Phase space approach to the use of integrator rods and optical arrays in illumination systems

We propose an algorithm to remove a parabolic wavefront from a convergent or divergent beam in the Wigner function. Using this approach we numerically collimate the beam. This avoids a dense sampling in phase space to describe a convergent wavefront. Thereby we reduce the required computer memory, but maintain computational accuracy and physical effects. Furthermore, we compare two algorithms, shearing and Radon transform, to propagate the Wigner function in free space. We use the fast Fourier transform to accurately perform shearing. However, zero-padding is necessary to circumvent aliasing. We prove that the Radon transform is a more efficient approach for a long propagated distance.

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“…, where z defines the propagated distance [8]. The signals in phase space before and after the propagation share a shearing relation, i.e.,…”

Section: Methods 2: Shearing and Radon Transformmentioning

confidence: 99%

Propagation algorithms for Wigner functions

Zhong

Groß

2016

J. Eur. Opt. Soc.-Rapid Publ.

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“…So with the help of a ray-tracer we can analyze the transformation of the input radiance from object (light source) to image in a phase space diagram. From the final radiance distribution all radiometric quantities, like irradiance E(x) can be calculated via a simple projection of the radiance distribution [13,14].…”

Section: Phase Space Definition and Radiance Propagationmentioning

confidence: 99%

“…This work presents an approach which includes the etendue of the source from the very beginning. To do so, the method of phase space in optics is employed, which allows for a direct visualization of the radiance distribution [13,14]. Phase space methods have already prooven to be promising for improved raytracing of illumination systems [15].…”

Section: Introductionmentioning

confidence: 99%

Design of a freeform uniformity corrector lens for extended sources in elliptical reflectors

Rausch¹,

Herkommer²

2019

J. Phys. Photonics

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Illumination design usually requires the collection of a large solid angle of radiation from the light source. However, it is known that elliptical reflectors in combination with extended uniform light sources result in a non-uniform irradiance profile at the secondary focus. Within this paper we propose a design method based on phase space transformations, which includes the source extension from the very beginning. We show that an analysis of the local mapping of the source to the target radiance distribution allows a profound understanding of the effects and in consequence a design concept for an additional freeform lens to correct the uniformity at the secondary focus.

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“…Obviously, the factor of homogenization increases with the number of reflections on the sidewalls. 14 …”

Section: Integrator Rodsmentioning

confidence: 99%

Design and applications of a phase space analyzer

Rausch

Herkommer

2016

SPIE Proceedings

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In the last few years the requirement of more special and complex optical system increases as the demand in industries for higher efficiency increases. To satisfy the demand more complex optical elements substitute continuously standard components. Therefore it is of high interest to develop new methods in evaluating optical systems. In classical illumination design a huge number of rays has to be traced to get enough information to evaluate the performance of the system. An other method is to investigate the transport of etendue in the phase space picture where we have direct access to the radiance, irradiance and radiant intensity without extensive ray tracing. The phase space analyzer offers a different way to illustrate directly the phase space diagram of an arbitrary light distribution restricted to two dimensions. This method is much faster than traditional ray tracing. Most often used illumination components like integrator rods and optical arrays can be understood in the phase space approach.

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Phase space approach to the use of integrator rods and optical arrays in illumination systems

Cited by 14 publications

References 17 publications

Propagation algorithms for Wigner functions

Propagation algorithms for Wigner functions

Design of a freeform uniformity corrector lens for extended sources in elliptical reflectors

Design and applications of a phase space analyzer

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