An Honest Optics Bound for Adjustable-Focus Spectacles: Delivered Power Range, Usable Field, and the Astigmatism Ceiling of Alvarez and Fluid-Membrane Lenses

Adjustable-focus spectacles (laterally shifted Alvarez lens pairs; fluid-filled membrane lenses) are promoted as one product that replaces individual refraction. This paper computes, from stated first-order optics and stated aberration models, what they can deliver. An Alvarez pair (cubic coefficient 1000 m-2, index 1.52, shift up to 3.25 mm per plate) gives a mechanical range of +/-6.76 D, is clean on axis (0.001 D mechanism blur), but spends half the 6/12 blur budget (0.8025 D) by 6 mm pupil eccentricity (12.5 degrees gaze) at +/-6.00 D. A fluid membrane lens (15 mm semi-aperture, fluid index 1.40) reaches +5.00 D at 1.419 mm centre deflection and about 0.26 kPa pressure, is capped at +/-5.11 D by a 1.45 mm deflection limit, and has negligible spherical aberration (at most 0.011 D). Neither spherical-only mechanism corrects astigmatism: uncorrected cylinder alone exhausts the 6/12 budget at 1.60 D and coverage is 0.0% at 2.00 D or more of cylinder in the less astigmatic eye. In a stated population of 91,106 adults with purely refractive impairment, the Alvarez design serves 94.2% (better eye) but only 66.4% with both eyes at 6/12; the membrane design serves 90.7% and 62.4%. At stated unit costs of $30 and $42, cost per both-eyes-served wearer is $45.18 and $67.31. Conclusion: sound bounded spherical adjusters; as replacements for refraction they fail, computably, on astigmatism for roughly one wearer in three. SIMULATED, NOT MEASURED.