Using the optical polarization state to control the ponderomotive phase plate

Abstract

The ponderomotive phase plate, also known as a laser phase plate or a standing wave optical phase plate, has a first mirror and a second mirror that define an optical cavity. An electron beam passes through the focal spot of the optical cavity. A laser with a variable polarization angle of the laser is coupled to the optical cavity. The standing wave of the polarized laser having an antinode at the focal spot of the optical cavity causes a variable modulation of the electron beam. The variable modulation of the electron beam can be controlled by the variable polarization angle of the laser. In a transmission electron microscope, the image plane receives the electron beam modulated by the standing wave optical phase plate. The image formed at the image plane is based on the variable polarization angle of the polarized laser.

Description

[0001] Cross - reference to related applications

[0002] This application claims the benefit of U.S. Patent Application No. 62 / 901,160, filed on September 16, 2019, under 35 U.S.C.§119(e), the entire content of which is incorporated herein by reference. This application also relates to U.S. Application No. 15 / 939,028, filed on March 28, 2018, and entitled "OPTICAL - CAVITY - BASED PONDEROMOTIVE PHASE PLATE FOR TRANSMISSION ELECTRON MICROSCOPY", which was issued as U.S. Patent 10,395,888 on August 27, 2019, and which claims the benefit of the priority of U.S. Provisional Application No. 62 / 479,044, filed on March 30, 2017, the entire contents of both of these applications being incorporated herein by reference.

[0003] Statement of government support

[0004] This invention was made with government support under Contract No. DE - AC02 - 05CH11231 awarded by the U.S. Department of Energy and Contract No. R01GM126011 awarded by the National Institute of General Medical Sciences of the National Institutes of Health. The government has certain rights in this invention. Technical field

[0005] The present invention generally relates to transmission electron microscopy (TEM), and more particularly to an optical - cavity phase plate for use in TEM. Background art

[0006] Modern transmission electron microscopes have become powerful imaging tools capable of achieving a resolution approximately 1000 times higher than that of optical microscopes; however, their imaging performance for thin biological specimens remains relatively poor. Such specimens are weakly scattering "phase objects", i.e., they do not actually exhibit absorption of the impinging electrons. As a result, the intensity of the transmitted electron beam remains equal to the intensity of the incident electron beam, and a perfect image of such an object does not exhibit contrast. Historically, electron microscopes thus required specially prepared samples with contrast provided by "staining" with heavy metals. These processes were difficult and time - consuming; moreover, these processes are known to alter the structure and thus limit the resolution at which meaningful information can be obtained.

[0007] Even for unstained phase objects, the object (specimen) structure is imprinted on the phase of the matter wave that describes the transmitted electrons. As Zernike discovered for optical microscopes, the invisible phase modulation can be converted into visible amplitude contrast. The light passing through the specimen is decomposed into a non-diffracted component and a diffracted component. The non-diffracted light is focused by the objective lens onto a bright spot at the center of this plane. The diffracted light is arranged around this center. Diffraction caused by the fine structure of the object results in a larger diffraction angle. Thus, the diffraction orders corresponding to the fine details of the image (i.e., having small dimensions) are far from the center, while large-scale structures cause diffracted light near the center. Mathematically, the intensity distribution in this back focal plane is given by the spatial Fourier transform of the transmission of the specimen (which is called the Fourier transform plane).

[0008] If the specimen is a pure phase object, there is a special phase relationship between these components. By canceling this phase relationship, the phase modulation is converted into amplitude modulation. The maximum conversion is obtained in the case of a 90-degree or π / 2 phase shift, and thus the maximum phase contrast is obtained. In an optical device, this is done by a phase plate, which is essentially a glass plate coated such that the light passing through a small central region receives an additional phase shift.

[0009] Unfortunately, there is no simple phase plate for an electron beam, which makes it difficult to view unstained biological specimens. The cryo-electron microscopy method gives a partial solution. These avoid the associated generation of staining and structural artifacts and generate a certain amount of phase contrast by deliberately viewing the specimen under defocus conditions combined with intentional spherical aberration. By optimizing the trade-off between the phase distortion caused by defocus and the phase distortion caused by spherical aberration, the desired conversion of phase to amplitude contrast can be achieved. However, the phase shift varies continuously over the spectrum of spatial frequencies. As a result, this "simple" method is suitable for small features in the image but results in loss of contrast for larger features. Since a fairly large contrast is also required for large features, a much larger defocus amount is usually needed to see biological macromolecules. Unfortunately, this leads to a reduction in resolution. In addition, the contrast transfer function oscillates many times in the region of higher spatial frequencies. Thus, defocus is an imperfect way to generate phase contrast in images of biological macromolecules.

[0010] A traditional technique uses a thin carbon film as a phase plate in transmission electron microscopy. The thickness of the film causes the scattered electrons to undergo a π / 2 phase shift, while the axial electrons pass through a central hole with a 1-μm diameter. The main drawback of this technique is that these phase plates "age" on a time scale of days or weeks. It is also difficult to fabricate these phase plates reproducibly. Additionally, a small fraction of the useful signal is lost when the scattered electrons pass through the thin carbon film.

[0011] Recently, microfabrication techniques have allowed the construction of electron microscope phase plates. The focused non-diffracting beam passes through a small aperture in an electrode that is biased with tens to hundreds of millivolts according to a specific electrode geometry in the device, thereby generating the desired phase shift. The electrostatic shielding of the electrode prevents interaction with scattered electrons, such that the scattered electrons do not experience an additional phase.

[0012] Another embodiment of the phase plate uses a very thin strip magnet placed adjacent to the non-diffracting electron beam across the electron diffraction pattern. A phase shift is generated by the Aharonov-Bohm effect due to the difference in the magnetic vector potential on either side of the strip magnet.

[0013] All these efforts are currently limited by the short time required for the physical device to become charged, which may be caused by the accumulation of contaminants on the surface when the device is hit by a strong electron beam. This results in an unwanted electric field, which causes uncontrolled phase shifts of the electron beam at various scattering angles. This effectively makes the image non-reproducible and non-interpretable. In addition, the electrode blocks the diffracting beam closest to the center, thereby reducing the contrast of large structures in the image. Thin film phase plates face similar problems. Summary of the Invention

[0014] In one embodiment, a system for transmission electron microscopy has a transmission electron microscope (TEM). The TEM has a back focal plane. A mirror forms an optical cavity. The focus of the optical cavity is positioned at the back focal plane of the TEM. The optical cavity is positioned to allow an electron beam provided by the TEM to pass through the focal spot of the optical cavity. The optical cavity is operable to allow a laser beam to enter. A laser having a variable polarization angle of the laser is coupled to the optical cavity. The laser is operable to provide a laser beam of a specified wavelength and variable polarization angle to enter the optical cavity. The laser beam is reflected from the mirror and provides a standing wave optical phase plate focused at the back focal plane of the TEM. The standing wave optical phase plate causes modulation of the electron beam. The image plane of the TEM is positioned to receive the electron beam modulated by the standing wave optical phase plate. The image plane forms an image with variable image contrast enhancement according to the variable polarization angle of the laser.

[0015] In one embodiment, a transmission electron microscope generates an electron beam. The TEM has a back focal plane. The electron beam is allowed to enter along an axis passing through the center of the optical cavity. The optical cavity is positioned at the back focal plane. The optical cavity is defined by a first mirror and a second mirror. A laser beam having a variable polarization angle of the laser is allowed to enter the optical cavity. The laser beam is reflected from the first mirror in the second mirror to generate a standing wave optical phase plate focused at the back focal plane of the TEM. The standing wave optical phase plate causes modulation of the electron beam. The TEM images the electron beam in the image plane. The image plane is positioned to receive the electron beam modulated by the standing wave optical phase plate. Changing the polarization angle of the laser changes the contrast enhancement of the image.

[0016] In one embodiment, a ponderomotive phase plate has a first concave mirror, a second concave mirror, and a laser. The first concave mirror and the second concave mirror are positioned to define an optical cavity. The optical cavity can be positioned to enable an electron beam to pass through a focal spot of the optical cavity. The laser has a variable polarization angle of the laser light. The laser and the laser light are coupled to the optical cavity. The laser is operable to cause an antinode of a standing wave of the laser light to be at the focal spot of the optical cavity to cause a variable modulation of the electron beam. The variable modulation of the electron beam can be controlled by the variable polarization angle of the laser light.

[0017] Other aspects and advantages of the embodiments will become apparent from the following detailed description taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the described embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The described embodiments and their advantages are best understood from the following description when read in conjunction with the accompanying drawings. These drawings in no way limit any changes in form and detail that may be made to the described embodiments by those skilled in the art without departing from the spirit and scope of the described embodiments.

[0019] Figure 1 Schematic geometry depicting an embodiment of a phase contrast TEM. The optical cavity mode with a narrow waist is focused in the back focal plane of the TEM objective, thereby imposing a delay on the transmitted wave but not on the scattered wave.

[0020] Figure 2 Depicting the dependence of the circulating power in the cavity on the input laser power measured experimentally. The grey shading represents the measurement uncertainty.

[0021] Figure 3 Depicting the intensity distribution of the fundamental mode of a near-concentric Fabry-Pérot cavity. The inset stretched in the horizontal direction shows the fringes of the standing wave.

[0022] Figure 4 Depicting the contrast transfer function (CTF) of a TEM with a cavity-based laser phase plate averaged over the azimuthal angle.

[0023] Figure 5 Is a schematic diagram of an embodiment of a laser system that includes a cavity and coupling optics, a feed laser system, and a cavity characterization tool within an electron microscope column.

[0024] Figure 6It is a cross-sectional view of an optical cavity including a housing, a cavity mirror, and a coupling aspherical lens in an embodiment.

[0025] Figure 7 Depicts a cavity mount in an embodiment. The shown wires are connected to a piezoelectric actuator for precise alignment of the cavity mirror.

[0026] Figure 8 It is a perspective view of a laser phase plate composed of three cavities with overlapping focal volumes in an embodiment.

[0027] Figure 9A Depicts the interference pattern generated by a three-cavity arrangement, which is characterized by a hexagonal lattice of interference peaks.

[0028] Figure 9B Depicts the rotation-averaged contrast transfer function of a three-cavity phase plate (upper curve) compared to a single cavity (black) with f = 2.5 mm (lower curve).

[0029] Figure 10 Shows an embodiment of a transmission electron microscope including an optical cavity phase plate according to an embodiment of the present invention.

[0030] Figure 11 Shows the intensity pattern of a resonant optical cavity phase plate according to an embodiment of the present invention.

[0031] Figure 12 Shows a system for generating an optical phase plate for modulating the phase of an electron beam according to an embodiment of the present invention.

[0032] Figure 13 It is a flowchart of a method for enhancing phase contrast in an electron beam image.

[0033] Figure 14 Depicts the schematic geometry of another embodiment of a phase contrast TEM, which is characterized by laser light with a variable polarization angle coupled to the optical cavity.

[0034] Figure 15A Depicts a half-wave plate with a rotator, which is used to change the polarization angle of the laser in embodiments of a phase contrast TEM and an embodiment of a ponderomotive phase plate.

[0035] Figure 15B Depicts an optical fiber coupler with a rotator, which is used to change the polarization angle of the laser in embodiments of a phase contrast TEM and an embodiment of a ponderomotive phase plate.

[0036] Figure 15C Depicts a laser with polarized laser light and a rotator, which is used to change the polarization angle of the laser in embodiments of a phase contrast TEM and an embodiment of a ponderomotive phase plate.

[0037] Figure 16 A schematic diagram depicting an action, which shows a sensor at the image plane of a phase-contrast TEM or a variant thereof, and a controller for analyzing a Ronchigram, which is used to control the polarization angle of a laser in an embodiment of a phase-contrast TEM and an embodiment of a ponderomotive phase plate. Figure 14 is a flowchart of a method for transmission electron microscopy, which can be performed by various embodiments of a TEM having a ponderomotive phase plate.

[0038] Figure 17 Specific embodiments Specific embodiments

[0039] Embodiments of a laser phase plate having an optical cavity and phase-contrast transmission electron microscopy using the laser phase plate are described herein. Figures 1 - 13 Relates to a ponderomotive phase plate based on an optical cavity for use in transmission electron microscopy. Figures 14 - 16 Relates to using an optical polarization state to control a ponderomotive phase plate. Examples of these specific embodiments are illustrated in the accompanying drawings. Although specific variants are described in connection with these specific embodiments, it should be understood that no limitation of the described embodiments is intended. Instead, it is intended to cover alternatives, modifications, and equivalents that may be included within the spirit and scope defined by the appended claims.

[0040] In the following description, numerous specific details are set forth to provide a thorough understanding of the present embodiments. Specific example embodiments may be implemented without some or all of these specific details. In other instances, well-known processing operations are not described in detail so as not to unnecessarily obscure the invention.

[0041] For clarity, various techniques and mechanisms of the present embodiments will sometimes be described in the singular. However, it should be noted that unless otherwise stated, some embodiments include multiple iterations of a technique or multiple instantiations of a mechanism.

[0042] Terms such as "about" or "approximately" are synonymous and are used to indicate that a value modified by the term has an understood range associated with the value, where the range can be ±20%, ±15%, ±10%, ±5%, or ±1%. The term "substantially" is used to indicate that a value is close to an object value, where close can mean, for example, that the value is within 80% of the object value, within 90% of the object value, within 95% of the object value, or within 99% of the object value.

[0043] This document describes an optical power amplification cavity, which is suitable for use as a phase mask for an electron beam in an electron-based imaging system or an electric-based spectroscopic system (such as a transmission electron microscope (TEM), etc.). According to this configuration, such a phase mask can be used as a plurality of electron optical elements for the coherent manipulation of an electron beam, and the phase mask includes:

[0044] · A phase plate used in Zernike-type phase contrast electron microscopy;

[0045] · A Bragg beam splitter for coherently splitting an electron beam into two parts with a controllable beam splitting ratio;

[0046] · A transmission diffraction grating for an electron beam, which splits an input beam into multiple diffraction orders;

[0047] · A time phase modulator similar to an electro-optic modulator used in a conventional optical device;

[0048] · A local time phase modulator, which in combination with an energy filter, can be used as a beam stopper for dark field electron microscopy;

[0049] · A spatio-temporal phase modulator similar to an acousto-optic modulator (deflector) used in a conventional optical device.

[0050] The design of an embodiment of the power amplification cavity includes cavity mirrors (e.g., spherical dielectric mirrors), and at least one of these cavity mirrors is characterized by a highly curved front surface. A reflective coating is disposed on the front (concave) surface of the mirror. An anti-reflective coating can be disposed on the rear (convex) surface of the mirror. The laser field in the cavity is configured to generate an effective potential for electrons, thereby imprinting a spatially patterned phase shift (which can also be modulated in time) onto the electron beam transmitted through the cavity.

[0051] The advantages of the optical cavity electron optical element relative to a conventional element based on a material structure (e.g., an optical cavity phase plate relative to a material phase plate) include: (1) the amount of phase shift remains substantially constant and does not change with the length of time of using the phase plate, as in the case of each previous device for bringing a physical object near or into the electron beam; (2) the amount of phase shift can be adjusted as desired to "tune" the phase shift from approximately zero degrees to 360 degrees; (3) negligible electron loss (undesired electron scattering) in the optical cavity element.

[0052] Advantages of the optical cavity electron optical element relative to elements based on pulsed laser systems include that the optical cavity phase plate can be used with continuous electron irradiation rather than a pulsed electron gun (as in previous pulsed laser phase plates). This feature makes the optical cavity phase plate uniquely suitable for use in standard continuous electron emission microscopes and for applications using very high electron exposures. The cavity-based system is also characterized by an accurately controllable phase shift pattern determined by the laser field configuration of the cavity mode. It is highly desirable to be free of the distortions and defects typically present in the laser beam profile to avoid unwanted scattering of electrons due to laser field irregularities.

[0053] The optical cavity phase plate can be characterized by:

[0054] · A near-concentric Fabry-Perot cavity configuration, or another cavity configuration characterized by a high-intensity focal spot;

[0055] · A highly reflective dielectric coating on the curved surface;

[0056] · An arrangement of three or more piezoelectric actuators to align the cavity and control the cavity mode shape;

[0057] · A phase plate for TEM, characterized in that it need not be a single spot but has a phase shift profile with multiple maxima and minima, which results in a contrast transfer function suitable for a particular purpose (e.g., a standing wave pattern with a waist at some wavelengths can be used as a Zernike phase plate, while a larger waist is preferably used as a Bragg beam splitter);

[0058] · A phase plate for TEM based on electron-optical interaction - one embodiment is a near-spherical cavity with a high finesse, high numerical aperture (high NA) mirror;

[0059] · A mirror with a rear (convex) surface concentric with the front (concave) surface for efficient coupling into the cavity mode;

[0060] · A mirror with a reflection-reducing coating on the rear surface for improving the coupling efficiency;

[0061] · The cavity with several support (resonance) frequencies input into the laser field simultaneously to achieve temporal modulation and temporal control of the phase pattern applied to the electron beam.

[0062] Feedback and alignment mechanisms and methods for the optical cavity phase plate can include:

[0063] · A feedback mechanism for maintaining the stability of the mode shape and size (e.g., a charge-coupled device (CCD) camera and / or a segmented detector monitoring the transmitted beam, the reflected beam, or both);

[0064] · A feedback topology in which, after fluctuations in cavity length and system variations, the laser frequency is kept locked to the cavity, or alternatively, the cavity length is varied to keep the resonance frequency of the cavity locked to the laser frequency;

[0065] · A method of aligning a cavity to an electron beam by monitoring a TEM image, a Fourier transform of the TEM image, or other mathematical constructs to determine the degree of misalignment and providing alignment feedback;

[0066] · Feedback on the cavity mode can help maintain alignment of the laser phase plate with the beam;

[0067] · Using a laser beam transmitted through the cavity to inject a master laser (e.g., as a frequency locking mechanism).

[0068] Other features of the optical cavity phase plate can include:

[0069] · A heat pipe for removing heat from the cavity;

[0070] · A thermal insulation screen for protecting the cavity structure;

[0071] · Controlling the cavity length by temperature;

[0072] · Controlling the mirror curvature by means of controlled preheating using an auxiliary laser, a heating circuit, or a thermoelectric device;

[0073] · Using a near-IR wavelength;

[0074] · Using a multi-cavity arrangement to reduce the spot size and increase the intensity;

[0075] · Using an optical fiber to bring the laser to the cavity;

[0076] · Using an optical isolator to protect the laser system from reflected light;

[0077] · The laser focus size is larger than the electron focus size to avoid scattering of the electron beam;

[0078] · Controlling the configuration of the field inside the cavity by deforming the mirror (e.g., gently squeezing the mirror).

[0079] Additional applications / features can include:

[0080] · Varying the laser power to tune the amount of phase shift. This feature can be used to reverse or otherwise adjust the contrast.

[0081] · The optical cavity phase plate can be used for high electron doses in TEM. The volt phase plate generally cannot be used for high electron doses.

[0082] ·The rapid modulation of the phase shift can be achieved by modulating the laser power in the cavity. This results in a modulated electron wave function (i.e., in the form of a spectrum) that can be used to transfer an oscillating or pulsed electromagnetic field to a microscopic object.

[0083] ·The formation of sidebands in the focal spot in combination with an energy filter can be used to effectively block the transmitted (i.e., non-diffracted) electron beam for full-field dark-field TEM.

[0084] ·Non-destructive controllable electron beam splitter

[0085] Various embodiments have some or all of the following features:

[0086] ·At least one of the mirrors has a reflecting surface with a radius of curvature of 5 cm or less to produce a small focal spot in the cavity.

[0087] ·The reflectivity of each mirror including the cavity is about 0.9 or greater.

[0088] ·The mirror including the cavity has a reflecting surface coated with a reflective dielectric coating.

[0089] ·The plurality of mirrors includes a first mirror and a second mirror.

[0090] ·A cavity housing, wherein the optical cavity is positioned in the cavity housing, wherein one or more of the mirrors including the cavity are mounted in an adjustable suspension, and wherein the adjustable suspension is operable to adjust the angle and position of the mirror.

[0091] ·The adjustable suspension includes a piezoelectric actuator.

[0092] ·The power of the laser beam is amplified by the cavity by about 10 times or more.

[0093] In some embodiments, the geometry of the rear surface (i.e., the non-reflecting surface) of the mirror may not be important and may not need to be a convex surface concentric with the front surface of the mirror. For example, the rear surface of one or both of the mirrors can be flat. One feature that defines a cavity suitable for a phase plate (as opposed to a general optical cavity) in some embodiments is that the cavity is capable of focusing the beam to a small focal spot while being able to amplify the laser power by a large factor and withstand the resulting high power. This is not seen in known optical cavities. The features present in the optical cavity of the present embodiment include (1) a short radius of curvature of at least one of the mirrors and (2) a low round-trip loss, which is equivalent to a high reflectivity / low absorption of all the mirrors.

[0094] The advantages of an optical cavity phase plate in cryo - electron microscopy (cryo - EM) are that, at the start of data collection, the amount of phase contrast can be 100% of a specified value. Additionally, the amount of phase contrast can be maintained at the specified value throughout the data collection time period, which can extend up to 24 hours or more for each cryo - EM segment. This means that all parts of the data collected will have equal quality as opposed to some data being much worse than others. Other advantages of the optical cavity phase plate include greater versatility and reliability. Additionally, a 270 - degree rather than a 90 - degree phase shift is theoretically expected to give better performance.

[0095] Further details regarding the operation of an optical cavity phase plate according to one embodiment are described in U.S. Patent Application Serial No. 13 / 487,831, filed June 4, 2012, which is incorporated herein by reference.

[0096] Transmission electron microscopy (TEM) of unstained, rapidly frozen biological specimens (cryo - EM) has recently become a major source of structural information in molecular biology. The lower limit of the molecular weight of accessible ions has been reduced to 100 - 200 kDa, and in some cases below 100 kDa. Theoretical considerations suggest that reconstruction of particles as small as approximately 40 kDa should be possible. However, determining the structures of macromolecular complexes between 40 and 100 - 200 kDa in size, as well as resolving larger but flexible complexes, requires further improvement of cryo - EM techniques.

[0097] One approach towards TEM reconstruction of smaller particles is the development of a Zernike phase plate, which allows phase - contrast imaging without defocus. An important step in this direction ( Figure 2 ) was the development of the "Volta" phase plate.

[0098] However, significant opportunities for further improvement still exist. In the Volta design, the phase shift is caused by exposing an amorphous carbon foil to an electron beam and increases during data collection. Only a moderate number of images can be taken while the phase shift is within the available range of 40 - 120°; then, the carbon film must be moved to expose a new spot. Many images must be taken at non - optimal phase shifts. The phase shift and its drift rate vary from spot to spot even within the same phase plate. These properties make it difficult to use a carbon - foil phase plate in cryo - EM structural studies, which require high - throughput image acquisition with consistent parameters.

[0099] Placing a material structure in the path of a high - energy electron beam inevitably leads to charging and degradation. Thus, time - varying behavior is an inevitable drawback of phase - contrast devices for material objects in a TEM - based electron stream. As a side - drawback, there is a small but perceptible 18% electron scattering in the Volta phase plate.

[0100] Here, it is proposed to escape this limitation by using the strong laser focus as an electron wave retarder. This laser- or “ponderomotive”-based phase plate does not involve a material object inserted into or located near the electron beam. The phase plate can apply a constant phase shift indefinitely, has a predictable and reproducible contrast transfer function, and has the characteristic of almost no electron loss. The phase shift can be changed by varying the laser power as desired.

[0101] The central idea in various embodiments is that a laser beam focused in the back focal plane of the TEM objective 1018 (see the embodiments described in more detail below Figure 10 can be used to retard the phase of the transmitted wave relative to the scattered wave, thereby acting as a Zernike phase plate. The controllable and stable phase shift provided by the laser phase plate will enable the cryo-EM community to take full advantage of the improved image contrast in Zernike phase contrast TEM.

[0102] The physical mechanism of electron retardation is described below. The goal of the presently described embodiments is to construct a better Zernike (quarter-wave) plate for phase contrast TEM by controlling the phase of the electron wave with a laser. The concept is borrowed from the field of atomic physics, where lasers are used to manipulate both the motional and internal degrees of freedom of cold atomic ensembles. These methods have enabled many experiments aimed at testing the foundations of quantum mechanics and general relativity, searching for the fields responsible for dark energy, and precisely measuring fundamental constants.

[0103] The physical principle behind the laser-based coherent control of electron waves can be described from the aspect of classical physics as follows. A relativistic electron traveling through a strongly oscillating laser field experiences small-scale jitter motion, thereby generating an effective “ponderomotive” potential. This potential is described by the following expression:

[0104]

[0105] where: I is the laser intensity, e and m are the charge and mass of the electron, ε0 is the permittivity of free space, c is the speed of light, and ω is the optical frequency. This repulsive potential imparts a negative phase shift (retardation) to the passing electrons.

[0106] A more rigorous description of the interaction between relativistic electrons and intense laser beams can be given in terms of quantum electrodynamics (QED), where the phase shift is attributed to stimulated Compton scattering. In this treatment, the electron absorbs photons from the laser beam and then re-emits them via stimulated emission induced by the same beam, or the electron undergoes these two events in reverse. An electron undergoing stimulated Compton scattering on a monochromatic laser beam emerges with the same energy as it started with without losing coherence. In contrast, spontaneous Compton scattering causes the electron to lose coherence, but under the conditions relevant to the various embodiments, a small fraction of the electrons undergoing such an event is of the order of 10 -7 。We note that electrons can also be inelastically scattered via higher-order scattering processes involving three or more photons, thereby losing coherence. However, these processes are not expected to become significant until the laser intensity reaches I≈10 13 W / cm 2 (for a laser wavelength of 1μm), which is far beyond the intensities dealt with in the present embodiments).

[0107] The required laser intensity is described below. The proportionality coefficient between the ponderomotive potential and the laser intensity in Equation (1) is small, which requires a high laser intensity. For an electron beam orthogonally passing through a focused Gaussian beam with power P and focal waist w0 (the beam radius measured at 1 / e 2 of the peak intensity), the phase shift is given by:

[0108]

[0109] where: α is the fine structure constant, β = v e / c, v e is the electron velocity, and γ = (1 - β 2 ) -1 / 2 。To estimate the required optical power, an electron energy U = 300 keV is substituted, as is commonly used in cryo-EM studies. According to Equation (2), for a laser wavelength λ = 1064 nm and beam waist w0 = 7 μm, the laser power required to achieve a full 90° phase shift is P≈300 kW.

[0110] Achieving such optical power with a pulsed laser system is straightforward, but a pulsed phase plate will also be required to synchronize the pulsed electron gun 1024 (see Figure 10 ). The main objective of the present embodiment is to develop a laser phase plate based on a continuous wave (CW) laser system that is compatible with traditional cryo-EM equipment.

[0111] The resonance field enhancement in the optical cavity is described below.

[0112] Figure 1Schematic geometry depicting an embodiment of a phase contrast TEM. A narrow waist optical cavity mode is focused in the back focal plane (e.g., diffraction plane 104) of the TEM objective, thereby imposing a delay on the transmitted wave 106 and not on the scattered wave 108. Electrons from the scattered wave 108 are detected by the electron detector 112 and imaged as an increased contrast view of the specimen in the specimen plane 102 as a result of the delay in the transmitted wave 106.

[0113] In some embodiments, the laser intensity is established by resonance in a high finesse, near concentric Fabry - Perot cavity (see the optical cavity 110 in Figure 1 ). This type of resonator is characterized by an hourglass - shaped fundamental mode, where there is a small waist and a large spot size on the surfaces of the mirrors 114, 116. The small waist concentrates the power into a high - intensity focal spot and confines the phase shift to a narrow region around the focus of the transmitted wave 106. The large spot size on the mirrors 114, 116 prevents laser - induced breakdown of the mirror coatings and helps to spread the heat load over a wider area. Additionally, the two counter - propagating waves in the Fabry - Perot cavity form a standing wave where the intensity is quadrupled at the antinodes. For a wavelength λ of 1064 nm and a beam waist w0 = 7 μm, an intracavity circulating power 204 of P = 75 kW is sufficient to achieve a full 90° phase shift.

[0114] In recent work towards the above - mentioned goal, a near - concentric cavity operating at a wavelength of λ = 1064 nm was demonstrated, where the finesse was F = 22000. A specially designed flexure - based mount with three piezoelectric actuators was used for the sensitive alignment of the near - concentric cavity, which allowed reaching a waist of 7 μm (radius at 1 / e 2 intensity).

[0115] Figure 2 Depicts the dependence of the intracavity circulating power 204 on the input laser power 206 measured experimentally. The grey shading 206 represents the measurement uncertainty. At an input power 202 of P_0 = 2.2 W, the cavity reaches a circulating power 204 of P = 7.5 kW, which corresponds to a record CW light intensity of 40 GW / cm 2 (see Figure 2 ). For a 300 keV electron beam, the phase shift corresponding to these beam parameters is 9.2°. Thus, a realistic ten - fold power increase would be sufficient to reach the goal of providing a 90° phase shift.

[0116] The following describes the laser field configuration and the contrast transfer function.

[0117] Figure 3Depicts the intensity distribution 302 of the fundamental mode of a nearly concentric Fabry - Perot cavity. The insert 304 stretched in the horizontal direction shows the fringes of the standing wave. In an ideal Zernike phase plate, a 90° delay is applied only to the transmitted wave focused at the center of the electron diffraction plane 104, with no phase shift in the rest of the plane. This embodiment of the cavity - based laser phase plate has the Gaussian standing - wave intensity profile ([ Figure 3 Figure 3 shown), thus applying a harmonic - modulation phase shift to the strip - like region of the diffraction plane 104. The results of this phase profile and why this phase plate effectively serves as a Zernike phase plate in cryo - EM single - particle analysis are discussed below.

[0118] Phase contrast extends to low enough spatial frequencies to image small protein complexes (∼5 nm or smaller). The "cut - on" frequency at which phase contrast becomes effective is determined by the contrast transfer function (CTF) of the imaging system. The correspondence between the spatial frequency ν and the radius r in the back - focal plane of the TEM objective is:

[0119] r = νfλ e (3),

[0120] where: f is the focal length of the TEM objective and λ e is the electron wavelength. Typical parameters of the microscopes used in cryo - EM are λ e = 1.97 pm (which corresponds to an electron energy of U0 = 300 keV) and f = 2.5 mm. For the initial stages of the development of the embodiment (including the development of the first prototype and initial data collection), a custom - modified FEI Titan TEM was used, with relay optics added to magnify the electron diffraction pattern at the plane of the phase plate. This additional magnification results in an effective focal length of f = 20 mm, which relaxes the requirements for the tightness of the laser focus.

[0121] Figure 4 Shows the focused CTF 402 of the cavity - based phase - contrast TEM averaged over the azimuthal angle calculated for the electron microscope. For clarity, the figure shows the CTF at defocus, and spherical aberration is not considered. For very low spatial frequencies 404, the curve starts at zero contrast. The CTF 402 reaches 50% at a spatial frequency 404 as low as 1 / (240 nm) (i.e., on the scale set by Equation (3), where r = λ / 2 represents the size of the standing - wave ripple (see Figure 2 ). The oscillations are caused by the fringes of the laser standing wave. The CTF reaches almost complete (>80%) contrast at frequencies larger than 1 / (10 nm) (i.e., on the scale set by the radius of the laser beam). Thus, for a size D≈0.5ν -1Particles of = 5 nm or less transmit the information contained in the electron phase with almost maximum contrast. Many macromolecules with molecular weights below 100 - 200 kDa have diameters of about 5 nm or less. The cavity-based phase plate provides near-ideal contrast for these macromolecules. Imaging of even larger particles (100 nm) is performed with only a moderately reduced contrast.

[0122] Image artifacts due to the standing-wave phase profile do not significantly distort the particle image. Multilayer numerical modeling of cryo-EM imaging of hemoglobin (a 64 kDa particle embedded in 30 nm of amorphous ice) confirmed that the cavity-based phase plate is well-suited for small particles. The structure of the hemoglobin molecule was downloaded from the Protein Data Bank. Using the dose. The resulting image showed a significant increase in contrast using the laser phase plate compared to the defocused image generated with 1 μm of underfocus.

[0123] Numerical modeling enabled the assessment of possible artifacts due to the anisotropic phase-shift profile of the laser wave plate. Studies were conducted on images that included images of hemoglobin simulated with an ideal phase plate that only phase-shifted the transmitted wave and images simulated with the cavity-based laser phase plate. The simulation highlighted any differences by not showing shot noise or noise from ice density fluctuations. Even so, only a slight vertical trailing could be discerned. The simulation showed the difference between the two images on a gray scale that amplified the difference signal by a factor of ten to a visible level. This difference was far below the noise level and was thus not expected to affect particle identification and classification.

[0124] Another side effect of the standing-wave phase-shift pattern is that it acts as a diffraction grating for the electron wave, thus generating additional weak "ghost" images. These ghost images are shifted relative to the original image by a distance δx = 2nfλe / λ, where n is the diffraction order, f is the focal length, and λe is the electron wavelength. Even for a full 90° shift, the amplitude of such ghost images is far lower than the shot noise of the illumination. In a dense specimen, an overlap between the ghost image of one particle and the main image of another particle can be expected. However, the ghost images are too weak to be seen in individual micrographs and can be expected to be averaged according to the combined data, which results in a non-significant contribution to the noise in the averaged image used for density map reconstruction.

[0125] A tighter laser focus is required to adapt the laser phase plate to a standard cryo-EM system. At a later stage, embodiments were developed that included advanced phase plate prototypes with a narrower focus suitable for use in a conventional TEM system with a typical focal length f = 2.5 mm. To this end, the numerical aperture of the cavity mode was increased, thereby operating the cavity closer to concentricity. In one method, it was unclear whether this would compromise the cavity finesse. In another method, a multi-cavity configuration was used, which had a lower risk but involved additional steps of cavity alignment and frequency locking. Two schemes are described in the "Methods" section.

[0126] In summary, a Zernike phase plate for a TEM operating at 300 kV was developed based on the ponderomotive potential of a high-intensity CW laser field circulating in an optical cavity. It has been demonstrated that sufficient ~9° phase shift and a ten-fold increase in laser intensity (which would provide an optimal 90° phase shift) can be achieved using state-of-the-art mirror manufacturing techniques. Numerical simulations indicate that the cavity-based phase plate can effectively be used as a Zernike phase plate for cryo-EM single particle reconstruction. The following describes the method and includes a continuous wave laser phase plate module having a laser intensity sufficient to shift the phase of a 300 keV electron beam by 90°.

[0127] Constructing a laser phase plate based on a near-concentric cavity requires custom building highly curved cavity mirrors with high reflectivity and low loss. Additionally, a suitable feed laser and an opto-mechanical system for maintaining cavity alignment are employed. Embodiments of the system should also be compact, vacuum-compatible, and non-magnetic for operation within the TEM column. The strategy for constructing a system meeting these requirements is outlined below.

[0128] The following describes embodiments of the laser system.

[0129] Figure 5Schematic of an embodiment of a laser system that includes a cavity 110, coupling optics, a pump laser system, and a cavity characterization tool within an electron microscope column 526. For acronyms of the components of the system, FA = fiber amplifier 502, FC = fiber coupler 504, PDH_PD = Pound-Drever-Hall locking photodiode 506, FI = Faraday isolator 508, CL = coupling lens 510, CM = cavity mirror 512, BS = beam splitter 514, FPD = fast photodiode 516, and DA = digital data acquisition (e.g., of data from camera 524 and fast photodiode 516). In one embodiment, the Nd:YAG laser wavelength (1064 nm) is selected, which allows the use of commercially available narrow linewidth lasers and highly optimized optical coatings. A ytterbium fiber amplifier (FA) 502 manufactured by IPG Photonics or NuFern is used to amplify a low power (<100 mW) master laser 522. This provides up to 50 W of single mode, single frequency, polarization maintaining (PM) amplification.

[0130] The laser beam is coupled into a high power, single mode PM fiber from NKT Photonics, which is capable of conducting at least 20 W of optical power at 1064 nm. The power is delivered to a small assembly attached to the microscope that houses a Faraday isolator (to prevent laser radiation from being reflected back into the laser) and a beam steering mirror (to spatially match the fiber output to the cavity mode). Camera 524 and photodetectors (e.g., FPD 516) observe the mode shape transmitted by cavity 110 for optimization purposes and for measuring the cavity finesse using cavity ringdown spectroscopy.

[0131] As demonstrated by recent work, the master laser frequency is stabilized (“locked”) to the resonance of the optical cavity 110 using the Pound-Drever-Hall method. For this purpose, a portion of the light reflected from cavity 110 is detected by a photodetector (PDH_PD) 506 and used by the PDH locking circuit 520 to control the laser frequency.

[0132] The cavity mirror 512 is described below. For a Fabry-Perot cavity made of two identical mirrors 512, the power amplification factor M is determined by the cavity mirror transmission and reflection coefficients T and R and the mode overlap integral Q:

[0133]

[0134] Since |Q| ≤ 1, the power enhancement is limited by the quality of the cavity mirrors: the reflectivity must be as close to one as possible, and the transmittance must be as high as possible. These two coefficients are constrained by energy conservation to R + T + L = 1, where the loss L = S + A includes scattering S and absorption A. Absorption is usually a property of the dielectric material used to produce the mirror coating. In near-infrared reflective coatings produced by ion beam sputtering (IBS) by companies such as Advanced Thin Films, Inc. and Research Electro-Optics (both located in Boulder, CO), the absorption is typically less than three parts per million (ppm).

[0135] On the other hand, scattering mainly depends on the smoothness of the mirror substrate and is thus determined by the quality of the mirror polishing process. Scattering can be approximated as S = (4πδh) 2 / λ 2 , where δh is the root mean square (RMS) surface roughness. The methods for polishing flat fused silica substrates have been developed so well that surface roughnesses of less than 0.1 nm and scatterings on the order of 3 ppm are typically achieved. However, the polishing of high-curvature concave mirrors required for near-concentric cavities remains challenging.

[0136] One embodiment utilizes a recently developed polishing process that allows for an RMS surface roughness of approximately 0.1 - 0.2 nm to be achieved on substrates with a radius of curvature as short as 10 mm. This will result in S being much lower than 10 ppm. In one embodiment, the mirror 512 is coated with a prior art high-reflection IBS coating at Advanced Thin Films or Five Nines Optics. Based on these figures, these mirrors support magnification factors in the range of M = 8000 - 13000.

[0137] If the IBS coating process used by the above coating companies does not perform well on the new substrates produced by Perkins Precision, one plan is to purchase mirrors 512 with a radius of curvature small enough that can be obtained from Layertec and LaserOptik. It is expected that the reflectivity of these mirrors will be sufficient to achieve a magnification factor of M = 4000 - 6000. If neither of these two companies should be able to meet the performance goals specified in their quotes, there is a second backup option to purchase mirrors 512 with a larger radius of curvature that can be obtained from Advanced Thin Films, which can support a power magnification factor of 10000 for an 8 - 10 μm mode waist.

[0138] The mirror transmission coefficient will be measured directly before being installed in the cavity 110. The reflectivity of the mirror 512 will be measured using the cavity ring-down spectroscopy technique for this type of cavity.

[0139] For a cavity amplification factor M = 5000, an input power of 15 W is required to achieve a full 90° phase shift. Even at a full cycle power of 75 kW, direct laser damage to the mirror coating is impossible: using a mirror 512 with a radius of curvature Rcurv = 20 mm, the spot diameter on the mirror surface is w1 = (fλ) / (πw0) = 1 mm, which results in a maximum surface intensity of less than 0.5 MW / cm 2 , well below the laser damage threshold of high reflectivity mirror coatings in the near-infrared range; for example, an intensity of 100 MW / cm 2 is achieved.

[0140] The large mode size on the mirror surface makes it necessary to pay special attention to the surface quality, because any flaw in the central part of the mirror 512 will increase the round-trip loss. By specifying a surface quality with a surface finish (scratch-dig) of 10-5 or better, and by ordering the mirrors in batches of 10 or 12 to select the best performing mirrors, this risk can be mitigated.

[0141] The following describes cavity optomechanics.

[0142] Figure 6 is a cross-sectional view of an optical cavity including a housing 606, a cavity mirror 604, and a coupling aspherical lens 602 in an embodiment. The optical device on the right is positioned in a flexure suspension that can be tilted or moved along the axial direction.

[0143] The alignment of a near-concentric resonator with a small mode waist is extremely sensitive to the position and orientation of the mirrors 604 with respect to each other, because the desired configuration is very close to the degeneracy point, where a series of modes have the same frequency and the resonator becomes unstable. In this configuration, a small angular offset of the mirrors 604 results in a significant lateral displacement of the mode. In a near-concentric optical resonator, the mode waist size can be controlled by tuning the distance between the mirrors 604, which requires sub-micron accuracy.

[0144] Figure 7 depicts a cavity mount in an embodiment. The wire 702 shown is connected to a piezoelectric actuator (inside the housing 606) for precise alignment of the cavity mirror 604.

[0145] For various embodiments, see Figure 6 and Figure 7 , and it is planned to replicate the cavity mount used in previous work on a near-concentric resonator. It has been shown that a flexure suspension machined from a single aluminum block can be used to align a near-concentric cavity with a mode waist w0 = 7 μm. The mount is compact enough to allow the use of a diameter of The cylindrical access port is installed into the TEM cell. For the optical bench experiment, the cavity 110 is placed inside a compact vacuum chamber with anti-reflection coated laser quality input and output optical ports. One of the mirrors 604 is stationary in the mount, while the position of the second mirror 604 is controlled using three piezoelectric actuators paired with three fine-threaded screws for coarse alignment. The entire mount assembly is made of non-magnetic materials (aluminum body, type 316 stainless steel screws with silicon carbide tips, piezoelectric ceramics).

[0146] The following describes the thermal control. Operating under vacuum poses additional challenges in removing the heat dissipated in the cavity. The absorption in the IBS-coated mirrors is only 1 - 3 ppm of the circulating power, so each of the two cavity mirrors 604 needs to dissipate up to 200 mW in resonance. Attention should be paid to removing the heat deposited in the cavity mirrors to avoid thermal distortion. Numerical simulations show that the thermal conductivity of the fused silica substrate limits the temperature rise at the mirror center to about 30 K, where according to communication with the mirror manufacturer, this is highly unlikely to cause mirror damage.

[0147] The local temperature rise will also cause the local radius of curvature to increase by an amount of about δR ~ 300 nm. When the cavity 110 reaches the operating power, the distance between the mirrors 604 will increase by 2δR to keep the cavity 110 at the selected distance to concentricity (which determines the mode waist). Changing the cavity length will lower its resonance frequency by ~ 7 GHz. Since the master laser (NP Photonics Rock fiber laser module or equivalent) used in one embodiment has a frequency tuning range of about 30 GHz, the shift in the resonance frequency can be easily followed by the frequency-locked master laser.

[0148] However, an additional heat load is caused by the light scattered on the mirror surface, which is ultimately absorbed in the cavity. Assuming that at least half of the input power will be transmitted or reflected, it is necessary to be able to remove up to 10 W dissipated in the laser module. This task becomes more difficult due to the fact that the cavity needs to be suspended in a vacuum on a support structure about 200 mm long. Although the aluminum cavity mount body should provide sufficient thermal conductivity to limit the temperature rise to 10 K, it is planned to actively control the temperature of the cavity using a thermoelectric cooler to avoid fluctuations in the cavity alignment driven by temperature fluctuations. It is planned to use a thermoelectric module (cold plate and controller) from TE Technology that can absorb up to 28 W and can hold the temperature well within 0.1 K of the set point.

[0149] To promote external heat conduction, up to three copper / water heat pipes with a diameter of 4-6 mm extending in grooves along the support structure are planned to be used. Such heat pipes, which are commonly used for chip cooling in the electronics industry, have a thermal resistance much lower than 0.1 K / W, thus providing a greatly increased heat dissipation capacity compared to all-copper or aluminum rod suspensions without introducing vibrations associated with circulating liquid coolers. At the same time, copper / water heat pipes are both vacuum-compatible and non-magnetic, so they are suitable for use in TEM environments.

[0150] The tests are as described below. The following tests are planned to be carried out in an optical bench setup to confirm that the phase plate prototype meets its object specifications.

[0151] The numerical aperture of the cavity mode will be measured by recording the far-field image of the beam transmitted through the cavity and fitting it to a Gaussian profile. The inferred mode waist will be w0 = 7 μm or less.

[0152] The circulating optical power in the cavity will be at least 75 kW. This power will be calculated based on the measured transmission coefficient of the output cavity mirror and the measured transmission power using a calibrated power meter.

[0153] The system will operate in a vacuum chamber with a pressure measured using a vacuum gauge not exceeding 2·10 -7 mbar.

[0154] The system will be able to continuously maintain the circulating power and numerical aperture for at least two hours without manual adjustment of any degrees of freedom, and will be able to maintain these parameters for at least 10 hours with occasional adjustment of the controls.

[0155] In one embodiment, the electron microscope is a low-base FEI Titan TEM equipped with a side-entry Gatan cold forging machine, enabling the study of cryo-EM specimens. Images will be recorded using a 16-megapixel Gatan K2 Summit direct detection camera. As previously mentioned, the microscope has additional relay optics for magnifying the electron diffraction pattern, thus increasing the effective focal length to 20 mm. The microscope has four ports at the level of the conjugate back focal plane (three of these ports have acceptance), providing convenient access to the diffraction plane 104. One of the ports will be used to insert the cavity module, and the transmitted laser beam will be directed to a port (170° offset) almost radially opposite to the port where the prism is attached to the cavity mount.

[0156] The insertable laser module will be made of non-magnetic materials to avoid disturbing the magnetic fields of TEM electron optical components (aluminum alloy (cavity suspension system), piezoelectric ceramics, fused silica (mirrors, lenses)). The small micron screws planned to be used are made of type 316 stainless steel with silicon carbide ball heads. In the case where the extremely weak magnetic permittivity of stainless steel is found to interfere with TEM alignment, titanium screws can be used as an alternative option.

[0157] The laser beam source and frequency locking system will be placed adjacent to the electron microscope. A flexible, high-power polarization-maintaining single-mode fiber will be used to bring the light into the insertable module. One advantage of fiber optic coupling is that the alignment of the optical system with the electron beam can be performed by moving the entire optical insertable module without disturbing its internal alignment.

[0158] The insertable module will be suspended in a mount that permits three-axis position adjustment of the module relative to the TEM column. The laser focus and thus the module need to be vertically positioned within 100 μm of the diffraction plane 104. This ensures that the transmitted electron wave passes through the high-intensity region when it is focused to a size smaller than the fringes of the laser wave. The horizontal position in the direction orthogonal to the cavity optical axis needs to be controlled within 1 μm. This ensures that any misalignment is much smaller compared to the waist of the laser beam. Finally, the horizontal position along the cavity axis needs to be stabilized to better than 100 nm. This ensures that the unscattered electron beam passes through the largest part of the standing wave, since the half-maximum width of the standing wave fringes is only 266 nm. On the other hand, all the maxima within the range of ∼50 μm around the beam waist have approximately the same intensity (as Figure 5 shown), and any one of these maxima can be used to delay the transmitted wave. Piezoelectric actuators will be incorporated into the suspension system to keep the longitudinal position of the cavity stable.

[0159] To position the cavity focus at the center of the conjugate Fourier plane, a two-stage process is planned. First, for coarse alignment, a circular opening cut out in the cavity mount is planned to be used to allow the electron beam ("beam hole") to pass through, so that the cavity focus is centered below the electron beam in the case where no specimen is inserted. This position can be found by moving the components while observing the TEM image, noting the point where the electron beam is blocked by the edge of the beam hole. Then, for finer alignment, an amorphous carbon film can be used as the specimen. Observing the Fourier transform of the image under appropriate defocus reveals the position of the laser focus relative to the center of the TEM Fourier plane. Using the image as a guide, the center of the cigar-shaped focus can be brought into the center of the Fourier plane.

[0160] For fine-tuning the module position along the cavity axis, it is planned to again use the defocused image of amorphous carbon to observe the Thon ring. When the unscattered beam passes through the node of the standing wave, the Thon ring should have its normal pattern. However, when the unscattered electron beam is phase-shifted by the standing wave, the ring will be offset by the same phase, providing quantitative feedback for fine alignment.

[0161] Once the system is aligned, the power of the laser system can be calibrated by observing the offset of the Thon ring with varying laser power.

[0162] Precise alignment of the near-concentric resonator is vulnerable to vibration and thermal expansion. On the optical bench, alignment can be manually restored by piezoelectric actuators. However, for it to be useful to the TEM user community, the phase plate needs to be able to operate without frequent human intervention.

[0163] One goal is to overcome this difficulty by automating the minor adjustments required to maintain cavity alignment. As demonstrated in previous work, the major types of misalignment are easily observable using a CCD camera that monitors the laser beam transmitted through the cavity, and the necessary adjustments are straightforward. When cavity 110 is almost perfectly aligned, there are three major misalignment modes: (i) the pitch of the mode relative to the cavity axis, (ii) the yaw tilt of the mode relative to the cavity axis, and (iii) the change in the numerical aperture of the mode. These three modes can be measured by observing the output laser beam with a camera and fitting its intensity profile to a Gaussian in two coordinates, the centroid and the beam width. The coordinates of the beam center will be used to adjust the mirror tilt to realign the mode with the cavity axis, and the size of the mode will be used to stabilize the cavity length (and thus the mode waist). For these purposes, piezoelectric actuators are incorporated into the mirror mountings. The bandwidth of this feedback system does not need to be very high because on the optical bench, adjustments are only required once every few hours of operation. Given that the vibration isolation of the TEM system is at least as good as that of the optical table, it is expected that adjustments will not be required more frequently, so standard computer interface tools will be sufficient to provide the necessary bandwidth.

[0164] It will be necessary to periodically check the alignment of the unscattered electron beam with the maximum of the laser standing wave by monitoring the Thon ring pattern of the observed image, which is considered possible. One embodiment for implementing this feature is as a software plug-in that analyzes the TEM image and sends a feedback signal to the actuator that controls the alignment of the phase plate module with the electron beam.

[0165] In principle, the laser phase plate can be used in the back focal plane or any suitable conjugate plane on the column of the TEM.

[0166] Higher numerical apertures require highly curved mirrors that are beyond the scope of current polishing processes for high-precision mirrors, such as the mirrors planned for use in various embodiments. However, advanced processes (ion beam milling) can, in principle, perform this operation. Numerical apertures as high as 0.36 have been reported in near-concentric cavities corresponding to a mode waist of w0 = 0.94 μm (at λ = 1064 nm). A cavity-based ponderomotive phase plate with a focus as tight as this would enable phase contrast imaging in a conventional TEM with a focal length of f = 2.5 mm.

[0167] However, ion beam milling produces a surface that is not smooth enough for low-loss mirrors and must be super-polished before a reflective coating can be applied (one reported cavity had a finesse of only about 600). It may also not be clear whether substrates milled with very high NA can be polished to a small enough surface roughness to fabricate high-finesse cavity mirrors. Additionally, even if the substrate is smooth enough, it is not certain during planning that a highly reflective dielectric coating can be applied evenly enough to such a high numerical aperture mirror.

[0168] If the straightforward method of increasing the numerical aperture is not successful, another embodiment will use a compact assembly that includes two or more crossed cavities. One possible approach is to use a three-cavity configuration to produce an interference pattern characterized by narrow intensity peaks.

[0169] Figure 8 is a perspective view of a laser phase plate 800 composed of three cavities 802, 804, 806 with overlapping focal volumes. An electron beam 808 is shown as a vertical line. As Figure 8 shown, the cavities 802, 804, 806 are planned to be arranged in a horizontal plane with their axes at 60° to each other and their focal volumes intersecting. The numerical aperture of each cavity 802, 804, 806 can be moderate. Due to the constructive interference between these cavities, each cavity 802, 804, 806 only requires 1 / 9 of the laser power needed to produce the same phase shift using a single cavity.

[0170] It is planned to frequency lock the three cavities 802, 804, 806 to a single feed laser using the Pound-Drever-Hall method, thereby ensuring the mutual coherence of the fields within the cavities.

[0171] Figure 9A Depicts the interference pattern 900 produced by the three-cavity arrangement, which is characterized by a hexagonal lattice of interference peaks. The interference pattern of the three cavity modes forms a half-maximum diameter of 382 nm (see Figure 9A) of the hexagonal lattice of narrow intensity peaks. The transmitted electron wave will be aligned to pass through the highest intensity peak at the center. Although additional high-intensity peaks create "blind spots" (where the contrast transfer function is close to zero) in the diffraction plane 104, such regions are small and isolated. In Figure 9B The rotationally averaged CTF of this configuration is shown (assuming a focal length f = 2.5 mm).

[0172] Figure 9B The rotationally averaged contrast transfer function of a three-chamber phase plate (upper curve 902) is depicted compared to a single-chamber (black) (lower curve 904) with f = 2.5 mm. Due to the narrow central peak, the CTF has reached 90% of its maximum value at a spatial frequency of approximately ν = (20 nm)-1 and remains close to one at higher frequencies, with a moderate decrease due to the additional intensity peaks. Thus, the three-chamber configuration should be able to achieve full-contrast observation of particles up to approximately 10 nm in diameter, which is sufficient for most particles with a molecular mass of 200 kDa or less.

[0173] The chambers 802, 804, 806 can be positioned relative to the electron beam (and thus relative to each other) by closing all but one chamber, longitudinally translating that chamber until the phase shift of the transmitted wave (observed by the Thon ring shift) is maximized, and repeating the process for all chambers.

[0174] The following describes reaching milestones towards a prototype laser phase plate and achieving a continuous 40 GW / cm 2 laser intensity in a near-concentric optical cavity.

[0175] Manipulating free-space electron wave functions with a laser field can bring new electron optical elements to transmission electron microscopy. In particular, the Zernike phase plate will enable high-contrast imaging of soft matter, thus opening up new opportunities for structural biology and materials science. The Zernike plate can be realized using a tight, intense, continuous laser focus that shifts the phase of the electron wave through the ponderomotive potential. Here, a circulating laser power of 7.5 kW at 1064 nm is focused to a 7-μm waist using a near-concentric cavity, thus setting a record for continuous-wave laser intensity and establishing a path towards a ponderomotive phase-contrast TEM.

[0176] In both molecular biology and materials science, transmission electron microscopy (TEM) has become a key source of structural information with atomic resolution. One limitation of TEM is that specimens composed of light elements such as biological macromolecules are nearly transparent to the electron beam, resulting in weak image contrast. In optical microscopy, the invention of Zernike's phase-contrast microscopy solved the problem of observing thin transparent objects such as living cells. Introducing Zernike-type phase contrast into electron microscopy has been the goal of increasingly intensive research efforts. Recently, phase contrast in TEM has been spectacularly demonstrated using carbon foil-based phase plates. However, there remains significant potential for improvement: exposure to the electron beam changes the properties of the carbon foil over time, thus altering the contrast transfer function and limiting the time for which the phase plate can be optimally used for imaging.

[0177] Controlling free-space electron propagation with lasers provides an alternative to electron optics. Charged particles passing through a strong laser field undergo small-scale oscillatory motion, which results in an effective "ponderomotive" potential. Experiments using electron scattering on laser standing waves have shown that the ponderomotive potential can be used to create diffraction gratings and beam splitters for electron beams. Recently, it has been proposed that a laser beam focused in the back focal plane of a TEM objective can be used as a Zernike phase plate. Unlike material phase plates, laser phase plates are inherently immune to charging and electron-beam damage, and provide negligible electron losses. The possibility of rapidly changing the phase delay by varying the laser power is an additional advantage.

[0178] The free-space manipulation of high-energy electrons used in TEM requires very high laser intensities. The phase delay induced by a focused Gaussian laser beam can be calculated as follows:

[0179]

[0180] where: α is the fine-structure constant, c is the speed of light, m is the electron mass, β and γ are the relativistic factors of the electron, P is the beam power, ω is the laser angular frequency, and w is the beam waist (see also Eq. 2). Another possible requirement for a ponderomotive phase plate is that the focal spot size should not exceed a few micrometers. According to Eq. (5), imparting a π / 2 phase shift to electrons at a typical TEM energy of 200 - 300 keV over a distance of a few micrometers requires laser intensities in the range of several hundred GW / cm 2 Therefore, most experiments on electron scattering by light are carried out using pulsed laser systems. However, for cryo-EM and other high-resolution TEM applications where the signal-to-noise ratio is a limiting factor, continuous operation is desirable.

[0181] A power build-up cavity can be used to enhance the laser power of a continuous-wave (CW) system. Low-loss cavity mirrors have been shown to tolerate laser intensities up to 0.1 GW / cm 2The intensity. The much higher intensity required for the ponderomotive phase plate can be achieved in a focusing cavity (such as a near-concentric Fabry–Perot resonator, etc.). In this configuration, the fundamental mode has an hourglass shape, where the laser power is concentrated in a small focal spot at the center but spreads over a large area on the mirror surface, which prevents mirror damage. Low-power tight intracavity focusing is demonstrated in a near-concentric cavity with medium finesse. At the same time, an average circulating power of up to 670 kW is achieved in a focusing cavity that is constructed for amplifying ultrashort pulse trains for intracavity high-harmonic generation and optical frequency comb spectroscopy in the extreme ultraviolet spectral range. However, the combination of high power and tight intracavity focusing required for the laser phase plate has not been achieved.

[0182] Here, it is reported that a milestone has been reached towards a prototype laser phase plate implemented as a high-finesse, high-numerical-aperture near-concentric cavity. Its fundamental mode is characterized, and numerical models are used to analyze the properties of TEM in the presence of the intracavity laser field. Using a circulating CW laser power of 7.5 kW, a maximum intensity of 41 GW / cm 2 is demonstrated, which is sufficient to delay a 300 keV electron beam by 0.16 rad.

[0183] The experimental results are reported as follows. The optical system schematically shown in Figure 5 includes a near-concentric cavity 110 and a CW feed laser 522 operating at a wavelength γ = 1064 nm. The feed laser 522 in this embodiment is an external cavity diode laser frequency-locked to the cavity using the Pound–Drever–Hall method, as well as a fiber amplifier 502. The cavity 110 is designed to be inserted into a plane conjugate to the rear focal plane of a TEM objective, where the electron beam enters the cavity orthogonally to the optical axis. The cavity is formed by two concave mirrors 512 (LayerTec) with a diameter of 12.7 mm, a radius of curvature of 12.7 mm, and a specified reflectivity of R = 1-(10 ± 5)·10 -5 . The rear surface of the mirror is convex and concentric with the front surface. The meniscus shape enables efficient coupling into the high-numerical-aperture mode of the cavity using a single aspherical lens 510.

[0184] The cavity mount (see Figure 6 and Figure 7)Enables adjustment of the tilt and axial position of one of the mirrors 604 accommodated in the flexure suspension. The entire cavity housing 606 is machined from a single aluminum block to ensure that the mirror 604 is precisely centered and to provide effective heat conduction for cooling the cavity. Alignment of the near-concentric cavity 110, which requires an angular accuracy better than 1 μrad, is achieved by three fine-pitch micrometer screws that provide coarse alignment and thus press against three piezoelectric actuators positioned in cavities in the aluminum block. The high-power optical module including the cavity 110, the coupling lens 602, and the mirror alignment optics is made compact enough to fit into a 25-mm diameter cylindrical space, which helps with future integration into a TEM system.

[0185] The cavity 110 is suspended in a vacuum chamber evacuated to 2·10 -7 mbar, thus simulating the environment of an existing TEM column and preventing unwanted ionization of air molecules. Using the degrees of freedom of tilt and axial motion of one of the mirrors, the cavity 110 is brought into a near-concentric configuration. To characterize the size of the focus inside the cavity, the laser frequency is tuned to oscillate around the fundamental mode of the cavity 110. The transmitted beam is collimated by an aspherical lens (focal length 25 mm) and directed into a CMOS image sensor. The mode image is fitted with a two-dimensional Gaussian profile to obtain the width of the fundamental mode at the far field, which is the reciprocal of the size of the focal spot. The image exhibits a small degree of ellipticity determined by very slight astigmatism of the cavity mirrors. The two principal axes of the ellipse correspond to the numerical apertures NA a = 0.0469 ± 0.0005 and NA b = 0.0524 ± 0.0005. The mode waist corresponding to NA b is s = λ(πNA) -1 = 6.46 μm.

[0186] The reflectivities of the cavity mirrors 114, 116 are measured using the cavity ring-down (CRD) method, where light is briefly injected into the optical cavity 110 and the subsequent rise and decay of the power of the transmitted light are observed. To avoid the need for a pulsed laser source or an optical modulator, injection of light into the optical cavity 110 is achieved by rapidly sweeping the laser frequency across the longitudinal mode resonances of the TEM 00 mode of the cavity (rapidly swept cw-CRD).

[0187] Under these conditions, the transmitted electric field amplitude is well modeled by the inverse Fourier transform of the product of the transfer function of the cavity and the spectrum of the linearly-chirped laser field, such that the transmitted power is as follows:

[0188]

[0189] Where: R is the cavity mirror reflectivity, L is the cavity length, and η is the frequency sweep rate. This model is used to fit the experimentally measured CRD profile, where R is used as the fitting parameter of interest.

[0190] Shown in Figure 4 are the measured CRD profiles and their least-squares best fit to the model described by Equation (6). The cavity mirror reflectivity is expressed in terms of the cavity mirror transmissivity T and the loss L such that R, = 1 - (T + L), and the fitted profile corresponds to a cavity mirror transmissivity + loss of 137.9 ± 0.4 ppm.

[0191] This corresponds to the following cavity finesse.

[0192]

[0193] The seed laser is locked to the cavity using the Pound-Drever-Hall method, where sidebands are generated by direct RF modulation of the seed laser current (e.g., by RF generator 1216, see Figure 12 ). The reflected beam is separated by a Faraday isolator 508 and directed into a photodiode 506. The RF signal from the diode is demodulated and used as the error signal.

[0194] To estimate the circulating power in the cavity, in addition to the cavity finesse, the coupling efficiency of the mirror and the transmission loss ratio are required. These two parameters can be inferred from the measurement results of the cavity transmission coefficient T cav and the reflection coefficient R cav . Representing the mode overlap between the input beam and the fundamental cavity mode as Q leads to the following:

[0195]

[0196] With the laser frequency locked to the cavity resonance, the measured R cav = 0.34 ± 0.03, T cav = 0.32 ± 0.03. Extracting the cavity parameters results in |Q| 2 = 0.75 ± 0.05 and T / (T + L) = 0.65 ± 0.05. Considering these parameters together with the CRD data allows the mirror transmissivity T = 90 ± 7 ppm and the amplification factor to be determined as follows:

[0197]

[0198] With the cavity parameters determined, the input power is increased. With the chamber maintained at atmospheric pressure, increasing the input power by more than 300 mW does not result in a further increase in the transmitted power, apparently due to the onset of breakdown in air at a circulating power of approximately 1 kW and a maximum intensity of 5.5 GW / cm 2caused by the corresponding nonlinear optical effect. In the case of cavity evacuation, intracavity powers up to 7.5 ± 0.6 kW are achieved. At Figure 2 shows the intracavity circulating power 204 (inferred from the transmitted power) as a function of the input power 202. The curve is nearly linear, where the small deviation at higher powers may be due to thermally induced deformation of the cavity housing that modifies the cavity alignment. The maximum power is limited by concerns about the risk of thermal damage to the mirrors that are not well thermally coupled to the mount. Using the mode parameters measured above, the maximum measured power corresponds to a maximum intensity of (41 ± 4) GW / cm 2 which would result in a phase delay of 0.16 rad for a 300 kV electron beam. Repetitive CRD measurements at low power confirm that no mirror damage occurred during high-power operation.

[0199] The following describes numerical modeling. To evaluate the effect of the laser phase plate on TEM of biological macromolecules, numerical simulations of TEM imaging of human hemoglobin embedded in vitreous ice were performed. The peptide tetramer complex has a molecular weight of approximately 64 kDa, which is too small for conventional TEM reconstruction, but has recently been resolved to a resolution of 3.2 Å using phase-contrast TEM with a carbon foil phase plate.

[0200] Modeling of TEM images (not shown) of hemoglobin molecules with a cavity-based ponderomotive phase plate was examined, and (a) a ribbon diagram of the molecule, (b) a two-dimensional projection of the atomic potential, and (c) the phase shift caused by the fundamental mode of the optical cavity are shown. The magnified image shows the individual fringes of the standing wave. Panel (d) shows a simulated TEM image without shot noise of the molecule with the same orientation as in (a,b), where the offset "ghost" image corresponds to the first diffraction order. A simulated conventional TEM image defocused by 1 pm at a dose of 20 e / Å was generated. A focused image formed with a cavity-based ponderomotive phase plate at the same electron dose is shown. The numerical aperture of the cavity in the model is NA = 0.05, which is consistent with the experimentally demonstrated parameters. The model assumes that the intracavity power is scaled to achieve a maximum full 2-fold delay, which requires the optical power to be increased by about a factor of ten further.

[0201] Multilayer simulations were performed. An acceleration voltage of 300 kV, a pixel size of 0.2 Å, and a spherical aberration of 1.3 mm were used. Since shot noise and thermal tails of the potential dominate the information limit of the simulation, the finite spatial and temporal coherence of the electron beam was neglected in the simulation. The hemoglobin structure used was downloaded from the Protein Data Bank. The thermal vibrations of the protein atoms were assumed to be 0.1 Å, which was applied as an envelope function. A continuous model of vitreous ice developed by Shang and Sigworth was used to model the embedding potential around the hemoglobin structure numerically integrated in 3D.

[0202] The results of the modeling were studied. In Figure 3 a spatial plot of the phase shift caused by the Gaussian standing-wave cavity mode is shown, where the enlarged view (see insert 304) shows the individual minima and maxima of the standing wave.

[0203] A side effect of passing an electron beam through a laser standing wave is that the standing wave acts as a diffraction grating for the electrons, which produces additional weak "ghost" images. These ghost images are shifted from the original image by a distance δx = 2nfλ e / λ, where n is the diffraction order, f is the focal length of the TEM objective, and λ e is the electron wavelength. The first-order ghost images (not shown) presented in the absence of shot noise are visible, but would be invisible in the presence of shot noise. Since the amplitude of such ghost images is much lower than the shot noise, they will be invisible in individual images and will amount to an insignificant contribution to the noise in the averaged images used for density map reconstruction.

[0204] Simulated TEM images of hemoglobin molecules (not shown) were studied. Highly transparent biological macromolecules are typically made visible by defocusing the imaging system from the specimen plane 102 (see Figure 1 ), thereby using the oscillating contrast transfer function to produce phase-contrast images. Although higher defocus results in higher contrast at low spatial frequencies, this defocus also results in a loss of contrast at high spatial frequencies. The 1-μm defocus used here is a value that still allows reconstruction of the density map at near-atomic resolution. Assuming an effective dose of shot noise was modeled, which is typically used as the optimum point between radiation damage (which increases with dose) and shot noise (which decreases with dose) in TEM protein structure studies. Focused images of hemoglobin with a ponderomotive phase plate at the same electron dose were studied (not shown). A full π / 2 phase shift at the intensity maximum was assumed. The phase-contrast images exhibit a stronger signal at low spatial frequencies compared to the defocused contrast images, which are expected to enable particle projection classification and alignment of macromolecules at least as small as hemoglobin.

[0205] Refer to Figure 3 The numerical results of the study show that the standing wave established in the focused resonator produces a contrast transfer function suitable for phase-contrast imaging. Importantly, the well-defined spatial structure of the cavity mode ensures that the contrast transfer function can be accurately accounted for when interpreting EM images. Although the intensity ratio exhibited in the experiment is about an order of magnitude lower than the intensity required to impart a π / 2 phase shift to a 300-keV electron beam, it may be sufficient for an initial demonstration of ponderomotive delay. Additionally, using state-of-the-art mirrors, it should be possible to increase the cavity finesse to 2·10 5Increasing the input power to 30 W, which is possible using a commercial fiber amplifier at NIR wavelengths, should be sufficient to increase the focal intensity to well over 10 12 W / cm 2 .

[0206] In this work, one of the developed embodiments is a laser-based Zernike phase plate. However, many other tools can be envisioned using a high-intensity intracavity CW laser field. For example, quantum imaging methods based on interaction-free measurement schemes have been proposed. A significant obstacle to implementing this scheme lies in the lack of a high-quality beam splitter for the electron wave function. The CW standing wave in an optical cavity can act as a highly regular and nearly lossless phase grating, coherently splitting an electron beam into two paths via Kapitza-Dirac scattering in the Bragg mechanism. Such a beam splitter can also implement various electron interferometry schemes, mimicking different families of optical interferometers for metrology and sensing.

[0207] Finally, it should be noted that the type of cavity constructed may be of interest for a wide class of experiments. The combination of a small mode volume with the open and accessible geometry of a high-NA near-concentric resonator is useful for cavity QED experiments. Additionally, the ability to establish very high circulating powers can be used to implement ultra-deep dipole traps and for trapping and cooling nanoparticles.

[0208] In summary, a high-finesse optical cavity 110 with a tightly focused fundamental mode has been developed. Through numerical simulations, it has been verified that such a field configuration can be used as a ponderomotive phase plate for TEM. It has been shown that light intensities in the range of dozens of GW / cm 2 can be achieved in a CW laser system using a near-concentric Fabry-Perot resonator. These results represent an important step towards ponderomotive phase-contrast TEM and, more generally, pave the way for laser-based coherent control of free-space electron wave functions.

[0209] The following describes the research results and embodiments of a transmission electron microscope 1002 with an optical cavity phase plate.

[0210] Figure 10 An embodiment of a transmission electron microscope 1002 including an optical cavity phase plate according to an embodiment of the present invention is shown. An electron gun 1024 generates an electron beam 1012, which is collimated by a condenser 1020, focused by a specimen objective 1018, passes through a specimen at the specimen plane 102 (see Figure 1 ), passes through the Fourier transform plane 1004 in the laser cavity 1008, and is focused by a projection lens 1022 to generate an image 1016.

[0211] In an embodiment, a strong electric field in a tightly focused laser beam forms a phase plate (seeFigure 10 )。The phase plate in the Fourier transform plane 1004 of the electron microscope 1002 (i.e., Figure 1 the back focal plane or the diffraction plane 104 in

[0212] is constituted by a strongly focused laser beam 1014 from a laser 1006. An approximately spherical optical resonator (laser cavity 1008) is used to shape the focus and further enhance the intensity of the laser beam phase plate. The electron beam 1012 travels through holes at opposite ends (e.g., on the top and bottom) of the spherical optical cavity housing 1010. The interaction between the strong electric field of the laser beam and the charge of the electrons produces a phase shift in the electron beam corresponding to an increase in the "optical path length" of the electrons, which can be visualized as causing the electron trajectories to wobble to increase the traveled path distance. If the increase is 1 / 4 of the de Broglie wavelength of the electrons, the desired π / 2 phase shift is achieved.

[0213] Figure 11 FIG. 1102 shows the intensity pattern of the resonant optical cavity phase plate according to an embodiment of the present invention. The resonant enhancement of the laser beam in the spherical optical cavity housing 1010 reduces the high-power beam requirement. This provides a narrow intensity maximum 1104 at the center (about 0.5 wavelength radius, as Figure 11 shown), which matches well with the size of the non-diffracted electron beam in the Fourier transform plane. Electrons outside the center see a relatively low electric field and experience a negligible phase shift.

[0214] In a simple classical model, the laser is used as a phase plate because the alternating electric field of the laser causes the trajectories of the electrons to wobble and thereby increases their path length. The quantum mechanical treatment shows that the phase shift is as follows:

[0215]

[0216] Here, h is the reduced Planck constant, α is the fine structure constant, ρ is the photon density, λ is the laser wavelength, τ is the time required for the electrons to pass through the focus, and m is the electron mass. Away from the optical focus at the center of the cavity, the photon density ρ drops rapidly, such that there is no significant phase shift except at the optical focus. The photon density can be expressed in terms of the laser power P as where c is the speed of light. Assuming that the electric field has a Gaussian intensity profile with a 1 / e 2 intensity "waist" radius of w0 = λ / 2, which is a good approximation of the intensity distribution inside the cavity. This is the smallest focus that can be obtained for a laser of a given wavelength; larger foci are possible but result in higher required laser powers. To estimate the transit time τ, the same model is used to obtain τ = λ / v e , where v e is the electron beam velocity. Considering the actual intensity distribution of the cavity ( Figure 11A more accurate estimate is τ = sqrt(π / 2)λ / v e . For the insert type (1), the phase is as follows:

[0217]

[0218] The laser phase plate has the property of having almost no electron loss when passing through the phase plate. Through Compton scattering with photons, only about one electron is lost among one million electrons.

[0219] Equation (9) can be used to calculate the laser power P required to generate a δ = π / 2 phase shift as a function of electron velocity and laser wavelength. The electron velocity v of a 100 keV electron microscope e is about 10 8 m / s.

[0220] According to Equation (9), the desired π / 2 phase shift depends on the product of the laser wavelength and the laser beam power. It is desired to operate at the lowest possible laser power P, which can be traded off with a larger laser wavelength λ.

[0221] Conversely, the laser wavelength determines the size of the laser focus, which must be consistent with the size of the undiffracted electron beam. In particular, if the focus is too large, it will result in a loss of contrast of larger structures in the specimen. For example, consider a rod-shaped tobacco mosaic virus with a diameter of d = 18 nm. To obtain the contrast of all quantities on this diameter, the phase contrast of the spatial frequency needs to be as high as 1 / (2d) = 1 / (36 nm). For example, the electron optical focal length in an electron microscope (e.g., FEI Titan purchased from FEI Company, 5350 NE Dawson Creek Drive, Hillsboro, OR 97124) is f = 20 mm, and the electron wavelength λ e is 3.7 picometers (pm) at 100 keV. Resolving the spatial frequency 1 / (36 nm) will result in a maximum phase plate radius of about fλ e / (2d) = 20 mm x 36 nm / (3.7 pm) ≈ 2 μm, that is, the maximum wavelength is about 4 μm.

[0222] It is difficult to obtain a high-power laser at this wavelength. The selection of the laser wavelength is also restricted by the availability of reliable commercial high-power lasers. For example, according to Equation (9), a laser wavelength of 1064 nm requires a laser power of about 5 kW to generate the required π / 2 phase shift for a 100 keV electron beam. At this wavelength, a beam focus radius of about 0.5 μm is obtained. This will achieve the phase contrast of structures up to 80 nm in size, thus meeting the above requirements.

[0223] Pulsed lasers can easily achieve kW-level power within a duration of nanoseconds (ns), but the use of these pulsed lasers will also require a pulsed electron beam. However, such pulses are not available in most commercial TEM setups. However, most importantly, the cathode current density in the electron gun introduces new complexities in the operation of electron microscopes in pulsed mode. Therefore, a continuous-wave high-intensity light field is desired.

[0224] The intensity of a laser beam can be increased by using an optical cavity to obtain resonance enhancement. In such a cavity, the laser radiation bounces back and forth between the cavity mirrors. If the laser wavelength is a half-integer multiple of the mirror separation, the radiation on all round trips constructively adds up, providing resonance intensity enhancement. This occurs when the radiation has one of the following resonance frequencies:

[0225]

[0226] where: n = 1, 2, 3,... is the mode number (this equation applies with sufficient accuracy to the cavity when the length L is much larger than the wavelength). For a resonant laser, the intensity will increase by a factor of:

[0227] 1 / (1 - R) (11),

[0228] where: R is the reflectivity of the mirror. A perfect reflector would have a value of R = 1.

[0229] In addition to intensity enhancement, the cavity must provide a very tight focus of the laser beam. A tightly focused beam diverges rapidly, i.e., optical devices with a large numerical aperture (NA) are required. Therefore, the minimum focus is generated by the strongly diverging transverse electromagnetic mode TEMn01 in a spherical cavity that completely encloses the beam (see Figure 11 and Figure 12 ). The electromagnetic field in a strongly focused beam is non-trivial. Using this spherical cavity has the additional advantage of knowing the electric field in such a spherical cavity from analytical calculations.

[0230] Reference Figure 10, the optical cavity 1008 can be arranged, for example, such that the electron beam 1012 is directed vertically downward (e.g., along the z-axis), entering the cavity 1008 through a hole at the top and exiting through another hole at the bottom. The laser beam 1014 is shown as being directed horizontally, and its polarization can be made orthogonal to the plane of the figure. The electric field far from the center of the optical cavity is zero on a circle in the xy plane including the top and bottom of the cavity. Thus, the holes for the electron beam will not cause a perceptible loss of optical power. These holes are large enough so as not to inhibit the flow of electrons (e.g., with a radius of about 1 mm), but can be larger or smaller. If the cavity radius is 10 mm or greater, these holes will dissipate no more than 0.01% of the cavity circulating power. Additionally, this allows the cavity to be constructed from two hollow hemispheres that are joined after fabrication to form a single sphere. They are joined in the plane of the vanishing electric field such that even an imperfect join will not cause a perceptible loss of optical power.

[0231] The intensity enhancement factor is set by the reflectivity of the reflecting mirror surface (i.e., high internal surface reflectivity). For dielectric coatings, reflectivities of R = 99.99% and greater, which increase the intensity by 10,000 times and more, are prior art. However, unfortunately, dielectric coatings require precise thicknesses, which are difficult to achieve on highly curved surfaces such as two hemispheres, but can ultimately be achieved. Metal-coated mirrors are easier to fabricate because the thickness of the coating is not important. Conventionally, a metal reflectivity of 99% at 1 micron can be utilized, providing a 100-fold power enhancement. This may be sufficient for high-power lasers available in the prior art.

[0232] In an embodiment, the required power can be reduced by increasing the wavelength, but this will increase the spot size. At a CO2 laser wavelength of 10 μm, for a π / 2 phase shift, only 500 W of power is required to be circulated in the cavity, and the power enhancement factor of the metal mirror will be approximately 200. Thus, only 2.5 W of laser power is required. As discussed above, for a focus of ~5 μm size, some loss of contrast of the large-scale features of the specimen will occur. However, this configuration will be simpler in terms of the required laser power.

[0233] The laser cavity 1008 can be made by joining two hemispheres with a radius of, for example, 8 - 10 mm to form a spherical optical cavity housing 1010. The size is mainly determined by the space available in the electron microscope for placing the phase plate. The hemispheres can be ground into a square shape in a beryllium copper block to obtain good thermal conductivity and mechanical stability, or alternatively, Invar TMFor low thermal expansion. It should be noted that maintaining a perfectly spherical shape is secondary since, as described below, the cavity may anyway be deliberately deformed. The hemisphere is polished to λ / 10 and coated with gold on the inside. Since the loss of the gold mirror is relatively high, better polishing is not required. The hemispheres can be attached to each other by one or more piezoelectric transducers (PZTs) to tune the optical cavity for frequency stabilization at an optical frequency while suppressing other competing modes of the phase grating that may cause different standing wave period intensities. A laser power of about 50 W will be dissipated on the cavity walls. The heat can be removed by liquid cooling. For a 10 °C temperature rise (easily met with liquid cooling), a hemisphere with a 10 mm radius expands by about 160 nm for BeCu, or about 16 nm for Invar TM and expands by about 16 nm. This will cause a shift in the resonance frequency, which must be compensated for by active feedback (described below). In addition, the dynamic range of the PZT must be at least half of the laser wavelength to allow resonance to be obtained at any laser frequency (see Equation (10)). The gold surface at λ = 1 μm has R = 0.99, thus achieving a power enhancement factor of 100. According to Equations (9,10) and assuming 75% power transfer from the laser to the cavity, a 67 W laser will be required. A single-frequency fiber laser currently available from IPG Photonics (50 Old Webster Road, Oxford MA 01540) provides 50 W of laser at this wavelength. Since the phase contrast varies as the sine of the phase shift and thus as the sine of the laser power, a >90% optimal phase contrast can be obtained with 50 W of laser. A higher power laser 1006 will enable operation at a lower cavity coupling efficiency, thus reducing the cost of manufacturing the optical cavity.

[0234] To efficiently couple laser radiation into the cavity, it is desirable to obtain a near-spherically symmetric mode from the collimated laser beam. This is because in addition to the desired resonance mode with the tightest focus (see Figure 11 ), due to spherical symmetry, the cavity can resonate in a large number of other modes. For a perfect sphere, many of these modes have the same resonance frequency as the desired mode. Therefore, a slightly distorted cavity, which can be simply achieved by adjusting the distance between the hemispheres, breaks the degeneracy of the cavity modes, i.e., the desired mode now has a different resonance frequency. If the laser radiation has that frequency, the laser radiation will primarily excite that mode. The other modes that resonate at different frequencies are presented as cavity non-resonant and are thus suppressed.

[0235] Figure 12 A system for generating an optical phase plate for modulating the phase of an electron beam is shown. The coupled laser beam can simply pass through the radius r in cavity 1202 inis achieved through the aperture 1204. The transfer of power from the laser 1224 to the cavity mode is optimized when losses in other parts of its balanced cavity (i.e., losses due to the finite reflectivity of the metal surface) are considered. For Figure 11 the desired resonant mode shown, if 1 = (2 / 3)(4r cav 2 / r m 2 )(1 - R), this condition is satisfied, where r cav is the radius of the cavity 1202, and R is the reflectivity of the cavity mirror, or for R = 0.99, r in / r cav = [8(1 - R) / 3] 1 / 2 = 0.16.

[0236] Even when this condition is satisfied, the coupling efficiency may still not be 100%. Consider the time-reversed situation where the cavity generates light exiting through the coupler. The coupler is smaller compared to the size of the TEMn01 mode resonating inside the cavity. Therefore, the electric field exiting through the coupler has almost uniform intensity across the diameter of the coupler and is almost zero outside (neglecting diffraction at the edges, which is reasonable since the radius of the coupler is much larger than the wavelength, so the diffraction effect is basically negligible). By time-reversal, this defines the required shape of the laser beam impinging on the cavity with optimal power transfer. However, the laser generates a Gaussian mode. The optimal power transfer between the Gaussian mode and the truncated ("top-hat") cavity mode is 50.4%, and it occurs when the waist radius parameter of the Gaussian beam in the plane of the coupler is equal to the radius of the coupler. It is also assumed that the coupling lens has an appropriate focal length. By using a beam shaping device that is essentially a phase grating to transform the Gaussian beam into a beam with uniform intensity, this efficiency can be increased to the theoretical 100%. Such a technique with 84 - 90% efficiency has been reported.

[0237] To enable the cavity to provide maximum intensity enhancement, the frequency of the laser must match one of the resonances of the cavity. To obtain resonance despite thermal drift and other drifts in the laser and the cavity, a feedback mechanism based on the Pound-Drever-Hall method (e.g., as Figure 12 shown) is used. For this purpose, the electro-optic modulator 1206 applies a modulation with frequency ω m and modulation index β mPhase modulation. The beam is coupled into the cavity through a beam shaper 1220 and a coupling lens 1222, and a reflected signal due to the radiation exiting the optical cavity is detected by a detector 1218. An isolator 1208 can be used to couple the reflected signal to the detector 1218. In another embodiment, a beam splitter and a mirror can be used to couple the reflected signal to the detector 1218. The resonance characteristics of the cavity convert the phase modulation into amplitude modulation. When the laser and the resonance frequency are in agreement, the detected reflected component of the amplitude modulation (AM) reaches a minimum, ideally zero; otherwise, non-zero AM occurs. This is detected by a double-balanced mixer (DBM) 1210 through amplitude and phase, and its output is low-pass filtered to suppress the modulation frequency ω m . This results in a signal with a zero phase crossover at resonance. The signal is fed back to the laser frequency actuator via a suitable servo 1214 through feedback 1212, and the servo 1214 keeps the cavity resonance aligned with the laser 1224. Due to the high signal power in this system, a very slight modulation may be sufficient to obtain a feedback signal with a high signal-to-noise ratio.

[0238] Many uses and application methods can be considered. In biochemistry, significant improvements can be achieved in determining the structures of multi-protein complexes and macromolecular machines. In cell biology, significant improvements can be achieved in localizing such complexes and their spatial relationships within whole cells through EM tomography. In both cases, it is expected that Zernike phase contrast improves the ability to image unstained specimens embedded in vitreous ice (i.e., in a life-like state).

[0239] In an embodiment, the use method includes recording an image 1016 of a biological macromolecule and a supramolecular structure. Such research requires obtaining the maximum image contrast physically possible. Compared with the current defocusing method for imaging unstained samples in TEM, the contrast of the focused Zernike optical cavity phase contrast microscope can be ten times greater (see above), and it does not degrade or destroy the signal at high resolution like the use of defocusing.

[0240] In addition to biological applications, in an embodiment, the microstructure of soft materials can be characterized.

[0241] In an embodiment, an optical cavity phase plate can be applied to generate three-dimensional optical traps of extreme depth. The trap depth can be in the range of tens or even hundreds of Kelvin, thereby trapping, for example, room-temperature atoms and localizing them in space to better than 0.5 micrometers, even for substances that are difficult to cool. Such traps are useful for a wide range of atoms or molecules because the huge intensity in the cavity will make it unimportant to closely align the laser frequency with the atomic or molecular transition. This allows spectroscopy of very weak transitions of such atoms. An example is nuclear spectroscopy of thorium-229 atoms with a laser. The laser spectrum of the ∼5-6 eV transition in the thorium-229 nucleus could be a breakthrough in precision measurement because it allows the construction of a "nuclear" clock based on transitions between nuclear energy levels rather than transitions in electron shells. However, it has been hindered by the lack of a suitable method for localizing the atoms. Only using local atoms allows the probe laser to be focused tightly enough as needed to generate sufficient intensity. The dipole trap proposed here can solve this problem and enable direct laser spectroscopy of the transition. This could lead to higher-precision clocks (since the nucleus is less sensitive to the environment), as well as testing the time variability of fundamental "constants" with unprecedented accuracy.

[0242] Providing a dielectric coating technology capable of fabricating a uniform and controllable dielectric layer mirror on the inner surface of a high-NA cavity enables higher resonance enhancement and thus allows the use of a lower-cost, low-power laser or a longer laser wavelength (which would enable the use of a lower-NA cavity).

[0243] Compared with the conventional microstructured phase plates described above, it can be understood that the optical resonance cavity phase plate has several advantages. It does not use any mechanical electrodes inside the electron beam; the optical elements required to introduce the laser beam can be far enough away (1 mm or more), such that problems of image blurring and distortion are avoided; it overcomes the problem of short device lifetime that currently limits the performance of thin-film phase plates; it overcomes the problem of partial loss of scattered electrons that occurs for both thin-film phase plates and electrostatic or magnetic phase plates; and it will make electron microscopy more productive and efficient because it does not cause partial loss of the signal and because there are no interruptions due to the need to replace microstructures or thin-film phase plates that have aged or become contaminated when struck by the electron beam.

[0244] By converting phase into amplitude contrast, the resonant optical cavity phase TEM can capture meaningful signals from a very small amount of unstained and thus unaltered material. Therefore, this method is useful for all research programs that use electron microscopy to determine the structure of unstained biological materials or generally low atomic number materials, including organic polymers and other soft materials. These projects include biological and materials science research, medical schools, private research institutions, or chemical companies developing new polymer materials. Use may also grow to include research laboratories in the biotechnology and pharmaceutical sectors.

[0245] Figure 13 It is a flowchart of a method for enhancing phase contrast in an electron beam image. This method can be practiced using a transmission electron microscope, an optical cavity, and a laser.

[0246] In operation 1302, an electron beam is generated in a transmission electron microscope. In operation 1304, the electron beam is allowed to enter along an axis passing through the center of an optical cavity, which is defined by a first mirror and a second mirror and is positioned at the back focal plane of the transmission electron microscope.

[0247] In operation 1306, a laser beam is allowed to enter the optical cavity. The laser beam is reflected from the first mirror and the second mirror to generate a standing wave optical phase plate. The standing wave optical phase plate is focused at the back focal plane to cause modulation of the electron beam.

[0248] In operation 1308, the angle or position of the first mirror or the second mirror is adjusted using a piezoelectric actuator in an adjustable suspension. In operation 1310, the electron beam is imaged in the image plane of the transmission electron microscope. The image plane is positioned to receive the electron beam modulated by the standing wave optical phase plate.

[0249] The following reference Figures 14 - 16 The described embodiments extend the capabilities of the ponderomotive phase plate by allowing control of the spatial profile of the ponderomotive phase plate via control of the optical polarization state of the light used in the ponderomotive phase plate. In the case of transmission electron microscopy imaging, this control can be used to eliminate the presence of image artifacts due to electron diffraction in the phase plate. For the same reason, in one embodiment, this control can also be used as a switchable electron beam splitter. The various embodiments and variations described herein provide similar control of the spatial profile of the phase plate.

[0250] The spatial profile of the ponderomotive phase plate is caused by the spatial profile of the ponderomotive potential generated by light. However, the spatial profile of the ponderomotive potential depends not only on the intensity of the light, but also on the polarization state of the light when the velocity of the incident charged particles (e.g., electrons) is a significant fraction of the speed of light. Specifically, the depth of the standing wave of the phase plate can be changed by rotating the polarization angle. For particles with a velocity greater than 1 / sqrt(2) times the speed of light, the depth of the standing wave can be made zero.

[0251] Since the standing wave structure of the phase plate diffracts the passing-through particles, the embodiments described herein can be used to control the amount of diffraction that occurs in the phase plate. When the phase plate is used for transmission electron microscopy imaging, it may be desirable to eliminate the electron diffraction effect, as this eliminates the presence of image artifacts due to electron diffraction. It can also make the process of aligning the electron beam with the phase plate easier and faster, since the spatial profile of the phase plate becomes less rapidly varying. Controlling the depth of the standing wave also provides a way to control the maximum phase shift imparted to the electron beam, which adjusts the amount of image contrast enhancement provided by the phase plate for phase contrast transmission electron microscopy. It may be advantageous to use various embodiments to switch between two phase plate profiles (with and without a standing wave) during normal data collection to more accurately reconstruct data related to the sample.

[0252] Another application is as a switchable electron beam splitter (or beam splitter), since the standing wave structure can be switched ON and OFF as fast as the polarization state of light can be changed. One embodiment uses an electro-optic modulator to quickly switch the polarization of a laser, thus turning on and off the diffraction effect acting on the electron beam, which results in the beam splitter being turned on and off. The electro-optic modulator can be used in various embodiments of the ponderomotive phase plate or the laser phase plate (including in transmission electron microscopes and other embodiments described below).

[0253] Yet another application is electron pulse slicing. A laser beam strong enough causes the incident electron beam to be completely diffracted. None of the outgoing electron beams travel in the same direction as the incident electron beam. All of the incident electron beams are deflected by a certain specific angle. If the device is operating at this stage and then the polarization is switched, this action slices the electron beam. Rapidly switching the polarization results in electron pulse slicing.

[0254] Another application is time phase modulation of an electron beam focused on a single antinode of the standing wave of the laser in the laser phase plate. When the electron beam is focused and passes through the antinode of the standing wave (the position where the electric field of the wave is highest), the electron beam receives a phase shift. This phase shift depends on the polarization state of the laser. Rapidly changing the polarization state changes the amount of phase shift that the electron beam receives from the laser, and this occurs at the frequency at which the polarization state of the laser is changed. After the electron beam has propagated a certain distance, this effectively amplitude-modulates the electron beam. A sample located next to the electron beam experiences pulses of repulsion or attraction to the beam at the frequency of the change in the polarization state of the laser. A device designed and operated in this way can control the characteristics of the electron beam for use in the study of the chemical properties of specimens or other properties of substances.

[0255] By modifying Figures 1 - 13The ponderomotive phase plate arrangements described in [reference] are used to implement various embodiments, which allow the polarization state of the light sent into the Fabry - Perot optical cavity to be rotated to any angle with respect to the electron beam axis. Specifically, in some embodiments, a common optical element (half - wave plate) is inserted into the path of the laser beam input to the cavity and rotated. The rotation of the half - wave plate (or more generally the rotation of the polarization angle of the laser beam by various mechanisms) can be discrete preset or within a continuous range, and can be manually controlled or automatically controlled in various embodiments.

[0256] For several reasons, the embodiments are considered novel. First, the fact that the ponderomotive potential is polarization - dependent for fast particles is not generally obvious to those skilled in the art. However, prior to the present invention, there were several theoretical articles by other academic research groups that had confirmed the existence of the effect in computer simulations and discussed potential applications. Second, the embodiments described herein are considered to be the first experiments demonstrating this effect. Third, the application of the proposed effect in transmission electron microscopy has not been previously disclosed.

[0257] The various embodiments have potential uses. The most likely commercial use of the present invention is in the operation of the ponderomotive phase plate for image contrast enhancement in transmission electron microscopy, as a method for eliminating image artifacts caused by electron diffraction from the phase plate. The present group is currently in the process of signing a cooperative research and development agreement with Thermo Fisher Scientific to further develop the ponderomotive phase plate technology described herein.

[0258] There are no known competing technologies for removing the standing - wave structure from the ponderomotive phase plate. The advantages of the ponderomotive phase plate over other types of phase plates are described herein.

[0259] Figure 14 A schematic geometry depicting another embodiment of a phase - contrast TEM 1434 is characterized by a laser with a variable polarization angle coupled to an optical cavity 1424. Changing the polarization angle of the laser changes the image contrast enhancement of the image of the sample 1404 formed at the image plane 1428 of the transmission electron microscope 1434. The following references Figures 15A - 15C describe the mechanisms for changing the polarization angle of the laser, and further mechanical, electromechanical, and electro - optical embodiments can be readily designed in accordance with the teachings herein. In one embodiment, a laser 1412 with a variable polarization angle has an electro - optic modulator for changing the polarization.

[0260] In operation, the electron beam 1402 of the transmission electron microscope 1434 is directed at the sample 1404 at the object plane 1406. A portion of the electron beam 1402 is diffracted by the sample 1404 and travels as a diffracted electron beam 1436. The undiffracted portion of the electron beam 1402 is focused by the objective lens 1408 on the focal point 1422 of the optical cavity 1424, and the objective lens 1408 is typically made of an iron core magnet or an electromagnetic field coil. At the same time, the diffracted electron beam 1436 diverging from the sample 1404 cannot be focused by the objective lens 1408 at the focal point 1422 of the optical cavity 1424.

[0261] The polarized laser light from the laser 1412 with a variable polarization angle is coupled into the optical cavity 1424 by the coupler 1416, where the coupler 1416 can be air, gas, vacuum, or an optical fiber in various embodiments, and other types of couplers can be easily designed. As described above in various embodiments, the optical cavity 1424 is formed by two concave mirrors 1418, 1420 that focus the laser light at the focal point 1422 of the optical cavity 1424. The antinode of the polarized laser light at the focal point 1422 of the optical cavity 1424 causes modulation of the electron beam 1402. Most of the scattered diffracted electron beam 1436 from the sample 1404 does not pass through the focal point 1422 of the optical cavity 1424 and is not thus modulated by the polarized laser light.

[0262] The unscattered and undiffracted portion of the electron beam 1402 focused on the focal point 1422 undergoes a phase shift due to the focused polarized laser light, while the portion of the scattered beam that does not intersect with the light wave does not undergo a phase shift. The electron beam 1402 and the diffracted electron beam 1436 are guided by the projection lens 1426 to the image plane 1428, where an image can be formed and captured by the electron camera 1430 (or other sensors in alternative embodiments). Similar to the objective lens 1408, the projection lens 1426 is typically made of an iron core magnet or an electromagnetic field coil. Also, the electron camera 1430 operates on a principle similar to that of a photoelectric camera for capturing pixels, for example, using a charge-coupled device (CCD) or an optically exposed random access memory (RAM). The phase shift difference between the unscattered beam and a specific portion of the scattered diffracted electron beam 1436 determines how much contrast enhancement is provided by the ponderomotive phase plate 1410 (or laser phase plate) at the image plane 1428.

[0263] Changing the polarization angle of the laser affects how many standing wave structures are present in the ponderomotive phase plate 1410, which can be tuned from a maximum to zero. The lack of standing waves results in less image contrast enhancement but eliminates the presence of ghost images from the scattered diffracted electron beam 1436. In the case of maximum standing waves, the image contrast enhancement is maximum, and thus ghost images are present. Various trade - offs are obtained at intermediate settings. One potential side effect of setting the laser polarization angle such that the "ghost" images are eliminated is that it may be easier to align the electron beam to the laser beam antinode, as this operation can be difficult to achieve. In one embodiment, such alignment is useful for making phase - contrast images. It should be noted that this advantage can be independent of the other benefits mentioned herein.

[0264] Figure 15A Depicts a half - wave plate 1502 with a rotator 1504, which is used to change the polarization angle of the laser in embodiments of phase - contrast TEM and embodiments of ponderomotive phase plates. The polarized laser from the laser 1503 passes through the half - wave plate 1502, which is made of a birefringent material that affects the phase angle of the transmitted polarized light. The rotator 1504 sets the rotation angle of the half - wave plate 1502 and thereby sets the phase angle of the polarized laser. The rotator 1504 can be implemented as a wheel (whose friction or gear teeth engage with the gear teeth on the half - wave plate), or a belt drive, or other mechanism, and can be set manually, for example, with a shaft or knob, or actuated by a motor (e.g., a stepper motor or other electric motor). The motor - driven rotator 1504 can be manually controlled, for example, by a switch or button, or can be automatically controlled, for example, through a feedback path and controller as Figure 16 shown.

[0265] Figure 15B Depicts an optical - fiber coupler with a rotator 1512, which is used to change the polarization angle of the laser in embodiments of phase - contrast TEM and embodiments of ponderomotive phase plates. The ferrule 1506 of the optical - fiber coupler fixes one end of the optical fiber 1508 or cable to the laser 1503 with polarized laser. Another ferrule 1510 at the other end of the optical fiber 1508 or cable is rotated by the rotator 1512, which rotates the end of the optical fiber 1508 or cable relative to the end fixed to the laser 1503, thereby rotating the polarization angle of the polarized laser from the laser 1503. Similar to the Figure 15A rotator 1504, there are many possibilities for how the rotator 1512 can be implemented for manual, motorized, or automatic control.

[0266] Figure 15CDepict a laser 1503 with a polarized laser and a rotator 1516, which is used to change the polarization angle of the laser in embodiments of phase contrast TEM and embodiments of ponderomotive phase plates. By directly rotating the body of the laser 1503, the polarized laser generated by the laser 1503 exhibits the same rotation angle as the body. Similar to the rotator 1504 in Figure 15A , there are many possibilities for how the rotator 1516 can be implemented.

[0267] Figure 16 Depict a schematic diagram with actions, which shows a sensor 1606 at the image plane 1428 of a phase contrast TEM 1434 or a variant thereof in Figure 14 , and a controller 1602 for analyzing a Ronchi pattern, which is used to control the polarization angle of the laser in embodiments of phase contrast TEM 1434 and embodiments of ponderomotive phase plates 1410. A Ronchi pattern is formed at the image plane 1428, and the Ronchi pattern has standing wave fringes that vary with the polarization angle of the laser. At a specific polarization angle for a specific electron velocity, the standing wave fringes disappear. In one embodiment, the sensor 1606, which can be an electron camera 1430, detects the standing wave fringes at the image plane 1428 and sends a signal to the controller 1602. The controller 1602 performs various actions, which include analyzing the Ronchi pattern as action 1604 and controlling the polarization angle as action 1608. For example, software, firmware, or hardware in the controller 1602 can look for the intensity and placement of the standing wave fringes, direct an electric rotator to change the polarization angle of the laser, analyze the change of the standing wave fringes as the polarization angle changes, and associate the position of the rotator and the associated polarization angle with aspects of the standing wave fringes. For example, the controller 1602 can find the setting of the polarization angle of the laser that causes the standing wave fringes to disappear, where this setting and further settings are developed by the controller (or selected by the user) as the phase plate profile. In one embodiment, the controller 1602 can analyze the contrast in the image, and weigh the contrast and the ghost image, and then determine the optimal setting of the polarization angle.

[0268] Figure 17 Is a flowchart of a method for transmission electron microscopy, which can be performed by various embodiments of a TEM with a ponderomotive phase plate.

[0269] In action 1702, the TEM generates an electron beam. The electron beam can pass through the sample.

[0270] In action 1704, the electron beam is allowed to enter the optical cavity of the ponderomotive phase plate. The undiffracted and unscattered part of the electron beam is focused at the focal point of the optical cavity.

[0271] In operation 1706, a laser beam with polarized laser is allowed to enter the optical cavity to form a standing wave optical phase plate and cause modulation of the electron beam. Suitable mechanisms and techniques for doing so have been described above.

[0272] In operation 1708, the electron beam is imaged in the image plane of the TEM. When using a sample, the image shows the sample through phase contrast transmission electron microscopy. The image also shows a Ronchigram with standing wave fringes (which, as a degenerate case, can become zero amplitude at one or more specific settings of the polarization angle of the laser).

[0273] In operation 1710, the polarization angle of the laser is changed to change the contrast enhancement of the image. In various embodiments, this can be achieved by manual adjustment or automatic adjustment of the system.

[0274] Although the invention has been described in detail with its advantages, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. In addition, the scope of this application is not intended to be limited to the specific embodiments of the processes, machines, manufactures, compositions of matter, components, methods and steps described in the specification. As will be readily understood by those of ordinary skill in the art from the embodiments of the invention, processes, machines, manufactures, compositions of matter, components, methods or steps that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein can be utilized, whether currently existing or later developed, in accordance with the invention. Accordingly, the appended claims are intended to include such processes, machines, manufactures, compositions of matter, components, methods or steps within their scope.

[0275] In the foregoing specification, the invention has been described with reference to specific embodiments. However, those of ordinary skill in the art understand that various modifications and changes can be made without departing from the scope of the invention as set forth in the appended claims. Therefore, the specification and drawings are to be regarded as illustrative rather than restrictive, and all such modifications are intended to be included within the scope of the invention.

Claims

1. A transmission electron microscope system, comprising: A transmission electron microscope, i.e., a TEM, having a rear focal plane; A plurality of mirrors forming an optical cavity, the focal spot of the optical cavity being positioned at the rear focal plane of the TEM, the optical cavity being positioned to allow an electron beam provided by the TEM to pass through the focal spot of the optical cavity, and the optical cavity being operable to allow a laser beam to enter; A laser with a variable polarization angle of the laser, coupled to the optical cavity and operable to provide a laser beam with a specified wavelength and variable polarization angle to enter the optical cavity, the laser beam being reflected from the plurality of mirrors to provide a standing-wave optical phase plate focused at the rear focal plane of the TEM, thereby causing modulation of the electron beam, wherein the polarization angle of the laser is variable at least between a first phase plate profile and a second phase plate profile, the first phase plate profile having a standing wave in a Ronchigram formed at the image plane of the TEM, and the second phase plate profile having no standing wave in the Ronchigram; and The image plane of the TEM, positioned to receive the electron beam modulated by the standing-wave optical phase plate to form an image according to the variable polarization angle.

2. The transmission electron microscope system according to claim 1, further comprising: A half-wave plate; And A rotator arranged to hold and rotate the half-wave plate to provide a variable polarization angle of the laser.

3. The transmission electron microscope system according to claim 1, further comprising: An optical fiber member for coupling the laser to the optical cavity and being bendable or rotatable to provide a variable polarization angle of the laser.

4. The transmission electron microscope system according to claim 1, further comprising: An electron camera or one or more sensors positioned at the image plane and operable to analyze the Ronchigram and provide feedback for automatic control of the variable polarization angle of the laser.

5. The transmission electron microscope system according to claim 1, wherein, The polarization angle of the laser has two or more presets.

6. The transmission electron microscope system according to claim 1, wherein, The polarization angle of the laser has one or more of manual adjustment and automatic adjustment.

7. A method for a transmission electron microscope, comprising: Generating an electron beam in a transmission electron microscope, i.e., a TEM, having a rear focal plane; Allowing the electron beam to enter along an axis passing through the center of an optical cavity, the optical cavity being positioned at the rear focal plane and being defined by a first mirror and a second mirror; Allowing a laser beam with a variable polarization angle of the laser to enter the optical cavity, the laser beam being reflected from the first mirror and the second mirror to generate a standing-wave optical phase plate focused at the rear focal plane of the TEM, thereby causing modulation of the electron beam, wherein the variable polarization angle of the laser is variable at least between a first phase plate profile and a second phase plate profile, the first phase plate profile having a standing wave in a Ronchigram formed at the image plane of the TEM, and the second phase plate profile having no standing wave in the Ronchigram; Imaging the electron beam in the image plane of the TEM to form an image, the image plane of the TEM being positioned to receive the electron beam modulated by the standing-wave optical phase plate; and Changing the polarization angle of the laser to form the image according to the variable polarization angle.

8. The method for a transmission electron microscope according to claim 7, further comprising: Rotating a half-wave plate to provide a variable polarization angle of the laser.

9. The method for a transmission electron microscope according to claim 7, further comprising: Rotating or bending an optical fiber member for coupling the laser to the optical cavity to provide a variable polarization angle of the laser.

10. The method for a transmission electron microscope according to claim 7, further comprising: Analyzing the Ronchigram formed at the image plane based on the output of a sensor or an electron camera; and Controlling the variable polarization angle of the laser based on the analysis.

11. The method for a transmission electron microscope according to claim 7, wherein, Changing the polarization angle of the laser to change the contrast enhancement of the image.

12. The method for a transmission electron microscope according to claim 7, wherein, Changing the polarization angle of the laser includes: Determining the polarization angle of the laser based on two or more than two presets.

13. The method for a transmission electron microscope according to claim 7, wherein, Changing the polarization angle of the laser includes: Determining the polarization angle of the laser based on manual adjustment or automatic adjustment.

14. A ponderomotive phase plate, comprising: A first concave mirror and a second concave mirror, which are positioned to define an optical cavity, the optical cavity being capable of being positioned to allow an electron beam to pass through the focal spot of the optical cavity; and A laser with a variable polarization angle of the laser, which is coupled to the optical cavity and is operable to have a standing wave with an antinode at the focal spot, thereby causing a variable modulation of the electron beam that can be controlled by the variable polarization angle of the laser, wherein the variable polarization angle of the laser is variable at least between a first phase plate profile and a second phase plate profile, the first phase plate profile having a standing wave in the Ronchigram formed at the image plane of a transmission electron microscope, i.e., TEM, and the second phase plate profile having no standing wave in the Ronchigram.

15. The ponderomotive phase plate according to claim 14, wherein, The TEM positions the focal spot of the optical cavity at the back focal plane of the TEM; and An imaging device, which is positioned at the image plane of the TEM and is operable to form an image with a variable image contrast enhancement that can be controlled by the variable polarization angle of the laser.

16. The ponderomotive phase plate according to claim 14, further comprising: A half-wave plate, which is positioned to couple the laser to the optical cavity; and A rotator, which is operable to rotate the half-wave plate such that the laser has a variable polarization angle according to the rotation of the half-wave plate when the laser is incident on the half-wave plate and is coupled to the optical cavity to provide the standing wave with an antinode at the focal spot.

17. The ponderomotive phase plate according to claim 14, further comprising: An optical fiber coupler, which is arranged to couple the laser to the optical cavity; and A rotator, which is operable to rotate one end of the optical fiber coupler relative to the opposite end of the optical fiber coupler to change the polarization angle of the laser relative to the optical cavity.

18. The ponderomotive phase plate according to claim 14, further comprising: A rotator, which is coupled to the laser and is operable to rotate the laser to change the polarization angle of the laser relative to the optical cavity.

19. The ponderomotive phase plate according to claim 14, further comprising: An electron beam source, wherein the laser with a variable polarization angle of the laser can operate together with the first concave mirror and the second concave mirror as a switchable electron beam splitter or electron pulse slicing device.

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