Cemented Doublet Research Articles

Guidelines for predicting stress in cemented doublets undergoing temperature change: theory, practice, and data

Guidelines for predicting stress in cemented doublets undergoing temperature change: theory, practice, and data

Algebraic solution for aplanatic cemented doublets with aspherical surfaces of second degree.

An algebraic method of an initial design of the aplanatic cemented doublet with a unit focal length is described. Based on the third-order aberration theory, algebraic equations are derived for calculating the design parameters of an aplanatic thin cemented doublet with spherical surfaces and aspherical surfaces of the second degree. These equations make it easy to determine whether there exists a real solution of the doublet design for required parameters. The results of the calculations of selected cemented doublet solutions are presented in the examples. The obtained parameters can be used as the starting solution for the final optimization of doublet designs.

Method of initial design of a two-element double-sided telecentric optical system.

An algebraic method for finding fundamental parameters of a starting design of a two-element double-sided telecentric lens is introduced in this work. The telecentric lens is formed by two objectives composed of an afocal meniscus lens followed by a cemented doublet. It is used the third-order aberration theory to find the fundamental parameters of the starting configuration of a given optical system. The method gives results which make possible to obtain a good initial design of such a telecentric lens for further optimization using optical design software. The proposed method is presented on an example of finding initial design parameters of the double-sided telecentric lens.

Calculation automation of “cemented doublet with a singlet” and “singlet with a cemented doublet” objectives

Subject of study. Automating the synthesis of “cemented doublet with a singlet” and “singlet with a cemented doublet” objectives with an entrance pupil on the first surface of the system is studied. The design of this type of system is complex owing to a large number of possible solutions. Moreover, when changing over from an infinitely thin system to a system with a finite thickness of elements, the image quality of axial points significantly deteriorates in most cases. This feature should be considered when developing an algorithm for lens design. Aim of study. The aim is to develop a method and algorithm for automatic synthesis of “cemented doublet with a singlet” and “singlet with a cemented doublet” objectives and a ranking system for designed objectives. Changes in the axial point image quality of the considered objectives with two or three different materials for possible acceleration of the synthesis process are also studied. Method. The initial design of objectives is carried out on the basis of the third-order aberrations theory. An automated exhaustive search is used to rank all possible combinations of lens materials. Main results. The methodology and algorithm of the automatic design of “cemented doublet with a singlet” and “singlet with a cemented doublet” objectives have been developed. A ranking system is provided to rank the designed objectives by the main criterion based on the axial point image size and by the preliminary criterion that determines the technological stability of the objective to the manufacturing errors of the optical elements. It is determined that the “singlet with a cemented doublet” objectives are generally preferable to “cemented doublet with a singlet” objectives according to the proposed criteria. Based on the calculation results, it is demonstrated that solutions with only two materials can have a slight decrease in the image quality of the axial point. Practical significance. Based on the developed algorithm, the program for the automatic design of two- and three-lens objectives is upgraded. The developed program will help optical engineers to significantly simplify and accelerate the process involved in designing two- and three-lens objectives with the required image quality characteristics.

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.

Approach for designing thick cemented doublet lenses based on the caustic surface.

A new, to the best of our knowledge, method for designing a thick-lens achromatic doublet based on the concept of a caustic surface to correct both third- and fifth-order spherical aberration is presented. We consider two different wavelengths brought into coincidence at the back focal length instead of the effective focal length as it is usually done, to calculate the radii of curvature assuming predefined values for axial thicknesses and their indices of refraction for both lenses. Alternatively, we apply Taylor's series around the optical axis, and to vanish the approximate caustic surface, we obtain the values for the conic constants, which reduce at third- and fifth-order spherical aberration. Two designs for cemented doublets are provided assuming that the lenses are cemented. Finally, we propose a method to qualitatively test doublet lenses by using null screens, considering to place the detection plane at arbitrary positions.

Comparison of achromatic doublet on glass Fresnel lenses for concentrator photovoltaics.

Silicone on glass (SoG) Fresnel lenses are the reference technology in concentrator photovoltaics (CPV) because of their simplicity and low cost. Nevertheless, their performance is strongly limited by chromatic aberration. As an alternative, in order to overcome such limitation, achromatic doublet on glass (ADG) Fresnel lenses were proposed. Such lenses are achromatic cemented doublet specifically designed for CPV applications. In this paper, a novel ADG architecture is presented and its performance analyzed and compared to previous proposals. The results show that most of the intrinsic optical losses are minimized and a superior optical efficiency can be achieved. The novel ADG design provides an achromatic lens for CPV whose efficiency is almost equal to the reference SoG technology and, at the same time, maintains all the advantages provided by the achromatic design such as the higher maximum attainable concentration and the strongly reduced temperature dependency.

Design of the Cemented Doublet – Software Application

From optical point of view, an imaging application includes the sensor (CCD or CMOS) and the objective. The simplest objective consists of a cemented doublet. The paper proposes a design algorithm of the doublet and describes a software application based on this algorithm. The results provided by the original software are validated by means of a professional application in optical system analysis.

Automation of athermal cemented doublet synthesis

Automation of athermal cemented doublet synthesis

Simple method for determination of parameters of cemented doublet.

This paper proposes a simple noninvasive method that makes it possible to calculate the inner design parameters of the cemented doublet using measurements of its chosen paraxial optical and geometrical parameters without any damage to the system under testing (e.g., dismantling). Derived formulas are based on the knowledge of measured values of the lenses thicknesses, the radii of curvatures of the first and the last doublet's surfaces, the paraxial focal length, and positions of the object and the image focal point. Practical usefulness of the proposed method is demonstrated on the real measurement of a known doublet.

Experimental method of determination of parameters of cemented doublet.

This work analyzes a method to determine the internal parameters of an optical system of a classical cemented doublet or a three-element tunable-focus lens (a tunable-focus doublet), which is an equivalent of the classical cemented doublet. The method is noninvasive, and the parameters are calculated without any damage or dismantling of the lens.

Methods of solving aspheric singlets and cemented doublets with given primary aberrations.

Purely algebraic algorithms are proposed for solving aspheric singlets and cemented doublets with desired focal length and primary aberrations. Singlets can meet the focal length, spherical aberration and central coma; cemented doublets can even meet the longitudinal chromatic aberration. An aspheric surface can be defined by either a conic or a fourth-order aspheric coefficient. In some situations, conic surfaces must be adopted to satisfy the required aperture diameters. They may have one or multiple aspheric surfaces and the aberration equations indicate that these aspheric coefficients of different surfaces are linearly dependent. Four examples including a classical front-stop singlet landscape lens, a DVD-rewritable (DVD-RW) pickup head lens, a singlet with double conic surfaces, and a cemented doublet in a telescope system are demonstrated.

双胶合透镜法检测大相对孔径凸非球面透镜

It is difficult to fabricate and test convex aspherical surfaces,especially for steep convex aspheical surfaces.Based on the analysis of the conventional null test,a simple test system with cemented doublet for two steep convex ellipsoids was discussed.The wavefront of the both test system was less than 1/30λ RMS(Root Meat Square,λ=632.8nm).The convex aspheric lens had their successful application in practical optical system.The result showed that the null test for convex aspheric lens discussed in this paper is valid.Compared with the traditional test method,the cemented doublet offsets the spherical aberration generated by the sphere surface of the lens.So the proposed test method decreases the amount of the spherical aberration generated by the aspherical lens,with fewer elements, and reduces the system′s alignment difficulty.It was demonstrated to be an effective,high-precision testing method.

Rigorous analysis of axisymmetric transformation optics lenses embedded in layered media illuminated by obliquely incident plane waves

ABSTRACTA body of revolution, finite‐difference time‐domain (BOR‐FDTD) method is developed for rigorous analysis of axisymmetric transformation optics (TO) lens devices. For normal incidence, a one dimensional (1‐D) FDTD method based on the total‐field scattered‐field (TFSF) technique was proposed to model the propagation of a plane wave launched from the top of a layered medium in cylindrical coordinates. The 1‐D FDTD solutions were employed to efficiently inject normally incident plane waves into the BOR‐FDTD method. For oblique incidence, analytical formulations were derived and presented by expanding the plane wave into a series of cylindrical modes via Fourier series expansion of the ϕ‐dependent variables, which were then used to introduce obliquely incident plane waves into the TFSF formulas associated with the BOR‐FDTD method. These procedures allowed for accurate simulations of BOR TO lenses embedded in layered media illuminated by obliquely incident waves. The accuracy and efficiency of the proposed method were verified by comparing numerical results with either analytical solutions or a commercial software (COMSOL) package. Thereafter, the developed BOR‐FDTD code was utilized to study the imaging properties of (a) radial gradient‐index (GRIN) lenses with a parabolic index profile, (b) a flat TO GRIN lens, (c) a spherical Luneburg lens, and (d) a cylindrical TO Luneburg lens both in free space and on top of a substrate. Here the TO GRIN lenses were designed by using the quasi‐conformal transformation optics (QCTO) technique. It was found that the flat TO lens was able to provide identical focusing properties as a cemented doublet in both free space and over a dielectric substrate. Moreover, the numerical results demonstrated that the flattened TO Luneburg lens possessed the desired imaging properties under different illuminations for both polarizations.

The primary structure design of a birefringent lens with the concept of pseudo-chromatic aberration

Much attention has been paid to the optical design of a birefringent lens and analysis of its polarization aberration due to its essential application in bifocal interferometric microscopes. To investigate a practical way of designing a birefringent lens with large separation between the two foci, a novel concept named ‘pseudo-chromatic aberration’ is proposed, which results from the difference of refractive indices between the ordinary and extraordinary rays when they pass through the birefringent lens. As the concept is similar to normal chromatic aberration, the existing primary aberration theory to design a thin cemented lens can also be adopted on the design of a birefringent lens. A table of primary structure of cemented doublet birefringent lenses is consequently obtained. Different combinations of three kinds of birefringent crystals and optical glasses can satisfy various requirements. A concrete example of a birefringent lens with the compactness factor γ of 0.25 is given using the glass of SF2 and calcite.

Cemented doublet lens with an extended focal depth

A method of designing a lens with an extended focal depth is studied. The lens is a cemented doublet composed of a birefringent lens and a conventional lens. The crystal optical axis of the birefringent lens is perpendicular to the axis of the optical system. By properly selecting the parameters of the birefringent lens and the conventional lens, we can flexibly configure an imaging system that simultaneously has a large focal depth and high resolution. We also provide a theoretical analysis which shows that the focal depth of the lens is approximately 1.5 times that of a conventional lens.

Longitudinal chromatic aberration in tangent doublets

A condition has been theoretically deduced to achieve the correction of the so-called tangent doublets for paraxial chromatism as well as for marginal and zonal chromatism up to the fifth order. Furthermore, results obtained for the chromatic aberrations in these systems confirm the correct behaviour of the theoretical formula deduced to calculate the longitudinal spherical aberration in cemented doublets.

Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets

The authors use a genetic algorithm in the structural design of cemented doublets in accordance with a prespecified set of Gaussian characteristics and primary aberration targets. Actual glasses are taken as variables. Suitable modifications in the algorithm are sought with which to explore the solution space in search of the global as well as useful local optima. Some illustrative examples of structural design are given.

Selection of glasses for achromatic doublets with reduced secondary spectrum I Tolerance conditions for secondary spectrum, spherochromatism, and fifth-order spherical aberration

We describe a way of selecting pairs of glasses for both thin cemented achromatic doublets and thin aplanatic achromatic doublets with a reduced secondary spectrum. By taking one pair of glasses at a time, we can compute and display the secondary spectrum in increasing value. The number of solutions based on the magnitude of the secondary spectrum alone is huge: 40,804 pairs. Some tests are applied at different stages of the design procedure to reduce the number of acceptable solutions. Aberrations that cannot be corrected, namely, spherochromatism and fifth-order spherical aberration, are further calculated to reduce drastically the number of acceptable solutions. To do this, we establish tolerance conditions based on the relationship between the Strehl intensity ratio and the rms wave-aberration error so that the rms wave error is minimized in the presence of the secondary spectrum, spherochromatism, and the fifth-order spherical aberration.

Stability of the spherical aberration up to the fifth order in cemented doublets

A theoretical method is proposed to calculate variations in the spherical aberration up to fifth order in cemented doublets when some of the parameters that specify the system are modified. This method permits the evaluation of the stability of the spherical aberration with variations in the refractive indices and Abbe numbers of the glasses and radii of the lenses. Using this procedure we have verified that the so-called tangent doublets have a higher stability than those which are not of a tangent type.