Automatic software-based 3D-angular measurement for weight-bearing CT (WBCT) is valid.

BACKGROUND: The purpose of this study was to compare automatic software-based angular measurement (AM) with validated measurement by hand (MBH) regarding angle values and time spent for Weight-Bearing CT (WBCT) generated datasets. METHODS: Five-hundred WBCT scans from different pathologies were included in the study. 1st - 2nd intermetatarsal angle, talo-1st metatarsal angle dorsoplantar and lateral, hindfoot angle, calcaneal pitch angle were measured and compared between MBH and AM. RESULTS: The pathologies were ankle osteoarthritis/instability, n = 147 (29%); Haglund deformity/Achillodynia, n = 41 (8%); forefoot deformity, n = 108 (22%); Hallux rigidus, n = 37 (7%); flatfoot, n = 35 (7%); cavus foot, n = 10 (2%); osteoarthritis except ankle, n = 82 (16%). The angles did not differ between MBH and AM (each p > 0.36). The time spent for MBH / AM was 44.5 / 1 s on average per angle (p < .001). CONCLUSIONS: AM provided angles which were not different from validated MBH and can be considered as a validated angle measurement method. The time spent was 97% lower for AM than for MBH. LEVELS OF EVIDENCE: Level III.

Fabrication of large-scale scaffolds with microscale features using light sheet stereolithography.

The common characteristics that make scaffolds suitable for human tissue substitutes include high porosity, microscale features, and pores interconnectivity. Too often, however, these characteristics are limiting factors for the scalability of different fabrication approaches, particularly in bioprinting techniques, in which either poor resolution, small areas, or slow processes hinder practical use in certain applications. An excellent example is bioengineered scaffolds for wound dressings, in which microscale pores in large surface-to-volume ratio scaffolds must be manufactured - ideally fast, precise, and cheap, and where conventional printing methods do not readily meet both ends. In this work, we propose an alternative vat photopolymerization technique to fabricate centimeter-scale scaffolds without losing resolution. We used laser beam shaping to first modify the profile of the voxels in 3D printing, resulting in a technology we refer to as light sheet stereolithography (LS-SLA). For proof of concept, we developed a system from commercially available off-the-shelf components to demonstrate strut thicknesses up to 12.8 ± 1.8 µm, tunable pore sizes ranging from 36 µm to 150 µm, and scaffold areas up to 21.4 mm × 20.6 mm printed in a short time. Furthermore, the potential to fabricate more complex and three-dimensional scaffolds was demonstrated with a structure composed of six layers, each rotated by 45° with respect to the previous. Besides the demonstrated high resolution and achievable large scaffold sizes, we found that LS-SLA has great potential for scaling-up of applied oriented technology for tissue engineering applications.

Freeform optics: introduction.

This feature issue of Optics Express highlights 28 state-of-the-art articles that capture a snapshot of the recent developments in the field of freeform optics. As an introduction, the editors provide an overview of all published articles, which cover a broad range of topics in freeform optics. The wide variety of applications presented here demonstrates that freeform optics is a growing and vibrant field with many more innovations to come.

Semi-automatic software-based 3D-angular measurement for Weight-Bearing CT (WBCT) in the foot provides different angles than measurement by hand.

BACKGROUND: The purpose of this study was to compare semi-automatic software-based angular measurement (SAM) with previously validated measurement by hand (MBH) regarding angle values and time spent for the investigator for Weight-Bearing CT (WBCT). METHODS: In this retrospective comparative study, five-hundred bilateral WBCT scans (PedCAT, Curvebeam, Warrington, PA, USA) were included in the study. Five angles (1st - 2nd intermetatarsal angle (IM), talo-metatarsal 1-angle (TMT) dorsoplantar and lateral projection, hindfoot angle, calcaneal pitch angle) were measured with MBH and SAM (Bonelogic Ortho Foot and Ankle, Version 1.0.0-R, Disior Ltd, Helsinki, Finland) on the right/left foot/ankle. The angles and time spent of MBH and SAM were compared (t-test, homoscesdatic). RESULTS: The angles differed between MBH and SAM (mean values MBH/SAM; IM, 9.1/13.0; TMT dorsoplantar, -3.4/8.2; TMT lateral. -6.4/-1.1; hindfoot angle, 4.6/21.6; calcaneal pitch angle, 20.5/20.1; each p < 0.001 except the calcaneal pitch angle, p = 0.35). The time spent for MBH / SAM was 44.5 ± 12 s / 12 ± 0 s on average per angle (p < 0.001). CONCLUSIONS: SAM provided different angles as MBH (except calcaneal pitch angle) and can currently not be considered as validated angle measurement method (except calcaneal pitch angle). The investigator time spent is 73% lower for SAM (12 s per angle) than for MBH (44.5 s per angle). SAM might be an important step forward for 3D-angle measurement of WBCT when valid angles are provided.

Automatic software-based 3D-angular measurement for Weight-Bearing CT (WBCT) provides different angles than measurement by hand.

BACKGROUND: Purpose of this study was to compare automatic software-based angular measurement (AM, Autometrics, Curvebeam, Warrington, PA, USA) with previously validated measurement by hand (MBH) regarding angle values and time spent for the investigator for Weight-Bearing CT (WBCT). METHODS: Five-hundred bilateral WBCT scans (PedCAT, Curvebeam, Warrington, PA, USA) were included in the study. Five angles (1st - 2nd intermetatarsal angle, talo-metatarsal 1-angle (TMT) dorsoplantar and lateral projection, hindfoot angle, calcaneal pitch angle) were measured with MBH and AM on the foot/ankle (side with pathology). Angles and time spent of MBH and AM were compared (t-test, homoscedatic). RESULTS: The specific pathologies were ankle osteoarthritis/instability, n = 147 (29%); Haglund deformity/Achillodynia, n = 41 (8%); forefoot deformity, n = 108 (22%); Hallux rigidus, n = 37 (7%); flatfoot, n = 35 (7%); cavus foot, n = 10 (2%); osteoarthritis except ankle, n = 82 (16%). The angles differed between MBH and AM (each p < 0.001) except the calcaneal pitch angle (p = 0.05). The time spent for MBH / AM was 44.5 ± 12 s / 1 ± 0 s on average per angle (p < 0.0011). CONCLUSIONS: AM provided different angles as MBH and can currently not be considered as validated angle measurement method. The investigator time spent is 97% lower for AM (1 s per angle) than for MBH (44.5 s per angle). Cases with correct angles in combination with almost no time spent showed the real potential of AM. The AM system will have to become reliable (especially in diminishing positive and negative angle values as defined) and valid which has to be proven by planned studies in the future. LEVEL OF EVIDENCE: Level III.

Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation.

Recently, freeform optics has been widely used due to its unprecedented compactness and high performance, especially in the reflective designs for broad-wavelength imaging applications. Here, we present a generalized differentiable ray tracing approach suitable for most optical surfaces. The established automated freeform design framework simultaneously calculates multi-surface coefficients with merely the system geometry known, very fast for generating abundant feasible starting points. In addition, we provide a "double-pass surface" strategy with desired overlap (not mutually centered) that enables a component reduction for very compact yet high-performing designs. The effectiveness of the method is firstly demonstrated by designing a wide field-of-view, fast f-number, four-mirror freeform telescope. Another example shows a two-freeform, three-mirror, four-reflection design with high compactness and cost-friendly considerations with a double-pass spherical mirror. The present work provides a robust design scheme for reflective freeform imaging systems in general, and it unlocks a series of new 'double-pass surface' designs for very compact, high-performing freeform imaging systems.

Freeform imaging systems: Fermat's principle unlocks "first time right" design.

For more than 150 years, scientists have advanced aberration theory to describe, analyze and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design methods for and manufacturing techniques of imaging systems with ever-increasing complexity and performance up to the point where they are now including optical elements that are unrestricted in their surface shape. These so-called optical freeform elements offer degrees of freedom that can greatly extend the functionalities and further boost the specifications of state-of-the-art imaging systems. However, the drastically increased number of surface coefficients of these freeform surfaces poses severe challenges for the optical design process, such that the deployment of freeform optics remained limited until today. In this paper, we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat's principle and solved using power series. The method allows calculating the optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method with catoptric and catadioptric design examples. As such we introduce a disruptive methodology to design optical imaging systems from scratch, we largely reduce the "trial-and-error" approach in present-day optical design, and we pave the way to a fast-track uptake of freeform elements to create the next-generation high-end optics. We include a user application that allows users to experience this unique design method hands-on.

Compact illumination optic with three freeform surfaces for improved beam control.

Multi-chip and large size LEDs dominate the lighting market in developed countries these days. Nevertheless, a general optical design method to create prescribed intensity patterns for this type of extended sources does not exist. We present a design strategy in which the source and the target pattern are described by means of "edge wavefronts" of the system. The goal is then finding an optic coupling these wavefronts, which in the current work is a monolithic part comprising up to three freeform surfaces calculated with the simultaneous multiple surface (SMS) method. The resulting optic fully controls, for the first time, three freeform wavefronts, one more than previous SMS designs. Simulations with extended LEDs demonstrate improved intensity tailoring capabilities, confirming the effectiveness of our method and suggesting that enhanced performance features can be achieved by controlling additional wavefronts.

Freeform optical design for a nonscanning corneal imaging system with a convexly curved image.

Most existing techniques that are typically used by specialists to image the cornea are based on point, slit, or annular scanning due to a narrow field of view. The difficulty in achieving a larger field of view comes from the convex shape of the human eyeball. Field curvature for a refractive imaging system with positive power is typically negative and thus a concave image surface. In order to view the full cornea and sclera with snapshot imaging, we calculate qualified two- and three-mirror solutions from Seidel aberration theory. A three-mirror solution is further optimized as a high-resolution off-axis imaging system using freeform surfaces, which can obtain a full-field tailored image shell without scanning. The lateral resolution on the cornea is about 10 µm with good modulation transfer function (MTF) and spot performance. To ease the assembly, a monolithic design is achieved with slightly lower resolution, leading to a potential mass production solution.

Multifield direct design method for ultrashort throw ratio projection optics with two tailored mirrors.

In this work, we present a multifield direct design method for ultrashort throw ratio projection optics. The multifield design method allows us to directly calculate two freeform mirror profiles, which are fitted by odd polynomials and imported into an optical design program as an excellent starting point. Afterward, these two mirrors are represented by XY polynomial freeform surfaces for further optimization. The final configuration consists of an off-the-shelf projection lens and two XY polynomial freeform mirrors to greatly shorten the regular projection distance from 2 m to 48 cm for a 78.3 inch diagonal screen. The values of the modulation transfer function for the optimized freeform mirror system are improved to over 0.6 at 0.5 lp/mm, in comparison with its rotationally symmetric counterpart's 0.43, and the final distortion is less than 1.5%, showing a very good and well-tailored imaging performance over the entire field of view.

Analytic design of a zoom XY-beam expander with freeform optical surfaces.

Many laser applications require specific irradiance distributions to ensure optimal performance. In addition, some applications can benefit from time-varying distributions. In this work, we present the analytic design of a zoom XY-beam expander based on movable freeform optics that allows to simultaneously vary the magnification in x- and y-direction, respectively. This concept is not new: the new is to design and optimally exploit freeform lenses to achieve such an optical functionality. In comparison with zoom beam expanders that use combinations of rotated cylindrical lenses, a freeform system can be more compact, yet achieving excellent overall optical performance throughout the full zoom range.

Optical modeling of changeable laser image functionality with analysis of the viewing performance.

Changeable laser image is a security feature commonly used on personalized documents. To understand and to predict the influence of different design parameters, a holistic optical modeling approach is essential. In this work a two-stage modeling process is performed using geometric ray tracing methods. The first stage, based on a basic optical model, allows us to identify the influencing parameters and to determine optimum solutions. The second stage, based on an advanced model, allows us to evaluate the optimum performance quantitatively in terms of the viewing angles and the contrast between two images. Simulation results are verified by experiments.

Multi-fields direct design approach in 3D: calculating a two-surface freeform lens with an entrance pupil for line imaging systems.

Including an entrance pupil in optical systems provides clear benefits for balancing the overall performance of freeform and/or rotationally symmetric imaging systems. Current existing direct design methods that are based on perfect imaging of few discrete ray bundles are not well suited for wide field of view systems. In this paper, a three-dimensional multi-fields direct design approach is proposed to balance the full field imaging performance of a two-surface freeform lens. The optical path lengths and image points of numerous fields are calculated during the procedures, wherefore very few initial parameters are needed in advance. Design examples of a barcode scanner lens as well as a line imaging objective are introduced to demonstrate the effectiveness of this method.

Refractive laser beam shaping by means of a functional differential equation based design approach.

Many laser applications require specific irradiance distributions to ensure optimal performance. Geometric optical design methods based on numerical calculation of two plano-aspheric lenses have been thoroughly studied in the past. In this work, we present an alternative new design approach based on functional differential equations that allows direct calculation of the rotational symmetric lens profiles described by two-point Taylor polynomials. The formalism is used to design a Gaussian to flat-top irradiance beam shaping system but also to generate a more complex dark-hollow Gaussian (donut-like) irradiance distribution with zero intensity in the on-axis region. The presented ray tracing results confirm the high accuracy of both calculated solutions and emphasize the potential of this design approach for refractive beam shaping applications.

Tailored free-form optics with movement to integrate tracking in concentrating photovoltaics.

The economic use of high-efficiency solar cells in photovoltaics requires high concentration of sunlight and therefore precise dual-axis tracking of the sun. Due to their size and bulkiness, these trackers are less adequate for small- to mid-scale installations like flat rooftops. Our approach to combine concentrating and tracking of sunlight utilizes two laterally moving lens arrays. The presented analytic optics design method allows direct calculation of the free-form lens surfaces while incorporating the lateral movement. The obtained concentration performance exceeds a factor of 500. This demonstrates that one can benefit from high-efficiency solar cells and more compact and flexible single-axis trackers at the same time.

Potential benefits of free-form optics in on-axis imaging applications with high aspect ratio.

Including free-form optical components in imaging systems provides numerous opportunities for enhanced performance and compact, lightweight packaging. This applies especially to the use of free-form optics in off-axis imaging applications. In case of on-axis imaging, rotationally symmetric lenses are typically used, as they greatly simplify the design and manufacturing process. However, for imaging applications with high aspect ratio, free-form optics can help to provide solutions with clearly better overall imaging performance. For such cases, the ray tracing simulations in this work demonstrate superior imaging performance of basic free-form lenses in comparison to conventional rotationally symmetric lenses, each consisting of two surfaces.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces.

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576-5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat's principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles.

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat's principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Tracking integration in concentrating photovoltaics using laterally moving optics.

In this work the concept of tracking-integrated concentrating photovoltaics is studied and its capabilities are quantitatively analyzed. The design strategy desists from ideal concentration performance to reduce the external mechanical solar tracking effort in favor of a compact installation, possibly resulting in lower overall cost. The proposed optical design is based on an extended Simultaneous Multiple Surface (SMS) algorithm and uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. It achieves 500× concentration, outperforming its conventional concentrating photovoltaic counterparts on a polar aligned single axis tracker.