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.

Version: v1 · 2026-09-28 · History
Domain-specific #: 11872
Domain group: Natural Sciences
Origin domain: Physics
Subdomains: Radiation Thermometry, Thermal Radiation, Radiometry → Physics

Core Idea¶

Sakuma–Hattori equation is treated here as the recurring mathematics and formal science identity summarized by this source-grounded definition: 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.

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. S(T) is the temperature dependent electromagnetic signal output of a radiation thermometer (units depend on the instrument but typically V or mV). c_2 = hc/k_\text{B} is the second radiation constant (0.014387752 m⋅K ).

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. They are listed in the chart below in order of quality of curve-fit to actual radiometric data.

For Sakuma–Hattori equation, the abstraction is narrower than the article's general subject matter: a positive case must preserve 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. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in mathematics and formal science, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982.
Constitutive relation — The signal can be electromagnetic flux or signal produced by a detector measuring this radiation.
Operating condition — The Planckian form is realized by the following substitution.
Recognition evidence — 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.
Admissible variation — In 1996, a study investigated the usefulness of various forms of the Sakuma–Hattori equation.
Characteristic consequence — This study showed the Planckian form to provide the best fit for most applications.
Failure boundary — This study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables.

What It Is Not¶

Not the whole field of mathematics and formal science. The node requires the specific identity stated by 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.
Not an over-broad reading. This study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables.
Not an over-broad reading. However the Sakuma–Hattori equation becomes very useful when considering low-temperature, wide-band radiation thermometry.
Not an over-broad reading. The 1996 paper investigated 10 different forms.
Not automatically Thermal emittance. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Sakuma–Hattori equation applies literally inside mathematics and formal science wherever the source-defined carrier and relation can be established. Its documented habitats include:

General form. It has been suggested that below the silver point, a method using the Sakuma–Hattori equation be used.
Discussion. The inverse Sakuma–Hattori function can be used without iterative calculation.
History. This study showed the Planckian form to provide the best fit for most applications.
Discussion. This integral yields an incomplete polylogarithm function, which can make its use very cumbersome.
History. The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982.
History. In 1996, a study investigated the usefulness of various forms of the Sakuma–Hattori equation.

Outside mathematics and formal science, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Pattern or should be marked as analogy.

Clarity¶

A clear use of Sakuma–Hattori equation names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is 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 strongest recognition evidence in the frozen account is: 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. A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification This study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Sakuma–Hattori equation compresses multiple mathematics and formal science details into a stable diagnostic relation. The source shows both the central mechanism—the signal can be electromagnetic flux or signal produced by a detector measuring this radiation.—and the practical consequence—this study showed the Planckian form to provide the best fit for most applications. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the mathematics and formal science entities to which the claim applies.
State the relation. Use the source-grounded identity: 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.
Check operation and conditions. The Planckian form is realized by the following substitution.
Demand recognition evidence. 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.
Test variation. Change an implementation or setting while preserving in 1996, a study investigated the usefulness of various forms of the Sakuma–Hattori equation.
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Pattern.

Knowledge Transfer¶

Within the home domain. Knowledge about Sakuma–Hattori equation transfers literally when a new case preserves the same carrier type, relation, and recognition test. It has been suggested that below the silver point, a method using the Sakuma–Hattori equation be used. The inverse Sakuma–Hattori function can be used without iterative calculation.

Beyond the home domain. No canonical parent is asserted for Sakuma–Hattori equation. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982. This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → 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; recognition evidence → 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

Applied / In Practice¶

In 1996, a study investigated the usefulness of various forms of the Sakuma–Hattori equation. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → History; invariant → 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; boundary → the case exits the class when this study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables

Structural Tensions¶

T1 — Stable identity versus admissible variation. This study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. However the Sakuma–Hattori equation becomes very useful when considering low-temperature, wide-band radiation thermometry. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. The 1996 paper investigated 10 different forms. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Sakuma–Hattori equation literally, co-instantiate Pattern, or only resemble it?

T6 — Autonomy versus reduction. The signal can be electromagnetic flux or signal produced by a detector measuring this radiation. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Sakuma–Hattori equation distinguish that the broader parent Pattern leaves together?

Structural–Framed Character¶

Sakuma–Hattori equation is structural-leaning. Its structural side is the repeatable organization summarized by 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. Its framed side is the mathematics and formal science vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: The Planckian form is realized by the following substitution. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Pattern. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. 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 stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: The Sakuma–Hattori equation was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1982. The signal can be electromagnetic flux or signal produced by a detector measuring this radiation. It further constrains recognition and variation through: The Planckian form is realized by the following substitution. 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.

What is domain-bound. mathematics and formal science supplies the operative entities, technical vocabulary, warrants, and exceptions that make Sakuma–Hattori equation literal. Its documented scope includes the condition that It has been suggested that below the silver point, a method using the Sakuma–Hattori equation be used. Another bounded application condition is that The inverse Sakuma–Hattori function can be used without iterative calculation. These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—In 1996, a study investigated the usefulness of various forms of the Sakuma–Hattori equation.—and future graph densification may discover a defensible relation only if it preserves that boundary.

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Sakuma–Hattori equation. The reviewed identity is: 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 accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Neighborhood in Abstraction Space¶

Sakuma–Hattori equation sits in a sparse region of the domain-specific corpus (89^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Named Physical Phenomena & Theoretical Constructs (16 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Pattern. The parent omits the specialist differentia. Tell: Can the case establish 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?
Thermal emittance. The ratio of thermal radiant flux emitted by a particular surface to that emitted by a blackbody at the same temperature under specified spectral and directional conditions. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Albedo. The dimensionless fraction (0 to 1) of incident shortwave radiation a surface reflects — so its complement, the absorbed fraction, drives temperature, and its self-reinforcing feedback gives it disproportionate climate leverage. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Hata Propagation Model. A closed-form empirical model that estimates median land-mobile path loss from frequency, distance, antenna heights, and environment-specific corrections inside a declared validity envelope. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Sakuma–Hattori equation remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside mathematics and formal science lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Pattern?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Sakuma%E2%80%93Hattori_equation (revision 1360118566).
Preserved source candidate: http://www.eudict.com/?word=silver+point+melting&lang=engchi
Preserved source candidate: http://www.bipm.org/wg/CCT/CCT-WG5/Allowed/Miscellaneous/Low_T_Uncertainty_Paper_Version_1.71.pdf
Preserved source candidate: http://physics.nist.gov/cuu/index.html
Preserved source candidate: https://www.astm.org/e2758-15ar21.html
Preserved source candidate: http://msl.irl.cri.nz/sites/all/files/training-manuals/tg22-july-2009v2.pdf
Preserved source candidate: https://web.archive.org/web/20110724195532/http://msl.irl.cri.nz/sites/all/files/training-manuals/tg22-july-2009v2.pdf
Preserved source candidate: https://www.measurement.govt.nz/download/28

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.