![](https://uploads-us-west-2.insided.com/zemax-en/attachment/c566c8e1-29f9-4b56-b76c-eba5a3ad8b2f.jpg)
The definition of a solid angle can be found in the Wiki.
https://en.wikipedia.org/wiki/Solid_angle
From the Wiki, you may know a solid angle can be calculated from the following formula.
(Eq.1)
![](https://uploads-us-west-2.insided.com/zemax-en/attachment/7d6ebf6d-54f8-4f5a-a18a-4909f242ef6e.jpg)
And the relationship between (θx,θy) and (θ,φ) is as shown in the following equation.
![](https://uploads-us-west-2.insided.com/zemax-en/attachment/1b881102-5bab-4a74-9578-8823fef75757.jpg)
The variables in (Eq 1) are (θ,φ). We will convert them to (θx,θy) by the way of variable transformation.
![](https://uploads-us-west-2.insided.com/zemax-en/attachment/6b0281ea-325f-422b-b6d4-62e613e229ab.jpg)
Finally we can get the result as below.
(Eq. 2)
![](https://uploads-us-west-2.insided.com/zemax-en/attachment/20cf17ed-c500-4c7a-87a9-1a7c962748c6.jpg)
(Eq. 2) can be used to calculate the solid angle from a specific pixel coordinate.
However, there is no analytical solution for this equation. We know that a numerical solution can be calculated.
In fact, our algorithm is not this method. When OpticStudio calculate the radiant intensity, a iteration method is used.
Theoretically, the result is the same. One of our users has verified this.