Milena Nikolic

Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study

Abstract. 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.

Super-resolution optics for virtual reality

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.

Design of three freeform mirror aplanat

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.

Design of compact optical systems using multichannel configurations

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.

Optical design through optimization using freeform orthogonal polynomials for rectangular apertures

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.

On the Degrees of Freedom of Freeform Optics

We address here the problem of the number of freeform surfaces and the degrees-of-freedom they provide in optics design. We analyze the degrees-of-freedom lost when prescribing a mapping between object-and-image or source-and-receiver.

Ultra-compact multichannel freeform optics for 4xWUXGA OLED microdisplays

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%).

Three surface freeform aplanatic systems

We address, in detail, the system of differential equations determining a freeform aplanatic system with illustrative examples. We also demonstrate how two optical surfaces, in general, are insufficient in achieving freeform aplanatism through the use of integrability condition for a given reflective freeform aplanatic configuration. This result also alludes to the fact that a freeform aplanatic system fulfills a broader set of conditions than its rotationally symmetric counterpart. We also elaborate on the above results with two illustrative examples (1) A semi aplanatic system which satisfies the generalized sine condition in only one direction and (2) A fully freeform aplanatic reflective system.

Advanced freeform optics enabling ultra-compact VR headsets

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.

Recent advances in the SMS method: diffraction and 3D aplanatism

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.