We recently introduced the edge-imaging condition, a necessary condition for all generalized lenses (glenses) [ J. Opt. Soc. Am. A 33 , 962 ( 2016 ) JOAOD6 0740-3232 10.1364/JOSAA.33.000962 ] in a ray-optical transformation-optics (RTO) device that share a common edge [ Opt. Express 26 , 17872 ( 2018 ) OPEXFF 1094-4087 10.1364/OE.26.017872 ]. The edge-imaging condition states that, in combination, such glenses must image every point to itself. Here we begin the process of building up a library of combinations of glenses that satisfy the edge-imaging condition, starting with all relevant combinations of up to three glenses. As it grows, this library should become increasingly useful when constructing lens-based RTO devices.

We discuss new effects related to relativistic aberration, which is the apparent distortion of objects moving at relativistic speeds relative to an idealized camera. Our analysis assumes that the camera lens is capable of stigmatic imaging of objects at rest with respect to the camera, and that each point on the shutter surface is transparent for one instant, but different points are not necessarily transparent synchronously. We pay special attention to the placement of the shutter. First, we find that a wide aperture requires the shutter to be placed in the detector plane to enable stigmatic images. Second, a Lorentz-transformation window [Proc. SPIE9193, 91931K (2014)PSISDG0277-786X10.1117/12.2061415] can correct for relativistic distortion. We illustrate our results, which are significant for future spaceships, with raytracing simulations.

We present a new type of cloak, the abyss cloak, a lens structure that maps interior physical-space position to the exterior. We show that two nested abyss cloaks can form a perfect invisibility cloak.

Previously [Courtial et al., Opt. Express 26, 17872 (2018)] we presented the theory of transformation optics (TO) with ideal lenses and demonstrated an example, an omnidirectional lens.Here we interpret this omnidirectional lens in two different parameter regimes as ideal-lens cloaks that employ different cloaking strategies: a standard "shrink cloak" in which objects appear smaller (ideally zero) and a novel "abyss cloak" in which interior physical-space positions are mapped to the exterior and thus are visible only from certain directions.We proceed to combine two nested abyss cloaks into another novel, omnidirectional, "bi-abyss cloak."Our work significantly extends the arsenal of cloaking strategies.

We present the theory of ray-optical transformation optics (RTO) with ideal thin lenses and show that ideal-thin-lens RTO devices are omnidirectional lenses. Key to designing such devices are two theorems, the loop-imaging theorem, and the edge-imaging theorem, which ensure that the interior physical space is distorted in the same way for all viewing directions. We discuss the possibility of realising such devices using lens holograms or Fresnel lenses, as both are in principle capable of changing the directions of rays incident from a specific point precisely like an ideal thin lens, thereby enabling macroscopic and broad-band RTO devices that work for at least one viewing position. Even when restricted in this way, our work opens up new possibilities in ray optics. Our devices have the potential to form the basis of new microscope objectives, virtual-reality headsets, and medical spectacles.

We recently showed how to construct omni-directional ray-optical transformation-optics devices out of ideal thin lenses. These devices can be seen as theoretical generalisations of the paraxial, four-lens, "Rochester cloak". Here we investigate the practical realisability of such devices. We use ray-tracing simulations to compare combinations of skew lenses of different types, including ideal lenses and phase holograms of lenses.

We present a structure of ideal thin lenses that acts as an omnidirectional transformation-optics cloak and an omnidirectional lens. We present the design principles, and discuss experimental realisability and potential applications.

We describe pairs of skew ideal thin lenses as a single thin lens with non-coinciding, non-parallel, principal planes. This description facilitates the understanding of structures of skew lenses such as the ideal-lens cloak.

Many of the properties of thick lenses can be understood by considering these as a combination of parallel ideal thin lenses that share a common optical axis. A similar analysis can also be applied to many other optical systems. Consequently, combinations of ideal lenses that share a common optical axis, or at least optical-axis direction, are very well understood. Such combinations can be described as a single lens with principal planes that do not coincide. However, in recent proposals for lens-based transformation-optics devices the lenses do not share an optical-axis direction. To understand such lens-based transformation-optics devices, combinations of lenses with skew optical axes must be understood. In complete analogy to the description of combinations of pairs of ideal lenses that share an optical axis, we describe here pairs of ideal lenses with skew optical axes as a single ideal lens with sheared object and image spaces. The transverse planes are no longer perpendicular to the optical axis. We construct the optical axis, the direction of the transverse planes on both sides, and all cardinal points. We believe that this construction has the potential to become a powerful tool for understanding and designing novel optical devices.

We recently showed how structures of ideal (thin) lenses can act as (ray-optical) transformation-optics devices. This was done by breaking the structure down into all sets of ideal lenses in the structure that share a common edge, and showing that these sets have very specific imaging properties. In order to start the development of a general understanding of the imaging properties of sets of ideal lenses that share a common edge, we investigate here particularly simple and symmetric examples of combinations of ideal lenses that share a common edge. We call these combinations ideal-lens stars. An ideal-lens star is formed by N identical ideal lenses, each placed such that they share a principal point (which lies on the common edge) and such that the angles between all neighbouring lenses are the same. We find that that passage through every single ideal lens in the ideal-lens star images any point to itself. Furthermore, light-ray trajectories in ideal-lens stars are piecewise linear approximations to conic sections. (In the limit of N approaching infinity, they are conic sections.)

We present a design for an omnidirectional transformation-optics (TO) cloak comprising thin lenses and glenses (generalized thin lenses) [J. Opt. Soc. Am. A33, 962 (2016)1084-7529JOAOD610.1364/JOSAA.33.000962]. It should be possible to realize such devices in pixelated form. Our design is a piecewise nonaffine generalization of piecewise affine pixelated-TO devices [Proc. SPIE9193, 91931E (2014)PSISDG0277-786X10.1117/12.2061404; J. Opt18, 044009 (2016)]. It is intended to be a step in the direction of TO devices made entirely from lenses, which should be readily realizable on large length scales and for a broad range of wavelengths.

We study, theoretically, omni-directional Euclidean transformation-optics (TO) devices comprising planar, light-ray-direction changing, imaging, interfaces. We initially studied such devices in the case when the interfaces are homogeneous, showing that very general transformations between physical and electromagnetic space are possible. We are now studying the case of inhomogeneous interfaces. This case is more complex to analyse, but the inhomogeneous interfaces include ideal thin lenses, which gives rise to the hope that it might be possible to construct practical omni-directional TO devices from lenses alone. Here we report on our progress in this direction.

We describe a way to realise transformation-optical devices from structures of micro-structured sheets called generalised confocal lenslet arrays. The resulting devices should work for all visible light, and they should be relatively easy and cheap to (mass-) produce on the scale of metres, but they suffer from field-of-view limitations and significant transmission loss. Furthermore, the mapping between electromagnetic space and physical space is not through stigmatic imaging, but integral imaging. As an example application of this technology, we design and simulate an architectural window that cloaks insulation material with the aim of reducing heat loss.

In a photo taken with a camera moving at relativistic speed, the world appears distorted. That much has long been clear, but the details of the distortion were slow to emerge correctly. We recently added relativistic raytracing capability to our custom raytracer, Dr TIM, resulting in unique combinations of capabilities. Here we discuss a few observations. In particular, photos can be sharp only if the shutter is placed correctly. A hypothetical window that changes light-ray direction like a change of inertial frame, when combined with suitable shutter placement, can correct for all relativistic-aberration effects.

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text J. Courtial, S. Oxburgh, E. N. Cowie, C. D. White, and T. Tyc, "Transformation optics with lenses," in Imaging and Applied Optics 2016, OSA Technical Digest (online) (Optica Publishing Group, 2016), paper MTh2H.3. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Johannes Courtial, Tomáš Tyc, Stephen Oxburgh, Jakub Běĺın, Euan N. Cowie, and Chris D. White School of Physics & Astronomy, College of Science & Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom∗ Institute of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno, Czech Republic Centre for Research in String Theory, Queen Mary University of London, 327 Mile End Road, London E1 4NS, United Kingdom (Dated: November 4, 2016)

We study the possibilities of direct (using one intersection with each light ray) stigmatic imaging with a curved surface that can change ray directions in an arbitrary way. By purely geometric arguments we show that the only possible case of such imaging is the trivial one where the image of any point is identical to the point itself and the surface does not perform any change of the ray direction at all. We also discuss an example of a curved surface which performs indirect stigmatic imaging after twice intersecting each light ray.

All simulations shown in the paper were performed with our custom ray tracer Dr TIM [1, 2] (Fig. 1). With the instructions provided in this section, the reader should be able to run all simulations described in this paper, shown again in Fig. 2. Further information on how to use Dr TIM can be found in the user guide [3]. Dr TIM runs on any computer capable of running Java programs that require the Java Virtual Machine (JVM) 1.6. To run Dr TIM, download the Java Archive (JAR) file from the supplementary material and open it. Provided Java is correctly installed, Dr TIM should start up and display the window shown in Fig. 1. Two sets of parameters need to be adjusted to repeat our simulations, namely the parameters describing the scene, and the parameters describing the camera. This is outlined below. To render the view with new parameters, press the Render button on Dr TIM’s home screen. Pressing the Edit scene button on Dr TIM’s main screen allows editing of the scene. The basic scene we used to illustrate the pinch-transformation window can

Ray-optically, optical components change a light-ray field on a surface immediately in front of the component into a different light-ray field on a surface behind the component. In the ray-optics limit of wave optics, the incident and outgoing light-ray directions are given by the gradient of the phase of the incident and outgoing light field, respectively. But as the curl of any gradient is zero, the curl of the light-ray field also has to be zero. The above statement about zero curl is true in the absence of discontinuities in the wave field. But exactly such discontinuities are easily introduced into light, for example by passing it through a glass plate with discontinuous thickness. This is our justification for giving up on the global continuity of the wave front, thereby compromising the quality of the field (which now suffers from diffraction effects due to the discontinuities) but also allowing light-ray fields that appear to be (but are not actually) possessing non-zero curl and thereby significantly extending the possibilities of optical design. Here we discuss how the value of the curl can be seen in a light-ray field. As curl is related to spatial derivatives, the curl of a light-ray field can be determined from the way in which light-ray direction changes when the observer moves. We demonstrate experimental results obtained with light-ray fields with zero and apparently non-zero curl.

Identity certification in the cyberworld has always been troublesome if critical information and financial transaction must be processed. Biometric identification is the most effective measure to circumvent the identity issues in mobile devices. Due to bulky and pricy optical design, conventional optical fingerprint readers have been discarded for mobile applications. In this paper, a digital variable-focus liquid lens was adopted for capture of a floating finger via fast focusplane scanning. Only putting a finger in front of a camera could fulfill the fingerprint ID process. This prototyped fingerprint reader scans multiple focal planes from 30 mm to 15 mm in 0.2 second. Through multiple images at various focuses, one of the images is chosen for extraction of fingerprint minutiae used for identity certification. In the optical design, a digital liquid lens atop a webcam with a fixed-focus lens module is to fast-scan a floating finger at preset focus planes. The distance, rolling angle and pitching angle of the finger are stored for crucial parameters during the match process of fingerprint minutiae. This innovative compact touchless fingerprint reader could be packed into a minute size of 9.8*9.8*5 (mm) after the optical design and multiple focus-plane scan function are optimized.