# Uniform Illumination Using Single-Surface Lens through Wavefront Engineering

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{chief}− L

_{sp}− L

_{pt},

_{chief}, L

_{sp}and L

_{pt}correspond to chief ray (the shortest), source to principal plane, and principal plane to target optical path lengths, respectively. Figure 2a demonstrates the OPDs of some rays (purple lines).

^{®}Square, GH CSSRM4.24). In this simulation, the target plane is a square-shaped area of $1{\mathrm{m}}^{2}$ located 25 cm from the source, perpendicular and centered to the optical axis. The detector plane (target plane) resolution is 200 by 200, and the lens refractive index is assumed to be 1.4880 (PMMA @660 nm). Analyzing the results and calculating the uniformity and power in the specified target plane were carried out using MATLAB.

## 3. Results and Discussion

## 4. Conclusions

## 5. Patents

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Haitz, R.; Tsao, J.Y. Solid-state lighting:‘The case’10 years after and future prospects. Phys. Status Solidi
**2011**, 208, 17–29. [Google Scholar] [CrossRef] - Gupta, S.D.; Agarwal, A. LED Supplementary Lighting. In Light Emitting Diodes for Agriculture, 1st ed.; Springer: Singapore, 2017; pp. 27–36. [Google Scholar]
- Bula, R.J.; Morrow, R.C.; Tibbitts, T.; Barta, D.; Ignatius, R.; Martin, T. Light-emitting diodes as a radiation source for plants. HortScience
**1991**, 26, 203–205. [Google Scholar] [CrossRef] [PubMed] - Nelson, J.A.; Bugbee, B. Economic analysis of greenhouse lighting: Light emitting diodes vs. high intensity discharge fixtures. PLoS ONE
**2014**, 9, e99010. [Google Scholar] [CrossRef] - Kusuma, P.; Pattison, P.M.; Bugbee, B. From physics to fixtures to food: Current and potential LED efficacy. Hortic. Res.
**2020**, 7, 56. [Google Scholar] [CrossRef] - Wu, B.-S.; Hitti, Y.; MacPherson, S.; Orsat, V.; Lefsrud, M.G. Comparison and perspective of conventional and LED lighting for photobiology and industry applications. Environ. Exp. Bot.
**2020**, 171, 103953. [Google Scholar] [CrossRef] - Paucek, I.; Appolloni, E.; Pennisi, G.; Quaini, S.; Gianquinto, G.; Orsini, F. LED lighting systems for horticulture: Business growth and global distribution. Sustainability
**2020**, 12, 7516. [Google Scholar] [CrossRef] - Katzin, D.; Marcelis, L.F.; van Mourik, S. Energy savings in greenhouses by transition from high-pressure sodium to LED lighting. Appl. Energy
**2021**, 281, 116019. [Google Scholar] [CrossRef] - Shelford, T.J.; Both, A.-J. On the technical performance characteristics of horticultural lamps. AgriEngineering
**2021**, 3, 716–727. [Google Scholar] [CrossRef] - Runkle, E. The Importance of Light Uniformity; Michigan State University: East Lansin, MI, USA, 2017. [Google Scholar]
- Poorter, H.; Niinemets, Ü.; Ntagkas, N.; Siebenkäs, A.; Mäenpää, M.; Matsubara, S.; Pons, T. A meta-analysis of plant responses to light intensity for 70 traits ranging from molecules to whole plant performance. New Phytol.
**2019**, 223, 1073–1105. [Google Scholar] [CrossRef] [PubMed] - Balázs, L.; Dombi, Z.; Csambalik, L.; Sipos, L. Characterizing the Spatial Uniformity of Light Intensity and Spectrum for Indoor Crop Production. Horticulturae
**2022**, 8, 644. [Google Scholar] [CrossRef] - Both, A.; Ciolkosz, D.E.; Albright, L. Evaluation of light uniformity underneath supplemental lighting systems. In Proceedings of the IV International ISHS Symposium on Artificial Lighting 580, Québec City, QC, Canada, 7 November 2000; pp. 183–190. [Google Scholar]
- Ciolkosz, D.E.; Both, A.J.; Albright, L.D. Selection and placement of greenhouse luminaires for uniformity. Appl. Eng. Agric.
**2001**, 17, 875. [Google Scholar] [CrossRef] - Pan, J.; Li, Q.; Li, X.; Wen, Y. Spatial light distribution characterization and measurement of LED horticultural lights. In Proceedings of the 29th CIE Session, Washington, DC, USA, 14–16 June 2019; pp. 14–22. [Google Scholar]
- Ding, Y.; Liu, X.; Zheng, Z.-r.; Gu, P.-f. Freeform LED lens for uniform illumination. Opt. Express
**2008**, 16, 12958–12966. [Google Scholar] [CrossRef] - Fang, F.; Zhang, X.; Weckenmann, A.; Zhang, G.; Evans, C. Manufacturing and measurement of freeform optics. CIRP Ann.
**2013**, 62, 823–846. [Google Scholar] [CrossRef] - Desnijder, K.; Hanselaer, P.; Meuret, Y. Ray mapping method for off-axis and non-paraxial freeform illumination lens design. Opt. Lett.
**2019**, 44, 771–774. [Google Scholar] [CrossRef] - Bösel, C.; Gross, H. Ray mapping approach for the efficient design of continuous freeform surfaces. Opt. Express
**2016**, 24, 14271–14282. [Google Scholar] [CrossRef] [PubMed] - Feng, Z.; Cheng, D.; Wang, Y. Iterative wavefront tailoring to simplify freeform optical design for prescribed irradiance. Opt. Lett.
**2019**, 44, 2274–2277. [Google Scholar] [CrossRef] - Bösel, C.; Gross, H. Double freeform illumination design for prescribed wavefronts and irradiances. JOSA A
**2018**, 35, 236–243. [Google Scholar] [CrossRef] [PubMed] - Gannon, C.; Liang, R. Ray mapping with surface information for freeform illumination design. Opt. Express
**2017**, 25, 9426–9434. [Google Scholar] [CrossRef] - Bruneton, A.; Bäuerle, A.; Wester, R.; Stollenwerk, J.; Loosen, P. High resolution irradiance tailoring using multiple freeform surfaces. Opt. Express
**2013**, 21, 10563–10571. [Google Scholar] [CrossRef] [PubMed] - Feng, Z.; Huang, L.; Gong, M.; Jin, G. Beam shaping system design using double freeform optical surfaces. Opt. Express
**2013**, 21, 14728–14735. [Google Scholar] [CrossRef] - Feng, Z.; Cheng, D.; Wang, Y. Iterative freeform lens design for prescribed irradiance on curved target. Opto-Electron. Adv.
**2020**, 3, 200010-200011–200010-200019. [Google Scholar] [CrossRef] - Romijn, L.B.; ten Thije Boonkkamp, J.H.; IJzerman, W.L. Freeform lens design for a point source and far-field target. JOSA A
**2019**, 36, 1926–1939. [Google Scholar] [CrossRef] - Byzov, E.V.; Kravchenko, S.V.; Moiseev, M.A.; Bezus, E.A.; Doskolovich, L.L. Optimization method for designing double-surface refractive optical elements for an extended light source. Opt. Express
**2020**, 28, 24431–24443. [Google Scholar] [CrossRef] - Ma, D.; Feng, Z.; Liang, R. Freeform illumination lens design using composite ray mapping. Appl. Opt.
**2015**, 54, 498–503. [Google Scholar] [CrossRef] - Bruneton, A.; Bäuerle, A.; Wester, R.; Stollenwerk, J.; Loosen, P. Limitations of the ray mapping approach in freeform optics design. Opt. Lett.
**2013**, 38, 1945–1947. [Google Scholar] [CrossRef] - Wei, S.; Zhu, Z.; Fan, Z.; Ma, D. Least-squares ray mapping method for freeform illumination optics design. Opt. Express
**2020**, 28, 3811–3822. [Google Scholar] [CrossRef] [PubMed] - Oliker, V.I.; Rubinstein, J.; Wolansky, G. Ray mapping and illumination control. J. Photonics Energy
**2013**, 3, 035599. [Google Scholar] [CrossRef] - Ma, D.; Feng, Z.; Liang, R. Tailoring freeform illumination optics in a double-pole coordinate system. Appl. Opt.
**2015**, 54, 2395–2399. [Google Scholar] [CrossRef] - Wu, R.; Feng, Z.; Zheng, Z.; Liang, R.; Benítez, P.; Miñano, J.C.; Duerr, F. Design of freeform illumination optics. Laser Photonics Rev.
**2018**, 12, 1700310. [Google Scholar] [CrossRef] - Wang, K.; Liu, S.; Chen, F.; Qin, Z.; Liu, Z.; Luo, X. Freeform LED lens for rectangularly prescribed illumination. J. Opt. A Pure Appl. Opt.
**2009**, 11, 105501. [Google Scholar] [CrossRef] - Zhenrong, Z.; Xiang, H.; Xu, L. Freeform surface lens for LED uniform illumination. Appl. Opt.
**2009**, 48, 6627–6634. [Google Scholar] [CrossRef] [PubMed] - Sorgato, S.; Chaves, J.; Thienpont, H.; Duerr, F. Design of illumination optics with extended sources based on wavefront tailoring. Optica
**2019**, 6, 966–971. [Google Scholar] [CrossRef]

**Figure 1.**Ray-mapping algorithm demonstration. (

**a**) 3D presentation of the principal plane and target plane. (

**b**) Cross section of the LED, the principal plane, and the target plane. d1 to dN are the widths of each ring on the principal plane, while L is the width of the corresponding rings on the target plane. (

**c**) Principal plane rings and sample points (yellow and green crosses). (

**d**) Corresponding mapped rings and sample points on the target plane.

**Figure 2.**Wavefront tailoring process. (

**a**) cross section of the incident (solid red curve), refracted (blue curve) and free-space propagated (dashed red curve) wavefronts to calculate optical path differences. Lens to principal plane and principal plane target plane rays have been illustrated with orange and green line, respectively. (

**b**) Required OPD based on wavefront tailoring (purple curve) for each point of the principal plane cross section (gray line on (

**a**)) and the corresponding lateral momentum change on the lens cross section (red graph).

**Figure 3.**Lens surface construction. (

**a**) 2D presentation of the numerical lens surface calculation by translation of refraction surface (purple lines) on principal plane (gray line) to the lens surface. (

**b**) Final lens design cross-section on xz-plane. (

**c**) manufactured lens and the LED assembly image.

**Figure 4.**The experimental setup computer-aided design (CAD). (

**a**) Dimetric view of the photodetector and the 2D translation stage, which measures the light intensity and its uniformity. (

**b**) 2D view (yz-plane) of the setup. The source placed 25 cm above the center point of the scanner to obtain experimental results. (

**c**) 2D view (xz-plane) of the setup. The source placed 25 cm above the center point of the scanner to obtain experimental results.

**Figure 5.**Simulation and experimental results for a target plane located 25 cm away from the source. (

**a**) ZEMAX simulation result for OSRAM LED rayfile without the lens. Dashed purple line indicates the middle row. (

**b**) Simulation result for OSRAM LED rayfile with the lens. (

**c**) Comparing middle rows’ irradiances (dashed horizontal lines on Figure 2a,b) of the simulation result with (green curve) and without (purple curve) the lens. (

**d**) Normalized irradiance for experimental result without the lens. (

**e**) Normalized irradiance for experimental result with the lens. (

**f**) Comparing middle rows’ irradiances of the experimental result with (green line) and without (purple line) the lens.

**Figure 6.**Simulation and experimental results for a 1 by 25 LED array, oriented along the x-axis. (

**a**) Simulation result for a 1 m

^{2}target plane, located 25 cm away from the LED array. (

**b**) Simulation result for a 4 m

^{2}target plane, located 50 cm away from the LED array. (

**c**) Experimental result for a 1 m

^{2}target plane, located 25 cm away from the LED array. (

**d**) Experimental result for a 4 m

^{2}target plane, located 50 cm away from the LED array.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Moaven, A.; Pahlevaninezhad, H.; Pahlevaninezhad, M.; Pahlevani, M. Uniform Illumination Using Single-Surface Lens through Wavefront Engineering. *Horticulturae* **2022**, *8*, 1019.
https://doi.org/10.3390/horticulturae8111019

**AMA Style**

Moaven A, Pahlevaninezhad H, Pahlevaninezhad M, Pahlevani M. Uniform Illumination Using Single-Surface Lens through Wavefront Engineering. *Horticulturae*. 2022; 8(11):1019.
https://doi.org/10.3390/horticulturae8111019

**Chicago/Turabian Style**

Moaven, Aria, Hamid Pahlevaninezhad, Masoud Pahlevaninezhad, and Majid Pahlevani. 2022. "Uniform Illumination Using Single-Surface Lens through Wavefront Engineering" *Horticulturae* 8, no. 11: 1019.
https://doi.org/10.3390/horticulturae8111019