Variable aberration generators using rotated Zernike plates

Dynamic correction of astigmatism

For the correction of defocus and astigmatism, mechanical approaches are well known, but there is a need for a non-mechanical, electrically tunable optical system that could provide both focus and astigmatism power correction with an adjustable axis. The optical system presented here is composed of three liquid-crystal-based tunable cylindrical lenses that are simple, low cost, and having a compact structure. Potential applications of the concept device include smart eyeglasses, virtual reality (VR)/ augmented reality (AR) head-mounted displays (HMDs), and optical systems subject to thermal or mechanical distortion. Details of the concept, design method, numerical computer simulations of the proposed device, as well as characterization of a prototype, are provided in this work.

Astigmatic Stokes lens revisited

Stokes lenses are variable power astigmatic lenses comprising of, in its standard version, two pure cylindrical lenses of equal but contrary power that rotate in opposite directions. Here, we present an optical device with variable and continuous astigmatic power which is based on a modified Stokes lens where two sphero-cylindrical lenses (in the form of pure astigmatic lenses) are combined in the classical way but merged with another fixed pure astigmatic lens for improving the capabilities of the resulting optical device concerning the expansion of the astigmatic range without worsening the dioptric power step resolution. The performance of this device is theoretically analyzed in virtue of the power vectors formalism including a three-dimensional (3-D) representation of the generated dioptric power as a function of both the meridian and the rotation angle between the cylinder's axes. In addition, we have assembled a lab-made prototype of the proposed modified Stokes lens and validated its theoretical behavior by dioptric power measurements with an automatic focimeter. As conventional Stokes lenses, the applications of this new optical device range from astigmatism compensation in optical instruments to measurement of refractive error in subjective routines with the previously commented improved capabilities.

Diffractive tunable lens for remote focusing in high-NA optical systems

Remote focusing means to translate the focus position of an imaging system along the optical axis without moving the objective lens. The concept gains increasing importance as it allows for quick 3D focus steering in scanning microscopes, leaves the sample region unperturbed and is compatible with conjugated adaptive optics. Here we present a novel remote focusing approach that can be used in conjunction with high numerical aperture optics. Our method is based on a pair of diffractive elements, which jointly act as a tunable auxiliary lens. By changing the mutual rotation angle between the two elements, we demonstrate an axial translation of the focal spot produced by a NA = 0.95 air objective (corresponding to NA = 1.44 for an oil immersion lens) over more than 140 µm with largely maintained focus quality. We experimentally show that for the task of focus shifting, the wavefront produced by the high-NA design is superior to those produced by a parabolic lens design or a regular achromatic lens doublet.

Characterization of a compact low-cost Stokes lens for astigmatism compensation in optical instruments

Variable power cross-cylinder lenses (or Stokes lenses) have been widely known in the literature for decades. In this paper, we describe how to build a low-cost Stokes lens and discuss its calibration and its application to two significant cases. The construction is in virtue of a phoropter's Risley prism mount for assembling a couple of equal but opposite sign cylindrical lenses (we have selected $\,\pm 1.50$±1.50 D). Thus, variable astigmatic power is achieved by relative rotation of the lenses in opposite directions, and the resulting astigmatic axis is defined by the global rotation of the device. Calibration measurements are performed using an automatic lensmeter (Topcon CL-300) and an aberrometer (Zeiss iProfiler plus) for low and high order, respectively, aberration characterization. The proposed device has been adapted to a manual Topcon LM-8 lensmeter and to a regular Olympus BX-60 upright microscope for experimental validation concerning astigmatism compensation in a digital microscope and astigmatism cancellation in ophthalmic lenses, respectively. The device can be easily adapted to any ophthalmic/optic instrument for the compensation and/or measurement of astigmatism up to a maximum range of $|3|$|3| D of astigmatism.

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.

Reconfigurable optical null based on counter-rotating Zernike plates for test of aspheres

In off-axis subapertures of most aspheres, astigmatism and coma dominate the aberrations with approximately quadratic and linear increase as the off-axis distance increases. A pair of counter-rotating Zernike plates is proposed to generate variable amount of Zernike terms Z4 and Z6, correcting most of the astigmatism and coma for subapertures located at different positions on surfaces of various aspheric shapes. The residual subaperture aberrations are then reduced within the vertical dynamic range of measurement of the interferometer. The plates are fabricated with computer generated holograms and the experimental results show the variable aberration correction effect without ghost fringes. The same plates are reconfigurable by counter-rotating to enable near-null test of various aspheres flexibly.

Generation of spherical aberration with axially translating phase plates via extrinsic aberration

We show that spherical aberration of all orders can be generated as an extrinsic aberration in a system of axially translating plates. Some practical examples are provided. In particular for two phase plates that are 10 mm in diameter it is possible to generate from -10 to 10 waves of fourth-order spherical aberration with an axial displacement of +/- 0.65 mm. We also apply the phenomenon of extrinsic aberration for the generation of a conical wavefront and other non-axially symmetric wavefronts, in other words we propose what can be called a generalized zoom plate.

Stability of a laser cavity with non-parabolic phase transformation elements

In this paper we present a general approach to determine the stability of a laser cavity which can include non-conventional phase transformation elements. We consider two pertinent examples of the detailed investigation of the stability of a laser cavity firstly with a lens with spherical aberration and thereafter a lens axicon doublet to illustrate the implementation of the given approach. In the particular case of the intra-cavity elements having parabolic surfaces, the approach comes to the well-known stability condition for conventional laser resonators namely 0 ≤ (1-z/R(1))(1-z/R(2)) ≤ 1.

Low-cost adaptive astigmatism compensator for improvement of eye fundus camera

In this work we show a conceptually simple and cheap means by which to improve retinal image quality in fundus cameras. We will explain how to build a low-cost variable astigmatism-correcting device with a pair of identical commercial ophthalmic lenses. We have developed and tested a low order aberration compensation device capable of correcting astigmatism prescriptions up to -8.00 D with no significant addition of higher order aberrations. A theoretical description of the device, calibration, and improvement in retinal images without employing any image restoration technique will be shown.

Adaptive astigmatism-correcting device for eyepieces

PURPOSE

We describe how to construct a low-cost and robust variable astigmatism-correcting device manufactured using a pair of identical commercial ophthalmic lenses.

METHODS

Variable astigmatism power can be obtained by relative rotation of two cross cylinders with the same prescription (for this work: S = +2.00 D, C = -4.00 D was used). The rotation of the whole ensemble allows the user to choose the astigmatism axis.

RESULTS

The lens system presented here is able to correct astigmatism for eyepieces, compensating eyeglasses prescriptions from -8.00 to 0.00 D without generation of higher order aberrations and always with mean sphere power close to 0. Theoretical description of the piece, calibration, measurement of aberrations, and examples of use within a microscope are included.

CONCLUSIONS

An inexpensive and robust variable-astigmatism device for eyepieces can be manufactured using two equal ophthalmic lenses. The system is robust in the sense that small misalignments only minimally affect mean sphere power and do not affect higher order aberrations. This unique device can be adapted to many users.

Conditions under which two-element variable power lenses can be created. Part 1. Theoretical analysis

The conditions under which a two-element variable power lens can be created are examined. Such a lens is defined as one in which the functional form of the optical effect created does not change as the elements translate with respect to one another--only the magnitude of the effect changes. It is found that only variable power optical effects that can be described by quadratic functions can be formed by laterally translating two-element variable power lenses. In the case of rotationally translating two-element variable power lenses, possible designs are found by mapping possible laterally translating designs from a Cartesian space to the polar coordinate space of the rotationally translating lens.

Phase plates for generation of variable amounts of primary spherical aberration

We discuss a set of phase plate-pairs for the generation of variable amounts of primary spherical aberration. The surface descriptions of these optical plates are provided, and their aberration-generating properties are verified with real ray-tracing. These plate-pairs are robust in that they allow large tolerances to spacing as well as errors in the relative displacement of the plates. Both primary spherical aberration (r4) and Zernike spherical aberration (6r4- 6r2 + 1) can be generated. The amount of spherical aberration is proportional to the plate-pair displacement and in our example it reaches up to 48 waves (~8 waves Zernike) for a clear aperture of 25 mm.

Spherical aberration gauge for human vision

Spherical aberration affects vision in varying degrees depending on pupil size, accommodation, individual eye characteristics, and interpretations by the brain. We developed a spherical aberration gauge to help evaluate the correction potential of spherical aberration in human vision. Variable aberration levels are achieved with laterally shifted polynomial plates from which a user selects a setting that provides the best vision. The aberration is mapped into the pupil of the eye using a simple telescope. Calibration data are given.

Design and fabrication of an off-axis see-through head-mounted display with an x-y polynomial surface

An off-axis optical system with an x-y polynomial surface for a see-through head-mounted display (HMD) is presented. With the use of an x-y polynomial surface, an off-axis see-through HMD system with one tilted spherical combiner and six relay optical lenses is designed. An off-axis see-through HMD with a 15 mm exit pupil, a 40 degrees x 30 degrees FOV, and 70 mm eye relief is achieved. Furthermore, a binocular off-axis see-through HMD prototype is fabricated and the performance of the system is experimentally tested; 972 cd/m(2) of luminance is measured at the position of the exit pupil of the HMD. A typical augmented reality image captured outdoors with the HMD prototype is also demonstrated.

Direct transformation of Zernike eye aberration coefficients between scaled, rotated, and/or displaced pupils

In eye aberrometry it is often necessary to transform the aberration coefficients in order to express them in a scaled, rotated, and/or displaced pupil. This is usually done by applying to the original coefficients vector a set of matrices accounting for each elementary transformation. We describe an equivalent algebraic approach that allows us to perform this conversion in a single step and in a straightforward way. This approach can be applied to any particular definition, normalization, and ordering of the Zernike polynomials, and can handle a wide range of pupil transformations, including, but not restricted to, anisotropic scalings. It may also be used to transform the aberration coefficients between different polynomial basis sets.