Optics, Refractometry, and Contact Lenses
Refractive Error and Lens Power
Emmetropia is the unaccommodated eye focused at infinity. Myopia is corrected with minus (diverging) lenses, hyperopia with plus lenses, and regular astigmatism with a spherocylinder. Spherical equivalent equals sphere plus half the cylinder. Transposition converts plus-cylinder to minus-cylinder form without changing the lens: keep the sphere, add the cylinder to it, change the cylinder sign, and rotate the axis 90 degrees.
Measurement and Contact Lens Fitting
Retinoscopy, autorefraction, and subjective refinement all estimate the correction; vertex distance matters most above about plus or minus 4 D, because moving a minus lens away from the eye increases its effective power and a plus lens decreases it. Keratometry measures central corneal curvature; topography maps the whole surface and flags irregular astigmatism such as keratoconus.
Soft lenses are fit with a base curve slightly steeper than the flattest keratometry reading, adequate diameter for centration, and oxygen transmission expressed as Dk/t. Rigid gas permeable lenses are judged by fluorescein pattern: apical alignment with peripheral clearance. Daily-wear and extended-wear schedules, replacement frequency, and care solutions must be documented.
Traps: axis transposition errors (180 becomes 090, not 000), forgetting that with-the-rule astigmatism has the steeper meridian near 90 degrees, and assuming higher water content always means more oxygen.
Rule of thumb: transposition check - the two written forms of the same lens must produce the same spherical equivalent.
Worked example: +2.00 −3.00 × 180 transposes to −1.00 +3.00 × 090. Sphere: 2.00 + (−3.00) = −1.00; cylinder sign flips; axis rotates 90 degrees.