Optically-Thin Thermal Free-Free Emission (Preliminary)

Note: The procedures described in this subsection are under testing. Comments are welcome for improvement.

Based on Dulk (1985)'s approximation model, the relation between the physical variables of emitting region and the emission can be derived.

(a) From Physical Variables to Emission

Inputs; electron temperature (K), line-of-site component of magnetic field (G), and volume emission measure (cm$^{-3}$) Outputs; flux density (SFU), circular polarization degree:
IDL> dulk_frfr,te,b_loc,vem,freq,fi,rc $<$CR$>$
If the size of emitting source (by solid angle in unit of sterad) is given additionally, optical depth is also obtained
IDL> dulk_frfr,te,b_loc,vem,freq,fi,rc,omega,tau $<$CR$>$

(b) From Emission to Physical Variables

Inputs; I-component (R$+$L) and V-component (R$-$L) of flux density (SFU): Outputs; line-of-sight component of magnetic field (G), $VEM/\sqrt{T_e}$ where $VEM$ is volume emission measure, $T_e$ is electron temperature:
IDL> norh_frfr_inv,fi,fv,b_los,vem_over_sqrtte $<$CR$>$
If one of $VEM$ or $T_e$ is assumed, the other is derived:
IDL> norh_frfr_inv,fi,fv,b_los,tein,vem,/assumete $<$CR$>$
IDL> norh_frfr_inv,fi,fv,b_los,vemin,te,/assumevem $<$CR$>$
Adding to this, if the size of emission source is given (as surface angle. Unit is sterad), optical thickness is derived
IDL> norh_frfr_inv,fi,fv,b_los,tein,vem,/assumete,omega,tau $<$CR$>$
IDL> norh_frfr_inv,fi,fv,b_los,vemin,te,/assumevem,omega,tau $<$CR$>$