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Transmissivity is an important property of material films. In this Letter an inverse transmissivity problem is proposed. Its exact solution formula and a Möbius inversion solution are obtained along with a convergent solution series and some exact solutions. A possible application is suggested and discussed. A related practical solution method is developed and shown to have useful properties for applications.
The black-body radiation inversion (BRI) problem is ill-posed and requires special techniques to achieve stable solutions. In this Letter, the universal function set method (UFS), is developed in BRI. An improved unique existence theorem is proposed. Asymptotic behavior control (ABC) is introduced. A numerical example shows that practical calculations are possible with UFS.
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