Designing lenses using stress birefringence performance criterion

• US 8,504,328 B2
• Filed: 05/21/2010
• Issued: 08/06/2013
• Est. Priority Date: 05/21/2010
• Status: Active Grant

• Current Assignee: IMAX Theatres International Limited (IMAX Corporation)
• Original Assignee: Eastman Kodak Company
• Inventors: Bietry, Joseph R., Kurtz, Andrew F., Silverstein, Barry D., Mazzarella, James
• Primary Examiner(s): Craig, Dwin M
• Application Number:
  US12/784,521
• Publication Number:
  US 20110288824A1
• Time in Patent Office: 1,173 Days
• Field of Search: 703/1, 353/20
• US Class Current: 703/1
• CPC Class Codes: G02B 13/16 for use in conjunction with image converters or intensifiers , or for use with projectors, e.g. objectives for projection TV
• CPC Class Codes: G02B 13/22 Telecentric objectives or lens systems
• CPC Class Codes: G02B 7/028 with means for compensating for changes in temperature or for controlling the temperature; thermal stabilisation

Abstract

A method for designing an imaging lens having reduced susceptibility to thermally-induced stress birefringence, the imaging lens having first and second groups of lens elements located either side of an aperture stop, the method comprising: defining a set of lens design attributes; defining a set of lens performance criteria including a thermally-induced stress birefringence performance criterion; defining a first set of candidate glasses having a negligible susceptibility to thermal stress birefringence and a second set of candidate glasses having at most a moderate susceptibility to thermal stress birefringence; selecting glasses for lens elements that are located adjacent to the aperture stop from the first set of candidate glasses; selecting glasses for the remaining lens elements from the first or second sets of candidate glasses; and using a computer processor to determine a lens design for the imaging lens.

Claims

1. A method for designing an imaging lens having reduced susceptibility to thermally-induced stress birefringence for imaging an object plane to an image plane, the imaging lens having an aperture stop positioned between the object plane and the image plane, a first group of lens elements located on the object plane side of the aperture stop, and a second group of lens elements located on the image plane side of the aperture stop, the method comprising:

defining a set of lens design attributes that describe the geometrical properties of the lens;

defining a set of lens performance criteria, including one or more image quality performance criteria and a thermally-induced stress birefringence performance criterion;

defining a first set of candidate glasses having a negligible susceptibility to thermal stress birefringence as characterized by a thermal stress birefringence metric;

defining a second set of candidate glasses having more than a negligible susceptibility to thermal stress birefringence but at most a moderate susceptibility to thermal stress birefringence as characterized by the thermal stress birefringence metric;

selecting glasses for lens elements in the first and second groups of lens elements that are located immediately adjacent to the aperture stop from the first set of candidate glasses;

selecting glasses for the lens elements in the first and second groups of lens elements that are not located immediately adjacent to the aperture stop from the first or second sets of candidate glasses; and

using a computer processor to determine a lens design for the imaging lens which achieves the lens design attributes while satisfying the defined lens performance criteria, wherein the lens design specifies thicknesses, spacings, shapes, and glasses for the lens elements in the first and second groups of lens elements, wherein the thermal stress birefringence metric includes factors relating to a coefficient of thermal expansion of the glass, a stress optical coefficient of the glass and a light absorption coefficient of the glass.

2. The method of claim 1 wherein the thermal stress birefringence metric further includes at least one additional factor relating to a modulus of elasticity of the glass, a thermal conductivity of the glass, a Poisson'"'"'s ratio of the glass, an optical power density in the glass, a thickness of the lens element or a clear aperture size of the lens element.

3. The method of claim 1 wherein the thermal stress birefringence metric is given by:

M₁′

=ρ

κ

α

where ρ

is the coefficient of thermal expansion, κ

is the stress optical coefficient, and α

is the light absorption coefficient.

4. The method of claim 1 wherein the thermal stress birefringence metric is given by:

M₁=ρ

κ

α

E/(K·

(1−

μ

)).

where ρ

is the coefficient of thermal expansion, κ

is the stress optical coefficient, α

is the light absorption coefficient, E is the modulus of elasticity, K is the thermal conductivity, and μ

is Poisson'"'"'s ratio.

5. The method of claim 4 wherein glasses in the first set of candidate glasses satisfy the condition that M₁≦

0.1×

10<sup>−

6</sup> W<sup>−

1</sup> and glasses in the second set of candidate classes satisfy the condition that 0.1×

10<sup>−

6</sup> W<sup>−

1</sup>≦

M₁≦

1.60×

10<sup>−

6</sup> W<sup>−

1</sup>.

6. The method of claim 1 wherein the lens design attributes describing the geometrical properties include a lens focal length, F/#, a lens magnification or a lens working distance.

7. The method of claim 1 wherein the image quality performance criteria include a modulation transfer function criterion or a point spread function criterion.

8. The method of claim 1 wherein the thermally-induced stress birefringence performance criterion is based on an aggregate thermal stress birefringence metric which combines intensity-weighted thermal stress birefringence metrics determined for each of the lens elements in the imaging lens.

9. The method of claim 8 wherein the intensity-weighted thermal stress birefringence metric is given by:

M₂=I₀ L ρ

κ

α

E/(K·

(1−

μ

)).

where I₀ is the optical power density in the glass, L is the thickness of the lens element, ρ

is the coefficient of thermal expansion, κ

is the stress optical coefficient, α

is the light absorption coefficient, E is the modulus of elasticity, K is the thermal conductivity, and μ

is Poisson'"'"'s ratio.

10. The method of claim 1 wherein the step of selecting the glasses for the lens elements includes:

specifying a nominal lens design which achieves the lens design attributes but which includes lens elements using glasses that are not in the first and second sets of candidate glasses;

identifying glasses from the first and second sets of candidate glasses that most closely match the refractive index and dispersive properties of the glasses that are not in the first and second sets of candidate glasses; and

substituting the identified glasses for the glasses that are not in the first and second sets of candidate glasses.

11. The method of claim 1 wherein the step of using the computer processor to determine the lens design for the imaging lens includes iteratively adjusting the selected glasses and optimizing the lens design until the defined performance criteria are satisfied.

12. The method of claim 1 wherein glasses for the lens elements having the highest optical power densities are selected from the first set of candidate glasses.

13. The method of claim 1 wherein glasses for the thinnest lens elements are selected from the second set of candidate glasses.

14. The method of claim 1 wherein the step of using the computer processor to determine the lens design for the imaging lens includes determining an aspheric surface profile or a diffractive optical surface profile for one or more of the lens elements.

15. The method of claim 1 wherein the lens design includes a polarization compensator.

16. The method of claim 1 wherein the lens design include a mirror with a multi-layer dielectric coating which differentially alters the path length for different wavelength bands, thereby reducing chromatic aberrations.

17. The method claim 1 wherein the imaging lens is used to image polarized light.

18. The method of claim 1 wherein the imaging lens is a relay lens or a projection lens for a digital projection system.

19. A method for designing a lens system having reduced susceptibility to thermally-induced stress birefringence, the method comprising:

defining a set of lens design attributes that describe the geometrical properties of the lens;

defining a set of lens performance criteria, including one or more image quality performance criteria and a thermally-induced stress birefringence metric, wherein the thermal stress birefringence metric includes factors relating to a coefficient of thermal expansion of the glass, a stress optical coefficient of the glass and a light absorption coefficient of the glass;

defining a first set of candidate glasses having a negligible susceptibility to thermal stress birefringence as characterized by a thermal stress birefringence metric;

defining a second set of candidate glasses having more than a negligible susceptibility to thermal stress birefringence but at most a moderate susceptibility to thermal stress birefringence as characterized by the thermal stress birefringence metric;

defining an arrangement of lens elements relative to an aperture stop, wherein the lens elements are arranged in at least one group of lens elements;

selecting glasses for lens elements in the at least one group of lens elements that experience the highest optical power densities from transiting light or are located proximate to the aperture stop from the first set of candidate glasses;

selecting glasses for the other lens elements in the at least one group of lens elements from the first or second sets of candidate glasses;

using a computer processor to determine a lens design for the lens system which achieves the lens design attributes while satisfying the defined lens performance criteria, wherein the lens design specifies thicknesses, spacings, shapes, and glasses for the lens elements in the at least one group of lens elements.

20. The method of claim 19 wherein the thermal stress birefringence metric further includes at least one additional factor relating to a modulus of elasticity of the glass, a thermal conductivity of the glass, a Poisson'"'"'s ratio of the glass, an optical power density in the glass, a thickness of the lens element or a clear aperture size of the lens element.

21. The method of claim 19 wherein the thermal stress birefringence metric is given by:

M₁=ρ

κ

α

E/(K·

(1−

μ

)).

where ρ

is the coefficient of thermal expansion , κ

is the stress optical coefficient, α

is the light absorption coefficient, E is the modulus of elasticity, K is the thermal conductivity, and μ

is Poisson'"'"'s ratio.

22. The method of claim 19 wherein at least some of the lens design attributes and the lens performance criteria are expressed in a lens design merit function that is used during a lens design optimization process by the computer processor.

23. The method of claim 19 wherein thermal-mechanical modeling is used to assess the thermal load applied to one or more of the lens elements from absorption of a portion of the transiting light, the thermal-mechanical modeling accounting for the effects of heat conduction, convection, and radiation, including lens system cooling, as appropriate.

24. The method of claim 23 wherein the thermal-mechanical modeling estimates the stress birefringence levels that are thermally induced in one or more lens elements.

25. The method of claim 23 wherein the selection of glasses is based at least in part on the results of the thermal-mechanical modeling of the lens elements.

26. The method of claim 19 wherein the lens system is an F-theta lens or a zoom lens having multiple lens groups.

27. The method of claim 19 wherein lens system includes a first group of lens elements located one side of the aperture stop, and a second group of lens elements located on other side of the aperture stop.

28. The method of claim 19 wherein less restrictive glasses, relative to thermally induced stress birefringence, are selected for at least one lens element of the lens system based upon a thickness of the lens element.

29. A method for designing an imaging lens having a plurality of lens elements for imaging an object plane to an image plane, the imaging lens having reduced susceptibility to thermally-induced stress birefringence, the method comprising:

defining a set of lens design attributes that describe the geometrical properties of the lens;

defining a merit function, including one or more image quality performance terms and a thermally-induced stress birefringence performance metric, wherein the thermal stress birefringence metric includes factors relating to a coefficient of thermal expansion of the glass, a stress optical coefficient of the glass and a light absorption coefficient of the glass;

defining a first set of candidate glasses having a negligible susceptibility to thermal stress birefringence as characterized by the thermal stress birefringence metric;

defining a second set of candidate glasses having more than a negligible susceptibility to thermal stress birefringence but at most a moderate susceptibility to thermal stress birefringence as characterized by the thermal stress birefringence metric; and

using a computer processor to determine a lens design for the imaging lens which achieves the specified lens design attributes by applying an optimization process responsive to the merit function, wherein the lens design specifies thicknesses, spacings, shapes, and glasses for the lens elements, and wherein the glasses for the lens elements are selected from the first and second sets of candidate glasses, and wherein the glass for at least one of the lens elements is selected from the first set of candidate glasses.