Sakuma–Hattori equation

In physics, the Sakuma–Hattori equation is a mathematical model for predicting the amount of thermal radiation, radiometric flux or radiometric power emitted from a perfect blackbody or received by a thermal radiation detector. The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982. In 1996, a study investigated the usefulness of various forms of the Sakuma–Hattori equation. This study showed the Planckian form to provide the best fit for most applications. This study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables. In 2008, BIPM CCT-WG5 recommended its use for radiation thermometry uncertainty budgets below 960 °C. The Sakuma–Hattori equation gives the electromagnetic signal from thermal radiation based on an object's temperature. The signal can be electromagnetic flux or signal produced by a detector measuring this radiation. It has been suggested that below the silver point, a method using the Sakuma–Hattori equation be used. In its general form it looks like where: is the scalar coefficient is the second radiation constant (0.014387752 m⋅K) is the temperature-dependent effective wavelength in meters is the absolute temperature in kelvins The Planckian form is realized by the following substitution: Making this substitution renders the following the Sakuma–Hattori equation in the Planckian form. Sakuma–Hattori equation (Planckian form) Inverse equation First derivative The Planckian form is recommended for use in calculating uncertainty budgets for radiation thermometry and infrared thermometry. It is also recommended for use in calibration of radiation thermometers below the silver point. The Planckian form resembles Planck's law. However the Sakuma–Hattori equation becomes very useful when considering low-temperature, wide-band radiation thermometry. To use Planck's law over a wide spectral band, an integral like the following would have to be considered: This integral yields an incomplete polylogarithm function, which can make its use very cumbersome.