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==== Radiant Intensity ====
**Definition:** The [[yanding:成像基础知识:光学:辐射度学与光度学:辐射通量|radiant flux]] emitted by a radiation source in a specific direction per unit [[yanding:成像基础知识:光学:辐射度学与光度学:立体角|solid angle]], denoted by the symbol $I$.\\
{{ :yanding:成像基础知识:光学:辐射度学与光度学:辐射强度.png?400 |}}
**Mathematical expression:** $$I = \frac{d\Phi}{d\Omega}$$
**Radiant intensity is a core property of point sources**\\
**1. For stars,** the observation distance r is measured in light-years. To a detector, the angular size of a star is extremely small (measured in milliarcseconds), so it can be treated as a point source. For a spherical surface centered on the star, the difference between the detector's planar area and the spherical surface area is negligible. Thus, the solid angle $\Omega$ can be calculated from the detector area $A$ and the distance $r$: $\Omega = \frac{A}{r^2}$, and the radiant intensity can be calculated from the radiant flux $\Phi $ and the solid angle $\Omega$: $ I = \frac{d\Phi}{d\Omega}$.\\

**2. For radiation sources at a finite distance,** when the observation distance r >> the maximum characteristic dimension of the source $D$, the angular size of the source as seen by the detector is relatively small (e.g., a car headlight with a diameter of 20 cm at a distance of 25 m has an angular size of about 0.46°). The effect of the source's geometry on the spatial distribution of radiation can be neglected, and all radiation can be considered as originating from a single point using the "far-field approximation." In this case, the radiant intensity can still be calculated as: $ I = \frac{d\Phi}{d\Omega}$.\\