Direct, stigmatic, imaging with curved surfaces

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

Dr TIM: Ray-tracer TIM, with additional specialist scientific capabilities

We describe several extensions to TIM, a raytracing program for ray-optics research. These include relativistic raytracing; simulation of the external appearance of Eaton lenses, Luneburg lenses and generalized focusing gradient-index (GGRIN) lenses, which are types of perfect imaging devices; raytracing through interfaces between spaces with different optical metrics; and refraction with generalised confocal lenslet arrays, which are particularly versatile METATOYs.Comment: 12 pages, 16 figure

Imaging with Pairs of Skew Lenses

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

Complex Imaging with Ray-rotating Windows

We study the imaging properties of windows that rotate the direction of transmitted light rays by a fixed angle around the window normal [A. C. Hamilton et al., J. Opt. A: Pure Appl. Opt. 11,085705 (2009)]. We previously found that such windows image between object and image positions with suitably defined complex longitudinal coordinates [J. Courtial et al., Opt. Lett. 37, 701 (2012)]. Here we extend this work to object and image positions in which any coordinate can be complex. This is possible by generalising our definition of what it means for alight ray to pass through a complex position: the vector from the real part of the position to the point on the ray that is closest to that real part of the position must equal the cross product of the imaginary part of the image position and the normalised light-ray-direction vector. In the paraxial limit, we derive the equivalent of the lens equation for planar and spherical ray-rotating windows. These results allow us to describe complex imaging in more general situations, involving combinations of lenses and inclined ray-rotating windows. We illustrate our results with ray-tracing simulations

Lorentz-transformation and Galileo-transformation Windows

We define Lorentz-transformation windows as windows that change the direction of transmitted light rays like a Lorentz transformation. Similarly, Galileo-transformation windows change the direction of transmitted light rays like a Galileo transformation. This light-ray-direction change distorts the scene seen through such a window in the same way in which the scene would be distorted in a photo taken with a camera moving through the scene. Lorentz-transformation windows can also undo the distortion of the scene when moving at relativistic velocity relative to it. For small angles between the direction of the light rays and the direction of the velocity, Galileo-transformation windows can be realised with relatively simple telescope windows, which consist of arrays of identical micro-telescopes

Ideal-Lens Stars

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.

What Do Forbidden Light-ray Fields Look Like?

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 there by 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

Law of refraction for generalised confocal lenslet arrays

We derive the law of generalised refraction for generalised confocal lenslet arrays, which are arrays of misaligned telescopes. We have implemented this law of refraction in TIM, a custom open-source ray tracer.Comment: 4 pages, 3 figure