parametric modeling of free-form surfaces for progressive ...€¦ · for progressive addition lens...

DAUR – Laboratory of Design Tools and Methods in Industrial Engineering Faculty of Engineering – University of Padua

[email protected]

IMProve 2011 Innovative Methods in Product Design

Venice June, 15th 17th

Parametric Modeling of Free-Form Surfaces for Progressive Addition Lens

G. Savio, G. Concheri, R. Meneghello

Open source code available at http://www.food4rhino.com/project/rp

http://www.food4rhino.com/project/rp



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th


G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Introduction: what’s PAL?

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example

- Influence of the parameters

- Industrial application

- Conclusion

The ability of the eye to bring near objects into focus is called accommodation.

Presbyopia: By the mid-40s, due to the growth of the lens, the accommodation decrease. “…Like death and taxis presbyopia is inevitable…” D. A. Atchison

Best solution for the presbyopia : Progressive Addition Lenses (PAL)

Astigmatic power Power

- Power increase continuously along the corridor. - Low astigmatism in the vision portion => Umbilics. - Low astigmatism and its gradient in the blending regions.


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Introduction: PAL & habits

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

- Different tasks required different amplitude of the near vision and the distance vision portion. - Different characteristics of the wearers (e.g. head or eye movement amplitude and velocity) require different designs.

In the vision the visual axis should cover only the optical zone which have low astigmatism.


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Introduction: Limits of the Trade SW?

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Several companies provide trading software for progressive lens design as: - Indizen Optical Technologies - Crossbows Optical Ltd - Scopus Optical Industries - Seiko - Shamir All these softwares give good solution for different habits for the mean of the population. The lenses design is characterized by the astigmatic power map and the power map. Usually these companies provide only few (3-4) different design.

These softwares do not allow a continuous variation of the amplitude of the distance or near vision portion or of the corridor length in order to better fit the characteristics of the wearer.

Moreover the mathematics involved are complex and often proprietary.

Astigmatic power Power

Off

ice

S

ho

rt c

orr

ido

r

(Crossbows web site)


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Method

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

To overcame the limit of the available trading softwares a specific modeling procedure was developed, which is based on a discrete definition of the points on the surface.

The proposed modeling process involves 3 steps: - geometric and optical parameters setting, - lens shape modeling -geometric models export and analysis.

In this work the method for designing a back progressive surface is explained. Analogously it is possible to design a front surface or a mould.


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Method: means of the parameters

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Geometric parameters A Lens diameter

B Y-coordinate of distance reference point

C Off-center (X-coordinate of distance

reference point)

D Inset (X-distance between distance

and near reference point)

E Corridor height

F Fitting cross

G Amplitude of the edge distance zone

H Amplitude of the edge near zone

Optical parameters P Power [D]

Add Addition [D]

n Refractive Index

PFS Front surface power (n=1.523) [D]

KD Distance aspheric coefficient

KN Near aspheric coefficient

FSFS PR /523

1)-(n10001)-(nCT-Rn1/1

FS

PncR DD

1)-(n10001)-(nCT-Rn1/1

FS

AddPncR NN


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Method: Shape Modeling

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Steps of the shape modeling procedure: 1) Aspheric far vision zone

The distance portion is delimited by a quadratic curve

2

,

2

,

2

2

,

2

,

,

ijiijiiii

ijiiji

ji

ycyxcxKcRcRc

ycyxcxz


G. Savio et. al.



G. Savio et. al.


AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Steps of the shape modeling procedure: 1) Aspheric far vision zone 2) Curvature equation along the corridor definition The curvature equation is defined as a polynomial equation. Coefficients are derived by geometrical constraints. Higher order derivative equal to zero means higher order polynomial.

Equation Constraints

DDN

DNDNa

ctcc

tcctcctc

3

45

)(10

)(15)(6)(

0t

c(t)d ,0

t

dc(t) ,cc(1)

0t

c(t)d ,0

t

dc(t) ,cc(0)

1

2

2

1

N

0

2

2

0

D

tt

tt

DDN

DNDNb

ctcc

tcctcctc

4

56

)(15

)(24)(10)(

As ca and 0t

c(t)d

0

3

3

t

DDNDN

DNDNc

ctcctcc

tcctcctc

45

67

)(35)(84

)(70)(20)(

As cb and 0t

c(t)d

1

3

3

t

DDNDN

DNDNd

ctcctcc

tcctcctc

56

78

)(56)(140

)(120)(35)(

As cc and 0t

c(t)d

0

4

4

t


G. Savio et. al.



G. Savio et. al.


AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Steps of the shape modeling procedure: 1) Aspheric far vision zone 2) Curvature equation along the corridor definition 3) Quadratic curves (x, y) in the intermediate area

A set of quadratic curves is used to cover the blending portion and the intermediate corridor.

01

2

2

01

2

2

)(

)(

t+bbtb

t+aata

ty

tx


G. Savio et. al.



G. Savio et. al.


AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Steps of the shape modeling procedure: 1) Aspheric far vision zone 2) Curvature equation along the corridor definition 3) Quadratic curves (x, y) in the intermediate area 4) Sampling and z-value calculation of the quadratic curves

The quadratic curves are sampled and then the z-coordinate value is calculated using the aspheric equation. The points of each quadratic curve are rotated in order to align the normal along the corridor.

2

,

2

,

2

2

,

2

,

,

ijiijiiii

ijiiji

ji

ycyxcxKcRcRc

ycyxcxz


G. Savio et. al.



G. Savio et. al.


AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Steps of the shape modeling procedure: 1) Aspheric far vision zone 2) Curvature equation along the corridor definition 3) Quadratic curves (x, y) in the intermediate area 4) Sampling and z-value calculation of the quadratic curves 5) Aspheric near vision zone


G. Savio et. al.



G. Savio et. al.


AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Steps of the shape modeling procedure: 1) Aspheric far vision zone 2) Curvature equation along the corridor definition 3) Quadratic curves (x, y) in the intermediate area 4) Sampling and z-value calculation of the quadratic curves 5) Aspheric near vision zone 6) Progressive surface orientation

To reduce the edge thickness the discrete surface is rotated.


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Method: analysis and data exchange

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Data exchange format Extension

File Version=1.2

[Properties]

Count=77

Interval=0.8

[Data]

3.723,3.578,3.436,3.299,…

3.674,3.529,3.388,3.250,…

…

*.hmf

-30.4 30.4 3.723

-30.4 29.6 3.578

-30.4 28.8 3.436

-30.4 28.0 3.299

-30.4 27.2 3.165

-30.4 26.4 3.036

…

*.xyz

21)1( kknSA

2)1( 21 kk

nSP

Surface optical power

Surface power Astigmatic surface power

Both optical properties and data to exchange are derived by a local quadratic fitting.


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Results: Examples

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

A plug-in for Rhinoceros V4 has been developed. Output: - Shape (mesh) - Astigmatic surface power (3D map and contour map) - Surface power (3D map and contour map) - Hmf file - xyz file


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Results: Influence of the parameters

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Increasing the order of the polynomial equation of the corridor, the maximum value of astigmatic surface power increases, while its variation is more smooth. P = 3.00 D, Add = 2.00 D 0 0.5 1

0

2 103

•

4 103

•

6 103

•

[1/m

m]

ca t( )

cb t( )

cc t( )

cd t( )

t

ca(t) Order 5 Max SA 1.58 D

cb(t)

Order 6 Max SA 1.64 D

cc(t) Order 7 Max SA 1.84 D

cd(t)

Order 8 Max SA 1.89 D


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Results: Influence of the parameters

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

1) Increasing addition, a proportional variation in the astigmatism map has been found.

2) Increasing the optical power of the lens, no significant change in astigmatism map has been found

3) Increasing the amplitude of the distance vision portion, the maximum astigmatic surface power increases.

4) Increasing the amplitude of the near vision area, the maximum astigmatic surface power increases.

5) Decreasing the corridor length, the maximum astigmatic surface power increases.

P = 3 D, Add = 2 D Max SA 1.92 D

P = 3 D, Add = 3 D Max SA 2.87 D

P = -3 D, Add = 2 D Max SA 1.92 D


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Results: Industrial application

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

Measurement of a manufactured mould by optical instrument (courtesy of IODA srl)

Theoretical Addition: 2.00 D Measured Addition: 1.99 D

Rotlex Class Plus


G. Savio et. al.



G. Savio et. al.

IMProve 2011 Venice June, 15th 17th Conclusion

AGENDA

- Introduction

- What’s PAL

- PAL & habits

- Limits

- Method

- Parameters

- Modeling

- Analysis

- Results

- Example



- Conclusion

In this work a method for the parametric design and analysis of progressive addition lens has been proposed. Both the optical and the geometrical parameters have been taken into account. In this way it is possible to better fit different characteristics and task of the wearer. Moreover the exchange data formats for the CNC manufacturing process and the method for numerical optical properties estimation were described. These are both based on a quadratic fitting. Numerical analyses highlight that, compared to the software available in the market, the proposed approach gives similar results. Preliminary experimental measurements show actual results are in good agreement with the numerical results. Next steps: - Establishing a correlation between geometric parameters and wearer characteristics. - Statistical evaluations on the wearer are needed. - Comparing the virtual results with the actual measurements given by optical or mechanical instruments.

DAUR – Laboratory of Design Tools and Methods in Industrial Engineering Faculty of Engineering – University of Padua

[email protected]

Thank you for your attention


G. Savio, G. Concheri, R. Meneghello

Open source code available at http://www.food4rhino.com/project/rp



parametric modeling of free-form surfaces for progressive ...€¦ · for progressive addition lens...

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