Identify the true temperature among permitted solutions without emissivity information

Determine which temperature–emissivity pair among the continuum of permitted solutions that exactly reproduce multiwavelength spectral radiance measurements corresponds to the actual physical temperature when no a priori emissivity information about the emissivity spectrum is available.

Background

Multiwavelength thermometry (MWT) is intrinsically underdetermined: at n wavelengths there are n emissivity values plus temperature to recover from only n radiance measurements, yielding a continuous infinity of exact solutions ("permitted solutions"). The paper emphasizes that this multiplicity persists even when measurement noise is present, as noise simply propagates to the inferred emissivity spectra without removing the non-uniqueness.

In the random-error analysis, the authors underline that any temperature combined with its corresponding permitted emissivity spectrum can perfectly explain the measured (noisy) radiance. Without introducing external emissivity information, the true solution cannot be singled out from the infinite set of permitted solutions. This explicit knowledge gap motivates the need for emissivity information to localize the true temperature.