 Solution

For a displayed width $D$ representing a scanned specimen width $d$, the linear image magnification isThe user changes the scan-coil excursion, hence $d$. A smaller raster displayed at the same width gives larger magnification. Changing the display or print size also changes displayed magnification, so the calibrated scale bar is more portable than a magnification label. This is the scan/display principle described in the manufacturer's microscope guide.^[ref]

At the low-magnification extreme, the probe scans the widest accessible field. Coil range, apertures, scan distortion and maintaining focus constrain the actual usable width. Formally increasing $d$ without bound would make $M$ arbitrarily small, but a real column has a finite accessible field.

At the high-magnification extreme, the scan covers a very small region. Formally $d\to 0$ makes $D/d$ diverge, but exactly zero scan width samples one location and supplies no spatial image. Electron microscope resolution, finite probe size, pixel spacing, drift, noise and specimen damage set the useful limit. Enlarging a field already sampled more finely than its resolvable information produces empty magnification, not new structural detail. For $N$ pixels across a field, the specimen sampling interval is $d/N$; this is distinct from the probe's spatial resolution.