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I was reading a thread where you have comprehensively answered about radiometric units (Deriving radiance from irradiance and intensity).

My question is whether we can convert from W/cm2 ( or W/m2) to W/sr. We are measuring the irradiance (W/cm2) at 1 meter distance. Please explain. Thanks

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  • $\begingroup$ As there are 4pi steradians in the solid angle subtended but a sphere and 4pi m2 in surface area for a sphere with 1 m radius does that not mean that at 1 m distance W/m2 is equal to (numerically) W/sr? $\endgroup$ Feb 3, 2023 at 23:44

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In general $W/m^2$ and $W/sr$ are different units of measure for radiant energy so can not be converted between.

However, given the geometry of the area to be measured and the radiant energy for that area then conversion can be done:

To convert from watts per square meter (W/m²) to watts per steradian (W/sr), you would need to determine the solid angle subtended by the surface. The solid angle can be calculated from the surface area and the distance from the surface to the point at which the radiation is being measured.

Once you have the solid angle, you can convert W/m² to W/sr by dividing by the surface area:

$W/sr = (W/m²) / (surface area / (distance)^2)$

where surface area is expressed in square meters and distance is expressed in meters.

Note that the resulting unit will depend on the surface area and distance, and the formula is only valid for isotropic radiators, i.e., radiators that emit energy uniformly in all directions.

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  • $\begingroup$ This expression is a bit confusing: "W/sr=(W/m²)/(surface area/(distance)2)". What is the "surface area" here? And is the "distance" here source to target distance? Also what is the role of the aperture of the detector in this calculation (from W/m2) to W/sr? $\endgroup$
    – NKR
    Feb 7, 2023 at 4:58
  • $\begingroup$ Distance is the from the radiator. So it should be 1 meter in this case. Surface area is the surface area of the radiator. surfacearea/distance^2 is the solid angle. Surface area is expressed in square meters. And distance is expressed in meters. $\endgroup$
    – pmw1234
    Feb 7, 2023 at 21:58
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If the irradiance is constant over the surface considered (or if the surface is small enough), one steradian corresponds to an area of $1/4\pi\,m^2$ on the unit sphere so that $1 W/m^2$ is equivalent to $4\pi\,W/sr$ at $1\,m$.

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