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 − δ)cosδ 102 i +∆−( z i) cos ( 12 ii + ) 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 κδ x0
′ ′ ∆ ∆ξx0 = 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 λ ∆ δ x0= x 0 / N ≈ 3 ∆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