Polarization-based filters with angle-sensitive transmission having circular polarizers

1. An angle-filter, comprising:

exactly two polarizers that function as circular polarizers along a same light beam path, comprising:

an input circular polarizer; and

an analyzing circular polarizer; and

a retarder positioned between the circular polarizers, the retarder having a thickness-direction retardation;

wherein the thickness-direction retardation of the retarder (R1h) is selected to produce a prescribed angle-of-incidence dependent transmission function, and

wherein the circular polarizers reduce the amount of azimuth-dependence in the transmission function.

2. An angle-filter as defined in claim 1 , wherein the retarder has R1h<0 or R1h>0.

3. A pair of eyewear containing an angle-filter as defined in claim 1 , wherein the angle-filter has a prescribed angle-dependent transmission function reducing the amount of stray-light.

4. An image-capture device containing an angle-filter as defined in claim 1 , wherein the angle-filter has a prescribed angle-dependent transmission function for reducing the amount of stray-light.

5. A display device containing an angle-filter as defined in claim 1 , wherein the angle-filter has a prescribed angle-dependent transmission function for reducing the amount of stray-light reflected by the display, reduces the etendue of the backlight unit, or both.

6. A radiometric system, wherein an angle-filter as defined in claim 1 is placed in a receiver-path, an illumination-path, or both, for the purpose of reducing the etendue.

7. An angle-filter as defined in claim 1 , wherein the retarder is one of a C-Plate, an O-Plate, or a Biaxial retarder.

8. An angle-filter as defined in claim 7 , wherein the retarder is a C-Plate with magnitude |Rth|>400 nm.

9. An angle-filter as defined in claim 1 , wherein the transmission function is one of a low-pass filter, a band-pass filter, or a high-pass filter.

10. An angle-filter as defined in claim 9 , wherein the azimuth variation in a 50% transmission angle varies by less than ±10%.

11. An angle-filter as defined in claim 9 , wherein the azimuth variation in a 50% transmission angle varies by less than ±20%.

12. An angle-filter as defined in claim 1 , wherein the circular polarizers are each constructed of a linear-polarizer combined with a quarter-wave retarder.

13. An angle-filter as defined in claim 12 , wherein each of the linear polarizer are one of an absorptive polarizer, a reflective polarizer, or a crystalline polarizer.

14. An angle-filter as defined in claim 12 , wherein the analyzing circular polarizer is the input circular polarizer flipped about the polarizer axis.

15. An angle-filter as defined in claim 12 , wherein the quarter-wave retarders have reverse-dispersion, such that the optical-pathlength-difference in the red exceeds that in the blue.

16. An angle-filter as defined in claim 12 , wherein the quarter-wave retarders have R1h<Re/2.

17. An angle-filter as defined in claim 12 , wherein the quarter-wave retarders have R1h=0.

18. An angle-filter as defined in claim 12 , wherein the polarizers are parallel, and the QW optic-axes are crossed at ±45°.

19. An angle-filter as defined in claim 12 , wherein the quarter-wave retarders are one of a stretched polymer, a reactive-mesogen retarder, or a crystalline retarder.

20. An angle-filter as defined in claim 12 , wherein a geometric compensator is placed between the input linear-polarizer and the quarter-wave retarder, between the analyzing linear-polarizer and quarter-wave retarder, or between both.

21. A two-stage angle-filter arranged in series, comprising:

exactly four circular polarizers;

a first stage, comprising:

two of the four circular polarizers, comprising:

a first input circular polarizer; and

a first analyzing circular polarizer; and

a first retarder between the first circular polarizers;

a second stage, comprising:

two of the four circular polarizers, comprising:

a second input circular polarizer; and

a second analyzing circular polarizer; and

a second retarder between the second circular polarizers;

wherein the thickness-direction retardation of the first retarder (R1h I) and of the second retarder (R1h2) are selected to produce a prescribed angle-of-incidence dependent transmission function, and

wherein the circular polarizers reduce the amount of azimuth-dependence in the transmission function.

22. An angle-filter as defined in claim 21 , wherein the transmission function is one of a low-pass filter, a band-pass filter, or a high-pass filter.

23. An angle-filter as defined in claim 21 , wherein the azimuth variation in a 50% transmission angle varies by less than ±10%.

24. An angle-filter as defined in claim 21 , wherein the azimuth variation in a 50% transmission angle varies by less than ±20%.

25. An angle-filter as defined in claim 21 , wherein the retarders are one of a C-Plate, an O-Plate, or a Biaxial retarder.

26. An angle-filter as defined in claim 25 , wherein the first retarder and the second retarder are C-Plates with magnitude |Rth|>400 nm.

27. An angle-filter as defined in claim 21 , wherein the circular polarizers are constructed of a linear-polarizer combined with a quarter-wave retarder.

28. An angle-filter as defined in claim 27 , wherein a geometric compensator is placed between the input linear-polarizer and the quarter-wave retarder, the analyzing linear-polarizer and quarter-wave retarder, or both, in one or both stages.

29. An angle-filter as defined in claim 27 , wherein the analyzing circular polarizer of the first stage and the input circular polarizer of the second stage share a common linear polarizer.

30. An angle-filter as defined in claim 29 , wherein the polarizers are all parallel, and the QW optic-axes in the first and second stage are crossed at ±45°.