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An Optical Device with Variable Astigmatic Power
Abstract
A new variable power cross-cylinder lens set is described. It differs from the well known Stokes variable power cross-cylinder lens set, which is made of cylinder lenses of equal but opposite power, in that in the new variable power cross-cylinder lens set both lens elements are identical. These elements can be sphero cylindrical of any type and can be designed to give the same effect as a Stokes lens set or create a spherical bias or offset of a desired amount. The action of this lens set is analyzed using 3-dimensional refractive space.
... In addition, the concept behind the Stokes lens instrument has been applied to some other devices based on the rotation of different optical elements for providing a variable and continuous generation of different optical effects such as variable aberration generation based on two rotating phase elements [25,26], variable prism compensator (Risley prism mount) [27], tunable zoom system based on toroidal lens rotation [28,29], and, of course, variable dioptric power using both refractive and diffractive optical elements [30][31][32][33][34]. Focusing on the Stokes lens itself, some versions have been proposed with different features and uses. ...
... In addition, the concept behind the Stokes lens instrument has been applied to some other devices based on the rotation of different optical elements for providing a variable and continuous generation of different optical effects such as variable aberration generation based on two rotating phase elements [25,26], variable prism compensator (Risley prism mount) [27], tunable zoom system based on toroidal lens rotation [28,29], and, of course, variable dioptric power using both refractive and diffractive optical elements [30][31][32][33][34]. Focusing on the Stokes lens itself, some versions have been proposed with different features and uses. It is of special interest to remember Foley and Campbell's variable power astigmatic lens which was made from the combination of two identical cylinders instead of being equal but opposite powers [32], and Arines and Acosta's one which combined two identical cross-cylinder lenses [33,34]. Regarding the different uses that have been given to this type of lenses of variable astigmatic power, we found the enhancement of peripheral fundus images [35] and eye fundus camera [34], user's astigmatism compensation in device eyepieces [33] or in a Hartmann-Shack sensor [36], residual astigmatism compensation in digital microscopy systems [37] and dioptric power measurement in focimetry applications [38,39]. ...
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.
... The cylindrical axes of the maximum and minimum powers of the cylindrical lens are orthogonal. [1][2][3][4][5][6][7][8][9][10][11][12] Sphero-cylindrical lenses, which are spherical lenses combined with cylindrical lenses, have proved effective in correcting astigmatism. 13 A toric lens is an optical element having two different powers in two orientations that are perpendicular to one another. ...
... (10) and (11). The principal curvature R N can be obtained by solving Eq. (9). The value of the minor principal curvature is the minimum normal curvature at a point, where the minimum normal curvature is the inverse of the radius of the minimum normal curvature. ...
... Conventional correction methods for astigmatism and defocus typically involve the use of mechanically driven, bulky lenses. [3][4][5] However, modern optics research aims to replace these traditional mechanical correction methods with compact, low-cost, non-mechanical solutions. 6 In the field of adaptive optics, several methods have been developed over the past four decades to adjust the focal length of optical systems. ...
... Consequently, two sphere equivalents cancel each other, which causes zero spherical power [8]. Foley and Campbell showed a variable astigmatic lens with two identical spherocylindrical lenses [9]. In contrast to Stokes' lens, Campbell's proposed lens can generate any mean spherical power depending on the rotation of the lenses in the set [10]. ...
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.
... Since then, the Stokes lens has been used successfully in many ophthalmic and optometric applications and instruments, and some evolutions of the original system have been proposed across the years. Foley and Campbell proposed a new variable power astigmatic lens set equivalent to the Stokes lens but composed of two identical cylindrical lenses instead of cylinders of equal but opposite powers [2]. As a consequence, the system exhibits another essential difference from the Stokes lens: there is a remaining mean sphere power that is equal in magnitude to twice the mean spherical power of one of the cylinders in the set. ...
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.
... The optical correction of astigmatism can take many forms, including spectacles, contact lenses, and refractive surgery [1,3,10]. Spectacle lenses used to correct astigmatism are described as cylindrical or toroidal, and the axes of the maximum and minimum powers of the cylindrical lens are orthogonal [1,3,4,[6][7][8][9][10][11]. The axes of the cylindrical lens are aligned with the axes of the astigmatism of the eye to provide optical correction [6]. ...
Toroidal, spherocylindrical, ellipsoidal, and combined surfaces were used to correct astigmatism in aspheric spectacle lenses, and the differences among the proposed techniques were compared. Four astigmatic spectacle lenses were designed with the same optical parameters. A freeform measuring machine was used to evaluate posterior surfaces of aspheric spectacle lenses, and spherical and cylindrical power maps were generated and compared. The measured data were analyzed via commercial software. The toroidal lens helped to extend the clear vision range around the lens, and the ellipsoidal and spherocylindrical surfaces resulted in a more accurate centering of the lens around the optical axis of the eye, avoided astigmatism, and provided better visual perception.
While the near‐to‐eye HMDs are advancing in display resolution, there are active challenges related to accommodation‐convergence (AC) conflict correction as well as prescription correction (Rx). Many approaches are reported previously to solve AC conflict using variable focal lenses, however, very few of them included dynamic Rx correction. While AC correction requires only adjustment of focal plane, Rx correction requires simultaneous correction of focal length and astigmatism. In this report, we have shown concept, design, fabrication, and demonstration of liquid crystal based tunable lens that is capable of dynamic correction of both the issue without needing any mechanical moving parts. The device is lightweight, thin, flat, low voltage driven and has potential to replace the eyeglasses worn by the users with the HMDs.
The main two optical aberrations seen in any imaging system are defocus and astigmatism. Traditionally, the approaches to correct both aberrations utilize the mechanical movement of fixed power spherical and cylindrical lenses. In this report, we have proposed a non-mechanical, electrically tunable optical system that can provide both focus and astigmatism power correction with an adjustable axis. The concept device is comprised of stripe electrodebased gradient refractive index liquid crystal lens. Dynamic astigmatism and focus correction are demonstrated upon application of electric field on the designed device. Unlike complex, bulky, and curved shape lens systems, the proposed device is flat, low cost, and low voltage driven.
Dioptric power measurement is classically achieved using manual focimeters. In this contribution, we present vectofocimetry as a novel methodology to be easily implemented in manual focimeters for improving their capabilities regarding dioptric power measurement. The new procedure is conceptually based on power vector formalism of dioptric power which represents the dioptric power as three values in the form of [M, J0, J45], it uses an iterative process of blur reduction, and it only requires a few modifications in the device that are easy-to-adapt and cost-effective. As a result, dioptric power measurements are easily and quickly obtained with comparable results to the reported ones using the traditional method but with some improvements concerning: i) comfortability/usability (no need to see through the device), ii) elimination of the accommodation user's error (no need to adjust the ocular for every user), and iii) elimination of the measurement error coming from wrong interpretation/annotation of the cylinder axis (the test reticle is focused at once as a whole). The new device is presented, the measurement methodology is rigorously described, and proof-of-principle validation is included showing comparable results between the proposed procedure/device and the conventional ones for dioptric power determination. In addition, definition of the marking methodology has been also included and described. Next steps can be directed towards automatization of the measurement process at both levels (decision for final measurement point and avoiding the manual use of the device) thus opening the gate as a potential technology for a new generation of automatic focimeters.
Every dioptric power of the usual form sphere/cylinder x axis may be represented by means of a point in three-dimensional space. Graphical representation of data in this manner is important for statistical analysis. In particular, graphical representation may be used to display confidence regions about a mean power, for example. A disadvantage of these representations, however, is that simply changing the reference meridian for cylinder axes changes distances in the space and, therefore, changes the shapes of the confidence regions. Because the shapes define the nature of the variation and give, in particular, the principal components of variation, a researcher who happens to measure the orientation of cylinder axes from the 20 degree meridian, for example, instead of the conventional horizontal meridian, could be led to different statistical conclusions. The implication is that such conclusions are unlikely to have much physical meaning. A representation is described here in which distances and shapes do not depend on the meridian that happens to be chosen as reference. Each dioptric power is represented by a point in Euclidean 3-space. Several examples of graphical representation are given. The spherical powers occupy a particular line in the space, the Jackson crossed cylinders occupy a plane, the cylindrical powers occupy a cone, and so on, for all types of conventional dioptric power. These lines and surfaces are illustrated. The statistical implications are discussed briefly. The representation satisfies the requirements of the statistics and is proposed as the standard one for future use.
The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.