Kevin P. Thompson

A new family of optical systems employing φ-polynomial surfaces

Unobscured optical systems have been in production since the 1960s. In each case, the unobscured system is an intrinsically rotationally symmetric optical system with an offset aperture stop, a biased input field, or both. This paper presents a new family of truly nonsymmetric optical systems that exploit a new fabrication degree of freedom enabled by the introduction of slow-servos to diamond machining; surfaces whose departure from a sphere varies both radially and azimuthally in the aperture. The benefit of this surface representation is demonstrated by designing a compact, long wave infrared (LWIR) reflective imager using nodal aberration theory. The resulting optical system operates at F/1.9 with a thirty millimeter pupil and a ten degree diagonal full field of view representing an order of magnitude increase in both speed and field area coverage when compared to the same design form with only conic mirror surfaces.

Theory of aberration fields for general optical systems with freeform surfaces

This paper utilizes the framework of nodal aberration theory to describe the aberration field behavior that emerges in optical systems with freeform optical surfaces, particularly φ-polynomial surfaces, including Zernike polynomial surfaces, that lie anywhere in the optical system. If the freeform surface is located at the stop or pupil, the net aberration contribution of the freeform surface is field constant. As the freeform optical surface is displaced longitudinally away from the stop or pupil of the optical system, the net aberration contribution becomes field dependent. It is demonstrated that there are no new aberration types when describing the aberration fields that arise with the introduction of freeform optical surfaces. Significantly it is shown that the aberration fields that emerge with the inclusion of freeform surfaces in an optical system are exactly those that have been described by nodal aberration theory for tilted and decentered optical systems. The key contribution here lies in establishing the field dependence and nodal behavior of each freeform term that is essential knowledge for effective application to optical system design. With this development, the nodes that are distributed throughout the field of view for each aberration type can be anticipated and targeted during optimization for the correction or control of the aberrations in an optical system with freeform surfaces. This work does not place any symmetry constraints on the optical system, which could be packaged in a fully three dimensional geometry, without fold mirrors.

An analytic expression for the field dependence of Zernike polynomials in rotationally symmetric optical systems

Zernike polynomials have emerged as the preferred method of characterizing as-fabricated optical surfaces with circular apertures. Over time, they have come to be used as a sparsely sampled in field representation of the state of alignment of assembled optical systems both during and at the conclusion of the alignment process using interferometry. We show that the field dependence of the Zernike polynomial coefficients, which has to-date been characterized essentially by aperture dependence, can be introduced by association to the field dependent wave aberration function of H.H. Hopkins.

Design of a free-form single-element head-worn display

Compact and lightweight optical designs achieving visually acceptable image quality, field of view, eye clearance, eye box diameter and operating across the visible spectrum, are the key to the success of next generation head-worn displays. There have been several approaches in the design of head-worn displays including holographic optical elements and laser scanner systems. For example, Minolta has pursued a monochromatic display (green) with a 3 mm exit pupil realized by a 3.4 mm thick light guide with a holographic optical element to achieve an eyeglass form-factor head-worn display [1]. Our approach in this paper is to investigate the field of view, eyebox diameter, and the performance limit of a single element magnifier comprised of freeform surfaces. The surface shape is a major variable in such a constrained system with respect to the optimization degrees of freedom. Typical optical surfaces are functions mapping vectors in R2 to real numbers representing the sag of the surface. A majority of optical designs to-date have relied on conic sections to which are added polynomials as the functions of choice. The choice of conic sections is easily justified, since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from an image quality analysis point of view is understood since the wavefront aberration function is typically expanded in terms of polynomials. Therefore, a polynomial surface description may link a designers understanding of the wavefront aberrations and the surface shape. However, from the point of view of shape optimization and representation, polynomial shape descriptions can be challenged. In Section 2, we briefly describe the radial basis function approach to represent freeform optical surfaces. In Section 3, we apply the RBF to design a single element see-through compatible head-worn display.

Assembly of a freeform off-axis optical system employing three φ-polynomial Zernike mirrors

We report on the assembly of an off-axis reflective imaging system employing freeform, φ-polynomial optical surfaces. The sensitivity of the system to manufacturing errors is studied for both a passive and active alignment approach. The as-built system maintains diffraction-limited performance in the long-wave infrared.

MEMS-based handheld scanning probe with pre-shaped input signals for distortion-free images in Gabor-domain optical coherence microscopy

High-speed scanning in optical coherence tomography (OCT) often comes with either compromises in image quality, the requirement for post-processing of the acquired images, or both. We report on distortion-free OCT volumetric imaging with a dual-axis micro-electro-mechanical system (MEMS)-based handheld imaging probe. In the context of an imaging probe with optics located between the 2D MEMS and the sample, we report in this paper on how pre-shaped open-loop input signals with tailored non-linear parts were implemented in a custom control board and, unlike the sinusoidal signals typically used for MEMS, achieved real-time distortion-free imaging without post-processing. The MEMS mirror was integrated into a compact, lightweight handheld probe. The MEMS scanner achieved a 12-fold reduction in volume and 17-fold reduction in weight over a previous dual-mirror galvanometer-based scanner. Distortion-free imaging with no post-processing with a Gabor-domain optical coherence microscope (GD-OCM) with 2 μm axial and lateral resolutions over a field of view of 1 × 1 mm2 is demonstrated experimentally through volumetric images of a regular microscopic structure, an excised human cornea, and in vivo human skin.

Interferometric measurement of a concave, φ-polynomial, Zernike mirror

We report on the surface figure measurement of a freeform, φ-polynomial (Zernike) mirror for use in an off-axis, reflective imaging system. The measurement utilizes an interferometric null configuration that is a combination of subsystems each addressing a specific aberration type, namely, spherical aberration, astigmatism, and coma.

Ray-based optical design tool for freeform optics: coma full-field display

The field of optical fabrication has progressed to a point where manufacturing optical quality freeform surfaces is no longer prohibitive. However, to stimulate the development of freeform systems, optical designers must be provided with the necessary tools. Full-field displays are an example of such a tool. Identifying the field dependence of the dominant aberrations of a freeform system is critical for a controlled optimization and with the help of full-field displays, this can be accomplished. Of specific interest is coma, an often system-limiting aberration and an aberration that has recently been directly addressed with freeform surfaces. In this research, we utilize nodal aberration theory to develop a ray-based method to generate a coma full-field display that circumvents wavefront fitting errors that can affect Zernike polynomial-based full-field displays for highly aberrated freeform starting designs.

57.3: Invited Paper: Head-worn Displays - Lens Design

There is a growing and sometimes critical need to ubiquitously process, visualize, and merge information with the world around us, in real-time. This need has created a renewed interest in see- through (as opposed to look-at) augmented mobile viewing systems that are compact, low cost, and convenient, with resolution that approaches that of the human visual system extending into the peripheral field of view. We will review key technology paths that build on historical highlights and discuss some market barriers to the emergence of eyewear format head- worn displays (HWDs). Finally, we will focus on freeform approaches and feature emerging solutions in freeform combiners that build on a novel description of freeform surfaces and provide a key competitive advantage in the ability to separate the see- through scene and the user by a seamless thin plastic window.

A new generation of optical systems with φ-polynomial surfaces

Recent advances have made it viable to fabricate optical surfaces that are not rotationally symmetric using a new generation of diamond-turning machines. These surfaces can greatly extend the field of view of optical systems and provide compact solutions. Through the use of optimization and analysis methods that track aberration content throughout the field of view, two non-rotationally symmetric designs that provide a compact mirror based geometry with a 10 degree full field of view are presented and compared. It is shown that a φ-polynomial surface provides superior optical performance to an anamorphic asphere because the surface can be made comatic.