Probabilistic Spectacle Performance Framework

Prescription and task

Right eye

Sphere (D) Cylinder (D) Axis (deg)

Left eye

Sphere (D) Cylinder (D) Axis (deg)

Task gaze H (deg) Task gaze V (deg) Gaze SD (deg)

Position of wear

RE monocular PD (mm) LE monocular PD (mm) COR separation (mm) RE height (mm) LE height (mm) Lens box B (mm) RE BVD (mm) LE BVD (mm) COR depth (mm) Pantoscopic tilt (deg) Face-form angle (deg) Lens index

Random variation

σ horizontal (mm) σ vertical (mm) σ depth (mm) σ tilt (deg) σ wrap (deg) σ twist (deg) PD observation SD (mm) Height observation SD (mm) BVD observation SD (mm)

Optical field and criteria

Corridor centre v (mm) dM/dv (D/mm) dJ₀/dv (D/mm) dJ₄₅/du (D/mm) |ΔM| limit (D) Cylinder-equivalent limit (D) Binocular-change limit (D) Prism excursion limit (Δ) Magnification limit (%)

Systematic error

Apply Rx error to Rx sphere error (D) Rx cylinder error (D) Rx error axis (deg) RE PD error (mm) LE PD error (mm) RE height error (mm) LE height error (mm) RE BVD error (mm) LE BVD error (mm) Panto error (deg) Wrap error (deg)

Simulation field

Trials per gaze cell Meaningful Q* deterioration ε Gaze step (deg) H minimum (deg) H maximum (deg) V minimum (deg) V maximum (deg) Seed

Ready.

Run the server model to calculate the paired comparison.

Rejection-risk index—model-derived optical risk

States crossing a criterion—integrated criteria

Baseline compatibility—at task gaze

Error compatibility—at task gaze

Signed difference—error minus baseline

Paired harm probability—Q* deterioration > ε

Systematic-error comparison across gaze

Results will be calculated on the server.

Interpretation boundary

The rejection-risk index is 1 − mean(Q*). It is an uncalibrated optical risk index and must not be interpreted as the percentage of patients who will reject the spectacles.

The intended and error scenarios use common random states. Signed differences therefore estimate the consequence of the stated systematic change rather than independent Monte Carlo noise.