probes in the sample plane like Figure 1(c), and the specimen-induced phase-difference is swept. Sub figure (a) shows the normalized intensity of the modes, in which mode -1 and 0 correspond to the dark and bright port, respectively. Sub figure (b) is the corresponding Fisher information for each respective mode. The outer modes should be ideally suppressed.
Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.
Interaction-free measurement (IFM) is a promising technique for low-dose detection and imaging, offering the unique advantage of probing an object with an overall reduced absorption of the interrogating photons. We propose an experiment to demonstrate IFM in the single x ray photon regime. The proposed scheme relies on the triple-Laue (LLL) symmetric x ray interferometer, where each Laue diffraction acts as a lossy beam splitter. In contrast to many quantum effects which are highly vulnerable to loss, we show that an experimental demonstration of this effect in the x ray regime is feasible and can achieve detection with reduced dose and high IFM efficiency even in the presence of substantial loss in the system. The latter aspect is claimed to be a general property of IFM based on our theoretical analysis. We scrutinize two suitable detection schemes that offer a dose reduction of up to half compared with direct detection. The successful demonstration of IFM with x rays promises intriguing possibilities for measurements with reduced dose, mainly advantageous for biological samples, where radiation damage is a significant limitation.
Abstract Reducing radiation damage is becoming a crucial factor in the development of future electron microscopes. The concept of interaction-free imaging utilizing a Mach–Zehnder interferometer has been proposed originally in. 1993 by Elitzur and Vaidman. Using the quantum Zeno effect the quantum efficiency for interaction-free measurements can be increased to near 100 % with increasing number of interrogations provided the sample is a perfect (thick) absorber. However, for an electron beam the sample is in general semi-transparent depending on the thickness. In electron microscopy the interaction-free experiment is complicated by the presence of elastic and inelastic scattering processes in the electron-sample interaction. The ratio of inelastically versus elastically scattered electrons is determined by the nature of the sample and the thickness and cannot be reduced arbitrarily. Because inelastically scattered electrons transfer energy to the sample and cause radiation damage this puts a limit to the elastically scattered electrons and consequently to the resolution of electron imaging. In this paper, the inelastic scattering is modeled as an “absorption” function on the modulus of the electron wave. Image simulations and Argand plots are used to investigate the convergence rate of the Zeno iterations versus different type of samples, in particular a double strained DNA helical sample. It is found that the stronger objects reach maximum quantum efficiency faster than weaker objects for which more interrogations are needed to reach the maximum quantum efficiency. For a general hybrid amplitude/phase object the “phase” information tends to converge to zero as the number of interrogation increases.
Feynman once asked physicists to build better electron microscopes to be able to watch biology at work. While electron microscopes can now provide atomic resolution, electron beam induced specimen damage precludes high resolution imaging of sensitive materials, such as single proteins or polymers. Here, we use simulations to show that an electron microscope based on a multi-pass measurement protocol enables imaging of single proteins, without averaging structures over multiple images. While we demonstrate the method for particular imaging targets, the approach is broadly applicable and is expected to improve resolution and sensitivity for a range of electron microscopy imaging modalities, including, for example, scanning and spectroscopic techniques. The approach implements a quantum mechanically optimal strategy which under idealized conditions can be considered interaction-free.
We discuss the effect of semitransparency in a quantum-Zeno-like interaction-free measurement setup, a quantum-physics based approach that might significantly reduce sample damage in imaging and microscopy. With an emphasis on applications in electron microscopy, we simulate the behavior of probe particles in an interaction-free measurement setup with semitransparent samples, and we show that the transparency of a sample can be measured in such a setup. However, such a measurement is not possible without losing (i.e., absorbing or scattering) probe particles in general, which causes sample damage. We show how the amount of lost particles can be minimized by adjusting the number of round trips through the setup, and we explicitly calculate the amount of lost particles in measurements which either aim at distinguishing two transparencies or at measuring an unknown transparency precisely. We also discuss the effect of the sample causing phase shifts in interaction-free measurements. Comparing the resulting loss of probe particles with a classical measurement of transparency, we find that interaction-free measurements only provide a benefit in two cases: first, if two semitransparent samples with a high contrast are to be distinguished, interaction-free measurements lose less particles than classical measurements by a factor that increases with the contrast. This implies that interaction-free measurements with zero loss are possible if one of the samples is perfectly transparent. A second case where interaction-free measurements outperform classical measurements is if three conditions are met: the particle source exhibits Poissonian number statistics, the number of lost particles cannot be measured, and the transparency is larger than approximately 12\frac{1}{2}21​. In all other cases, interaction-free measurements lose as many probe particles as classical measurements or more. Aside from imaging of gray levels, another possible application for interaction-free measurements is the detection of arbitrarily small phase shifts in transparent samples.