# Measuring Diffuse Sky Radiance with An Affordable and Open-Source All-Sky Imager

Valentin Bauer, Yehia Eissa, Yves-Marie Saint-Drenan, Philippe Blanc

► To cite this version:

Valentin Bauer, Yehia Eissa, Yves-Marie Saint-Drenan, Philippe Blanc. Measuring Diffuse Sky Radiance with An Affordable and Open-Source All-Sky Imager. Young Scientist Symposium 2025, Nov 2025, Klosterneuburg, Austria., 2025, 10.34726/11416. [https://hal.science/hal-05385520v1](https://hal.science/hal-05385520v1)

HAL Id: hal-05385520

Submitted on 27 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Measuring Diffuse Sky Radiance with An Affordable and Open-Source All-Sky Imager

<figure><img src="image_2.png" /></figure>

YSS
2025

Unlocking Nature's Genius

## Authors

**Valentin BAUER**
Yehia EISSAª
Yves-Marie SAINT-DRENANª
Philippe BLANCª

## Partners

ª Centre O.I.E.,
MINES Paris PSL

## Contact & Publication

valentin.bauer@tuwien.ac.at

<figure><img src="image_3.png" /></figure>

https://doi.org/
10.34726/hss.2025.120149

## References

[1] M. Sengupta et al., "Best Practices Handbook for the Collection and Use of Solar Resource Data for Solar Energy Applications: Fourth Edition," NREL/TP-5D00-88300, 2448063, Mainld: 89075, Sep. 2024. doi: 10.2172/2448063.

[2] N. Lindsay, Q. Libois, J. Badosa, A. Migan-Dubois, and V. Bourdin, "Errors in PV power modelling due to the lack of spectral and angular details of solar irradiance inputs," Solar Energy, vol. 197, pp. 266-278, Feb. 2020, doi: 10.1016/j.solener.2019.12.042.

[3] H. Vasquez, py-OCamCalib. Accessed: May 24, 2024. [Online]. Available: https://github.com/jakarto3d/py-OCamCalib/tree/main

[4] Ph. Blanc and L. Wald, "The SG2 algorithm for a fast and accurate computation of the position of the Sun for multi-decadal time period," Solar Energy, vol. 86, no. 10, pp. 3072-3083, Oct. 2012, doi: 10.1016/j.solener.2012.07.018.

[5] C. Emde et al., "The libRadtran software package for radiative transfer calculations (version 2.0.1)," Geoscientific Model Development, vol. 9, no. 5, pp. 1647-1672, May 2016, doi: 10.5194/gmd-9-1647-2016.

[6] "CAMS solar radiation time-series." Accessed: Mar. 04, 2025. [Online]. Available: https://ads.atmosphere.copernicus.eu/datasets/cams-solar-radiation-timeseries?tab=overview

## 1. A camera for sky radiance measurement?

State-of-the-art pyranometers and pyrheliometers can precisely measure broadband surface solar irradiance components [1]. However, their high cost is a barrier to widespread deployment. Also, characterizing the sky's radiance in greater **angular and spectral detail** is necessary [2] for solar forecasting and atmospheric analysis. We designed and assembled a **low-cost** (approx. 300€) fish-eye camera based on a **Raspberry Pi 4**, and propose a methodology using **open-source** software to estimate **pixel-wise diffuse sky radiances in three spectral bands** (Red, Green, Blue).

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>Low-Cost
All-Sky Camera</figcaption></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>RGB Color Image</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>RGB Radiance Estimates</figcaption></figure>

## 2. Geometric Calibration

*Which sky point does a pixel correspond to?*

<figure><img src="image_9.png" /></figure>

Image coordinates are mapped to local sky coordinates (azimuth φ, zenith θ) by using py-OCamCalib [3] for intrinsic geometric calibration, and a comparison of sun positions from the SG2 algorithm [4] against sun detections for extrinsic geometric calibration. The mapping error is estimated by **comparing detected and estimated sun positions**, and on average less than 1° of angular error is achieved.

<table><thead><tr><th>Angular Error<br>Camera Location</th><th>Mean Bias<br>Error [°]</th><th>Std. Deviation<br>of Error [°]</th><th>Sun Detections<br>#</th></tr></thead><tbody><tr><td>Sophia Antipolis, France</td><td>0.75</td><td>0.47</td><td>2854</td></tr><tr><td>Vienna, Austria</td><td>0.41</td><td>0.27</td><td>3956</td></tr></tbody></table>

## 3. Radiometric Calibration

*What radiance does a pixel value represent?*

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Clear Sky Camera Image Patches (left) and Simulated Radiances (right)
Camera in Vienna, Austria, single point in time, RGB combined)</figcaption></figure>

To calibrate raw image values to sky radiance in W/(m² sr), circular patches of 5° opening angle are extracted at fixed sky points from high dynamic range images under clear-sky conditions. For each patch, a corresponding diffuse sky radiance is simulated using libRadtran [5], parameterized with data of the atmospheric composition from the Copernicus Atmosphere Monitoring Service (CAMS) [6]. Image values are normalized pixel-wise by solid angle, patches are averaged, and the simulated radiances are filtered and integrated using the sensor's spectral response function.

## 4. Results and Outlook

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>Clear Sky Measured Brightness vs. Simulated Radiance

*(Camera in Vienna, Austria, 18 time points over two days, N=882 points per channel)*</figcaption></figure>

Each color channel's measured brightness are shown to relate linearly to the simulated radiances, which validates our methodology for computing diffuse sky radiance from sky images. Next steps include calibration and validation of the spectral (RGB) and broadband sky radiance with a high-quality pyranometer, and moving to applications like forecasting of the surface downwelling solar resource or atmospheric analysis

<figure><img src="image_15.png" /></figure>