Patricia Rosales and Susana Marcos, "Phakometry and lens tilt and decentration using a custom-developed Purkinje imaging apparatus: validation and measurements," J. Opt. Soc. Am. A 23, 509-520 (2006)
We present a Purkinje imaging system for phakometry and measurement of tilt and decentration of crystalline and intraocular lenses (IOLs). Crystalline lens radii of curvature were estimated by using both a merit function and the equivalent mirror approaches. Tilts and decentrations were estimated by using Phillips’s linear analysis. We present a complete validation of the technique through exhaustive computer simulations and control experiments, and measurements in 17 normal eyes (mean age ) and nine postcataract surgery eyes (mean age ). Crystalline lens radii ranged from 12.7 to 8.81 mm and from to for anterior and posterior surfaces, respectively. Crystalline lens tilt ranged from 2.8 to horizontally and from 2.58 to vertically. Crystalline lens decentration ranged from 0.09 to 0.45 mm horizontally and from 0.09 to vertically. IOL tilt ranged from 3.6 to horizontally and from 5.97 to vertically. IOL decentration ranged from 0.53 to horizontally and from 0.13 to vertically.
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Model Eye with Spherical Surfaces for 880 nm in Zemax with Herzberger Formula [Eq. (3)]
Retrieved Values
Eye Model Nominal Values
Equivalent Mirror
Merit Function
Anterior Corneal Radius (mm)
Posterior Corneal Radius (mm)
Anterior Chamber Depth (mm)
Lens Thickness (mm)
Lens Decentration (mm)
Lens Tilt (deg)
Anterior Lens Radius (mm)
Posterior Lens Radius (mm)
Anterior Lens Radius (mm)
Posterior Lens Radius (mm)
Anterior Lens Radius (mm)
Posterior Lens Radius (mm)
7.73
6.5
3.61
4
0
0
10
−6
10.15
−7.35
9.96
−6.51
7.73
6.5
3.61
4
0
0
12
−6
12.13
−7.04
11.94
−6.27
7.73
6.5
3.61
4
0
0
14
−6
13.99
−7.35
13.80
−6.53
7.73
6.5
3.61
4
0
0
10.45
−6
10.68
−7.12
10.32
−6.15
7.73
6.5
3.61
4
0
0
10.45
−5
10.68
−6.03
10.32
−5.28
7.73
6.5
3.61
4
0
0
10.45
−4
10.68
−5.06
10.32
−4.48
7.73
6.5
3.61
4
1
5
10.45
−6
10.18
−7.55
9.79
−6.46
8.5
6.5
3.61
4
0
0
10.45
−6
10.49
−7.03
10.23
−6.19
7.5
6.5
3.61
4
0
0
10.45
−6
10.55
−7.16
10.14
−6.14
6.5
6.5
3.61
4
0
0
10.45
−6
10.69
−6.88
10.08
−5.69
7.73
6.5
3.61
4
0
0
10.45
−6
10.56
−7.24
10.19
−6.24
7.73
6
3.61
4
0
0
10.45
−6
10.57
−7.21
10.19
−6.22
7.73
5.5
3.61
4
0
0
10.45
−6
10.48
−6.97
10.11
−6.03
7.73
6.5
4
4
0
0
10.45
−6
10.92
−7.52
10.54
−6.47
7.73
6.5
3.5
4
0
0
10.45
−6
10.58
−7.27
10.21
−6.27
7.73
6.5
2
4
0
0
10.45
−6
10.57
−7.19
10.19
−6.26
7.73
6.5
3.61
3
0
0
10.45
−6
10.7
−5.91
10.84
−5.17
7.73
6.5
3.61
3.5
0
0
10.45
−6
10.7
−6.64
10.84
−5.75
7.73
6.5
3.61
4
0
0
10.45
−6
10.7
−6.97
10.84
−6
Table 2
Realistic Model Eye with Aspheric Surfaces, Anterior Corneal Elevation from Corneal Topography, Gradient Refractive Index in the Lens, and Lens Tilt and Decentration
Asphericity defined for this surface is , where the Z axis is the optical axis, is the vertex radius of curvature, and Q is the surface asphericity.
Third- and higher-order corneal surface rms (fitted to a seventh-order Zernike polynomial), without spherical terms and .
Equivalent refractive index: gradient index (GRIN) profile in the equatorial plane defined by Garner et al.[23] , where is the refractive index in the center of the lens, b is the equatorial radius, and is the GRIN shape factor.
Tables (2)
Table 1
Model Eye with Spherical Surfaces for 880 nm in Zemax with Herzberger Formula [Eq. (3)]
Retrieved Values
Eye Model Nominal Values
Equivalent Mirror
Merit Function
Anterior Corneal Radius (mm)
Posterior Corneal Radius (mm)
Anterior Chamber Depth (mm)
Lens Thickness (mm)
Lens Decentration (mm)
Lens Tilt (deg)
Anterior Lens Radius (mm)
Posterior Lens Radius (mm)
Anterior Lens Radius (mm)
Posterior Lens Radius (mm)
Anterior Lens Radius (mm)
Posterior Lens Radius (mm)
7.73
6.5
3.61
4
0
0
10
−6
10.15
−7.35
9.96
−6.51
7.73
6.5
3.61
4
0
0
12
−6
12.13
−7.04
11.94
−6.27
7.73
6.5
3.61
4
0
0
14
−6
13.99
−7.35
13.80
−6.53
7.73
6.5
3.61
4
0
0
10.45
−6
10.68
−7.12
10.32
−6.15
7.73
6.5
3.61
4
0
0
10.45
−5
10.68
−6.03
10.32
−5.28
7.73
6.5
3.61
4
0
0
10.45
−4
10.68
−5.06
10.32
−4.48
7.73
6.5
3.61
4
1
5
10.45
−6
10.18
−7.55
9.79
−6.46
8.5
6.5
3.61
4
0
0
10.45
−6
10.49
−7.03
10.23
−6.19
7.5
6.5
3.61
4
0
0
10.45
−6
10.55
−7.16
10.14
−6.14
6.5
6.5
3.61
4
0
0
10.45
−6
10.69
−6.88
10.08
−5.69
7.73
6.5
3.61
4
0
0
10.45
−6
10.56
−7.24
10.19
−6.24
7.73
6
3.61
4
0
0
10.45
−6
10.57
−7.21
10.19
−6.22
7.73
5.5
3.61
4
0
0
10.45
−6
10.48
−6.97
10.11
−6.03
7.73
6.5
4
4
0
0
10.45
−6
10.92
−7.52
10.54
−6.47
7.73
6.5
3.5
4
0
0
10.45
−6
10.58
−7.27
10.21
−6.27
7.73
6.5
2
4
0
0
10.45
−6
10.57
−7.19
10.19
−6.26
7.73
6.5
3.61
3
0
0
10.45
−6
10.7
−5.91
10.84
−5.17
7.73
6.5
3.61
3.5
0
0
10.45
−6
10.7
−6.64
10.84
−5.75
7.73
6.5
3.61
4
0
0
10.45
−6
10.7
−6.97
10.84
−6
Table 2
Realistic Model Eye with Aspheric Surfaces, Anterior Corneal Elevation from Corneal Topography, Gradient Refractive Index in the Lens, and Lens Tilt and Decentration
Asphericity defined for this surface is , where the Z axis is the optical axis, is the vertex radius of curvature, and Q is the surface asphericity.
Third- and higher-order corneal surface rms (fitted to a seventh-order Zernike polynomial), without spherical terms and .
Equivalent refractive index: gradient index (GRIN) profile in the equatorial plane defined by Garner et al.[23] , where is the refractive index in the center of the lens, b is the equatorial radius, and is the GRIN shape factor.