Thin Lens Research Articles

An accurate determination of the refractive indices of water and glass by smartphone photography

A smartphone can be used for many physics experiments by using the sensors built into the phone. The complementary metal oxide semiconductor (CMOS) (charge-coupled device, CCD) sensor of the camera records the images of objects photographed in pixels. The width of the image can be read off with micron level accuracy with the help of software available freely from the internet. If the dimensions of the object in the direction transverse to the viewing direction of the camera are known, the magnification of the object photographed can be determined accurately. A smartphone camera is a compound lens comprising a number of very thin lenses. A single thin lens is equivalent, as far as the transverse magnification is concerned, to a compound lens of the smartphone, when the thin lens has the same focal length as the effective focal length of the compound lens and is placed at its first principal plane. This property allows us to find experimentally the effective focal length of the compound lens of the camera accurately, using the thin lens equation. Once the focal length of the camera is known, the distance of an object can be determined by finding its magnification from the photograph. We have determined the refractive index of water accurately by photographing the apparent position of an object immersed in it. By determining the magnifications, we have found the real and apparent depths of the object. The ratio of these depths gives the refractive index. We have determined the refractive index of glass also using some thin glass slides.

Ore Genesis of the Abu Ghalaga Ferro-Ilmenite Ore Associated with Neoproterozoic Massive-Type Gabbros, South-Eastern Desert of Egypt: Evidence from Texture and Mineral Chemistry

Massif-type mafic intrusions (gabbro and anorthosite) are known for their considerable resources of vanadium-bearing iron–titanium oxide ores. Massive-type gabbroic and anorthosite rocks are frequently associated with magmatic rocks that have significant quantities of iron, titanium, and vanadium. The most promising intrusions that host Fe-Ti oxide ores are the gabbroic rocks in the south-eastern desert. The ilmenite ore deposits are hosted in arc gabbroic and anorthosite rocks. They are classified into three types, namely black ore, red ore, and disseminated ore. The black ilmenite ore is located at the deeper level, while the oxidized red ore is mainly located at or near the surface. Petrographically, the gabbro and ilmenite ores indicate a crystallization sequence of plagioclase, titaniferous pyroxene, and ilmenite. This reveals that the ilmenite is a magmatic deposit formed by the liquid gravity concentration of ilmenite following the crystallization of feldspar and pyroxene. Meanwhile, quartz, tremolite, zoisite, and opaque minerals are accessory minerals. The Fe-Ti ores are composed of ilmenite hosting exsolved hematite lamellae of variable sizes and shapes, gangue silicate minerals, and some sulfides. The X-ray diffraction (XRD) data reveal the presence of two mineral phases: ilmenite and hematite formed by the unmixing of the ferroilmenite homogeneous phase upon cooling. As a result, the ore is mostly made up of hemo-ilmenite. Using an electron microscope (SEM), as well as by observing the textures seen by the ore microscope, ilmenite is the dominant Fe-Ti oxide and contains voluminous hematite exsolved crystals. Under the scanning electron microscope, ilmenite contained intergrowths of hematite as a thin sandwich and lens shape. The formation of hematite lamellae indicates an oxidation process. Mineral chemistry-based investigations reveal late/post-magmatic activity at high temperatures. The examined ilmenite plots on the ferro-ilmenite line were created by continuous solid solution over 800 °C, whereas the analyzed magnetite and Ti-magnetite plot near the magnetite line and were formed by continuous solid solution exceeding 600 °C.

Development of new methods for assessing the technical condition of power lines using digital image processing

An important role in satisfying the high quality of life of the population and modern industry is played by the reliability of power supply and ensuring uninterrupted delivery of electricity. As a result of a large number of emergency failures of elements caused by external factors, information about the technical state of elements in real time is not used by dispatching centers. These conditions cause difficulties in assessing the reliability of power lines and timely elimination of developing defects, which cause high transmission losses and lead to wire breaks and failures.Considering a digital photo or other raster image to assess the surface of power lines wires, we know that it is an array of numbers recorded by sensors of brightness levels, in a two-dimensional plane. Knowing that in mathematical terms a thin lens performs the Fourier transform of images placed in the focal planes, it is possible to create image processing algorithms, which are analogues of image processing by a classical optical system. An algorithm for automatic processing of scanning electron microscopy images aimed at detecting and describing surface defects in power line wires is proposed, which is implemented in the Python programming language. The algorithm proposes to use a Fourier transform procedure to eliminate the image brightness gradient and suppress high-frequency noise in the image by applying a two-dimensional bandpass filter. The necessity and parameters of the dynamic range normalization of the filtered image are determined. The binarization parameters of the normalized image are determined. A quantitative assessment of the degree of defectiveness of the investigated wire surface has been proposed. A quantitative assessment of the degree of elongation of defects on the surface of the investigated wire has been proposed.

Bistatic Radar Tracking With Significantly Improved Bistatic Range Accuracy

Tracking with bistatic radar measurements is a challenging problem due to the nonlinear relationship between the radar measurements and the Cartesian coordinates, especially for long distances. This nonlinearity leads, for 3-D bistatic radar, to a nonellipsoidal measurement uncertainty region in Cartesian coordinates, similar to a thin contact lens, that causes consistency problems for a tracking filter. The recently developed conversion of the bistatic radar measurements into Cartesian coordinates enables to maintain consistency by using a converted measurement Kalman filter. However, such a filter suffers from a poor bistatic range accuracy, limiting the multitarget tracking performance in a dense environment of targets or clutter. A solution is suggested by using a filter in the measurement coordinate system and converting its results into Cartesian coordinates. Consistent Cartesian estimation is obtained together with significantly improved filtered bistatic range accuracy. The latter is important in data association, resulting in a measurement-to-track association gates that are over an order of magnitude smaller compared to the Cartesian filters. It is shown that if the data association is performed in sensor coordinates, the (Cartesian) volume of the contact lens association region is over 20 times smaller than if it is performed in Cartesian coordinates because the ellipsoid in the latter case is extremely conservative.

Nonlinear focal shift due to the Kerr effect for a Gaussian beam focused by a lens.

When a low-power, monochromatic Gaussian beam is focused by a thin lens in air and the waist of the beam is in the plane of the lens, there is a shift of the focus position if the waist of the beam is much smaller than the size of the lens. The point of maximum intensity relative to the geometrical focal point shifts closer to the lens. We show that for ultra-intense light beams, when the Kerr effect is unavoidable, there is a nonlinear focal shift. The nonlinear focus position shifts closer to the lens for laser powers below the critical power. To avoid the nonlinear focal shift below the critical power, the correct combination of Gaussian beam waist and focal system has to be used in the experimental setup. It will be shown that as the Fresnel number N w associated with the Gaussian beam radius increases, the nonlinear focal shift first increases and then begins to decrease.

Analytical solutions for film stress and bending deformation of coated optical lenses

Axisymmetric film/substrate systems are irreplaceable for many applications, owing to special structural requirements. Stoney's formula is widely used to analyze the thin plate film/substrate system. Many researches have been presented to relax limitations of Stoney's formula, which considered the substrate as a thin plate without any curvature. For the optical lens, the axisymmetric thin shell substrate with different curvatures on its upper and lower surfaces is common due to the need of optical focusing. The film stress of the optical lens needs to be optimized and measured due to its effects on system deformations and optical performances. However, the optical lens cannot be solved by Stoney's formula and its extensions due to the curvatures. In this paper, analytical solutions for the thin shell optical lens with different curvatures on upper and lower substrate surfaces are developed by the thin shell theory with the axisymmetric distribution film stress resultant (FSR) in consideration. The FSR is modeled by thermal stress equivalent method, which allows the calculation for the axisymmetric distribution FSR induced by many factors. The forward and inverse solutions between the FSR and the bending deformation are provided in the form of simple formulas with correction coefficient vectors depending on the global substrate thickness, which enables its feasibility in practical applications. Moreover, the two solutions are verified by the finite element method considering the deformation normal to the substrate surface measured by the interferometer in inverse solution, and small errors are found when the optical lens conforms to the assumptions of the method in this paper. The proposed method is efficient to predict the optical lens’ bending deformations, and extends the usage of curvature-based techniques from plates to shells with different curvatures on upper and lower surfaces in the film stress measurement, which makes great significance to the thin film/substrate application.

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The work is devoted to the study of the characteristics of the optical-mechanical sensor for the measurement control of geometric characteristics of firearms bores. The results of the analysis of publications devoted to the structure and application of measuring devices based on the triangulation method of distances determining are given. The limited possibility of applying of the results obtained in known works in the creation of an optical-mechanical sensor for diagnosing of firearms bores was noted. Features of construction and basic geometric parameters of the optical-mechanical sensor are considered. A description of the measurement method is given, which provides for the calculation of the desired distance using the known parameters of the optical scheme of the optical-mechanical sensor and the linear and angular parameters of the triangles consisting of the elements of the optical scheme of the sensor. An expression for the dependence of the angle between the optical axis of the receiving lens and the light-sensitive detector from other basic geometric parameters of the optical-mechanical sensor was obtained using the basic formula for a thin lens. The expression determines the angular position of the light-sensitive detector in relation to the main optical axis of the receiving lens and should be taken into account as a limitation in the practical implementation of the sensor. The conversion function of the optical-mechanical sensor is determined, which establishes the dependence between the increment of the coordinate of the light spot on the surface of the light-sensitive detector of the sensor and the increment of the radius of the bore. An expression for solving the inverse problem � calculating the value of the input value based on measurement information about the output value � was obtained. Graphs of these functions for typical combinations of optical-mechanical sensor parameters are given. A study of the linearity of the conversion function of the optical-mechanical sensor and the nature of its sensitivity change within the range of measurement was conducted.

Different view on diffraction-limited imaging optics design.

The task of imaging optics design starts with choosing a subset of imaging parameters such as the object distance, the image magnification, the image resolution, and the depth of field. It is clear that the imaging parameters are inter-related and their appropriate trade-off is the key problem of final optical design. We provide a novel analysis of the optical design considering diffractive imaging phenomena and thin lens approximation, and we derive formulas for the solution of individual parameters. We show that combinations of three independent optical design input variables determine all other optical and geometrical parameters under diffraction-limited optical imaging. We also formulate an invariant relation in the object space if the depth of field is one of the design's target parameters.

Algebraic method for finding the initial design parameters of a two-element optical system with an afocal meniscus lens.

This work introduces an algebraic method of the calculation of an initial design of a two-element optical system composed of a thick afocal meniscus lens and a thin lens element, which can be formed, for example, by a cemented doublet. The third-order aberration theory is used to find the fundamental parameters of the starting configuration of a given optical system. The method gives results that make it possible to obtain a good starting design for further optimization of such imaging systems using optical design software. The proposed method is presented on two examples of finding the initial design parameters of the objective with an afocal meniscus lens and a cemented doublet.

Spectral singularities and threshold gain of a slab laser under illumination of a focused Gaussian beam

Spectral singularities of an infinite planar slab containing homogeneous optically active material at the focal plane of a thin lens are investigated. The field distribution of the beam behind the lens is Gaussian that we approximate by a plane wave concentrated near the optical axis at the focal plane of the lens, such that its phase and amplitude are distance-dependent. The consequences of this configuration are explored by determining the threshold gain of the active medium and tuning the resonance frequencies related to spectral singularities. We find that the spectral singularities and the threshold gain, besides that, vary with distance from the center of the Gaussian beam; also they change with the relative aperture of the focusing lens. Numerical studies show that for the central rays of the beam compared to the side rays, the resonances related to the spectral singularities occur at lower wavelengths (higher frequencies) with the highest threshold gain. Also, for the ray at a fixed distance from the center of the beam, increasing the relative aperture of the illuminating system leads to the same results. Numerical results confirm the theoretical findings.

Organization of residential space, site function variability, and seasonality of activities among MIS 5 Iberian Neandertals

Whether ethnoarcheological models of hunter-gatherer mobility, landscape use, and structuration of the inhabited space are relevant to the archeology of Neandertals and the Middle Paleolithic remains controversial. The thin lenses of hearth-associated stone tools and faunal remains excavated in sub-complex AS5 of Cueva Antón (Murcia, Spain) significantly advance these debates. Dated to 77.8–85.1 ka, these living floors are interstratified in river-accumulated sands and were buried shortly after abandonment by low-energy inundation events, with minimal disturbance and negligible palimpsest formation. Stone tools were made and ergonomically modified to fit tasks; their spatial distributions and use-wear reveal hearth-focused activities and a division of the inhabited space into resting and working areas. Site function varied with season of the year: units III-i/j1 and III-i/j2-3 record winter visits focused on filleting and hide processing, while woodworking predominated in unit III-b/d, which subsumes visits to the site over the course of at least one winter, one spring, and one summer. These snapshots of Neandertal behavior match expectations derived from the ethnographic and Upper Paleolithic records for the lifeways of hunter-gatherers inhabiting temperate regions with a markedly seasonal climate.

A Cost-Effective Triplet Lens Design with Chromatic Aberration Correction Based on Optimization Algorithm and Illustration Method

This paper proposes an optimization algorithm combined with an illustration method to select the three best glass materials for the design of a thickened triplet lens and a correction of the paraxial chromatic aberrations. In the thin lens thickening process, chromatic aberration arises from the deviation between the real and paraxial chromatic aberrations. To solve this problem, we propose an optimization algorithm and illustration method, which are integrated into a thickened triplet lens design. We optimize the eight thickened triplet lens groups to obtain the longitudinal chromatic aberration curve for the best group in the visible light range from 0.4861 μm to 0.6563 μm. The chromatic aberration curve area is 3.33 × 10−7 (μm × mm) for the longitudinal chromatic aberration and 2.11 × 10−5 (μm × mm) for the lateral chromatic aberration. Finally, the chromatic aberration of the thicken triplet lens is close to that of the thin triplet lens design, and the proposed method can obtain a good optical performance.

Knowledge and Practice Regarding Contact Lens Wear and Care Among Undergraduate Students in Universiti Sains Malaysia

Contact lenses are thin optical correction lenses worn on the eye and rest on the cornea’s surface. The number of individuals who wear contact lenses is growing every day, but many people are unaware of the benefits and drawbacks of wearing them. Contact lens wear and care that is not adhered to can lead to severe ocular complications and permanent vision loss [1]. Overall rates of non-compliance with good contact lens wear have been cited in the literature as ranging from 40-91% in the past [2]. Knowledge and practice regarding contact lens wear and care is very important to control its progression and its complication effectively.
 
 The objective of this cross-sectional study is to determine the knowledge and practice regarding contact lens wear and care and factor associated with the practice among undergraduate students in Universiti Sains Malaysia who have experienced wear contact lens. The questionnaire adopted from Abd Aziz et al [3] was distributed using the online method of Google form between January to May 2022. Data were analyzed using SPSS 26. Descriptive statistics were performed to determine the knowledge and practice. General linear regression modelling was used to analyze factors associated with practice.
 
 A total of 170 undergraduate students from various faculties on 3 campuses of USM aged 20-27 years old were involved in this study. Regularity of contact lens use showed most respondents used contact lens as occasionally (38.8%) and for 4-6 days per weeks (25.3%). Half of respondent mentioned their purpose of contact lens use as a refractive error (51.2%) and there is similar percentage in term of duration of contact lens use for less than 1 year and 5 years (30% and 30.6% respectively). Mean score of knowledge was 21.71 ± 2.46 with 51.8% of the respondents in this study have poor knowledge of contact lens wear and care. Mean score of practice was 22.49 ± 2.76 with majority of the respondent (74.1%) have poor practice regarding contact lens wear and care. In the final model of general linear regression, factors associated with the practice of contact lens wear and care were gender, course of study, purpose of using contact lens, duration of contact lens use and knowledge of contact lens wear and care (p < 0.05).This study indicate there is a need for health education and awareness program to contact lens wearers especially among young people regarding contact lens usage, care, and its related complications

Bifocal flat lens with different imaging characteristics for a dual-sensor imaging system

Wide field of view (FOV) images and magnified images can be taken simultaneously by dual-sensor imaging systems. Here, we propose an approach for creating a bifocal flat lens with different imaging characteristics of its two foci, which makes dual-sensor imaging systems more integrated and miniaturized. That is, two special parts of two different conventional ZP are extracted and then combine the two elements in a specific way. So that there are two foci with different characteristics along the optical axis, one is long focus with higher resolution, the other is short focus with long depth of focus (DOF). Under the proposed approach, a thin and light bifocal diffractive lens (BDL) with thickness of 0.6 μm is developed. The long and short focal lengths of the BDL are ~ 81 mm and ~ 27 mm, respectively, with a diameter of 6 mm. We experimentally demonstrate that the long focus of the BDL is capable of taking high-resolution magnified images, and its resolution is up to 21.90″. The short focus is able to take wide FOV with long DOF images, and two objects spread 2880 mm apart can be imaged clearly. The experiment results demonstrate that all of these metrics are better than those of a conventional refractive lens.

3-D Printed 3-D Near-Field Focus-Scanning Lens for Terahertz Applications

This article introduces a novel near-field focus (NFF) lens antenna with a three-dimensional (3-D) focus-steering capability operating at terahertz (THz) frequencies. The antenna consists of a pair of thin discrete dielectric lenses (DDLs) placed above a stationary feed horn. First, we demonstrate that the DDL doublet’s in- plane synchronous counter-rotation and co- rotation could scan its focus radially and azimuthally, respectively. A multi-focus synthesis method that compensates the required transmission phases at multi-focus points is developed to further improve its NFF-steering performance. The DDL-based antenna can realize 3-D focus-scanning using a combination of rotation and linear translation mechanisms. The 3-D printing is adopted to fabricate the THz antenna to simplify the manufacturing process and reduce the cost. Both numerical and experimental results demonstrate that the 15 mm-diameter antenna prototype can scan its focus in a 3-D cylindrical space with a diameter of 29 mm and a length of 8 mm at 300 GHz. The proposed 3-D focus-scanning antenna with a large field of view (FoV) of 72° will open new avenues for fast 3-D THz imaging applications.

Scalar diffraction analysis of the dispersion effect on the focal length of low-index thin flat lenses

We analyze the dispersion effect of the focal length of low-index thin lenses by using scalar diffraction and finite difference time domain (FDTD) methods. We compare the dispersion results obtained by using these methods with reported experimental results, and the well-known analytical formula for focal length (f) of diffractive lenses as a function of wavelength ( λ ) , f ( λ ) = f 0 λ 0 λ where f0 is the designed focal length for wavelength λ0. We show that when the analytical formula is applied to thin flat lenses with low-refractive index, the results are accurate for small numerical aperture (NA) up to 0.2. For larger NA, the error between the analytical approximation and the FDTD analysis remains around 8% over a wide range of NA.

VIS-NIR superachromatic triplet design with five-color correction for a broadband interferometer.

In general, k lenses with different materials can achieve at most (k+1) color correction (k≥2). A superachromat containing three lenses is designed to achieve five-color correction in the 600-1600 nm waveband, where the maximum chromatic focal shift is controlled within 1/100,000 of the focal length, achieving an almost unprecedented result. Conditions for lens power combination of three thin lenses in contact are first derived based on the Buchdahl dispersion equation; then a metric is introduced to verify the five-color correction, and a correction method is proposed to improve the refractive index fitting accuracy of the Buchdahl model from ∼10-3 to ∼10-7. By traversing 197 ecofriendly glass materials in the CDGM glass library iteratively, 113 initial structures are obtained in only 61.75 s, from which the structure with the minimum chromatic focal shift is selected to be optimized with Opticstudio. By setting up required operands, the final structure being within the diffraction limit in a field of view of ±0.05∘ is obtained within only 6 s, where the maximum longitudinal chromatic aberration is close to the maximum chromatic focal shift. We provide a complete theoretical basis and important guidance for designing broadband superachromats with (k+2) color correction using only k lenses and the smallest chromatic focal shift, and based on the theories, we have developed a broadband interferometer.

Inside-out and outside-in: Tips and tricks in posterior lenticonus.

Posterior lenticonus is a congenital condition characterized by the thinning and bowing of posterior lenticular capsule. Cataract develops when normal intra-lenticular pressure bulges the posterior capsule at the circumscribed portion of inherent thin posterior lens capsule, leading to derangement of lamellar lens fibers. This condition poses a surgical challenge as the presentation varies from thin, bulging posterior capsule to large, pre-existing posterior capsular dehiscence. This video highlights the tips for the surgical management of various scenarios of posterior lenticonus. In this video, tips for surgical management of various scenarios of posterior lenticonus are illustrated. Intraoperatively, ruptured posterior capsule is suspected by the presence of a fish-tail sign. The anterior capsulotomy is relatively easier in a flatter anterior lens capsule, owing to reduced intra-lenticular pressure. Hydro-dissection is avoided to prevent extension of pre-existing posterior capsular dehiscence or creation of rupture in a thinned-out capsule. The peripheral lens cortex aspiration is initiated first, followed by in each quadrant. In a presence of ruptured posterior capsule by vigilant inspection at this stage, the surgeon should change the direction of lens matter aspiration by aspirating the central lenticular matter first, followed by peripheral cortex like "inside-out". In absence of posterior capsule dehiscence, peripheral cortex is aspirated first, followed by central lens matter aspiration like "outside-in". Adequate anterior vitrectomy is performed until there are no vitreous tags. In the presence of pre-existing posterior capsular defect, the lens matter is aspirated from the center (inside-out), whereas in the absence of capsular defect, the lens matter is aspirated from the periphery (outside-in). https://youtu.be/8G6BCbFwr8Q.

Relative-phase simulated annealing for time-efficient and large-scale inverse design of achromatic thin lenses.

High-efficiency, broadband, wafer-size, and ultra-thin lenses are highly demanded, due to its great potential in abundant applications such as compact imaging modules. It is usually conceived that this target might be attainable given the advancement in nanofabrication, computation power and emerging algorithms, though challenging. Here, we reveal the inconvenient truth that for ultra-thin lenses, there actually exists intrinsic check-and-balance between size, broadband and performance. Unveiled by our inverse design algorithm, Relative-Phase Simulated Annealing (RPSA), focusing efficiency inevitably drops with refining wavelength intervals for better achromatic broadband features in optimized lens; and drops exponentially with increasing diameter and bandwidth, supported by our empirical formula. Meanwhile, with a slightly compromised goal, the powerfulness of RPSA is unlocked since it could provide a globally optimized design recipe whose time complexity relates to lens scale linearly rather than exponentially. This work, as a fast search engine for optimal solutions, paves the way towards practical large-scale achromatic ultra-thin lenses.

Using a smartphone camera to explore ray optics beyond the thin lens equation

Ray optics is a staple of introductory physics classes, but many students do not have the opportunity to explore optics beyond the thin lens equation. In this paper, we expand upon a successful remote experiment using a smartphone camera to explore both the successes and limitations of the thin lens equation. Application of the thin lens equation reveals a linear relationship between the object distance and the inverse image height in pixels. Using the open-source image analysis tool ImageJ to measure the image height, we can find the effective focal length of the smartphone camera lens. Our measured focal lengths agree well with the stated manufacturer values for the effective focal lengths. Further application of the thin lens equation is not successful, but a modification of the analysis leads to an explanation and experimental determination of the location of the principal planes in the smartphone camera systems. This experiment can work well at the introductory level, either in person or remote, and can be used as an introduction or motivation to explore more advanced topics in ray optics.