Application of the Alvarez-Humphrey concept to the design of a miniaturized scanning microscope

Modeling, fabrication, and metrology of 3D printed Alvarez lenses prototypes

In this work, we present the fabrication of two 3D printed plano-freeform prototypes, designed in such a way that, when assembled, an Alvarez lens is formed. The freeform surface of each element was mathematically described using Zernike polynomials and verified by implementing an off-axis null-screen test. Additionally, a characterization by refraction of the assembled lens was performed. Experimental images show the suitability of additive manufacturing engineering for prototyping freeform optics by providing a practical demonstration of the Alvarez lens concept.

Gradient-index Alvarez lenses

Gradient-index Alvarez lenses (GALs), a new, to the best of our knowledge, type of freeform optical component, are surveyed in this work for their unique properties in generating variable optical power. GALs display similar behavior to conventional surface Alvarez lenses (SALs) by means of a freeform refractive index distribution that has only recently been achievable in fabrication. A first-order framework is described for GALs including analytical expressions for their refractive index distribution and power variation. A useful feature of Alvarez lenses for introducing bias power is also detailed and is helpful for both GALs and SALs. The performance of GALs is studied, and the value of three-dimensional higher-order refractive index terms is demonstrated in an optimized design. Last, a fabricated GAL is demonstrated along with power measurements agreeing closely with the developed first-order theory.

General design method for dynamic freeform optics with variable functionality

We propose and demonstrate a general design method for refractive two-element systems enabling variable optical performance between two specified boundary conditions. Similar to the Alvarez lens, small, relative lateral shifts in opposite directions are applied to a pair of plano-freeform elements. The surface prescriptions of the boundary lenses and a maximum desired shift between freeform plates are the main design inputs. In contrast to previous approaches, this method is not limited to boundaries with similar optical functions and can enable a wide range of challenging, dynamic functions for both imaging and non-imaging applications. Background theory and design processes are presented both for cases that are conducive to analytical surface descriptions, as well as for non-analytic surfaces that must be described numerically. Multiple examples are presented to demonstrate the flexibility of the proposed method.

Freeform optics for variable extended depth of field imaging

Imaging depth of field is shallow in applications with high magnification and high numerical aperture, such as microscopy, resulting in images with in- and out-of-focus regions. Therefore, methods to extend depth of field are of particular interest. Researchers have previously shown the advantages of using freeform components to extend depth of field, with each optical system requiring a specially designed phase plate. In this paper we present a method to enable extended depth-of-field imaging for a range of numerical apertures using freeform phase plates to create variable cubic wavefronts. The concept is similar to an Alvarez lens which creates variable spherical wavefronts through the relative translation of two transmissive elements with XY polynomial surfaces. We discuss design and optimization methods to enable extended depth of field for lenses with different numerical aperture values by considering through-focus variation of the point spread function and compare on- and off-axis performance through multiple metrics.

Assessment of high-resolution 3D printed optics for the use case of rotation optics

We present design and manufacture of a 3D printed varifocal freeform optics. The optical refraction power can be tuned continuously by mutual rotation of two helically shaped lens bodies of azimuthally varying curvatures. Since no additional space for axial or lateral lens movement is required, rotation optics allow for a highly compact design of varifocal optics. Manufacturing of the optics was conducted by means of a high-resolution additive manufacturing process. Results of tactile surface measurements are presented as well as imaging through the lens.

MEMS-actuated metasurface Alvarez lens

Miniature lenses with a tunable focus are essential components for many modern applications involving compact optical systems. While several tunable lenses have been reported with various tuning mechanisms, they often face challenges with respect to power consumption, tuning speed, fabrication cost, or production scalability. In this work, we have adapted the mechanism of an Alvarez lens - a varifocal composite lens in which lateral shifts of two optical elements with cubic phase surfaces give rise to a change in the optical power - to construct a miniature, microelectromechanical system (MEMS)-actuated metasurface Alvarez lens. Implementation based on an electrostatic MEMS generates fast and controllable actuation with low power consumption. The utilization of metasurfaces - ultrathin and subwavelength-patterned diffractive optics - as optical elements greatly reduces the device volume compared to systems using conventional freeform lenses. The entire MEMS Alvarez metalens is fully compatible with modern semiconductor fabrication technologies, granting it the potential to be mass-produced at a low unit cost. In the reported prototype operating at 1550 nm wavelength, a total uniaxial displacement of 6.3 µm was achieved in the Alvarez metalens with a direct-current (DC) voltage application up to 20 V, which modulated the focal position within a total tuning range of 68 µm, producing more than an order of magnitude change in the focal length and a 1460-diopter change in the optical power. The MEMS Alvarez metalens has a robust design that can potentially generate a much larger tuning range without substantially increasing the device volume or energy consumption, making it desirable for a wide range of imaging and display applications.

Remote focusing in confocal microscopy by means of a modified Alvarez lens

Alvarez lenses are actuated lens-pairs which allow one to tune the optical power by mechanical displacement of subelements. Here, we show that a recently realized modified Alvarez lens design which does not require mechanical actuation can be integrated into a confocal microscope. Instead of mechanically moving them, the sublenses are imaged onto each other in a 4f-configuration, where the lateral image shift leading to a change in optical power is created by a galvo-mirror. The avoidance of mechanical lens shifts leads to a large speed gain for axial (and hence also 3D) image scans compared to classical Alvarez lenses. We demonstrate that the suggested operation principle is compatible with confocal microscopy. In order to optimize the system, we have drawn advantage of the flexibility a liquid-crystal spatial light modulator offers for the implementation. For given specifications, dedicated diffractive optical elements or freeform elements can be used in combination with resonant galvo-scanners or acousto-optic beam deflectors, to achieve even faster z-scans than reported here, reaching video rate.

Modified Alvarez lens for high-speed focusing

We present a modified configuration of a tunable Alvarez lens with a refocusing frequency of 1 kHz or more. In contrast to the classic Alvarez lens, the approach does not utilize a translational motion of two sub-lenses with respect to each other, but uses a 4f-setup to image two diffractive sub-lenses onto each other. Hereby focus tuning is achieved by rotating a galvo-mirror which affects the overlap of the two sub-lenses which together form an effective lens of refractive power which depends on the rotation angle of the galvo-mirror. We have demonstrated tuning of the optical power in a system where the diffractive Alvarez lens is realized by an LCOS-SLM. We consider our Alvarez setup especially suitable for applications where high refocusing rates are important, as for example in 3D life cell monitoring or tracking.

Metasurface Freeform Nanophotonics

Freeform optics aims to expand the toolkit of optical elements by allowing for more complex phase geometries beyond rotational symmetry. Complex, asymmetric curvatures are employed to enhance the performance of optical components while minimizing their size. Unfortunately, these high curvatures and complex forms are often difficult to manufacture with current technologies, especially at the micron scale. Metasurfaces are planar sub-wavelength structures that can control the phase, amplitude, and polarization of incident light, and can thereby mimic complex geometric curvatures on a flat, wavelength-scale thick surface. We present a methodology for designing analogues of freeform optics using a silicon nitride based metasurface platform for operation at visible wavelengths. We demonstrate a cubic phase plate with a point spread function exhibiting enhanced depth of field over 300 micron along the optical axis with potential for performing metasurface-based white light imaging, and an Alvarez lens with a tunable focal length range of over 2.5 mm corresponding to a change in optical power of ~1600 diopters with 100 micron of total mechanical displacement. The adaptation of freeform optics to a sub-wavelength metasurface platform allows for further miniaturization of optical components and offers a scalable route toward implementing near-arbitrary geometric curvatures in nanophotonics.

Optical performance simulation of free-form optics for an eye implant based on a measurement data enhanced model

This paper describes the application of a modeling approach for precise optical performance prediction of free-form optics-based subsystems on a demonstration model of an eye implant. The simulation model is enhanced by surface data measured on the free-form lens parts. The manufacturing of the free-form lens parts is realized by two different manufacturing processes: ultraprecision diamond machining and microinjection molding. Evaluation of both processes is conducted by a simulation of the optical performance on the basis of their surface measurement comparisons with the nominal geometry. The simulation results indicate that improvements from the process optimization of microinjection molding were obtained for the best manufacturing accuracy.

Robust Design of an Optical Micromachine for an Ophthalmic Application

This article describes an approach to the robust design of an optical micromachine consisting of a freeform optics, an amplification linkage, and an actuator. The robust design approach consists of monolithic integration principles to minimize assembly efforts and of an optimization of the functional components with respect to robustness against remaining assembly and manufacturing tolerances. The design approach presented involves the determination of the relevant tolerances arising from the domains manufacturing, assembly, and operation of the micromachine followed by a sensitivity analysis with the objective of identifying the worst offender. Subsequent to the above-described steps, an optimization of the functional design of the freeform optics with respect to a compensation of the effects of the tolerances is performed. The result leads to a robust design of the freeform optics and hence ensures a defined and optimal minimum performance of the micromachine in the presence of tolerances caused by the manufacturing processes and the operation of the micromachine. The micromachine under discussion is the tunable optics of an ophthalmic implant, an artificial accommodation system recently realized as a demonstration model at a scale of 2:1. The artificial accommodation system will be developed to replace the human crystalline lens in the case of a cataract.

Aberration analysis of optimized Alvarez-Lohmann lenses

In this paper aberrations in Alvarez-Lohmann lenses are analyzed, and a semi-analytical strategy for compensation is derived. An x-y polynomial model is used to describe the aberrations and classify them into static and dynamic components. The lenses are enhanced by higher-order polynomials, and a numerical optimization process is used to determine the most influential coefficients. Two simulations of corrected systems are presented. The first one is optimized for on-axis imaging. The second system is optimized for multiple field points and shows the limitations of a single Alvarez-Lohmann lens. Two systems overcoming these limitations by introducing additional optical surfaces are presented, and their performance is analyzed in simulations.

The Alvarez and Lohmann refractive lenses revisited

Alvarez and Lohmann lenses are variable focus optical devices based on lateral shifts of two lenses with cubic-type surfaces. I analyzed the optical performance of these types of lenses computing the first order optical properties (applying wavefront refraction and propagation) without the restriction of the thin lens approximation, and the spot diagram using a ray tracing algorithm. I proposed an analytic and numerical method to select the most optimum coefficients and the specific configuration of these lenses. The results show that Lohmann composite lens is slightly superior to Alvarez one because the overall thickness and optical aberrations are smaller.

[Triple-optic approach to the Artificial Accommodation System]

BACKGROUND

Use of an implantable mechatronic microsystem (artificial accommodation system) is a novel approach to restoration of the accommodative capacity of the human eye. One such system, based on the triple-optic approach, has been selected for investigation of its suitability.

METHODS

Optical modelling of the dioptric apparatus is carried out by means of an optical simulation tool. Postoperative refractive compensation plus at least 3 dpt of accommodation are required.

RESULTS

An axial shift of 300 microm or less is achieved for the entire range of biometric data ascertained before surgery. In addition, the defined requirements made of optical imaging quality are met.

CONCLUSIONS

The triple-optic approach is basically suitable for application in the restoration of accommodative capacity. It seems that flexure hinges could be used in association with conducting polymers as actuator material. One question that is still open concerns the deformability of such implants as this relates to minimally invasive corneal incisions.