The Dublin lens: a Cc = 1.0 mm objective lens intended for CryoEM at 100 keV

2.1 Approach

Here we sought to design a lens suitable for accommodating a liquid nitrogen cooled anti-contaminator system and standard cryo-specimen holders without touching the pole-piece which is kept at room temperature.

2.2 Design

To evaluate the performance of many lens geometries in parallel, a genetic algorithm (GA) tailored specifically for bespoke pole-piece design was written [17]. The GA is a metaheuristic that relies on the theory of natural selection, wherein the members of a population with the most favourable traits are the most likely to survive and reproduce. The algorithm emulates this by preserving the best-performing geometries, creating mutants and crossovers of high- and mid-ranked geometries, and discarding the worst candidates [18]. Performance was evaluated with a fitness function, specified by the user in accordance with the desired lens properties. Such a GA approach has previously been successfully implemented in magnetic and electrostatic lens design for objectives, electron guns and even MRI machines [19], [20], [21], [22], [23], [24].

Beginning with a Python-defined vectorised description of a stylised pole-piece geometry, various randomised mutations of the geometry were performed to create a population of candidates. Each candidate was used as the input for a magnetic flux simulation using COMSOL Multiphysics^®. The resulting magnetic flux profile along the optic axis was used as the input to a Julia script to determine values of the chromatic aberration coefficient (Cc) as well as spherical aberration (Cs) and focal length. These values were substituted into a fitness function, in our case prioritising Cc, and the candidates were then ranked from best to worst. This ranking was used to create a new generation of geometries, say by eliminating the worst-ranked half, followed by crossover and mutation of the remainder. The calculations continued in this iterative manner until the specified number of generations was reached.

Simulated aberration coefficients were calculated at a particular value of coil excitation just below magnetic saturation. This was obtained by evaluating the paraxial magnetic flux profile at two boundary excitation values to find the position of the image plane, which was above and below zero for the respective boundary values. Using these values as a starting point, paraxial flux analysis was performed iteratively at halfway points between boundary image plane positions until the coil excitation, for which the image plane lies at zero, i.e. the saturation excitation, was obtained. This value was used to calculate the final aberration coefficients utilised in the GA’s fitness function.

For this work, the GA was driven by a fitness function which prioritised the minimisation of Cc over Cs or focal length. The fabrication-ready design resulted from the evaluation of 250 generations, each comprised of 250 candidates, with minor adjustments made to the curvature of the pole-pieces for machining feasibility. The simulated physical and aberration properties of the lens are displayed in Table 1, alongside the values measured and described later in this paper. Some further examples of various calculated aberrations for different geometries are given in the Supplementary material.

2.3 Fabrication

Pole-pieces were fabricated in Ireland with assistance from Irish Manufacturing Research, a national centre of excellence and training in advanced manufacturing. Upper and lower poles were fabricated from an iron-cobalt alloy and a non-magnetic spacer placed between each pole. The complete pole-piece was heat-treated to obtain optimal magnetic properties before dimensional analysis was performed using a coordinate measuring machine (CMM).

Before installation, the pole-piece was cleaned using an ultrasonic bath with sequential rinses of CMOS-grade acetone (x1) and isopropyl alcohol (x3) followed by air drying in a laminar flow clean hood. The original JEOL pole-piece was removed through the TEM’s pole-piece access port, and the new design was lowered in its place using a bespoke installation tool. The original goniometer and aperture strip were replaced, and the column pumped.

2.4 Testing

The lens was installed on a standard JEOL 1400/HR microscope, which was equipped with two important modifications, namely a prototype hybrid pixel detector from DECTRIS and a Schottky FEG electron source from York Probe Sources.

The hybrid pixel detector was an experimental prototype that uses a gallium arsenide (GaAs) wafer as its sensitive layer with sub-50 μm pixels bump-bonded to the ASIC event counting architecture below, which consists of juxtaposed ASICs. The ion-pairs created by the electron track are collected by a voltage bias and converted into electron events that are read out at kHz frame rate. This gives the detector superb performance for its megapixel field-of-view, but a full description of its performance and properties are beyond the scope of this paper.

The field emission gun (FEG) from YPS is also a prototype. It represents a further improvement in terms of stability and reliability of the earlier design [25], used previously to demonstrate the promise of structure determination by cryoEM at 100 keV [4]. The most recent improvement involves the use of an improved high-voltage ceramic material and improved mechanical alignment designs in the FEG.

After installation of the lens, the illumination system was realigned by adjustment of the beam tilt to minimise the image motion by observing the rotation centre using the objective lens current wobbler. A Zemlin tableau would be useful to provide further characterisation and is planned soon [26].

Cc measurement was made by recording a series of images at a nominal magnification of 300 kX corresponding to a pixel size of 0.74 Å at the specimen, which was calibrated from the (111) fringes of the gold nanoparticles at 2.35 Å. The accelerating voltage was changed to be 30 V above and 30 V below the 100,000 V operating value in 30 V steps in both directions to eliminate any possibility of hysteresis. As in the earlier work [4], the voltage calibration was checked. The slope of defocus versus accelerating voltage gives Cc directly (Figure 2a), using the formula Cc = (ΔF/ΔE)*E, where (ΔF/ΔE) is the slope and E is the accelerating voltage, and was found to be 0.97 mm.

Figure 2:

(a) Measurement of Cc from change in underfocus as a function of electron energy; error bars on defocus are small. (b) Measurement of Cs by least-squares fitting of three CTF parameters shown in the box. The specimen was a carbon/gold/carbon sandwich.

Cs was estimated from a 300 kX magnification image (pixel size of 0.74 Å) of gold on carbon using the same C/Au/C sandwich specimen as used for Figure 3b, but with an exposure time of 40 s, corresponding to 256,000 frames. Multiple sub-frame (2048) summations were then aligned by cross-correlation to compensate for slight specimen drift during the full exposure to give a final image that showed good resolution in all directions. Small amounts of differential magnification or astigmatism were then eliminated computationally to give the radial power spectrum shown in Figure 2b. The values of defocus, Cs and amplitude contrast were then minimised computationally to produce the best agreement between the observed and fitted radii of the contrast transfer function (CTF) zeroes.

Figure 3:

(a) Young’s fringes FFT of the sum of a pair of PtIr images extending well beyond 2 Å. The images added together were 2025_03_06–21_31_03 and 2025_03_06–21_31_42. (b) FFT of gold in a carbon sandwich showing the 2.3, 2.0, 1.4 and 1.2 Å lattice fringes from Au (111), (200), (220), and (311) spacings in image 2025_03_19-17_55_02. Images were recorded at a nominal magnification of 400 kX using a DECTRIS prototype detector, with a calibrated pixel size of 0.55 Å at the specimen. The resolution at the edge of the image is 1.1 Å and the dashed circle is at 1.5 Å.

The two images shown in Figure 3 were recorded with slightly higher magnifications (nominally 400 kX, with a calibrated pixel size of 0.55 Å at the specimen). Figure 3a was made by adding together two images of amorphous platinum/iridium (Agar Scientific) recorded 40 s apart during which the specimen had drifted by about 35 Å, creating an electron imaging equivalent of the Young’s fringe experiment [27]. The fringes show good resolution beyond 2 Å. Figure 3b shows the FFT of an image of a specimen of gold nanoparticles sandwiched between thin films of amorphous carbon. This was made by floating carbon off mica, then evaporating gold followed by a final coating of carbon to create a C/Au/C sandwich in which the gold domain orientations were more stable than on a single layer. The real-space image is shown in Supplementary material Figure S1.