Design of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding process

Design of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding processDesign of multifocal contact lens with nurbs and shrinkage analysis on shell mold by injection molding process

DESIGN OF MULTIFOCAL CONTACT LENS WITH NURBS

AND SHRINKAGE ANALYSIS ON SHELL MOLD BY

INJECTION MOLDING PROCESS

DEPARTMENT OF MECHANICAL ENGINEERING PRECISION MANUFACTURING LABORATORY

Taipei, May 4 2 0

Dissertation defense for the Degree of Doctor of Philosophy

presented by Vu Thi Lien

Committee : Prof Sen-Yeu Yang (Chair)

Prof Jong-Woei Whang

Dr Kuo-Cheng Huang Prof Pei-Jen Chung

Dr Yi-Sha Ku Prof Chien-Yu Chen Prof Chao-Chang A Chen

Specific studies

Overview of contact lens design

Presbyopia and correction methods

A loss of accommodation with age (>40 ) to focus on nearby objects

when the crystalline lens becomes harder and loses elasticity and

causes light to focus behind the retina.

• More convenient (sport activities)

Two vision distances (near and far)

Power distributions of CLs for presbyopic correction [42-44]

Dop=6.0 mm

oneday-for-presbyopia/

5

Power profiles of commercial simultaneous multifocal CLs

Additional (Add) powers (low, mid, high) from +0.75 to 3.50 D

[87]

[89]

The power profile of a zonal-aspheric

multifocal CL

Problem statement

Current problems for multifocal CL designs:

with more and more requirements.

presents as the best design.

Lens shapes, materials and manufacture

methods need to be continuously improved.

The Add range of commercial soft multifocal CLs [68]

Continuity problem of zonal aspheric designs

Curvature continuity ?

Smooth connection

Research Objectives

 Development of a design method of symmetric simultaneous multifocal CLs with:

 A comprehensive method from clinical requirements for calculation and output data for analysis and manufacture.

Chapter 6: Conclusion and recommendation

Design & manufacture method of

multifocal CLs

Chapter 1

Overview of contact lens design

Contact lens history

Contact lens types

• Correction of Astigmatism

• Less comfortable, tough adaptation

• Larger & adhere more tight to the cornea

• Don’t correct astigmatic error

 Rigid Gas Permeable (RGP) CLs

 Soft CLs

 Hybrid CLs [109]

Fitting types of RGP contact lenses

Scleral contact lens

Fitting areas between CLs and eye (front view) [99]

Aspheric curves

2

2 2

i i

Aspheric design for CLs:

i i

Extended polynomial function

Conventional aspheric function

Conic curves with different conic constants

14

Freeform surfaces

Great flexibility and precision to present freeform shapes

Non Uniform Rational B-spline (NURBS)

,1

,1

( ) P ( )

( )

h

i p i i i

h

i p i i

1 ( )

NURBS commonly used in CAD, CAM, and CAE for generating

and representing freeform curves and surfaces.

( )

R u

k u



The curvature of an arbitrary point Q on the NURBS curve is:

The radius of curvature of point Q is:

Center of curvature of point Q is:

N(u) is an unit normal vector at point Q:

'( ) "( ) '( ) ( )

Anterior surface curvature: k a =1/R a  NURBS curve

Back vertex power (Pw):

A NURBS multifocal CLs with given

optical power distributions

sign: “-” for center-near and “+” for center-distance

Cumulative distribution function (CDF)

2 2

( )2center

20

2 2

2 mod

Two-zone optical power profiles

A.2 Functions of two-zone and one-zone optical power profiles

2 mod

A.3 Optimization problem

Given parameters (clinical requirement)

NURBS curve C(u)

(Three unknown parameters)

3

'( ) ''( ) ( )

1/2 2

1

1/2 2

i

m

i i i

Goal

C5 Optimization by Simulated Annealing algorithm

Initial conditions: X 0 , T 0 , Functions:F Obj , g(T,k), q(L,k), N(X) Stop conditions: T min , Max_Iter, k=0, Iter=0, L 0 , i=0

k=k+1 i=0

N N

1

m Obj i i

1/ v 0

A.5 Case study: Four PMMA multifocal CL designs

Table of given parameters

Generation of

power profiles

Case Center

power (D)

Add powers (D)

Base curves (mm)

Overall diameters (mm)

5.0 7.5 10.5 6.0 0.14 0 3

2 -4.0 (CD)

5 0 7.5 10.5 6.0 0.14 0 3

3 -4.0 (CD)

5 0 7.5 10.5 6.0 0.14 1.4 1.6

4 -2.0 (CN)

5.0 7.5 10.5 6.0 0.14 0.8 1.2

Note: CN: center-near; CD: center-distance The refractive index of PMMA:n=1.49

One-zone optical power profiles

Two-zone optical power profile Three-zone optical power profile

Optimization of NURBS curves

Large central zone

A.7 Optimized parameters of NURBS curves

NURBS curve vs Extended polynomial

In consideration of No of variables, 9 control

points are used for all designs

Selection of number control points

Higher precision and flexibility

Results of Case 1

No. Weights

w

Knot vector U

Control points NURBS curve

26

A.8 Generation of 3D lens models

Optimization

3D lens models (Case 1)

2D lens models (Case 1)

Optical

Simulation

Case 1Case 2Case 4Case 3

A.9 Optical simulation and manufacture

3D lens models

Simulation in ZEMAX

Power maps of four lens models

Manufacture

Design vs simulation power parameters

Ultra-precision ophthalmic lathe for contact lenses (Fantasee Incorporated, New Taipei City)

A.10 Results and discussions

Hard (PMMA) CLs samples

Power maps of four lens samples

Design, simulation, and measurement

power parameters

Measurement

developed method can be applied for multifocal CL design.

Case 4 Case 3

B NURBS multifocal contact lens with

uniform optical power in center-distance zone

30

B.1 Problems of soft multifocal CLs

Two measured power profiles of two different soft CL designs with the same requirement of the uniform powers in large central zones with radii of 1.2 mm

Non-uniform power in the central zones of soft multifocal contact lens samples

B.2 Solution for uniform power in center-distance zone

Weighted sum method:

where , , , and  are weighting factors and

Solving by SA algorithm

Priority High value

Smooth power profile

& high value

1 fitting_center

Total Add (D)

Base radius (mm)

Overall diameters (mm)

B.6 Four soft CLs with uniform power in center-distance zones

Spherical Aspheric

The allowable Addcenterof lens samples in Case 9 is 0.5 D

B.8 Simulation and measurement results of power profiles

Aspheric

Aspheric

• The power in the central zone of Case 6 (spherical central curve) is non-uniform.

• Small Addcenter values of Case 7 to 9  almost uniform

• The shape of NURBS curve in center-distance zones should be similar aspheric curves with small Add to obtain uniform power.

The power error curves in the central zones

39

B.10 Clinical test analysis

zones has been verified.

requirements.

C Minimization of shrinkage error of shell mold

(SM) in injection molding (IM) process

41

C.1 Problems of soft multifocal CL samples

The measured results of some soft lens samples of different designs that are designed by the developed method have non-uniform power in the large central zones

Z-shrinkage error of shell mold for casting CLs should be considered and minimized.

Measured power profiles with central zone radius of 1.2 mm: a) Center power

of -7.0D, b) Center power of -8.0D.

C.2 Solution

Clinical requirements of Soft multifocal CLs (Power distribution, material, diameters,

thickness ), scale factor s1and s2

Original design of soft multifocal CLs

Dry lens (DR lens)

casting Hydration

Reconstruction of DE

lens from shrinkage curve of shell mold

Minimization of shrinkage error by optimizing IM parameters

Z-Optical simulation and anslysis

Power compensation in the central zones (Compensated DE lenses)

Expansion (1/s 2 )

Reversed DE lens

Compensated DE lenses

Soft multifocal CLs samples

of original lens designs.

Minimization method of Z-shrinkage error of anterior shell molds (SMs)

Methodology flowchart

43

C.3 Injection molding design for PP polymer

Design parameters of optical region of soft multifocal CL

Case 10

Expansion factor S1

Design parameters of optical region

Centerpower(D)

TotalAdd(D)

Addcenter(D)

Centralzonediameter(mm)

Totalopticalregiondiameter(mm)

Centerthickness(mm)

Basecurve(mm)

Refractiveindex

SO lens -9.0 8.0 < 0.5 2.4 6.0 0.08 8.6 1.43

DE lens -9.0 12.0 0.4 3.0 7.4 0.08 8.6 1.43

Reduction factor S2

Mold flow simulation

Z-shrinkage error at the measured

point i-th where i is from 1 to 401

Warpage displacement

Z Zs m



 

the sags of the anterior SM profile and its

shrinkage profile corresponding to the point ith.

Results of ANOVA analysis DOE table and results of simulations

Optimal parameters

C.6 Z-shrinkage of original SM design

Highest Z-shrinkage

E.7 Compensation of Add power in central zone

Cases Case 10_V1 Case 10_V2 Case 10_V3

Added Add powers

Closest to the original curve

49

C.9 Optical power simulation after shrinkage

Optical power simulations in central zones of the reversed CLs

The most uniform

Manufacture

50

C.10 Manufacture

Original design Compensated deign with 25% Addcenter

a) One female mold insert b) Two male mold inserts c) Shell molds

d) Contact lens samples

51

C.11 Results and discussions

Power profiles of soft multifocal CLs of Case 10 (original

design) Power profiles of soft multifocal CLs of Case 10_V1 with 25% increasing in Addcenter

Conclusions and Recommendations

53

Conclusions

1 This study has developed a new and efficient design method of simultaneous multifocal CLs

to adapt various given smooth power distributions with high Add power values and uniform power in large central zones for different pupil diameters by optimizing three parameters of NURBS curves.

2 The mathematical functions have been developed to generate various smooth power profiles based on clinical requirements.

3 A solution for design of soft multifocal CLs with uniform optical power in large center– distance zones has been proven.

4 Z-shrinkage errors in IM process of the anterior SMs corresponding to the anterior surfaces

of multifocal CLs are minimized by both optimizing IM parameters and compensating Addcenter powers.

5 This developed method has been verified and proven the feasibility by experiment results of both rigid and soft multifocal CLs.

54

Recommendations

1 The current design program can be also developed

to simulate the optical performance directly in Matlab.

2 This method can be extended to design and

manufacture soft multifocal CLs having three optical

zones.

3 This method can be extended to design

non-symmetric CLs to correct astigmatism of human eye

with NURBS surface.

4 In addition, this method can be applied to design

other optical lenses with freeform surfaces.

Unsuccessful design

Commercial soft multifocal CLs

Design program of multifocal CLs in Matlab

2 L T Vu, C C A Chen, and C W Yu, "Optical design of soft multifocal contact lens with uniform optical power in center-distance zone with optimized NURBS," Optics Express 26(3): 3544-3556 (2018) SCI, IF: 3.307 (Q1: 17/92, Optics)

3 L T Vu, C C A Chen, and J T P Shum,"Analysis on multifocal contact lens design based on optical power distribution with NURBS," Applied Optics 56(28): 7990-7997 (2017) SCI, IF: 1.65 (Q2: 50/92, Optics).

4 C C A Chen, L T Vu, and Y T Qui, "Study on Injection Molding of Shell Mold for Aspheric Contact Lens Fabrication," Procedia Engineering 184: 344-349 (2017) SCOPUS

5 L T Vu, C C A Chen, and Y T Qui, “Optimization of aspheric multifocal contact lens by spline curve,” SPIE/COS Photonics Asia, SPIE (2016) EI

1 Present at Advances in Materials and Processing Technologies Conference (AMPT 2016), 8-11 November 2016 Kuala Lumpur, Malaysia.

2 Present at SPIE/COS Photonic Asia Conference, 12-14 October 2016, Beijing, China.

L T Vu, C C A Chen, and Y T Qui, “Progressive multifocal contact lens and producing method thereof” US 2018/0024380 A1 and TW I584022 (2017).

I am particularly grateful to Prof Chao-Chang A Chen, my advisor, who not only shared the

perspectives, knowledge, expertise, and passion, but also provided a genuine caring presence throughout the journey.

I would like to express my appreciation to Taiwan Tech for the scholarship during four years and

Department of Mechanical Engineering for the great academic environment.

I am thankful all members of Precision Manufacturing Lab, especially molding group members for

your encouragement and invaluable contributions.

I am deeply thankful to Dr Patrick Joi-Tsang Shum and his company, Fantasee Incorporated and to

Mr Shiang Yao, Jeng and his company, Seinoh Optical Co., Ltd for very important contributions to do

my experiments.

A special thanks to my family and friends Words cannot express how grateful I am to their encouragement, support and belief in me that help me overcome any hardships.

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