function ring_brightness,r_abs,rho_albedo_phase_index_ring_versus_r_sat,$ cos_inc_angle,cos_emm_angle, phase_angle,if_dark_side,$ ring_phase_lookup_table,label_lookup,tau_lookup,albedo_lookup,$ solar_elev_lookup,obs_elev_lookup,obs_azim_lookup,ss_phase_index_lookup,$ azimuth_inc_em_ring_plane_deg ;NOTE :cos_inc_angle,cos_emm_angle, should be positive if_lookup_table=1 ss_phase_index=3.092 tau=interpol(rho_albedo_phase_index_ring_versus_r_sat(*,1),$ rho_albedo_phase_index_ring_versus_r_sat(*,0),r_abs) albedo=interpol(rho_albedo_phase_index_ring_versus_r_sat(*,2)$ ,rho_albedo_phase_index_ring_versus_r_sat(*,0),r_abs) if (if_lookup_table) then begin n_tau=where((tau_lookup-tau)^2 eq min((tau_lookup-tau)^2)) n_albedo=where((albedo_lookup-albedo)^2 eq min((albedo_lookup-albedo)^2)) solar_elev=asin(cos_inc_angle)/!pi*180. if(if_dark_side) then solar_elev=solar_elev*(-1) n_solar_elev=where((solar_elev_lookup-solar_elev)^2 eq min((solar_elev_lookup-solar_elev)^2)) obs_elev=asin(cos_emm_angle)/!pi*180. n_obs_elev=where((obs_elev_lookup-obs_elev)^2 eq min((obs_elev_lookup-obs_elev)^2)) obs_azim=azimuth_inc_em_ring_plane_deg n_obs_azim=where((obs_azim_lookup-obs_azim)^2 eq min((obs_azim_lookup-obs_azim)^2)) n_ss_phase_index=where((ss_phase_index_lookup-ss_phase_index)^2 eq min((ss_phase_index_lookup-ss_phase_index)^2)) ;stop return, ring_phase_lookup_table(n_tau,n_albedo,n_solar_elev,n_obs_elev,n_obs_azim,n_ss_phase_index,1) endif else begin power_pf_fun=interpol(rho_albedo_phase_index_ring_versus_r_sat(*,3)$ ,rho_albedo_phase_index_ring_versus_r_sat(*,0),r_abs) ;was before: a formula P(s) = C_n s**power_ph_fun from ;Luke Dones where s = pi - the phase angle in radians ;now the one from Dones et. 93 ;the normalization coefficient C_n corresponds to n according to the following table ; (Dones et al 93) c_n_versus_n=[[1.000,1.257,1.860,2.624,3.092,3.301,3.642 ,4.300 ,5.108 ,7.518],$ [0.637,0.539,0.375,0.218,0.153,0.130,0.0993,0.0578,0.0289,0.00326]] c_n=interpol(c_n_versus_n(*,1),c_n_versus_n(*,0),power_pf_fun) ;help,c_n,tau if (if_dark_side(0) ne 0) then begin mu_0_minus_mu=(cos_emm_angle-cos_inc_angle) if (abs(mu_0_minus_mu) le 1.e-10) then mu_0_minus_mu=1.e-10 brightness=albedo/4.*c_n*phase_angle^power_pf_fun*$ (exp(-tau/cos_emm_angle)-exp(-tau/cos_inc_angle))*cos_inc_angle/mu_0_minus_mu ; brightness=0. endif else begin ;illuminated side brightness=albedo/4.*cos_inc_angle/(cos_emm_angle+cos_inc_angle)$ *(1.-exp(-tau*(1./cos_emm_angle+1./cos_inc_angle)))*c_n*phase_angle^power_pf_fun endelse ;stop return, brightness endelse end