Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method

Zhang, Yaqin; Wu, Rengmao; Liu, Peng; Zheng, Zhou; Li, Haifeng; Liu, Xu

doi:10.1016/j.optcom.2014.06.043

Cited by 37 publications

(33 citation statements)

References 19 publications

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“…However, detailed design procedures have been reported mainly for collimated laser beam shaping with plane wavefronts. [15][16][17][18][19][20][21][22][23][24] There is work 25 which can be used to generate a freeform wavefront; however, the irradiance is defined in the case at a plane close to the wavefront rather than on the wavefront itself. In our case, we have defined both the irradiance and the phase at the same plane, so that the design has a good accuracy even when the beam is strongly focused.…”

Section: Step Ii: Lens Design By Ray Mapping From the Input Plane To mentioning

confidence: 99%

Enhanced performance of refractive laser beam shapers through additional phase control at focus

Meuret

Vervaeke

et al. 2016

Opt. Eng

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Abstract. Laser beam shaping at focus or focal beam shaping is essential for many applications. The most common approach makes use of the Fourier transforming properties of lenses to generate at their focal planes the desired irradiance patterns, e.g., the flattop. There are two inherent limitations for this approach. First, the shaping quality depends strongly on the dimensionless parameter β. In the case of a long focal length or small beam sizes giving a small β value, additional beam expanders are needed to achieve a satisfying irradiance pattern at the focus. Second, without considering the phase, the irradiance patterns beyond the focal plane are not controlled. We propose a different approach with two plano-aspheric lenses that allow control of both irradiance and phase at focus. The design method comprises an extended ray mapping procedure combined with backward wave propagation from focus. With this design approach, the shaping quality is guaranteed without the possible need for extra beam expanders, offering the potential for a more compact system with fewer elements. Through the additional phase control, the depth of focus is enlarged to a large extent and the designed system becomes more tolerant.

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Section: Step Ii: Lens Design By Ray Mapping From the Input Plane To mentioning

confidence: 99%

Enhanced performance of refractive laser beam shapers through additional phase control at focus

Meuret

Vervaeke

et al. 2016

Opt. Eng

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“…Since an LED lens with a single freeform surface has a limitation in controlling the luminous flux emitted from an LED, as mentioned previously, design methods for an LED lens with double freeform surfaces (double freeform-surface lens) have received much attention recently [19][20][21][22][23][24]. Unfortunately, geometric optics cannot provide the necessary and sufficient conditions for making the simultaneous differential equations for a double freeform-surface lens complete, contrary to the case of a single freeform surface [19,25].…”

Section: Introductionmentioning

confidence: 99%

“…The combination of the edge-ray and luminance-engineering principles was used to resolve the problem in reference [22], and the so-called integrability condition for the surface normal vectors was used in reference [23]. A double freeform-surface lens for shaping a laser beam has been designed using two conditions on the intensity and phase distributions [24].…”

Section: Introductionmentioning

confidence: 99%

Design Method for a Total Internal Reflection LED Lens with Double Freeform Surfaces for Narrow and Uniform Illumination

Yang¹,

Park²,

Beom‐Hoan³

et al. 2016

Journal of the Optical Society of Korea

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In this paper, we propose a novel differential equation method for designing a total internal reflection (TIR) LED lens with double freeform surfaces. A complete set of simultaneous differential equations for the method is derived from the condition for minimizing the Fresnel loss, illumination models, Snell's Law of ray propagation, and a new constraint on the incident angle of a ray on the light-exiting surface of the lens. The last constraint is essential to complete the set of simultaneous differential equations. By adopting the TIR structure and applying the condition for minimizing the Fresnel loss, it is expected that the proposed TIR LED lens can have a high luminous flux efficiency, even though its beam-spread angle is narrow. To validate the proposed method, three TIR LED lenses with beam-spread angles of less than 22.6° have been designed, and their performances evaluated by ray tracing. Their luminous flux efficiencies could be obviously increased by at least 35% and 5%, compared to conventional LED lenses with a single freeform surface and with double freeform surfaces, respectively.

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“…Most of the studies are only applicable to the cases when the input and output beam irradiance distributions are rotationally symmetric or variables separable (see, e.g., [8][9][10][11][12][13][14][15][16]). For a more general beam-shaping problem that is nonrotational and nonseparable, one option is determining the governing equations in a rigorous manner and then solving them numerically [17,18]. An approximated but simpler approach is first computing a proper ray mapping and then following a simultaneous point-by-point procedure to construct the double freeform surfaces [19].…”

Section: Introductionmentioning

confidence: 99%

Creating unconventional geometric beams with large depth of field using double freeform-surface optics

Feng

Froese²,

Huang

et al. 2015

Appl. Opt.

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We consider here creation of an unconventional flattop beam with a large depth of field by employing double freeform optical surfaces. The output beam is designed with continuous variations from the flattop to almost zero near the edges to resist the influence of diffraction on its propagation. We solve this challenging problem by naturally incorporating an optimal transport map computation scheme for unconventional boundary conditions with a simultaneous point-by-point double surface construction procedure. We demonstrate experimentally the generation of a long-range propagated triangular beam through a plano-freeform lens pair fabricated by a diamond-tuning machine.

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Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method

Cited by 37 publications

References 19 publications

Enhanced performance of refractive laser beam shapers through additional phase control at focus

Enhanced performance of refractive laser beam shapers through additional phase control at focus

Design Method for a Total Internal Reflection LED Lens with Double Freeform Surfaces for Narrow and Uniform Illumination

Creating unconventional geometric beams with large depth of field using double freeform-surface optics

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