Light propagation through the : numerical considerations and applications to presbylasik surgery analysis

Julián Espinosa Tomás

Optics Department, University of Alicante Group of 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. patterns calculation inside the eye

Transmittance evaluation of

Transmittance evaluation of crystalline

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 =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 platform) Subjects

8 hyperopic

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