Here's an example of a 61-CoB lighting array.

And with just 2 linear connector modules, two square lighting arrays can be conjoined to form a perfect rectangular lighting array.

Visualizing Light Uniformity

Below are graphical representations that demonstrate the effectiveness of employing the UPFP in our patented technology to achieve truly uniform light distribution. Each set of graphs compares a traditional or less optimized approach (right) with our UPFP-based solution (left).

Beam Profile

These graphs illustrate the spatial distribution of light intensity, highlighting the "superfluous energy" outside the target PPFD range. The UPFP-based graph on the left demonstrates a more uniform beam spread with significantly reduced energy waste.

Figure 1: Comparison of Beam Profiles. Right: Traditional distribution. Left: Optimized UPFP distribution.

PPFD Surface Graphs

These 3D graphs illustrate the spatial distribution of PPFD, as presented in our research. The colors represent different intensity levels, with blue being low and red being high. The orange rectangle shows the target PPFD range. Note how the UPFP-based graph on the left exhibits a more uniform distribution with minimal "superfluous energy" (light outside the target PPFD range).

Figure 2: Comparison of PPFD Surface Graphs. Right: Traditional distribution. Left: Optimized UPFP distribution.

2D Variance Graphs

These graphs provide a top-down view of the PPFD distribution, highlighting the variance from the target PPFD. The UPFP-based approach (left) demonstrates significantly reduced variance in photon distribution, showcasing far superior uniformity.

Figure 3: Comparison of 2D Variance Graphs. Right: Traditional distribution. Left: Optimized UPFP distribution.

Heatmaps

Heatmaps offer another intuitive way to visualize PPFD distribution. Warmer colors (reds) represent higher PPFD, while cooler colors (blues) represent lower PPFD. The UPFP-based heatmap (left) displays a more consistent color across the growing area, signifying superior uniformity. While the competitor displays a pronounced concentration of photons toward the center of the illuminated area, as can be seen by the circular radiation pattern.

Figure 4: Comparison of PPFD Heatmaps. Right: Traditional distribution. Left: Optimized UPFP distribution.

Proprietary Machine Learning Algorithm

Central to our Uniform Photon Flux Principle (UPFP) is a sophisticated machine learning algorithm that dynamically optimizes LED intensities to ensure uniform Photosynthetic Photon Flux Density (PPFD) across the grow area. Below are key components of our algorithm:

Optimization Function

The optimization function minimizes the Mean Absolute Deviation (MAD) of PPFD from the target value while adhering to energy constraints. Here's a snippet of how the objective function is defined:

        def objective_function(light_intensities, target_ppfd):
            ppfd_values = calculate_ppfd(light_intensities)
            mad = np.mean(np.abs(ppfd_values - target_ppfd))
            energy_consumption = np.sum(light_intensities)
            return mad + 0.3 * energy_consumption
                        

        def lambertian_emission(intensity, distance, height):
            if distance == 0:
                return intensity
            return (intensity * height) / ((distance ** 2 + height ** 2) ** 1.5)
                        

        result = minimize(
            objective_function,
            initial_intensities,
            args=(target_ppfd,),
            method='SLSQP',
            bounds=bounds,
            constraints=constraints
        )
                        

Explanation:
The `minimize` function seeks the optimal light intensities for each concentric square layer of CoBs in our patented solution's LED arrangement that reduce the MAD, while respecting predefined bounds and constraints. The SLSQP method efficiently handles both equality and inequality constraints, making it suitable for our optimization needs.

Real-Time Adjustments

An integral component of our agentic AI platform, our algorithm continuously monitors environmental data from integrated sensors. Based on real-time feedback, it dynamically recalibrates LED intensities to maintain optimal PPFD levels, ensuring consistent plant growth conditions.

Benefits of Our Algorithm

Interactive Demo

Explore our optimization process through an interactive simulation. Adjust parameters such as floor dimensions and perimeter reflectivity to see how our algorithm adapts LED intensities to maintain uniform PPFD.

Technical Details

Our UPFP technology is based on rigorous mathematical modeling and optimization techniques. Here are some key technical aspects:

Experimental Validation

We are committed to rigorous experimental validation of our UPFP technology. We will be using Apogee Instruments spectroradiometers (PS series for lab testing and the MS-100 handheld for field testing) to empirically verify the principle across the 380–1000 nm range. These measurements will enable us to: