## Materials and Methods
### Irradiance Tilt Correction Using Multi View Angle Observations  
The novel aspect in AIRS irradiance measurement (Figure 1) is the method to mathematically correct for the tilt of the irradiance measurement using three (or more) tilted photodiode irradiance sensors. However, this method is not limited to exact hardware choices made for the FGI AIRS unit \begin{table}
\begin{tabular}{c c} \hline
**Component** & **Description** \\
**Spectrometer:** & For measuring irradiance spectrum in 350–1000 nm \\ _Ocean Optics USB2000+_ & range with 1 nm spectral resolution \\
**Photodiode (units):** & For measuring irradiance on RGB+Pan bands at three \\ _Grove I2C Color Sensor (TCS3414 CS)_ & different tilt angles \\
**Ground glass diffusers:** & Foreoptics with near-Lambertian field-of-view for the \\ _Edmund Optics 47717_ and _46105_ & spectrometer and photodiodes \\
**Inertial Navigation System:** & For providing orientation and GPS timing \\ _VectorNav VN-200 + Tallysman TW4421_ & for the system. \\
**Real time kinematic GNSS:** & For providing accurate single-band kinematic global \\ _uBlox NEO-M8T + Tallysman TW4421_ & navigation satellite system (GNSS) positioning \\
**Control computer:** & For data acquisition, general-purpose input/output (GPIO) interactions, data processing, \\ _Raspberry Pi 3 Model B_ & and real-time outputs. \\ \multirow{2}{*}{**Custom frame**} & Selective laser sintering (SLS) 3D printed in nylon \\  & and painted in black \\ \hline \end{tabular}
\end{table} 
Table 1: The main components of FGI AIRS. Figure 1: Enhanced photo of the Finnish Geospatial Research Institute Aerial Image Reference System (FGI AIRS) visualizing the view directions of the spectrometer and the photodiodes. but can be also employed in other suitable configurations. For the irradiance tilt correction, the critical AIRS components are the upward looking spectrometer, the three photodiodes, each tilted 10\({}^{\circ}\) from zenith in opposite directions (Figure 1), and the IMU. Firstly, the system tilt angles from IMU and the readings of the three photodiodes are used to calculate readings for virtual photodiodes in desired angles. By applying the boresight angle of each photodiode to the IMU roll and pitch angles of the whole system, the pointing direction of each photodiode in global coordinates can be calculated. These photodiodes provide 3 samples of an irradiance sensor reading at different known tilt angles. This data can be used to interpolate a reading of a virtual photodiode pointing to any direction within the real photodiode pointing directions. In our implementation, we chose to use bilinear interpolation, as it is the simplest type of interpolation and sets the least assumptions on the angular distribution of the illumination. This, however, assumes linear development of the irradiance sensor reading within the tilt angles of the photodiodes. In our testing, this was found to be sufficiently accurate, and no need was found for more advanced interpolation or irradiance modeling strategies. This interpolation is then used to calculate irradiance readings for a virtual photodiode pointing to zenith (\(E^{\prime}_{\frac{\cdot}{gen}}\)) and another virtual photodiode pointing to the view direction of the spectrometer (\(E^{\prime}_{\frac{\cdot}{spec}}\)). Using this information, the spectrometer irradiance spectrum (\(E_{\frac{\cdot}{spec}}(\lambda)\)) can be converted to tilt corrected irradiance spectrum (\(E_{\frac{\cdot}{gen}}(\lambda)\)):  
\[E_{\frac{\cdot}{gen}}(\lambda)=\frac{E^{\prime}_{\frac{\cdot}{gen}}}{E^{ \prime}_{\frac{\cdot}{gen}}}E_{\frac{\cdot}{spec}}(\lambda) \tag{1}\]  
The equation above uses only a single-band photodiode for the correction of the whole spectrum. As, in blue sky conditions, the angular distribution of irradiance is strongly wavelength dependent, taking advantage of the photodiode RGB bands can be useful.