Consider an airfoil blade sunshade (see the diagram below). It consists of multiple flat rectangular shapes which are parallel to each other but make an angle ($v$) to the horizontal plane. The blades are separated by a distance ($s$) and have length ($L$). The blades are placed so that light rays parallel to the blades can fully pass, but light rays with an angle larger than ($w$), $w>v$, are fully blocked. Rays with angles between $v$ and $w$ will pass partly.
How can the passing light fraction be expressed as a function of the angle of the incident light?
The situation is much simpler to conceptualize if we align our coordinate system so that the light rays are parallel to a coordinate axis:
Left: $\varphi \lt \beta$. Right: $\varphi \gt \beta$.
Above, $S$ is the distance between the pivot points, $L$ is the width of the louvres, $\beta$ is the solar elevation angle (the angle between horizontal and the light rays), and $\varphi$ is the angle between the louvres and horizontal.
Since the wall is vertical, $0 \le \beta \lt 90°$. We exclude negative angles based on the sun then being under the horizon. We exclude angles above $90°$ because they are directly above or behind the wall (shaded by the roof or the other side of the wall).
Let's make these really adjustable louvres, with $-90° \lt \varphi \lt 90°$. Thus, $$-90° \le \beta - \varphi \le 180°$$
As stated in the question, when $\beta = \varphi$ all light passes, so the louvres have no appreciable thickness. We also assume the louvres cover the entire wall we care about.
Perpendicular to the light, $d$ is the distance between louvres, and $h$ is the part shadowed by each louvre. The fraction of light passed through the louvres is therefore $$\alpha = \left \lbrace \begin{matrix} 1 - \frac{h}{d}, & h \lt d \\ 0, & h \ge d \end{matrix} \right.$$ Note that even though the wall is not vertical, the ratio of shadow per louvre, $h/d$, is still valid. The angle between the wall and the light just scales both $h$ and $d$ (by $1/cos(\beta)$), that's all.
Using the properties of the two right triangles, we have $$h = L \sin(\lvert\beta-\varphi\rvert)$$ and $$d = S \cos\beta$$ Therefore the fraction of light passing through the louvres is $$\alpha = \max\left( 0, \; 1 - \frac{L}{S} \frac{\sin \lvert\beta-\varphi\rvert}{\cos\beta} \right )$$
Even if the angle between the louvres and light was obtuse, the above still holds. In the illustration above, at $(\beta-\varphi) \gt 90°$ the louvres hang down left; at $0° \lt (\beta-\varphi) \lt 90°$ they hang down right, and when $-90° \lt (\beta-\varphi) \lt 0°$, they hang up right.