Freeform geometrical optics II: from parametric representation to CAD/CAM

Fractioned-pattern radiation mapping, Part I: modeling

Here, we present a technique that predicts the radiation's distribution in any optical system. It is based on decomposing the emitting source power by assigning a fraction of the total power to each emitted ray. All kinds of power losses in the rays' optical paths are considered. Fractioned radiation patterns are created in the last optical system surface, each associated with a single ray. We refer to fractioned patterns as those that conform to a whole radiating pattern. Thus, the irradiance of the completely illuminated surface is calculated by adding the optical system's fractioned radiation maps. This method is non-zero étendue. The result presented here allows for predicting the radiation patterns accurately with a handful of equations and can help design any image and non-image-forming optical systems.

Fractioned-pattern radiation mapping, Part II: assessment

In Part I, the authors proposed a theoretical background for predicting the radiation distribution in any optical system based on decomposing the emitting source power. Here, we describe the validity of this decomposition through a practical example that uses a radiating source and a single surface optical system. This source is calibrated in a metrology testbed that guarantees its traceability to the candela (cd), the International System (SI) base unit for luminous intensity I v. A second example, this time numerical, shows the method's performance in a multisurface optical system.

Freeform concentrator design for IR wireless-to-fiber link communications

Airplanes use heavy wired harnesses to provide multimedia services to the seats. Optical wireless communications (OWC) are a natural choice to reduce the amount of weight, reduce the wiring complexity, and avoid possible spurious electromagnetic radiation that risks affecting the airplane's navigation systems. The light's dual use as lighting and optical communications functionalities allows for providing light and multimedia content through the reading lamp. Thus, an optical system using optical fibers to replace wires and a reading lamp can provide a cabin seat with lighting and onboard connectivity. However, changing shielded harnesses by optical fibers is-from an optical design point of view-a challenging task as the reading lamp must also meet the stringent requirements to link the optical wireless transmissions to the optical fiber. The difficulty up to now lies in injecting the light emitted from the passenger's device into the optical fiber using the reading lamp as the receiving antenna and light injector. Here, we describe a proof-of-concept device that experimentally allowed for establishing a link between a transmitter and a photodetector coupled to an optical fiber-end, i.e., the link consisted of an optical wireless communication and the launching of the light modulated signal into an optical fiber. Additionally, from the experimental experience, we will describe the optical design strategies permitting designing a compound freeform concentrator to allow optical free space-to-fiber links.

Freeform optics characterization with surface registration and fitting algorithms for optical point-based spatial path 3D topography metrology

Accurate characterization of the form error for freeform optics is critical for controlled manufacturing and evaluation of optical properties. To solve the difficulty of current surface registration and fitting algorithms, and improve characterization accuracy of the form error of freeform optics for optical point-based spatial path 3D topography metrology, in this paper, improved surface registration and fitting algorithms are proposed, including a B-spline surface description of freeform optics, point orthogonal projection, registration parameter optimization, and B-spline fitting. Limited by the angular characteristics of an optical point-based sensor, the slope and reference frame of freeform optics must be flexibly adjusted, and polynomial surfaces are described and fitted as B-spline surfaces based on B-spline geometric invariance. To efficiently determine corresponding points on B-spline surfaces, the point orthogonal projection algorithm without Bezier subdivision is proposed using the first-order Newton method. Then, the iteration procedure of coordinate adjustment in sphere space using Lie algebra registration parameters is proposed to solve the difficulty of the current registration parameter optimization procedure. To fit a spatial path form error, the least squares B-spline fitting method is proposed to improve the Zernike method. Through simulation experiments, the proposed registration algorithm with good convergence can improve accuracy by one to two orders of magnitude compared with current registration algorithms. Through repeated experiments of a freeform prism, the proposed method can significantly improve the peak-to-valley and RMS accuracies compared with the stylus method, and characterize the mid-high frequency form error (about 200 nm) of a freeform prism.

Spatial Three-Mirror Off-Axis Freeform Optical System without Any Symmetry

In this manuscript, we have launched a study on the completely nonsymmetric freeform optical system with neither rotational symmetry nor planar symmetry. An off-axis three-mirror freeform optical system with nonsymmetric geometry is proposed and a direct design method is developed for the nonsymmetric freeform optical system. The design field points are sampled across the full FOV to control the imaging quality and object–image relationship. In this system, the center of the image plane is greatly away from the plane determined by the centers of the three mirrors. This nonsymmetric system with F/1.3, a focal length of 50 mm, and an 8° × 6° field of view can achieve imaging quality close to the diffraction limit. This work provides a feasible nonsymmetric system design idea for the optical community.

On-axis diffraction-limited bi-conical lenses

A diffraction-limited lens having both surfaces conic is shown. The analytical and numerical calculation for all possible solutions of the conical front and back surfaces is presented. Object and image distances, lens thickness, and refractive index are prescribed. The process to obtain on-axis diffraction-limited images with bi-conic lenses and the proof of the method, corroborated through an example in Oslo, are described here.

Roadmap for geometrical optics based on Taylor series expansion of skew ray

The skew ray R¯_n on the image plane of an optical system possessing n boundary surfaces has the form of an n-layered deep composite function. It is hence difficult to evaluate the system performance using ray tracing alone. The present study therefore uses the Taylor series expansion to expand R¯_n with respect to the source ray variable vector. It is shown that the paraxial ray tracing equations, point spread function, caustic surfaces and modulation transfer function can all be explored using the first-order expansion. Furthermore, the primary and secondary ray aberrations of an axis-symmetrical system can be determined from the third- and fifth-order expansions, respectively. It is thus proposed that the Taylor series expansion of the skew ray serves as a useful basis for exploring a wide variety of problems in geometrical optics.

Explicit Cartesian oval as a superconic surface for stigmatic imaging optical systems with real or virtual source or image

Cartesian ovals, also known as rigorously stigmatic surfaces, are the simplest optical systems capable of producing a perfect point image. Exist both implicit and explicit expressions to represent these surfaces, but they treat both refractive and reflective surfaces independently. Because of the complexity of explicit expressions, the ray-tracing techniques for these surfaces are implemented using third-party software. In this paper, we express Cartesian ovals as a degenerated superconic curve and get a new explicit formulation for Cartesian ovals capable of treating image formation using both object and image points, either real or virtual, and in this formulation can deal with both reflective and refractive rigorously stigmatic surfaces. Finally, using the resultant expressions and the vector Snell–Descartes Law, we propose a self-contained analytical ray-tracing technique for all these surfaces.