Data fields:

surface_r: The radial coordinates of the sampled points of the surfaces. Units: metres
spherical_y: The protrusion of the mirror with the best spherical curvature (from inline equation just preceding Eq. (9) in the manuscript). Units: metres
gaussian_y: The protrusion of the example Gaussian mirror. Units: metres
gaussian_spherical_y: The protrusion of the spherical profile with the same central curvature as the Gaussian profile. Units: metres
dual_curvature_y: The protrusion of the example dual curvature mirror. Units: metres
dual_curvature_central_sphere_y: The protrusion of the spherical profile that fits the centre of the dual curvature profile
dual_curvature_outer_sphere_y: The protrusion of the spherical profile that fits the outside of the dual curvature profile
spline_y: The protrusion of the example spline mirror. Units: metres 
spline_points_x: The radial coordinates of the optimised points on the spline mirror (which the profile must pass through). Units: metres
spline_points_x: The protrusion of the optimised points on the spline mirror (which the profile must pass through). Units: metres

density_z: The axial coordinate of samples in the mode density plot. A 2D array indexed in order (y_index, x_index). Units: metres
density_x: The transverse (for example 'x', but the cavity is radially symmetric) coordinate of samples in the mode density plot. A 2D array indexed in order (y_index, x_index). Units: metres
density_gaussian: The mode intensity at the corresponding axial and transverse coordinates of density_z and density_x for the mode of the cavity with the Gaussian mirror (sampled in gaussian_y). A 2D array indexed in order (y_index, x_index). Units: inverse metres squared
density_dual_curvature: The mode intensity at the corresponding axial and transverse coordinates of density_z and density_x for the mode of the cavity with the dual curvature mirror (sampled in dual_curvature_y). A 2D array indexed in order (y_index, x_index). Units: inverse metres squared
density_spline: The mode intensity at the corresponding axial and transverse coordinates of density_z and density_x for the mode of the cavity with the spline mirror (sampled in spline_y). A 2D array indexed in order (y_index, x_index). Units: inverse metres squared

emitter_r: The radial coordinates at which intensity samples were taken over the emitter plane. Units: metres
spherical_intensity: Intensity samples in the emitter plane for the cavity with the non-planar mirror with the best spherical curvature (from inline equation just preceding Eq. (9) in the manuscript). Units: inverse metres squared
retroreflective_optimised_intensity: Intensity samples in the emitter plane for the cavity with the retroreflective optimised mirror. Units: inverse metres squared
gaussian_intensity: Intensity samples in the emitter plane for the cavity with the Gaussian mirror. Units: inverse metres squared
dual_curvature_intensity: Intensity samples in the emitter plane for the cavity with the dual curvature mirror. Units: inverse metres squared
spline_intensity: Intensity samples in the emitter plane for the cavity with the spline mirror. Units: inverse metres squared

length_deltas: Changes in length from the nominal used for the length scan. Units: metres
spherical_cint: C_{int}^{0} for the cavity with the best spherical radius of curvature (from inline equation just preceding Eq. (9) in the manuscript) for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless
retroreflective_optimised_cint: C_{int}^{0} for the retroreflective optimised cavity for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless
gaussian_cint: C_{int}^{0} for the cavity with the Gaussian mirror for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless
dual_curvature_cint: C_{int}^{0} for the cavity with the dual curvature mirror for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless
spline_cint: C_{int}^{0} for the cavity with the spline mirror for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless



Figure plots:
Panel a):
all plots:
Black line: surface_r vs spherical_y (identical data plotted for negative r)
Blue line: surface_r vs gaussian_y/dual_curvature_y/spline_y for panel i/ii/iii respectively (identical data plotted for negative r)

i:
Green dashed line: surface_r vs gaussian_spherical_y (identical data plotted for negative r)

ii:
Green dashed line labelled 'R_c': surface_r vs dual_curvature_central_sphere_y (identical data plotted for negative r)
Green dashed line labelled 'R_o': surface_r vs dual_curvature_outer_sphere_y (identical data plotted for negative r)

iii:
Red crosses: spline_points_x vs spline_points_y (identical data plotted for negative r)

Panel b):
Heat map: density_gaussian/density_dual_curvature/density_spline (for panels i, ii, and iii respectively) on the coordinate grid laid out by density_z vs density_x. i.e. for all x and y indices in the arrays, the value density_gaussian/density_dual_curvature/density_spline[y_index, x_index] is placed at density_z[y_index, x_index] on the horizontal axis and density_x[y_index, x_index] on the vertical axis. 
Left white line: perfectly vertical
Right white line: surface_x vs gaussian_y, dual_curvature_y, spline_y for i, ii, and iii respectively (titled vertical, and with identical data plotted for negative x)

Panel c):
Black line: emitter_r vs spherical_intensity (identical data plotted for negative r)
Purple line: emitter_r vs retroreflective_optimised_intensity (identical data plotted for negative r)
Blue line: emitter_r vs gaussian_intensity (identical data plotted for negative r)
Red line: emitter_r vs dual_curvature_intensity (identical data plotted for negative r)
Yellow line: emitter_r vs spline_intensity (identical data plotted for negative r)


Panel c):
Black line: length_deltas vs spherical_cint
Purple line: length_deltas vs retroreflective_optimised_cint 
Blue line: length_deltas vs gaussian_cint 
Red line: length_deltas vs dual_curvature_cint 
Yellow line: length_deltas vs spline_cint 

