# Pushing the limits of beam-steering lens arrays

Håkon Jarand Dugstad Johnsen1, Astrid Aksnes2, Jan Torgersen1
1Department of Mechanical and Industrial Engineering, NTNU
2Department of Electronic Systems, NTNU

# How?

## Why?

• No rotation
• Small physical footprint
• Low power, fast, accurate tracking

## Old news?

• Johnsen, 2018
• Lin, 2012

• Objectives

# Choose an orientation Inspired by Ito et al.
Ito, A., Sato, D. and Yamada, N., “Optical design and demonstration of microtracking CPV module with bi-convex aspheric lens array,” Opt. Express, OE 26(18), A879–A891 (2018).

# Angular distribution of sunlight  # Average yearly efficiency # Objectives

Maximize average yearly efficiency
η
Minimize divergence
θmax
• Minimize cost & complexity

# Minimize cost & complexity

• Difficult to quantify
• Try a few different configurations:
1
2
3
4

# Design method

• Numerical optimization
• Scalarizing by fixing $\theta_{max}$
• Memetic programming
• Ray-tracing simulations
• Custom ray-tracer, Python & Numba
• Material: PMMA
$$\min\,\mathbf{f}\left(\mathbf{x},\theta_{max}\right)=\left(1-\overline{\eta}\left(\mathbf{x},\theta_{max}\right),\theta_{max}\right)^{T}\\\text{such that}\,\,g_{j}\left(\mathbf{x}\right)\le0,$$

# Optimization results # Selected example 1

 Average yearly efficiency: 74.4% Permitted divergence: 1° (Concentration limit $\frac{1}{\left(\sin 1^{\circ}\right)^2}$: ≈3300x)

# Selected example 2

 Average yearly efficiency: 74.6% Permitted divergence: 2.2° (Concentration limit $\frac{1}{\left(\sin 2.2^{\circ}\right)^2}$: ≈680x)

# Benefits

• Reduced physical footprint
• Low-power, high-accuracy, high-speed tracking

# Drawbacks

• Cosine projection effect # Outlook

• More configurations & orientations
• Alignment tolerances
• New proof-of-concept

# Conclusions

• New and promising configurations
• Comparison framework
• Design method
Interested?
hakon.j.d.johnsen@ntnu.no