PMC

Comparison of triangular lattice and quasi-crystal lattice in free space and reciprocal space. (a) Real-space lattice of square-triangle tiling random-Stampfli quasi-crystal lattice structure. (b) Real-space lattice of the triangular lattice structure. (c) Schematic cross-section showing normal incidence coupling to the waveguide mode. (d) Schematic cross-section showing near-normal incidence coupling to the waveguide mode. (e) Ewald circle construction of a quasi-crystal lattice in reciprocal space with normal incidence coupling. (f) Ewald circle construction of a quasi-crystal lattice in reciprocal space with near-normal incidence coupling. (g) Ewald circle construction of a triangular lattice in reciprocal space showing the light-line in red. (h) Ewald circle construction of a triangular lattice in reciprocal space with a large offset-incidence angle. Green circles represent the Ewald circle construction. Yellow arrows indicate the allowed coupled mode propagation directions and the width of the arrows schematically indicate the strength of each scattered beam.

Simple 2D lattice structures with the same trabecular separation and different volume fractions; Bone and marrow spaces were represented by white and black stripes, respectively; (a) bone space = 3, marrow space = 27; (b) variogram of the preceding lattice structure; (c) bone space = 6, marrow space =24; (d) variogram of the preceding lattice structure; (e) bone space = 9, marrow space = 21; (f) variogram of the preceding lattice structure.

Simple 2D lattice structures with the same volume fraction (30%) and different trabecular separation; Bone and marrow spaces were represented by white and black stripes, respectively; (a) bone space = 3, marrow space = 7; (b) variogram of the preceding lattice structure; (c) bone space = 6, marrow space =14; (d) variogram of the preceding lattice structure; (e) bone space = 9, marrow space = 21; (f) variogram of the preceding lattice structure.