Four Centuries, One Constant: The Resolution Bound of the Scheiner-Disc Self-Refractor

The Scheiner disc - two pinholes before the eye, through which a point of light appears double whenever focus is imperfect - is the oldest self-refraction principle in optics, described in 1619, and periodically reinvented as a low-cost refractor. This paper computes its resolution bound: the smallest defocus a user can detect, as a function of pinhole separation, against a stated criterion that a doubling separation of 2 minutes of arc is reliably seen. At a 2 mm separation the bound is 0.51 D; at 3 mm it is 0.34 D; at the largest separation a pupil admits, the principle cannot resolve the quarter-dioptre step that dispensing requires. The verdict is therefore bounded but real: a Scheiner device is a screening instrument that can sort eyes into half-dioptre bands and find gross error cheaply, and it is not a refractor, whatever its packaging claims. A design for the honest version - 3 mm separation, forced-choice doubling judgement, banded output - is specified. This study is simulated, not measured.