De Soto cover

Method

The accepted fraction of the direct sunlight is the transmittance of the module cover at the incidence angle divided by its transmittance at perpendicular incidence. Each layer of the cover refracts the light by Snell's law, reflects the average of the two polarisations given by Fresnel's equations, and absorbs along the refracted path by Bouguer's law. The direct light crosses a thin anti-reflective coating and then the glass. The incidence angle is held between 1° and 89°, and the fraction is capped at 1. The reference at perpendicular incidence is taken at 1°, and its glass layer is computed with air, not the coating, on the incoming side. When the next step integrates the diffuse light at effective angles, the sky and ground light are read at those angles through plain glass, divided by the same reference and capped at 1. With the other options of the Incidence-angle modifier, diffuse and albedo step, the curve of the direct light is averaged. With the anti-reflective coating switched off, the direct light and the reference cross plain glass too.

Settings

Setting	Value
Refractive index of the glass $n_g$	1.526
Thickness of the glass $\ell_g$	2 mm
Refractive index of the coating $n_c$	1.3
Thickness of the coating $\ell_c$	0.02 mm
Extinction coefficient $K$	4 /m, both layers
Incidence angles of the direct light	held between 1° and 89°
Anti-reflective coating	on (the Glass switch of the Module tab)

The math

1. Transmittance of one layer
2. Direct light through the coating and the glass
3. Reference at perpendicular incidence
4. Accepted fraction of the direct light
5. Accepted fractions of the sky and ground light

$$\tau(\theta_1;\,n_2, n_1, \ell) = \left[1 - \tfrac{1}{2}\left(\frac{\sin^2(\theta_2 - \theta_1)}{\sin^2(\theta_2 + \theta_1)} + \frac{\tan^2(\theta_2 - \theta_1)}{\tan^2(\theta_2 + \theta_1)}\right)\right] e^{-K \ell/\cos\theta_2},\qquad \sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 \tag{1}$$ $$\tau_b(\theta) = \tau(\theta;\,n_c, 1, \ell_c)\ \tau(\theta_c;\,n_g, n_c, \ell_g) \tag{2}$$ $$\tau_n = \tau(1°;\,n_c, 1, \ell_c)\ \tau(\theta_{c,1};\,n_g, 1, \ell_g) \tag{3}$$ $$F(\theta) = \min\!\left(1,\ \frac{\tau_b(\min(\max(\theta, 1°), 89°))}{\tau_n}\right) \tag{4}$$ $$F_{sky} = \min\!\left(1,\ \frac{\tau(\theta_{sky};\,n_g, 1, \ell_g)}{\tau_n}\right),\qquad F_{gnd} = \min\!\left(1,\ \frac{\tau(\theta_{gnd};\,n_g, 1, \ell_g)}{\tau_n}\right) \tag{5}$$

where

Symbol	Meaning	Unit
$\tau$	the transmittance of a layer	—
$\theta_1$	the angle of the light arriving at the layer	degrees
$\theta_2$	the angle of the light refracted into the layer	degrees
$n_1, n_2$	the refractive indices of the incoming medium and of the layer	—
$\ell$	the thickness of the layer	m
$K$	the extinction coefficient	1/m
$\tau_b(\theta)$	the transmittance of the cover for the direct light	—
$\theta$	the incidence angle of the direct light	degrees
$\theta_c$	the angle refracted into the coating	degrees
$n_c, n_g$	the refractive indices of the coating and of the glass	—
$\ell_c, \ell_g$	the thicknesses of the coating and of the glass	m
$\tau_n$	the reference transmittance	—
$\theta_{c,1}$	the angle refracted into the coating at 1°	degrees
$F(\theta)$	the accepted fraction of the direct light	—
$F_{sky}, F_{gnd}$	the accepted fractions of the sky and ground light	—
$\theta_{sky}, \theta_{gnd}$	the effective incidence angles of the sky and ground light, from the next step	degrees

References

1. De Soto, Klein & Beckman 2006, Improvement and validation of a model for photovoltaic array performance, Solar Energy 80(1) 78–88
2. Duffie & Beckman, Solar Engineering of Thermal Processes, 4th ed., Wiley 2013
3. NREL SAM Simulation Core (SSC) source code, release 2026.7.3, github.com/NatLabRockies/ssc: shared/lib_pv_incidence_modifier.cpp, functions transmittance() and calculateIrradianceThroughCoverDeSoto()

API

iam.kind = desoto, iam.ar_coating = true

Symbols follow the symbol registry.