Method for designing progressive addition lenses

• US 6,956,682 B2
• Filed: 06/26/2003
• Issued: 10/18/2005
• Est. Priority Date: 06/26/2003
• Status: Expired due to Term

• Current Assignee: Essilor International SA (EssilorLuxottica SA)
• Original Assignee: Johnson & Johnson Vision Care Incorporated (Johnson & Johnson)
• Inventors: Wooley, C. Benjamin
• Primary Examiner(s): Sugarman, Scott J.
• Assistant Examiner(s): Collins, Darryl J.
• Application Number:
  US10/606,391
• Publication Number:
  US 20040263778A1
• Time in Patent Office: 845 Days
• Field of Search: 351/159, 351/161, 351/169, 351/177
• US Class Current: 398/154
• CPC Class Codes: G02C 7/028 Special mathematical design techniques
• CPC Class Codes: G02C 7/061 Spectacle lenses with progressively varying focal power

Abstract

The invention provides a method for designing progressive surfaces and lenses produced using image blur to construct a merit function. The shape of a lens surface, or surfaces, is arbitrarily defined and optimized to minimize the image blur based merit function.

Claims

1. A method for designing a progressive addition lens, comprising a. ) describing a progressive addition surface;

and b.) optimizing the surface using a merit function of the formula;

MF=MF_blur+MF_power+MF_other

wherein;

MF_blur is a merit function that controls image blur;

MF_power is a merit function that controls the mean sphere power; and

MF_other is a merit function that controls constraints on cosmetics and manufacturability wherein the surface is described as a continuous, a differentially continuous, or a twice differentially continuous surface.

2. The method of claim 1, wherein the surface is described according to the equation:

${\mathrm{sag}}_{x,y}={\mathrm{Delta}}_{x,y}+\frac{c·<br><br>r^2}{1+\left[1-\left(1+k\right)·<br><br>c^2·<br><br>r^2\right]}+{\mathrm{\alpha <br><br>}}_1·<br><br>r^2+{\mathrm{\alpha <br><br>}}_2·<br><br>r^4+{\mathrm{\alpha <br><br>}}_3·<br><br>r^6+{\mathrm{\alpha <br><br>}}_4·<br><br>r^8+\mathrm{\dots <br><br>}$

wherein;

c is a surface curvature;

r is a radial distance from an optical axis of the lens;

k is a conic constant;

α

1, α

2, α

3, α

4 each are a coefficient; and

Delta_k,y is a delta sag that is a function of x and y.

3. A method for designing a progressive addition lens, comprising a.) describing at least two progressive addition surfaces;

and b.) optimizing the surfaces using merit functions of the formula;

MF=MF_blur+MF_power+MF_other

wherein;

MF_blur is a merit function that controls image blur;

MF_power is a merit function that controls the mean sphere power; and

MF_other is a merit function that controls constraints on cosmetics and manufacturability.

4. The method of claim 3, wherein the surfaces are each independently described as a continuous, a differentially continuous, or a twice differentially continuous surface.

5. The method of claim 3, wherein the surfaces are each described according to the equation:

${\mathrm{sag}}_{x,y}={\mathrm{Delta}}_{x,y}+\frac{c·<br><br>r^2}{1+\left[1-\left(1+k\right)·<br><br>c^2·<br><br>r^2\right]}+{\mathrm{\alpha <br><br>}}_1·<br><br>r^2+{\mathrm{\alpha <br><br>}}_2·<br><br>r^4+{\mathrm{\alpha <br><br>}}_3·<br><br>r^6+{\mathrm{\alpha <br><br>}}_4·<br><br>r^8+\mathrm{\dots <br><br>}$

wherein;

c is a surface curvature;

r is a radial distance from an optical axis of the lens;

k is a conic constant;

α

1, α

2, α

3, α

4 each are a coefficient; and

Delta_x,y is a delta sag that is a function of x and y.

6. The method of claim 3, 4, or 5, wherein MF_power is:

$\begin{array}{c}{\mathrm{MF}}_{\mathrm{power}}=<br><br>\underset{{\mathrm{\theta <br><br>}}_x}{\sum <br><br>}<br><br>\underset{{\mathrm{\theta <br><br>}}_y}{\sum <br><br>}<br><br>W<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varphi <br><br>}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{\Phi <br><br>}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-P_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2+\\ <br><br>{\mathrm{Wadd}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}<br><br>\left[{\left({\mathrm{AddF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-{\mathrm{PF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2+{\left({\mathrm{AddB}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-{\mathrm{PB}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2\right]\end{array}$

wherein

θ

_x is a horizontal eye rotation angle;

θ

_y is a vertical eye rotation angle;

RMS<sub>θ

x,θ

y</sub> is a RMS spot size calculated at an image of an eye lens;

Wrms<sub>θ

x,θ

y</sub> is a weight for a field position;

AddF<sub>θ

x,θ

y</sub> is a calculated add power on a front surface of the lens;

AddB<sub>θ

x,θ

y</sub> is a calculated add power on a back surface of the lens;

PF<sub>θ

x,θ

y</sub> is a target for an add power value for the front surface;

PB<sub>θ

x,θ

y</sub> is a target for an add power for the back surface; and

Wadd<sub>θ

x,θ

y</sub> is a weighting.

7. The method of claim 3, 4, or 5, wherein MF_power is:

$\begin{array}{c}{\mathrm{MF}}_{\mathrm{power}}=<br><br>{\mathrm{Wadd}}_{\mathrm{far}}<br><br>\left[{\left({\mathrm{AddF}}_{\mathrm{far}}-{\mathrm{PF}}_{\mathrm{far}}\right)}^2+{\left({\mathrm{AddB}}_{\mathrm{far}}-{\mathrm{PB}}_{\mathrm{far}}\right)}^2\right]+\\ <br><br>\left[\underset{{\mathrm{\theta <br><br>}}_x}{\sum <br><br>}<br><br>\underset{{\mathrm{\theta <br><br>}}_y}{\sum <br><br>}<br><br>W<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varphi <br><br>}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{\Phi <br><br>}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-P_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2\right]\end{array}$

wherein

θ

_x is a horizontal eye rotation angle;

θ

_y is a vertical eye rotation angle;

RMS<sub>θ

x,θ

y</sub> is a RMS spot size calculated at an image of an eye lens;

Wrms<sub>θ

x,θ

y</sub> is a weight for a field position;

AddF<sub>θ

x,θ

y</sub> is a calculated add power on a front surface of the lens;

AddB<sub>θ

x,θ

y</sub> is a calculated add power on a back surface of the lens;

PF<sub>θ

x,θ

y</sub> is a target for an add power value for the front surface;

PB<sub>θ

x,θ

y</sub> is a target for an add power for the back surface; and

Wadd<sub>θ

x,θ

y</sub> is a weighting.

8. The method of claim 3, 4, or 5, wherein MF_blur is:

$\begin{array}{cc}{\mathrm{MF}}_{\mathrm{blur}}=\underset{{\mathrm{\theta <br><br>}}_x}{\sum <br><br>}<br><br>\underset{{\mathrm{\theta <br><br>}}_y}{\sum <br><br>}<br><br>\left[{\mathrm{Wrms}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{RMS}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2+\text{\hspace{1em}<br><br>}<br><br>{\mathrm{Wast}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{AstF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-{\mathrm{AF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2\right]& \left(\mathrm{IX}\right)\end{array}$

wherein;

AstF<sub>θ

x,θ

y</sub> is either the surface astigmatism from the front surface or the contribution to the total lens astigmatism as seen by the eye from the front surface; and

Wast<sub>θ

x,θ

y</sub> are the weights placed on the unwanted astigmatism.

9. The method of claim 6, wherein MF_blur is:

$\begin{array}{cc}{\mathrm{MF}}_{\mathrm{blur}}=\underset{{\mathrm{\theta <br><br>}}_x}{\sum <br><br>}<br><br>\underset{{\mathrm{\theta <br><br>}}_y}{\sum <br><br>}<br><br>\left[{\mathrm{Wrms}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{RMS}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2+\text{\hspace{1em}<br><br>}<br><br>{\mathrm{Wast}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{AstF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-{\mathrm{AF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2\right]& \left(\mathrm{IX}\right)\end{array}$

wherein;

AstF<sub>θ

x,θ

y</sub> is either the surface astigmatism from the front surface or the contribution to the total lens astigmatism as seen by the eye from the front surface; and

Wast<sub>θ

x,θ

y</sub> are the weights placed on the unwanted astigmatism.

10. The method of claim 7, wherein MF_blur is:

$\begin{array}{cc}{\mathrm{MF}}_{\mathrm{blur}}=\underset{{\mathrm{\theta <br><br>}}_x}{\sum <br><br>}<br><br>\underset{{\mathrm{\theta <br><br>}}_y}{\sum <br><br>}<br><br>\left[{\mathrm{Wrms}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{RMS}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2+\text{\hspace{1em}<br><br>}<br><br>{\mathrm{Wast}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}·<br><br>{\left({\mathrm{AstF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}-{\mathrm{AF}}_{{\mathrm{\theta <br><br>}}_x,{\mathrm{\theta <br><br>}}_y}\right)}^2\right]& \left(\mathrm{IX}\right)\end{array}$

wherein;

AstF<sub>θ

x,θ

y</sub> is either the surface astigmatism from the front surface or the contribution to the total lens astigmatism as seen by the eye from the front surface; and

Wast<sub>θ

x,θ

y</sub> are the weights placed on the unwanted astigmatism.

11. The method of claim 3, further comprising c.) determining a set of coefficients to describe the lens surface to minimize e value of the merit function.

12. The method of claim 11, wherein step c.) is carried out by (i) selecting optimization variables that are a curve for a front surface and a curve for e back surface of the lens;

and (ii) minimizing MF_other.