This figure contains some panels labelled with I or II, which we will name 'short_array' and 'long_array' respectively
For figures labelled 'I', we will take '<N>' to mean 'short_array', and for figures labelled 'II', '<N>' will mean 'long_array'

Data fields
<N>_example_inverse_curvatures: The inverse curvatures of the spherical mirror investigated for the example geometry. Units: inverse metres
<N>_example_spherical_cints: The C_{int}^{min} of the cavities with spherical mirrors in the example geometry. Units: dimensionless
<N>_expected_spherical_performance: The expected maximum C_{int}^{min} achievable in the example geometry with a spherical mirror
<N>_expected_spherical_inverse_curvature: The inverse radius of curvature of the spherical mirror at this expected maximum achievable C_{int}^{min}. Units: inverse metres
<N>_example_optimised_cint: The C_{int}^{min} achievable through retroreflective optimisation in the example geometry. Units: dimensionless

<N>_spherical_r: Radial coordinate values to plot the spherical surface that maximises C_{int}^{min}. Units: metres
<N>_spherical_protrusion : The protrusion of the spherical surface that maximises C_{int}^{min}. Units: metres
<N>_surface_r: Radial coordinate values to plot the retroreflective optimised surface. Units: metres
<N>_surface_protrusion: The protrusion of the retroreflective optimised surface. Units: metres
<N>_surface_residuals: The residuals of the retroreflective optimised surface from the spherical surface that maximises C_{int}^{min} (i.e. surface_residuals = surface_protrusion - spherical_protrusion). Units: metres

<N>_density_zz: Axial coordinates of the intensity values for the density plot. Units: metres
<N>_density_xx: Transverse x coordinates of the intensity values for the density plot. Units: metres
<N>_spherical_mirror_mode_density: Intensities of the mode with the spherical mirror that maximises C_{int}^{min} for the density plot. Units: inverse metres squared
<N>_optimised_mirror_mode_density: Intensities of the mode with the optimised for the density plot. Units: inverse metres squared 
<N>_surface_r_reduced: Radial coordinate values to plot the retroreflective optimised surface in the density plot. Units: metres
<N>_surface_protrusion_reduced: The protrusion of the retroreflective optimised surface in the density plot. Units: metres
<N>_example_emitter_axial_positions: Linearly-spaced array of axial positions at which the emitters are placed. Units: metres
<N>_example_length: The length of the cavity in the example case

<N>_axial_intensity_zs: The axial coordinate values for the axial intensity scan. Units: metres
<N>_axial_intensities: The intensity values for the axial intensity scan. Units: inverse metres squared

<N>_example_emitter_range_to_length_ratio: The ratio of emitter array length to cavity length in the example case. Units: dimensionless
scan_lengths: The lengths over which the cavity geometry was scanned. Units: metres
scan_emitter_range_to_length_ratio: The ratios of emitter array legnth to cavity length over which the cavity geometry was scanned. Units: dimensionless
scan_spherical_cints: The values of C_{int}^{min} for the best spherical mirrors over the scan of geometry. Units: dimensionless
scan_optimised_cints: The values of C_{int}^{min} for the optimised mirrors over the scan of geometry. Units: dimensionless
single_emitter_s_crit_l_e_over_l: The emitter array length to cavity length ratios that correspond to s_crit for the separation between two adjacent emitters. Units: dimensionless
whole_array_s_crit_l_e_over_l: The emitter array length to cavity length ratios that correspond to s_crit for the separation between the emitters at each end of the array. Units: dimensionless
l_for_d_crit: The length at which the cavity mirror diameter is D_crit (a single value for the dataset). Units: metres
cint_improvement_factor: The factor by which C_{int}^{min} is improved over the best spherical case by performing retroreflective optimisation. i.e. cint_improvement_factor = scan_optimised_cints / scan_spherical_cints
 

Figure plots
Panel a:
Black line: <N>_example_inverse_curvatures vs <N>_example_spherical_cints
Black crosshair: x value: <N>_expected_spherical_inverse_curvature, y value: <N>_expected_spherical_inverse_curvature
Blue horizontal line: <N>_example_optimised_cint

Panel b:
Black line: <N>_spherical_r vs <N>_spherical protrusion (identical data plotted for negative r)
Blue line: <N>_surface_r vs <N>_surface_protrusion (identical data plotted for negative r)
Red line: <N>_surface_r vs <N>_surface_residuals (identical data plotted for negative r)

Panel c:
i:
Heat map: <N>_spherical_mirror_mode_density on the coordinate grid laid out by <N>_density_zz vs <N>_density_xx. i.e. for all x and y indices in the arrays, the value <N>_spherical_mirror_mode_density[y_index, x_index] is placed at <N>_density_zz[y_index, x_index] on the horizontal axis and <N>_density_xx[y_index, x_index] on the vertical axis. 
Right white line: <N>_spherical_r vs <N>_spherical_protrusion (titled vertical, placed at plus 0.5 * <N>_example_length, and with identical data plotted for negative x)
Left white line: The right white line reflected
ii:
Heat map: <N>_optimised_mirror_mode_density on the coordinate grid laid out by <N>_density_zz vs <N>_density_xx. i.e. for all x and y indices in the arrays, the value <N>_optimised_mirror_mode_density[y_index, x_index] is placed at <N>_density_zz[y_index, x_index] on the horizontal axis and <N>_density_xx[y_index, x_index] on the vertical axis. 
Right white line: <N>_surface_r_reduced vs <N>_surface_protrusion_reduced (titled vertical, placed at plus 0.5 * <N>_example_length, and with identical data plotted for negative x)
Left white line: The right white line reflected
both:
Cyan crosses: crosses at zero transverse coordinate and the axial coordinates of <N>_example_emitter_axial_positions

Panel d:
Blue line: <N>_axial_intensity_zs vs <N>_axial_intensities
Vertical black lines: <N>_example_emitter_axial_positions: Linearly-spaced array of axial positions at which the emitters are placed. Units: metres

Panel e:
i: 
Heat map: scan_spherical_cints (data) vs scan_lengths (x) and scan_emitter_range_to_length_ratio (y)
ii:
Heat map: scan_optimised_cints (data) vs scan_lengths (x) and scan_emitter_range_to_length_ratio (y)
both:
Vertical white line: l_for_d_crit
Diagonal white line (lower): scan_length vs whole_array_s_crit_l_e_over_l
Diagonal white line (upper): scan_lengths vs single_emitter_s_crit_l_e_over_l
Green crosses: <N>_example_length vs <N>_example_emitter_range_to_length_ratio

Panel f:
Heat map: Heat map: cint_improvement_factor (data) vs scan_lengths (x) and scan_emitter_range_to_length_ratio (y). Data only shown for length (x value) greater than l_for_d_crit
Vertical white line: l_for_d_crit
Diagonal white line (lower): scan_length vs whole_array_s_crit_l_e_over_l
Diagonal white line (upper): scan_lengths vs single_emitter_s_crit_l_e_over_l
Green crosses: <N>_example_length vs <N>_example_emitter_range_to_length_ratio



