Modulation patterns for surface scattering antennas

1. A method, comprising:

discretizing a hologram function for a surface scattering antenna that defines an aperture, where the discretizing includes

identifying a discrete plurality of locations on the aperture for a discrete plurality of scattering elements of the surface scattering antenna and

identifying a discrete set of states for each of the scattering elements corresponding to a discrete set of function values at each of the locations of the scattering elements; and

identifying an antenna configuration that reduces artifacts attributable to the discretizing, wherein the identifying of the antenna configuration includes applying an error diffusion algorithm to the discretized hologram function.

2. The method of claim 1 , further comprising:

adjusting the surface scattering antenna to the identified antenna configuration.

3. The method of claim 1 , further comprising:

operating the surface scattering antenna in the identified antenna configuration.

4. The method of claim 1 , further comprising:

storing the identified antenna configuration in a storage medium.

5. The method of claim 1 , wherein the plurality of locations is a sequence of locations, and the applying of the error diffusion algorithm includes, for each location in the sequence of locations:

identifying an error, if any, accumulated at the location from one or more locations earlier in the sequence of locations;

selecting a function value from the discrete set of function values, the selected value being that value in the discrete set of function values that is closest to a sum of the hologram function evaluated at the location and the accumulated error;

identifying a new error equal to the selected function value minus the sum of the hologram function evaluated at the location and the accumulated error; and

accumulating the new error at one or more locations, if any, later in the sequence of locations.

6. The method of claim 5 , wherein the plurality of scattering elements is a one-dimensional plurality of scattering elements, and the sequence of locations is a sequence of locations of adjacent scattering elements.

7. The method of claim 6 , wherein the accumulating of the new error at one or more locations later in the sequence of locations is an accumulating of the new error at a next location in the sequence of locations.

8. The method of claim 5 , wherein the plurality of scattering elements is a two-dimensional plurality of scattering elements.

9. The method of claim 8 , wherein the two-dimensional plurality of scattering elements is arranged in rows, and the sequence of locations is a row-by-row sequence of locations of adjacent scattering elements in each row.

10. The method of claim 9 , wherein the accumulating of the new error at one or more locations later in the sequence of locations is an accumulating of the new error at a next location in the sequence of locations.

11. The method of claim 10 , wherein:

if the location is at an end of one of the rows of scattering elements, the accumulating of the new error at the next location in the sequence locations is an accumulating of zero error at the next location in the sequence of locations.

12. The method of claim 9 , wherein the accumulating of the new error at one or more locations in the sequence of locations is an accumulating of the new error at multiple locations in a two-dimensional neighborhood of the location.

13. The method of claim 9 , wherein the surface scattering antenna includes a plurality of one-dimensional waveguides supporting the two-dimensional plurality of scattering elements, and the rows coincide with the plurality of one-dimensional waveguides.

14. The method of claim 9 , wherein the surface scattering antenna includes a plurality of one-dimensional waveguides supporting the two-dimensional plurality of scattering elements, and the rows are perpendicular to the plurality of one-dimensional waveguides.

15. The method of claim 9 , wherein the surface scattering antenna includes a waveguide supporting a waveguide mode, and the rows correspond to a set of constant phase fronts of the waveguide mode.

16. The method of claim 9 , wherein the rows correspond to a set of contours of the hologram function.

17. The method of claim 5 , wherein the identifying of the antenna configuration includes, for each scattering element in the plurality of scattering elements:

identifying a state for the scattering element selected from the discrete set of states and corresponding to the selected function value for the location of the scattering element.

18. A system, comprising:

a surface scattering antenna with a plurality of adjustable scattering elements that are adjustable between a discrete set of states corresponding to a discrete set of function values at each location in a plurality of locations for the plurality of adjustable scattering elements;

a storage medium on which a set of antenna configurations corresponding to a set of hologram functions is written, each antenna configuration being selected to reduce artifacts attributable to a discretization of the respective hologram function; and

control circuitry operable to read antenna configurations from the storage medium and adjust the plurality of adjustable scattering elements to provide the antenna configurations;

wherein at least one antenna configuration is an error-propagated discretization of the respective hologram function.

19. The system of claim 18 , wherein the error-propagated discretization is obtained by an algorithm that includes, for each location in a sequence of the plurality of locations:

identifying an error, if any, accumulated at the location from one or more locations earlier in the sequence of locations;

selecting a function value from the discrete set of function values, the selected value being that value in the discrete set of function values that is closest to a sum of the respective hologram function evaluated at the location and the accumulated error;

identifying a state for the adjustable scattering element at the location, the identified state being selected from the discrete set of states and corresponding to the selected function value for the location;

identifying a new error equal to the selected function value minus the sum of the respective hologram function evaluated at the location and the accumulated error; and

accumulating the new error at one or more locations, if any, later in the sequence of locations.

20. The system of claim 19 , wherein the plurality of adjustable scattering elements is a one-dimensional plurality of adjustable scattering elements, and the sequence of locations is a sequence of locations of adjacent scattering elements.

21. The system of claim 20 , wherein the accumulating of the new error at one or more locations later in the sequence of locations is an accumulating of the new error at a next location in the sequence of locations.

22. The system of claim 19 , wherein the plurality of adjustable scattering elements is a two-dimensional plurality of adjustable scattering elements.

23. The system of claim 22 , wherein the two-dimensional plurality of adjustable scattering elements is arranged in rows, and the sequence of locations is a row-by-row sequence of locations of adjacent scattering elements in each row.

24. The system of claim 23 , wherein the accumulating of the new error at one or more locations later in the sequence of locations is an accumulating of the new error at a next location in the sequence of locations.

25. The system of claim 24 , wherein:

if the location is at an end of one of the rows of scattering elements, the accumulating of the new error at the next location in the sequence locations is an accumulating of zero error at the next location in the sequence of locations.

26. The system of claim 23 , wherein the accumulating of the new error at one or more locations in the sequence of locations is an accumulating of the new error at multiple locations in a two-dimensional neighborhood of the location.

27. The system of claim 23 , wherein the surface scattering antenna includes a plurality of one-dimensional waveguides supporting the two-dimensional plurality of adjustable scattering elements, and the rows coincide with the plurality of one-dimensional waveguides.

28. The system of claim 23 , wherein the surface scattering antenna includes a plurality of one-dimensional waveguides supporting the two-dimensional plurality of adjustable scattering elements, and the rows are perpendicular to the plurality of one-dimensional waveguides.

29. The system of claim 23 , wherein the surface scattering antenna includes a waveguide supporting a waveguide mode, and the rows correspond to a set of constant phase fronts of the waveguide mode.

30. The system of claim 23 , wherein the rows correspond to a set of contours of the respective hologram function.

31. A method of controlling a surface scattering antenna with a plurality of adjustable scattering elements, comprising:

reading an antenna configuration from a storage medium, the antenna configuration being selected to reduce artifacts attributable to a discretization of a hologram function; and

adjusting the plurality of adjustable scattering elements to provide the antenna configuration;

wherein the adjustable scattering elements are adjustable between a discrete set of states corresponding to a discrete set of function values at each location in a plurality of locations for the plurality of adjustable scattering elements; and

wherein the antenna configuration is an error-propagated discretization of the hologram function.

32. The method of claim 31 , further comprising:

operating the antenna in the antenna configuration.

33. The method of claim 31 , wherein the error-propagated discretization is obtained by an algorithm that includes, for each location in a sequence of the plurality of locations:

identifying an error, if any, accumulated at the location from one or more locations earlier in the sequence of locations;

selecting a function value from the discrete set of function values, the selected value being that value in the discrete set of function values that is closest to a sum of the respective hologram function evaluated at the location and the accumulated error;

identifying a state for the adjustable scattering element at the location, the identified state being selected from the discrete set of states and corresponding to the selected function value for the location;

identifying a new error equal to the selected function value minus the sum of the respective hologram function evaluated at the location and the accumulated error; and

accumulating the new error at one or more locations, if any, later in the sequence of locations.

34. The method of claim 33 , wherein the plurality of adjustable scattering elements is a one-dimensional plurality of adjustable scattering elements, and the sequence of locations is a sequence of locations of adjacent scattering elements.

35. The method of claim 34 , wherein the accumulating of the new error at one or more locations later in the sequence of locations is an accumulating of the new error at a next location in the sequence of locations.

36. The method of claim 33 , wherein the plurality of adjustable scattering elements is a two-dimensional plurality of adjustable scattering elements.

37. The method of claim 36 , wherein the two-dimensional plurality of adjustable scattering elements is arranged in rows, and the sequence of locations is a row-by-row sequence of locations of adjacent scattering elements in each row.

38. The method of claim 37 , wherein the accumulating of the new error at one or more locations later in the sequence of locations is an accumulating of the new error at a next location in the sequence of locations.

39. The method of claim 38 , wherein:

if the location is at an end of one of the rows of scattering elements, the accumulating of the new error at the next location in the sequence locations is an accumulating of zero error at the next location in the sequence of locations.

40. The method of claim 37 , wherein the accumulating of the new error at one or more locations in the sequence of locations is an accumulating of the new error at multiple locations in a two-dimensional neighborhood of the location.

41. The method of claim 37 , wherein the surface scattering antenna includes a plurality of one-dimensional waveguides supporting the two-dimensional plurality of adjustable scattering elements, and the rows coincide with the plurality of one-dimensional waveguides.

42. The method of claim 37 , wherein the surface scattering antenna includes a plurality of one-dimensional waveguides supporting the two-dimensional plurality of adjustable scattering elements, and the rows are perpendicular to the plurality of one-dimensional waveguides.

43. The method of claim 37 , wherein the surface scattering antenna includes a waveguide supporting a waveguide mode, and the rows correspond to a set of constant phase fronts of the waveguide mode.

44. The method of claim 37 , wherein the rows correspond to a set of contours of the respective hologram function.