Wide-angle compensation of uniaxial retarder stacks
A compound retarder that creates independent control of R e and R th . This can be done by forming a three-layer compound retarder, including a pair of matched −A-plates, combined with single +A-plate. The +A-plate is typically an MD-stretched film, with retardation that is specific to the in-plane requirements (R e ) of the application. The pair of −A-plates have their optic axes crossed, such that R e =0, with an optic axis aligned parallel to the +A-plate. A single retardation value for the −A-plate can produce improved field-of-view performance over a broad range of R e values, making it a very practical means of universal compensation. While R th is typically associated with a single retarder, retarder stacks with a diverse range of optic-axis orientations can be considered to have a compound (or composite) R th value (R th c ). The three-layer compound retarder has the practical benefit of enabling field-of-view compensation across a broad range of normal-incidence polarization transformations.
1. A compound retarder, comprising:
a first planar retarder that has two dimensions parallel to a plane and a third or thickness dimension orthogonal to the plane, wherein the first retarder has a single optic-axis orientation that determines the in-plane retardation and wherein the first retarder has a first retardation in the thickness dimension;
a second planar retarder that has two dimensions parallel to a plane and a third or thickness dimension orthogonal to the plane, wherein the second retarder has a single optic-axis orientation that determines in-plane retardation and that is parallel to the optic-axis orientation of the first retarder and wherein the second retarder has a second retardation in the thickness dimension; and
a third planar retarder that has two dimensions parallel to a plane and a third or thickness dimension orthogonal to the plane, wherein the third retarder has a single optic-axis orientation that determines in-plane retardation and that is crossed with respect to the optic-axis orientation of the first retarder and wherein the third retarder has a third retardation in the thickness dimension;
wherein the first retardation is opposite in sign to the second retardation and the third retardation.
2. A compound retarder as defined in claim 1 , wherein the second retarder and the third retarder each have a same in-plane retardation.
3. A compound retarder as defined in claim 1 , wherein the second retarder and the third retarder each have an in-plane retardation that is half of the in-plane retardation of the first retarder.
4. A compound retarder as defined in claim 1 , wherein the second retarder and the third retarder each have an in-plane retardation that is between 20% and 80% of the in-plane retardation of the first retarder.
5. A retarder stack that includes two or more of the compound retarders of claim 1 .
6. A compound retarder, comprising:
a first retarder with a first single optic-axis orientation that determines a first retardation;
a second retarder with a second single optic-axis orientation that determines a second retardation; and
a third retarder with a third single optic-axis orientation that determines a third retardation, wherein the third optic-axis orientation is perpendicular to the second optic-axis orientation;
wherein one of the second single optic-axis orientation and the third single optic-axis orientation is perpendicular to the first single optic-axis orientation;
wherein the first retardation is opposite in sign to the second retardation and the third retardation.
7. A compound retarder as defined in claim 6 , wherein the second retarder and the third retarder each have a same in-plane retardation.
8. A compound retarder as defined in claim 6 , wherein the second retarder and the third retarder each have an in-plane retardation that is half of the in-plane retardation of the first retarder.
9. A compound retarder as defined in claim 6 , wherein the second retarder and the third retarder each have an in-plane retardation that is between 20% and 80% of the in-plane retardation of the first retarder.
10. A retarder stack that includes two or more of the compound retarders of claim 6 .
11. A retarder stack for wavelength-dependent manipulation of a state-of-polarization of light passing therethrough, the retarder stack comprising:
a first retarder-stack that includes two linear-retarder layers, each with a single optical axis that determines in-plane retardation, wherein the first retarder-stack has a thickness dimension in the direction that light passes therethrough, and wherein the first retarder-stack has a non-zero retardance in the thickness dimension;
a second retarder-stack that includes two linear-retarder layers, each with a single optical axis that determines in-plane retardation, wherein the second retarder stack has a thickness dimension in the direction that light passes therethrough, and wherein the second retarder-stack has a non-zero retardance in the thickness dimension; and
a pair of crossed A-plate retarders positioned between the first and second retarder-stacks, wherein the pair of crossed A-plate retarders have substantially matched in-plane retardance.
12. A retarder stack as defined in claim 11 , wherein the first and second retarder-stacks each have a birefringence of the same sign to one of the crossed A-plate retarders and of opposite sign to a birefringence of an other of the crossed A-plate retarders.
13. A retarder stack as defined in claim 11 , wherein the retarder stack has a composite in-plane retardance, and wherein the crossed A-plate retarders reduce the angle-of-incidence dependence of the composite in-plane retardance.
14. A retarder stack as defined in claim 13 , wherein the azimuth-dependent compensation is substantially matched in retardation and orientation to the compound retardation that exists between the retarder-stacks, minimizing the composite in-plane retardance.
15. A retarder stack as defined in claim 11 , wherein the retarder-stacks are arranged in a reverse-order reflection about 45 degrees configuration, wherein the retarder-stacks act to convert an input state-of-polarization of a predefined range of wavelengths to a state-of-polarization that is orthogonal to the input state-of-polarization, and wherein the pair of crossed A-plate retarders provide azimuth-dependent compensation that reduces the angle-of-incidence dependent change in the composite in-plane retardance.
16. A retarder stack as defined in claim 15 , wherein the retarder-stacks are composed of positive A-plates and the crossed A-plate retarders are composed of negative A-plates.
17. A retarder stack as defined in claim 15 , wherein the combination of retarder stacks and crossed A-plates produce a normal-incidence composite polarization transformation that is substantially insensitive to angle-of-incidence.
18. A retarder stack as defined in claim 11 , wherein the retarder stacks do not convert the input state-of-polarization over a predefined range of wavelengths, and wherein the crossed A-plate retarders do not contribute adversely to the angle-of-incidence dependent change in the composite in-plane retardance.