Fabian Duerr

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermats principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Tracking integration in concentrating photovoltaics using laterally moving optics

In this work the concept of tracking-integrated concentrating photovoltaics is studied and its capabilities are quantitatively analyzed. The design strategy desists from ideal concentration performance to reduce the external mechanical solar tracking effort in favor of a compact installation, possibly resulting in lower overall cost. The proposed optical design is based on an extended Simultaneous Multiple Surface (SMS) algorithm and uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. It achieves 500× concentration, outperforming its conventional concentrating photovoltaic counterparts on a polar aligned single axis tracker.

Potential benefits of free-form optics in on-axis imaging applications with high aspect ratio

Including free-form optical components in imaging systems provides numerous opportunities for enhanced performance and compact, lightweight packaging. This applies especially to the use of free-form optics in off-axis imaging applications. In case of on-axis imaging, rotationally symmetric lenses are typically used, as they greatly simplify the design and manufacturing process. However, for imaging applications with high aspect ratio, free-form optics can help to provide solutions with clearly better overall imaging performance. For such cases, the ray tracing simulations in this work demonstrate superior imaging performance of basic free-form lenses in comparison to conventional rotationally symmetric lenses, each consisting of two surfaces.

Tailored free-form optics with movement to integrate tracking in concentrating photovoltaics

The economic use of high-efficiency solar cells in photovoltaics requires high concentration of sunlight and therefore precise dual-axis tracking of the sun. Due to their size and bulkiness, these trackers are less adequate for small- to mid-scale installations like flat rooftops. Our approach to combine concentrating and tracking of sunlight utilizes two laterally moving lens arrays. The presented analytic optics design method allows direct calculation of the free-form lens surfaces while incorporating the lateral movement. The obtained concentration performance exceeds a factor of 500. This demonstrates that one can benefit from high-efficiency solar cells and more compact and flexible single-axis trackers at the same time.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576-5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermats principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Refractive laser beam shaping by means of a functional differential equation based design approach.

Many laser applications require specific irradiance distributions to ensure optimal performance. Geometric optical design methods based on numerical calculation of two plano-aspheric lenses have been thoroughly studied in the past. In this work, we present an alternative new design approach based on functional differential equations that allows direct calculation of the rotational symmetric lens profiles described by two-point Taylor polynomials. The formalism is used to design a Gaussian to flat-top irradiance beam shaping system but also to generate a more complex dark-hollow Gaussian (donut-like) irradiance distribution with zero intensity in the on-axis region. The presented ray tracing results confirm the high accuracy of both calculated solutions and emphasize the potential of this design approach for refractive beam shaping applications.

Miniaturization of Fresnel lenses for solar concentration: a quantitative investigation

Sizing down the dimensions of solar concentrators for photovoltaic applications offers a number of promising advantages. It provides thinner modules and smaller solar cells, which reduces thermal issues. In this work a plane Fresnel lens design is introduced that is first analyzed with geometrical optics. Because of miniaturization, pure ray tracing may no longer be valid to determine the concentration performance. Therefore, a quantitative wave optical analysis of the miniaturizations influence on the obtained concentration performance is presented. This better quantitative understanding of the impact of diffraction in microstructured Fresnel lenses might help to optimize the design of several applications in nonimaging optics.

Direct design approach to calculate a two-surface lens with an entrance pupil for application in wide field-of-view imaging

Abstract. In this work, a multifields optical design method aiming to calculate two high-order aspheric lens profiles with an embedded entrance pupil is proposed. This direct design algorithm is capable of partially coupling more than three ray bundles that enter the same pupil with only two surfaces. Both infinite and finite conjugate objectives can be designed with this approach. Additional constraints such as surface continuity and smoothness are taken into account to calculate smooth and accurate surface contours described by point clouds. The calculated points are then fitted with rotationally symmetric functions commonly used in optical design tools. A presented subaperture sampling strategy that introduces a weighting function for different fields allows for a very well-balanced imaging performance over a wide field of view (FOV). As an example, a ±45  deg f/7.5 wide-angle objective is designed and analyzed to demonstrate the potential of this design method. It provides an excellent starting point for further optimization of the surfaces’ coefficients and initial design parameters, resulting in a very good and well-balanced imaging performance over the entire FOV.

Analytic design of a zoom XY-beam expander with freeform optical surfaces.

Many laser applications require specific irradiance distributions to ensure optimal performance. In addition, some applications can benefit from time-varying distributions. In this work, we present the analytic design of a zoom XY-beam expander based on movable freeform optics that allows to simultaneously vary the magnification in x- and y-direction, respectively. This concept is not new: the new is to design and optimally exploit freeform lenses to achieve such an optical functionality. In comparison with zoom beam expanders that use combinations of rotated cylindrical lenses, a freeform system can be more compact, yet achieving excellent overall optical performance throughout the full zoom range.

Analytic free-form lens design for imaging applications with high aspect ratio

A new three-dimensional analytic optics design method is presented that enables the coupling of three ray sets with only two free-form lens surfaces. Closely related to the Simultaneous Multiple Surface method in three dimensions (SMS3D), it is derived directly from Fermat’s principle, leading to multiple sets of functional differential equations. The general solution of these equations makes it possible to calculate more than 80 coefficients for each implicit surface function. Ray tracing simulations of these free-form lenses demonstrate superior imaging performance for applications with high aspect ratio, compared to conventional rotational symmetric systems.