Most virtual reality (VR) headsets nowadays use conventional, rotationally symmetric optics to create a wide field of view
(FOV > 90°) virtual scene enabling the required “immersion” or “presence” feeling. These optics require a long total track
length (TTL, distance between the actual panel displaying the contents and user’s pupil) to work well, and headsets become
very bulky. The so-called CLOVER is an optic, compatible with VR and video-see-through mixed reality (MR) able to
work around the TTL problem by using a freeform multi-channel, light folding approach. In its simplest version, it can
reduce the TTL down to a half, compared to conventional solutions, for the same FOV and angular resolution. Along with
a review of the original 4-channel CLOVER, this work shows recent results of upscale versions of the optic that utilize
myopia and color correction, pupil tracking and staggered surfaces to, respectively, avoid the need of prescription lenses,
improve the image quality for all colors, rise the resolution (by a 20%) and reduce the size (20% TTL reduction) of the
precursor.
Reducing the size of Virtual Reality head-mounted displays is of main interest to improve the comfort of users, which is a particularly complex design problem due to the very large field of view needed to feel the immersion. High compactness with high transmission efficiency and high contrast can be achieved by multichannel optics, whose design for high performance is carried out at LIMBAK introducing intensively freeform optical surfaces, increased resolution via variable magnification, dynamic mapping control and super-sampling via pixel interlacing. This presentation will cover the growing variety of geometries, how to address their challenges and envision their future.
Reducing the size of Virtual Reality head-mounted displays is of main interest to improve the comfort of users, which is a particularly complex design problem due to the very large field of view needed to feel the immersion. Such reduction can be achieve via folded polarization “pancake” optics, but at the expense of a very low transmission efficiency and poor contrast. High compactness without those drawbacks can be achieved by multichannel optics, whose design for high performance is carried out at LIMBAK intensively introducing freeform optical surfaces, adding variable magnification to maximize the VR display resolution where it is to be normally gazed, and applying two-dimensional distortion software corrections to each channel. This presentation will cover the recent advances in these systems, the growing variety of geometries, the benefits obtained when including gaze-tracking and the resolution boosts obtained by the application of pixel interlacing strategies.
Compared to conventional, rotationally-symmetric optics, free-form optics provide additional degrees of freedom that enable special geometrical and performance features. For instance, in AR and VR, some approaches based on free-forms have shown their ability to reduce the display to pupil distance (total track length, or TTL), to increase the Field of view (FOV) or to improve the apparent resolution of the VR scene. This work will discuss different forms to treat design problems with free-forms, ranging from the direct calculation of point-clouds using the so-called SMS method (followed by a NURBS representation of results) to the combination of direct calculation + optimization. In the latter approach, different types of polynomial descriptions of the free-form surfaces will be considered, with special emphasis on the importance of using a basis that is orthogonal, either with a sag metric or a gradient one.
We present an advanced optical design for a high-resolution ultra-compact VR headset for high-end applications based on multichannel freeform optics and 4 OLED WUXGA microdisplays developed under EU project LOMID [1]. Conventional optical systems in VR headsets require large distance between lenses and displays that directly leads to the rather bulky and heavy commercial headsets we have at present. We managed to dramatically decrease the required display size itself and the display to eye distance, making it only 36 mm (to be compared to 60-75 mm in most conventional headsets). This ultra-compact optics allows reducing the headset weight and it occupies about a fourth of volume of a conventional headset with the same FOV. Additionally, our multichannel freeform optics provides an excellent image quality and a large field of view (FOV) leading to highly immersive experience. Unlike conventional microlens arrays, which are also multichannel devices, our design uses freeform optical surfaces to produce, even operating in oblique incidences, the highest optical resolution and Nyquist frequency of the VR pixels where it is needed. The LOMID microdisplays used in our headsets are large-area high-resolution (WUXGA) microdisplays with compact, high bandwidth circuitry, including special measures for high contrast by excellent blacks and low-power consumption. LOMID microdisplay diagonal is 0.98” with 16:10 aspect ratio. With two WUXGA microdisplays per eye, our headset has a total of 4,800x1,920 pixels, i.e. close to 5k. As a result, our multichannel freeform optics provides a VR resolution 24 pixels/deg and a monocular FOV of 92x75 degs (or 100x75 with a binocular superposition of 85%).
We address freeform aplanatic designs both as solutions of a differential system of equations and as limiting cases of SMS designs. We conclude that, in general, freeform aplanatic systems need at least 3 optical-surfaces with illustrative examples.
In present commercial Virtual Reality (VR) headsets the resolution perceived is still limited, since the VR pixel density (typically 10-15 pixels/deg) is well below what the human eye can resolve (60 pixels/deg). We present here novel advanced optical design approaches that dramatically increase the perceived resolution of the VR keeping the large FoV required in VR applications. This approach can be applied to a vast number of optical architectures, including some advanced configurations, as multichannel designs. All this is done at the optical design stage, and no eye tracker is needed in the headset.
We introduce a time multiplexing strategy to increase the total pixel count of the virtual image seen in a VR headset. This translates into an improvement of the pixel density or the Field of View FOV (or both) A given virtual image is displayed by generating a succession of partial real images, each representing part of the virtual image and together representing the virtual image. Each partial real image uses the full set of physical pixels available in the display. The partial real images are successively formed and combine spatially and temporally to form a virtual image viewable from the eye position. Partial real images are imaged through different optical channels depending of its time slot. Shutters or other schemes are used to avoid that a partial real image be imaged through the wrong optical channels or at the wrong time slot. This time multiplexing strategy needs real images be shown at high frame rates (>120fps). Available display and shutters technologies are discussed. Several optical designs for achieving this time multiplexing scheme in a compact format are shown. This time multiplexing scheme allows increasing the resolution/FOV of the virtual image not only by increasing the physical pixel density but also by decreasing the pixels switching time, a feature that may be simpler to achieve in certain circumstances.
We present novel advanced optical designs with a dramatically smaller display to eye distance, excellent image quality and a large field of view (FOV). This enables headsets to be much more compact, typically occupying about a fourth of the volume of a conventional headset with the same FOV. The design strategy of these optics is based on a multichannel approach, which reduces the distance from the eye to the display and the display size itself. Unlike conventional microlens arrays, which are also multichannel devices, our designs use freeform optical surfaces to produce excellent imaging quality in the entire field of view, even when operating at very oblique incidences. We present two families of compact solutions that use different types of lenslets: (1) refractive designs, whose lenslets are composed typically of two refractive surfaces each; and (2) light-folding designs that use prism-like three-surface lenslets, in which rays undergo refraction, reflection, total internal reflection and refraction again. The number of lenslets is not fixed, so different configurations may arise, adaptable for flat or curved displays with different aspect ratios. In the refractive designs the distance between the optics and the display decreases with the number of lenslets, allowing for displaying a light-field when the lenslet becomes significantly small than the eye pupil. On the other hand, the correlation between number of lenslets and the optics to display distance is broken in light-folding designs, since their geometry permits achieving a very short display to eye distance with even a small number of lenslets.
The Freeform RXI collimator is a remarkable example of advanced nonimaging device designed with the 3D Simultaneous Multiple Surface (SMS) Method. In the original design, two (the front refracting surface and the back mirror) of the three optical surfaces of the RXI are calculated simultaneously and one (the cavity surrounding the source) is fixed by the designer. As a result, the RXI perfectly couples two input wavefronts (coming from the edges of the extended LED source) with two output wavefronts (defining the output beam). This allows for LED lamps able to produce controlled intensity distributions, which can and have been successfully applied to demanding applications like high- and low-beams for Automotive Lighting.
Nevertheless, current trends in this field are moving towards smaller headlamps with more shape constraints driven by car design. We present an improved version of the 3D RXI in which also the cavity surface is computed during the design, so that there are three freeform surfaces calculated simultaneously and an additional degree of freedom for controlling the light emission: now the RXI can perfectly couple three input wavefronts with three output wavefronts. The enhanced control over ray beams allows for improved light homogeneity and better pattern definition.
Compacting devices is an increasingly demanding requirement for many applications in both nonimaging and imaging optics. “Compacting” means here decreasing the volume of the space between the entry and the exit aperture without decreasing the optical performance. For nonimaging optical systems, compact optics is mainly important for reducing cost. Its small volume means less material is needed for mass-production and small size and light weight save cost in transportation. For imaging optical systems, in addition to the mentioned advantages, compact optics increases portability of devices as well, which contributes a lot to wearable display technologies such as Head Mounted Displays (HMD). After reviewing the different techniques to design compact systems, we analyze here the multichannel strategies. These type of designs split the incoming bundle of rays in different sub-bundles that are optically processed (independently) and then recombined in a single outgoing bundle. The optics volume decreases rapidly with the number of sub-bundles. These designs usually need to be combined with freeform optics in order to get optimum performance.
Recent advances in the Simultaneous Multiple Surfaces (SMS) design method are reviewed in this paper. In particular,
we review the design of diffractive surfaces using the SMS method and the concept of freeform aplanatism as a limit
case of a 3D SMS design.
Several applications of freeform optics call for deeper analysis of systems with rectangular apertures. We study the behavior of a freeform mirror system by comparing four orthogonal polynomial surface representations through local optimization. We compare polynomials with different orthogonal areas (rectangular-circular) and different metrics (sag-gradient). Polynomials orthogonal inside a rectangle converge faster or to a better local minimum than those orthogonal inside a circle in the example considered. This is the most likely due to the loss of the good properties of orthogonality when the orthogonality area does not coincide with the surface area used.
Axisymmetric aplanatic systems have been used in the past for solar concentrators and condensers (Gordon et. al, 2010).
It is well know that such a system must be stigmatic and satisfy the Abbe sine condition. This problem is well known
(Schwarzschild, 1905) to be solvable with two aspherics when the system has rotational symmetry.
However, some of those axisymmetric solutions have intrinsically shading losses when using mirrors, which can be
prevented if freeform optical surfaces are used (Benitez, 2007).
In this paper, we explore the design of freeform surfaces to obtain full aplanatic systems. Here we prove that a rigorous
solution to the general non-symmetric problem needs at least three free form surfaces, which are solutions of a system of
partial differential equations (PDE). We also present the PDEs for a three surface full aplanat. The examples considered
have one plane of symmetry, where a consistent 2D solution is used as boundary condition for the 3D problem. We have
used the x-y polynomial representations for all the surfaces, and the iterative algorithm formulated for solving the above
said PDE has shown very fast convergence.
With the increasing interest in using freeform surfaces in optical systems due to the novel application opportunities and manufacturing techniques, new challenges are constantly emerging. Optical systems have traditionally been using circular apertures, but new types of freeform systems call for different aperture shapes. First non-circular aperture shape that one can be interested in due to tessellation or various folds systems is the rectangular one. This paper covers the comparative analysis of a simple local optimization of one design example using different orthogonalized representations of our freeform surface for the rectangular aperture. A very simple single surface off-axis mirror is chosen as a starting system. The surface is fitted to the desired polynomial representation, and the whole system is then optimized with the only constraint being the effective focal length. The process is repeated for different surface representations, amongst which there are some defined inside a circle, like Forbes freeform polynomials, and others that can be defined inside a rectangle like a new calculated Legendre type polynomials orthogonal in the gradient. It can be observed that with this new calculated polynomial type there is a faster convergence to a deeper minimum compared to “defined inside a circle” polynomials. The average MTF values across 17 field points also show clear benefits in using the polynomials that adapted more accurately to the aperture used in the system.
Freeform optical surfaces have been in much demand recently due to improved techniques in their manufacturability and design methodology, and the degrees of freedom it gives the designers. Specifically in the case of off-axis mirror systems, freeform surfaces can considerably reduce the number of surfaces and compensate for some of the higher order aberrations as well, which improves the overall system performance. In this paper, we explore the design of freeform surfaces to obtain full aplanatic mirror systems, i.e., free of spherical aberration and circular coma of all orders. It is well know that such a system must be stigmatic and satisfy the Abbe sine condition. This problem is well known (Schwarzschild, 1905) to be solvable with two aspheric when the system has rotational symmetry. Here we prove that a rigorous solution to the general non-symmetric problem needs at least three free form surfaces, which are solutions of a system of partial differential equations. The examples considered have one plane of symmetry, where a consistent 2D solution is used as boundary condition for the 3D problem. We have used the x-y polynomial representations for all the surfaces used, and the iterative algorithm formulated for solving the above mentioned partial differential equations has shown very fast convergence.
Axisymmetric aplanatic concentrators have been used in the past for solar concentrators and condensers (Gordon et. al, 2010). It is well know that such a system must be stigmatic and satisfy the Abbe sine condition. This problem is well known (Schwarzschild, 1905) to be solvable with two aspherics when the system has rotational symmetry. However, some of those axisymmetric solutions have intrinsically shading losses when using mirrors, which can be prevented if freeform optical surfaces are used (Benitez, 2007). In this paper, we explore the design of freeform surfaces to obtain full aplanatic systems. Here we prove that a rigorous solution to the general non-symmetric problem needs at least three free form surfaces, which are solutions of a system of partial differential equations (PDE). We also present the PDEs for a three surface full aplanat. The examples considered have one plane of symmetry, where a consistent 2D solution is used as boundary condition for the 3D problem. We have used the x-y polynomial representations for all the surfaces, and the iterative algorithm formulated for solving the above said PDE has shown very fast convergence.
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic
Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an
image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object
plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive
refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break
the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power
transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus
by a distance much smaller than the wavelength. Although these systems can detect displacements up to λ/3000, they
cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and
drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW
with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show
that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.
The previous publications (Miñano et al, 2011) have shown that using a Spherical Geodesic Waveguide (SGW), it can be
achieved the super-resolution up to λ /500 close to a set of discrete frequencies. These frequencies are directly connected
with the well-known Schumann resonance frequencies of spherical symmetric systems. However, the Spherical Geodesic
Waveguide (SGW) has been presented as an ideal system, in which the technological obstacles or manufacturing
feasibility and their influence on final results were not taken into account. In order to prove the concept of superresolution
experimentally, the Spherical Geodesic Waveguide is modified according to the manufacturing requirements
and technological limitations. Each manufacturing process imposes some imperfections which can affect the
experimental results. Here, we analyze the influence of the manufacturing limitations on the super-resolution properties
of the SGW. Beside the theoretical work, herein, there has been presented the experimental results, as well.
Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of
arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a receptor called “perfect drain” (PD) located at the corresponding MFE image point. The PD has the property of absorbing the complete radiation without radiation or scattering and it has been claimed as necessary to obtain super-resolution (SR) in the MFE. However, a prototype using a “drain” different from the PD has shown λ/5
resolution for microwave frequencies (Ma et al, 2010). Recently, the SR properties of a device equivalent to the MFE,
called the Spherical Geodesic Waveguide (SGW) (Miñano et al, 2012) have been analyzed. The reported results show
resolution up to λ /3000, for the SGW loaded with the perfect drain, and up to λ /500 for the SGW without perfect drain. The perfect drain was realized as a coaxial probe loaded with properly calculated impedance. The SGW provides SR only in a narrow band of frequencies close to the resonance Schumann frequencies. Here we analyze the SGW loaded with a small “perfect drain region” (González et al, 2011). This drain is designed as a region made of a material with complex permittivity. The comparative results show that there is no significant difference in the SR properties for both perfect drain designs.
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye
(MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of
arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point
source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution
(SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this
prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution
property. However, neither software simulations nor experimental measurements for a broad band of frequencies have
yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt
and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE,
called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system
loaded with the perfect drain, and up to λ /500 for a not perfect load. In both cases super-resolution only happens for
discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried
out.
Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.)
design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function
called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is
obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the
linearity of the integral transformation which allows us to derive new solutions from linear combinations of known
lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the
Abel integral equation with fixed limits, which is an ill-posed problem.
A metal-less RXI collimator has been designed using the Simultaneous multiple surface method (SMS). The collimator
is completely made of plastic (PMMA) and does not include any mirrored surface, unlike to the convectional RXI
collimators, whose back surface is metalized to provide a specular reflection. The back surface of the V-groove RXI is
designed as a grooved surface providing two TIR reflections for all rays impinging on it. The main advantage of the
presented design is lower manufacturing cost since there is no need for the expensive process of metalization. Also,
unlike to the conventional RXI collimators this design performs good colour mixing. The experimental measurements of
the first prototype are presented.
A metal-less RXI collimator has been designed. Unlike to the conventional RXI collimators, whose back surface and
central part of the front surface have to be metalized, this collimator does not include any mirrored surface. The back
surface is designed as a grooved surface providing two TIR reflections for all rays impinging on it. The main advantage
of the presented design is lower manufacturing cost since there is no need for the expensive process of metalization.
Also, unlike to the conventional RXI collimators this design performs good colour mixing. The first prototype of V-groove
RXI collimator has been made of PMMA by direct cutting using a five axis diamond turning machine. The
experimental measurements of the first prototype are presented.
The Simultaneous Multiple Surface design method (SMS) is applied to the design of free-form V-groove reflectors. The
general design problem is to achieve perfect coupling of two wavefronts after two reflections at the groove, no matter
which side of the groove the rays hit first. All possible 2D designs are listed and used as a basis for the 3D free-form
reflector analysis. The extension to the 3D case is given, and illustrative particular canonical examples are developed.
Besides the theory and design work, first prototypes were produced of a mirrorless TIR device using V-grooves that
emulates a parabolic reflector. The experimental measurements of the TIR reflector show reflectance up to 98%.
A novel waveguide-optical integrator is introduced for applications to LEDs. The concept is based upon a Kohler illuminator made of Luneburg lenses. Typical Kohler illuminators are formed by pairs of thin lenses, and perform badly when the paraxial approximation is rough, i.e., when the angular span of the incoming rays is wide. In contrast, the new illuminator performs ideally for angular spans up to 90o (±45o), and has only a 3% loss for a 180o angular span. In general such an illuminator cannot be made in 3D, because adjacent Luneburg lenses overlap. It can, however, be implemented in planar optics, by using Rinehart geodesic lenses, which moreover do not use gradient index material. This waveguide device has application in illumination engineering as a light mixer, particularly for LEDs. Another light mixer using a combination of two kaleidoscopes with a geodesic lens is also presented. Irradiance at the exit of a kaleidoscope has good light mixing if the kaleidoscope is long enough, but the intensity is never well mixed, irrespective of the length. Inserting a Rinehart geodesic lens produces a 90-degree phase-space rotation of the rays, i.e., it exchanges irradiance and intensity. A further kaleidoscope assures complete mixing in both irradiance and intensity.
A novel waveguide-optical integrator is introduced for applications to LEDs. The concept is based upon a Kohler illuminator made of Luneburg lenses. Typical Kohler illuminators are formed by pairs of thin lenses, and perform badly when the paraxial approximation is rough, i.e., when the angular span of the incoming rays is wide. In contrast, the new illuminator performs ideally for angular spans up to 90° (±45°), and has only a 3% loss for a 180° angular span. In general such an illuminator cannot be made in 3D, because adjacent Luneburg lenses overlap. It can, however, be implemented in planar optics, by using Rinehart geodesic lenses. This waveguide device has application in illumination engineering as a light mixer, particularly for LEDs. Another light mixer using a combination of two kaleidoscopes with a geodesic lens is also presented. Irradiance at the exit of a kaleidoscope has good light mixing if the kaleidoscope is long enough, but the intensity is never well mixed, irrespective of the length. Inserting a Rinehart geodesic lens produces a 90-degree phase-space rotation of the rays, i.e., it exchanges irradiance and intensity. An further kaleidoscope assures complete mixing in both irradiance and intensity.
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