1. The determination of the plasma parameters in the sunspot photosphere using the inversion code

2. Contents Introduction to the inversion code
Derivation of the reponse functions
The inversion process
Error estimation
Examples of response functions
Results

3. Inversion code SIR (Stokes Inversion based on Response functions)
one-dimensional code
local termodinamic equilibrium assumed
one-component model atmosphere
Ruiz Cobo, B. & del Toro Iniesta, J.C. 1992, ApJ, 398,543

4. Response functions RTE for polarised light Formal solution of RTE
Both the propagation matrix and the source function are
dependent on the atmospheric parameters. The integrand
is so-called contribution function, which inform us how the
different atmospheric layers contribute to the observed
spectrum.

5. Response functions
If we change the input parameters, the propagation matrix and the source functions change at first approximation as
The asociated changes in the intensities follow the transfer
equation. If we neglect the second order terms, we gain
We define effective source function as

6. Response functions
The last equation was formally identical to RTE and therefore the solution must be formally the same
The integrand is now the contribution function to the
perturbations of Stokes profiles. If we define the response
function
we gain

7. Inversion process

8. Error estimation
The error of the plasma parameter is proportional to the merit function (quality of the fit) and to the inverse of the response function
The basic assumtion required for the derivation of this equation
is, that the plasma parameters are independent, so changes of
one parameter do not influence the remaining ones.

9. Relative response function of Stokes I

10. Relative response function of Stokes Q

11. Relative response function of Stokes U

12. Relative response function of Stokes V

13. Averaged models of atmosphere

14. Absolute response functions to temperature

15. Absolute response functions to magnetic field strength

16. Absolute response functions to velocity

17. Individual profiles and corresponding stratification of plasma parameters

18. Maps of magnetic field configuration (Area 1, horizontal cuts)

19. Maps of magnetic field configuration (Area 2, horizontal cuts)

20. The canopy scheme