Ptychography Setup

Defocus is referenced to the entrance surface, z = 0. C1 > 0 puts the crossover above the sample at z = −C1. In the alternate convention, df = −C1. Do not assume the microscope display has the same sign without checking.

Geometric diameter: D(z) = 2α|z + C1|, with α in radians. This ray construction reaches zero at focus; the real probe remains finite. The ideal aberration-free Airy intensity FWHM, 0.514λ/α, is reported separately and is not used as a measured footprint.

Detector: Δθ ≈ λΔq, with λ in Å and q in Å⁻¹ (spatial frequency, no 2π). W = λ/Δθ = 1/Δq is the unpadded Fourier real-space window. Pixel spacing dx = W/N. Axis-edge angle = NΔθ/2; square-corner angle is √2 times this. Detector padding refines dx but does not enlarge W at fixed Δq.

Overlap: the notes use the linear estimate max(0, 1 − step/D). Equal-circle area overlap is calculated separately. Neither is an overlap integral of the real probe. When the geometric diameter is zero, these geometric estimates are unavailable.

Dose: electrons/pattern = I × dwell / e; average raster dose = electrons/pattern / step². This is an interior, uniform-raster average, not local peak dose. Collection time excludes detector and scan overhead.

Use D ≤ W/2 (at most 50%) as the support-based diffraction-sampling limit: W = 1/Δq is the real-space period, and diffraction intensity is the Fourier transform of the exit-wave autocorrelation, whose support diameter is approximately twice the exit-wave support diameter D. The geometric cone is only a proxy for that support: probe tails and multiple scattering must be considered. The earlier 80% target and the 0.73 margin in the design notes do not establish this condition. The ideal probe has nonzero tails, so a practical support definition or tolerance is also needed. Scattering, aberrations, coherence, probe tails and sample-dependent damage are not modeled.

Reference files: Ptychography_overfocus_design_300kV_40nm.pdf (document identifies itself as version 4) and Ptychography_overfocus_design_300kV_40nm_v2.pdf. The first note's preset is 430 mm / +10 nm; the second uses 550 mm / +20 nm. The supplied Chen et al. (2021) supplementary material, pp. 5 and 9 and Fig. S2, discusses finer diffraction sampling for thick specimens; it does not explicitly state the half-window diameter condition. Camera-length dropdown values come from Spectra Ultra 300 kV Camera_Length_Calibration.docx (21 Aug 2026); the note presets use the matching measured values. The document’s reciprocal-space column is in 1/nm per pixel, equivalent to one tenth that value in Å⁻¹ per pixel. Unit conversion here is computed from the relativistic wavelength.