# 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

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**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.

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**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