Light propagation through the eye: numerical considerations and applications to presbylasik surgery analysis Julián Espinosa Tomás Optics Department, University of Alicante Group of Optics and Vision Science Carlos Illueca, PhD. David Mas, PhD. Jorge Pérez, PhD. Julián Espinosa, MSc. Vissum Corporation, Alicante Jorge Alió, PhD. Dolores Ortiz, PhD. Esperanza Sala, OD. Light patterns calculation inside the eye Transmittance evaluation of cornea Transmittance evaluation of crystalline lens Wave propagation (angular spectrum) up to the plane of interest. Applications to presbylasik surgery analysis Corneal transmittance evaluation: - Geometrical configuration 2 surfaces 1st surface: Corneal topography 2nd surface: Dubbelman 2003 =6.6 − 0.005 × 2 2 2 R2 age xy+ +(1 + Qz2 ) − 2 Rz 2 = 0 Q2 = −0.1 − 0.007 × age Corneal transmittance evaluation: - Optical path length Crystalline lens transmittance evaluation Dubbelman 2001 (Scheimpflug photography ) x2+ y 2 +(1 + Qz ) 2 − 2 Rz = 0 = − × =−6.4 + 0.03 × Rant 12.9 0.057 age ; Qant age =− + × =−6.0 + 0.07 × Rpost 6.2 0.012 age ; Qpost age Crystalline lens transmittance evaluation opznzzii≈+1( 21 ii −)cosδ 102 i +∆−( z i) cos ( δ 12 ii + δ ) Wave propagation Convergent patterns calculation λz exp −iπ m ɶ 2 × ()∆x 2 0 ()u∝ DFT −1 z µ 2 m∆ x m2 ()∆ x ×DFT u0 − i π 0 1 0 exp 2 N λ N z c ∆x2 z≤0 ≤ z Nyquist condition λN c zc = 20mm λ = 633nm Total eye ∆x= 6.7mm N = 3600 0 Φ =3 ∆x p()4 0 Wave propagation 2 ∆x0 Nyquist condition: Nλ ≥ zc N κ >1 N′ = λ′ = κλ Let us define , κ and 1 1 ∆ξ ∆ξ = ∆ξ ′ = = ′ δ x0 δx0 κ ′ ′ ∆x0 ∆ξ = N ∆x0 = ∆ x z ∆ξ′ ∆x= N ′ z Wave propagation Rectangle function κ=1 vs. κ=4 zc= 20 mm ∆x0=6.7 mm N=3600 Prop. distance (mm) Intensity error (sd) Phase error (sd) 18 4.47% 1.12% 19 3.61% 0.48% 20 0.52% 1.98% 21 3.98% 4.73% 22 4.70% 10.28% Wave propagation Wave propagation Wave propagation zc = 20mm λ = 633nm Total eye ∆x= 6.7mm N = 3600 0 Φ =3 ∆x p()4 0 mm-1 −1 δx0= ∆ x 0 / N ≈ 3 λ ∆ξ ≈ 540 ≈ 82 cdeg −1 Visual Acuity =1.3 40c deg Lossless subsampling by a factor κ = 2 Application Optical quality of the eye after presbylasik surgery Correction for presbyopes with hyperopia Multifocal corneal ablation Decimal VA estimation Pseudo accommodation range Application Optical quality of the eye after presbylasik surgery Chaubard 2003 Application Optical quality of the eye after presbylasik surgery Chaubard 2003 Application Optical quality of the eye after presbylasik surgery Far Vision Correction Combined Treatment Near Vision Correction Chaubard 2003 Application Optical quality of the eye after presbylasik surgery Central Presbylasik surgery (H. Eye Tech. Technovision excimer laser platform) Subjects 8 hyperopic eyes Mean age: 57 years Mean preoperative spherical equivalent refraction: 1.28 ±±± 0.87 D Mean preoperative VA: 1.02 ±±± 0.13 (corrected) 0.37 ±±± 0.15 (uncorrected) Presbyopia: <2 D Clinical results Mean postoperative spherical equivalent refraction: -0.46 ±±± 0.49 D Mean postoperative VA: 0.95 ±±± 0.09 (corrected) 0.72 ±±± 0.18 (uncorrected) Results 1 y = 0,925x + 0,060 R2 = 0,740 0,8 0,6 0,4 0,2 Subjective Subjective Visual Acuity 0 0 0,2 0,4 0,6 0,8 1 Calculated Visual Acuity Objective results φ=4 mm Pseudo accommodation range: 1.3 ±±± 0.4 D Near distances φ=3 mm Acc=+1 D Far distances φ=5 mm.