Crossed laser phase plates for transmission electron microscopy

Abstract

For decades since the development of phase-contrast optical microscopy, an analogous approach has been sought for maximizing the image contrast of weakly-scattering objects in transmission electron microscopy (TEM). The recent development of the laser phase plate (LPP) has demonstrated that an amplified, focused laser standing wave provides stable, tunable phase shift to the high-energy electron beam, achieving phase-contrast TEM. Building on proof-of-concept experimental demonstrations, this paper explores design improvements tailored to biological imaging. In particular, we introduce the approach of crossed laser phase plates (XLPP): two laser standing waves intersecting in the diffraction plane of the TEM, rather than a single beam as in the current LPP. We provide a theoretical model for the XLPP inside the microscope and use simulations to quantify its effect on image formation. Using simulations, we find that the XLPP increases information transfer at low spatial frequencies while also suppressing the ghost images formed by Kapitza-Dirac diffraction of the electron beam by the laser beam. We also present a simple acquisition scheme, enabled by the XLPP, which dramatically suppresses unwanted diffraction effects. Finally, we discuss important practical considerations of XLPP design and show experimental results from a prototype. The results of this study chart the course for future developments of LPP hardware.

Figures (21)

• Figure 1: Crossed laser phase plates (XLPP) concept. (a) Schematic of a TEM with a XLPP in the conjugate diffraction plane. The incident electron beam (green) is focused at the focus of the XLPP laser beams (blue) while scattered electrons (yellow) are not. Blue double-headed arrows indicate horizontal laser polarization. (b-c) Comparisons of the phase shifts $\eta$ produced by the single laser phase plate (SLPP, b) and XLPP (c) as a function of spatial frequency $(s_x,s_y)$. Insets progressively zoom in on lowest spatial frequencies. Purple circles in (b) illustrate the cut-on frequencies $s_2$ (left) and $s_1$ (right). (d) Azimuthally-averaged modulus of the CTF. Vertical dashed lines indicate $s_2$ for the SLPP (red) and XLPP (blue), as well as $s_1$ (purple), which is the same for both. (e-f) Normalized, simulated in-focus images of one apoferritin protein formed using the SLPP (e) and XLPP (f) show ghost images spaced by $d_g$ from the main image. Insets zoom in on main image (solid border) and right ghost image (dashed border). The SLPP has $N_A=0.05$ while the XLPP has $N_A=0.08$. Additional calculation parameters are provided in Table \ref{['Table:Parameters']}. Color scale ranges from 0 (white) to $\frac{\pi}{2}$ (black) in (b,c) and from 0.08 (black) to 1.1 (white) in (e,f).
• Figure 2: Improvements of signal power. Dependence of the square modulus of the CTF, proportional to the power spectral density, on (a) $N_A$ and (b) $\lambda_l$ for a XLPP. In (a), a fixed value of $\lambda_l=1064nm$ is used. In (b), a fixed value of $N_A=0.05$ is used. Dashed vertical lines indicate the values of $s_2$ in (a) and both $s_1$ and $s_2$ in (b). Additional calculation parameters are provided in Table \ref{['Table:Parameters']}. For the condition plotted in red in both panels, $s_1=9.6e-4/\angstrom$ and $s_2=2.4e-2/\angstrom$.
• Figure 3: Ghost suppression by the XLPP. Simulated noiseless main images (first row) and first-order ghost images (second row) of apoferritin. Color scale ranges from 0.08 (black) to 1.1 (white) in all panels and each panel side length is 250. Phase plate and $N_A$ are indicated at the top of each column. Arrows point to the light "halo" around the main image, which is reduced from left to right in the top row. (c) PSDs of main images (solid) and first-order ghost images (dashed). Line colors in (c) correspond to panel border colors in (a) and (b). PSD of the object is shown in (c) as a gray line indicated by an arrow. It closely follows the other solid lines, departing near 1/(1) due to signal attenuation by the CTF envelope.
• Figure 4: Two-image scheme for ghost suppression. (a) Zoomed-in XLPP phase shift $\eta(\mathbf{s})$ showing the location of the unscattered beam for the two images in the two-image sequence, with the color scale ranging zero (white) to $\frac{\pi}{2}$ (black). Panels (b,c) show the first and second image, and (d) shows their average. Color scale in (b-d) is [0.46 (black), 1.06 (white)] and field of view is 1565 along each side. Panel (e) shows the ratio of the power spectral densities of a first-order ghost image and the main image for the case of a SLPP, XLPP, and the two-image result from panel (d). Line scans along the horizontal through the main image (f) and first-order ghost image (g) are shown for the three different cases plotted in (e).
• Figure 5: Prototype XLPP. (a) Section through a model of a prototype XLPP showing the two laser cavities, each consisting of two mirrors (red), integrated into a single mount. The laser beams (not shown) cross within the bore in the center of the mount. The electron beam (not shown) propagates through the bore, along $\hat{\mathbf{r}}_z$ (into the page). Flat mirrors (gray) steer the two laser beams into and out of the XLPP. (b) Experimental Ronchigram image of the two intersecting standing waves in the XLPP, each with a circulating power of $\mathord{\sim}$14kW. Inset shows the central region, indicated by the blue box, rotated slightly for comparison to Figure \ref{['Fig:Main']}c.