The Pinhole Aperture That Minimises Blur: An Optimum Diameter, Its Acuity Ceiling, and a Test of the Claim That Smaller Is Sharper

Pinhole spectacles are sold in fixed apertures, often with the suggestion that a smaller hole gives sharper sight. That suggestion does not survive a standard blur calculation. For an eye with defocus, geometric blur grows in proportion to aperture while diffraction blur grows as aperture shrinks; combining the two at 550 nm gives, for 2 D of defocus, a minimum total blur of 7.96 minutes of arc at an aperture of 0.82 mm - an acuity near 20/159, and 3.46 times sharper than the naked 4 mm pupil, though still well short of a proper lens. A 0.5 mm hole is 1.24 times blurrier than the optimum, not sharper, and passes only a small fraction of normal light. Because the optimum moves with the wearer's defocus - 1.16 mm at 1 D, 0.67 mm at 3 D - the design rule is a compromise aperture near 1.0 mm for general stock, with the table below showing what each defocus level gains and loses by it. This study is simulated, not measured.