Model scanning run AF (optically thin inner disk), and the model parameters of the best model AF1 with minimum , which is calculated by comparing each model with the data set. Panel a: Parameter ranges of model scanning run AF, number of tested parameter values (steps) per parameter, and parameters of the best model AF1. The listed parameters are: L_∗ = stellarluminosity; i = inclination of the disk; PA = positionalangleofrotationaxisthedisk; and the following parameters for the inner sub-AU disk; R_in = innerradiusoftheinnerdisk; W_ring = (R_out−R_in) /R_in (relative radial width of the inner component); R_out = outerradiusoftheinnerdisk; h_in = scaleheightoftheinnerdiskatitsinnerradius; q = scale - heightpower - lawindexoftheinnerdisk; p = surface - densitypower - lawindex; τ = Planck - averagedmidplaneopticaldepthat7500 K; n = power - lawindexofgrainsizedistribution; f_carbon = fractionofcarboninthedust. Panel b: maps of Model run AF.For each subset of parameters, the shown is the lowest value for all combinations with other paramters. For example, for each pair of (R_in, τ) values, the values for all possible (L_∗, n, f_carbon) combinations within the described ranges were compared and the minimum value found is plotted into the map at left panel. Panel c: SED of HD 169142. The lines denote the model contributions from different radial regions. The red dots are the observations. 5% uncertainty is assumed for each observation. Panel d: NIR visibilities (red dots: observations; black lines: model) from our VLTI/PIONIER observations.