Astigmatism

Strong structure factors at low spatial frequencies can lead to CTF determination bias. Direct CTF determination at high frequency using the ‘1S2R’ procedure might fail in the case of large astigmatism due to severe oscillation of CTF. Two options are provided to deal with CTF determination at near-atomic resolution for micrographs that have very large astigmatism. They both make the ‘1S2R’ procedure more robust in such challenging case. One option is ‘resolution–extension (RE)’ and the other is ‘Bfactor-switch (BS)’. In the first method, Gctf determines initial CTF parameters using a relatively lower resolution ring (e.g. 50–10 Å by default). These parameters are passed as input to the next step of CTF refinement using a higher range (e.g. 15–4 Å). In the second method, Gctf uses a larger Bfactor (e.g. 500 Å²) to significantly down-weight high frequency for initial CTF determination. Then it switches to a smaller Bfactor (e.g. 50 Å²) to refine the previously determined CTF parameters. Either method shows its power to deal with some challenging cases (detailed results in Section 3.5). The combination (‘REBS’) can even work slightly better in certain cases.

The accuracy of defocus determination is very important for high-resolution cryoEM reconstructions. Assuming the difference between the true defocus of a micrograph and the estimated defocus is $\mathrm{\Delta }z$ , the phase error $\mathrm{\Delta }\gamma (s)$ is calculated by Eq. (4): $\mathrm{\Delta }\gamma (s)=\pi \lambda \mathrm{\Delta }{\mathit{zs}}^2$
Derived from Eq. (4), the defocus-inaccuracy dependent phase error is proportional to frequency squared for a certain micrograph Eq. (5). $\frac{\mathrm{\Delta }\gamma (s_1)}{\mathrm{\Delta }\gamma (s_2)}=\frac{s_1^2}{s_2^2}$
Obviously from Eqs. (4), (5), an error in CTF determination, which can be ignored for a lower resolution reconstruction, might cause a critical error at high resolution. If the CTF is not properly determined, there are increasing phase errors against the frequency. The contrast of CTF is inverted for a 180 degree phase error. When this error is smaller than 90 degree, the probability to have the correct contrast of CTF is more than 50%. Gctf uses such a 90 degree criterion in order to guarantee at least half of information from the EM images after CTF correction. Based on this criterion, CTF phase error versus frequency for different defocus errors between 10 nm and 200 nm were plotted (Fig. 1a). The maximum allowed CTF defocus errors were plotted against frequency for three typical voltages used in cryoEM reconstruction s (Fig. 1b).
In practice, defocus inaccuracy is only one of the factors that cause CTF phase error. Magnification distortion, chromatic or comatic aberration (Glaeser et al., 2011 (link)), astigmatism inaccuracy, mechanical and beam induced movement of the samples, curvature or deformation of the carbon substrate (Shatsky et al., 2014 (link)), sample thickness (DeRosier, 2000 (link)) can all contribute to the phase error during an experiment. Data processing can also lead to large phase errors, especially at high frequency. Although Gctf uses this 90 degree criterion, it should be noted that the highest quality micrographs might need a stricter criterion in practice.

Participants were recruited from the movement disorder clinic of the Samsung Medical Center. The Institutional Review Board of Samsung Medical Center approved this study, and all subjects provided written informed consent. Patients were enrolled if they were diagnosed with PD based on the United Kingdom Brain Bank Criteria for PD^{38 (link)}. Patients with any of the following conditions were excluded: any neurologic disorder other than PD, systemic vasculitis, cardiovascular disease, musculoskeletal disease, end-stage renal disease, peripheral nervous system autonomic failure (diabetic neuropathy, Guillain-Barre syndrome, amyloid neuropathy, surgical sympathectomy, and pheochromocytoma, etc.), ocular pathology that could affect OCTA measurements (glaucoma, a refractive error >+6.0 diopters of spherical equivalent or <−6.0 diopters of spherical equivalent, astigmatism ≥ 3.0 diopters, epiretinal membrane, age-related macular degeneration, diabetic retinopathy, hypertensive retinopathy, retinal artery/vein occlusion, or optic neuropathy) or previous retinal surgery. Exact age- and sex-matched controls were recruited. The healthy controls were required to have normal visual acuity, normal intraocular pressure ≤21 mm Hg, and normal optic discs. The same exclusion criteria were applied to healthy controls and PD patients. Demographic and clinical data, including age, sex, and comorbid vascular risk factors (hypertension, diabetes mellitus, dyslipidemia), were collected for all enrolled participants. The UPDRS III^{39 (link)}, H&Y scale^{40 (link)}, LEDD^{41 (link)}, and MoCA^{42 (link)} were investigated in all enrolled PD patients.

All patients underwent a comprehensive ophthalmological examination. The preoperative examination data included uncorrected distance visual acuity (UDVA), corrected distance visual acuity (CDVA), intraocular pressure, axial length, and corneal astigmatism measured by the IOL Master 700 (Carl Zeiss, Jena, Germany) and corneal spherical aberration measured by the iTrace aberrometer (Tracey Technologies, Houston, TX, USA) in a 6-mm range. The Barrett Universal II formula was used to determine the IOL power, and the postoperative target diopter was set to mild myopia (0–0.5D).
Postoperative examinations were conducted 3 months after cataract surgery. The data included UDVA, CDVA, uncorrected intermediate visual acuity (UIVA) at a distance of 80 cm, uncorrected near visual acuity (UNVA) at a distance of 40 cm, using Snellen visual charts and then converted into logarithm of the minimum angle of resolution (logMAR) notation. Astigmatism, and postoperative ocular spherical aberration, coma, trefoil in a 4-mm range was also recorded. After correcting refractive errors, CSV-1000HGT (Vector Vision, Dayton, OH, USA) was applied to measure the contrast sensitivity (CS) with and without glare after adapting the patient to scotopic conditions. Spatial frequencies of 3, 6, 12, and 18 cpd (cycle/degree, cpd) were used, which were then converted into base 10 logarithmic units for statistical analysis. Objective visual quality parameters, that is, the objective scatter index (OSI), modulation transfer function (MTF), and Strehl ratio (SR) using an optical quality analysis system (OQAS, Visiometrics SL, Terrassa, Spain) were recorded. Subjective visual quality was evaluated using the Catquest-9SF questionnaire with four response options for perceived difficulty in vision (4 = very great difficulty; 3 = great difficulty; 2 = some difficulty; 1 = no difficulty), and the Quality of Vision (QoV) questionnaire wherein the patients rated 10 visual symptoms with four response levels (0, 1, 2, 3; higher scores indicated worse photic phenomena).

In order to measure the VUV transmission, the crystals were cut and polished. Cutting was done using a Wiretec DWS100 with a 0.08 mm diamond coated wire. Facets cut with the wire saw were flat enough to be polished in a 1-step process. Polishing was done with a Buehler polishing machine and a Buehler SiC P4000 Silicon Carbide polishing paper. As CaF₂ is hygroscopic and adsorbed water decreases transmisson, the polishing paper was wetted with isopropanol instead of water³⁷ . All operations were performed with personal protective equipment in a radionuclide type C lab in well ventilated boxes.
Transmission measurements were performed using a dedicated setup. The light of a Hamamatsu L15094 D₂ lamp is focused with a toroidal mirror onto the entrance slit of a McPherson 234/302 monochromator. The light is separated into its spectral components by the grating and is focused onto the exit slit. By rotating the grating the exit wavelength can be selected. The exit slit cuts out a small portion of the spectrum effectively creating a narrow wavelength light source with a linewidth down to 0.1 nm. The linewidth can be changed by changing the entrance/exit slit width (0.01–2.50 mm). This light travels through the crystal, and is recorded by a Hamamatsu R6835 head-on CsI photomultiplier tube (PMT) which is mounted close to the crystal.
Although conceptually simple, measuring a wavelength-dependent absolute absorption is burdened with several experimental challenges. These are connected with geometrical changes in the beam paths due to the presence of the sample (beam shifts and astigmatism), strong spectral intensity modulations and overall intensity instabilities in the VUV source (deuterium lamp). These lead to an overall systematic error on the following transmission measurements of ± 5%.