Various possibilities are available to define coatings - listed from simplest to most complex:

• the “I.X” notation: where X represents the transmitted intensity, irespective of angle/wavelength/polarization. Reflected intensity is assumed R=1-T and no absorption (A=0)  
• the “IDEAL name T R” notation : where T is the transmitted intensity and R reflected intensity, irrespective of angle/wavelength/polarization and A=1 - T - R
• the “IDEAL2 <name> s_rr s_ri s_tr s_ti p_rr p_ri p_tr p_ti no_pi_flag” notation : here the amplitude (not power!) coefficients are defined, for polarization p and s, and using real and imaginary parts - again irrespective of angle/wavelength, and A=1 - T - R
• the “TABLE” notation : allows to specify, for any couple of wavelength/angles, the module and phase angles as Rs Rp Ts Tp Ars Arp Ats Atp, where Rs/Rp/Ts/Tp are the squared modules of the complex r/t coefficients, and Ars/Arp/Ats/Atp are their phase angle. Absorptions Ap=1-Rp-Tp and As=1-Rs-Ts

My question is how do all these definitions are converted into the same “coefficient framework” ?

What are the low-level quantities that are defined from those definitions ? Are they complex-amplitude coefficents r_s, r_p, t_s, t_p ?

If so, using the TABLE notation, does r_s = Rs^0.5 * exp(j Ars) ? (and similarly for the other coefficients)