Double freeform surfaces design for beam shaping with non-planar wavefront using an integrable ray mapping method

Wei, Shili; Zhu, Zhengbo; Fan, Zichao; Yan, Yiming; Ma, Donglin

doi:10.1364/oe.27.026757

Cited by 37 publications

(8 citation statements)

References 32 publications

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“…As far as we know, there are no methods in category (2.B). (3.B) Examples of ray mapping techniques are: Wei et al [37] consider source distributions with wavefronts of general shape (i.e., non-collimated and non-spherical source intensities). The authors use the leastsquares algorithm in [3] to compute an initial mapping and a point-by-point procedure to compute an initial approximation to the first freeform surface.…”

Section: Research Articlementioning

confidence: 99%

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Generating-function approach for double freeform lens design

et al. 2021

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Section: Research Articlementioning

confidence: 99%

“…The computation of m is an iterative procedure; in every iteration, we minimize four functionals, displayed in Eq. (37). First, to solve Eq.…”

Section: A Generalized Least-squares Algorithmmentioning

confidence: 99%

Generating-function approach for double freeform lens design

et al. 2021

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“…Another approach by Feng et al uses ray mapping to calculate the shapes and positions of the surfaces [14]. A ray mapping method has been used to construct optical systems with two freeform surfaces for arbitrary input and output wavefronts [15].…”

Section: Introductionmentioning

confidence: 99%

Design of a freeform two-reflector system to collimate and shape a point source distribution

van Roosmalen,

Anthonissen,

IJzerman

et al. 2021

Preprint

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In this paper we propose a method to compute a freeform reflector system for collimating and shaping a beam from a point source. We construct these reflectors such that the radiant intensity of the source is converted into a desired target. An important generalization in our approach compared to previous research is that the output beam can be in an arbitrary direction. The design problem is approached by using a generalized Monge-Ampère equation. This equation is solved using a least-squares algorithm for non-quadratic cost functions. This algorithm calculates the optical map, from which we can then compute the surfaces. We test our algorithm on two cases. First we consider a uniform source and target distribution. Next, we use the model of a laser diode light source and a ring-shaped target distribution.

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“…ere are few recent papers dealing with the controlled transformation of both irradiance and wavefront [21][22][23][24]; however the applied mathematical approaches are based also on optimal mass transportation and corresponding ray mapping. e presented algorithm differs from all the discussed methods, since it is based purely on ray propagation and ray-distribution-to-irradiance transformations.…”

Section: Introductionmentioning

confidence: 99%

Simplified Geometric Approach to Freeform Beam Shaper Design

Wojtanowski

Drozd

2020

International Journal of Optics

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Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily. In order to keep these two quantities determined simultaneously, it is required to apply at least two powered refractive or reflective surfaces. In this paper, a fully geometric design method of double-freeform beam shapers is discussed briefly. The presented algorithm is based on two stages. First, integrable input-output ray mapping is calculated by the application of the novel GATMA (Geometric Approach to Monge–Ampere equation) method. It allows us to determine the shape of the first freeform surface. Then, according to the condition of constant optical path length between input and output plane, corrected by wavefront phases at those planes, the second surface is determined. GATMA algorithm combines advantages of Monge–Ampere (MA) equation and ray-tracing efficient apparatus. Compared to the state-of-the-art freeform design methods, GATMA does not need to solve MA equation directly but uses this equation as an error function. Such approach makes the computation algorithm simpler and more robust and convergent. The application of the proposed method in a challenging design example of a beam shaper, transforming uniform collimated beam into a beam having a triangular cross section and flat wavefront, is presented as a case study.

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Double freeform surfaces design for beam shaping with non-planar wavefront using an integrable ray mapping method

Cited by 37 publications

References 32 publications

Generating-function approach for double freeform lens design

Generating-function approach for double freeform lens design

Design of a freeform two-reflector system to collimate and shape a point source distribution

Simplified Geometric Approach to Freeform Beam Shaper Design

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