Finite Conjugate Research Articles

Study of lens design method for narrowing primary aberration variation during conjugate change for a finite conjugate system

Currently, maintaining image quality during conjugate change is most frequently achieved through careful lens design with the multiconfiguration optimizing method and physical shifts of the lenses within the system such that the system remains in focus. However, in applications with operational limitations, such as endoscopy where the space available cannot allow for moving parts, the lens system needs to be designed such that the system is in focus over a wide range of conjugates. A lens design method that is integrable into existing commercial lens design software is presented. This method derives and maintains an optimal condition for astigmatism and distortion to control and reduce the overall aberration variation during the conjugate change, and extends the depth of field of the system. A side-by-side lens design comparison between the method illustrated in this study and the conventional lens design method commonly employed by designers of zoom lenses is also presented and is demonstrated to produce better results in designing conjugate change optical systems.

基于显微光杠杆技术的微结构偏转角测量系统

A microscope system for the deflection angle measurement of microstructures is presented.The microscope consists of an infinite conjugate imaging system and an integrated optical lever.The laser beam of the optical lever is focused by the infinite objective to a size less than 10μm.A current-mode circuit is designed for signal processing for the optical lever,and 5MHz in bandwidth is achieved.The measurement range and resolution of the system are±4°and 1.2″, respectively.As a test,the system is used to measure the deflection angles at the free end of a cantilever probe of atomic force microscope under step load.The measurement results are consistent well with the calculation by using Timoshenko beam theory.

Thermal expansion recovery microscopy: Practical design considerations

A detailed study of relevant parameters for the design and operation of a photothermal microscope technique recently introduced is presented. The technique, named thermal expansion recovery microscopy (ThERM) relies in the measurement of the defocusing introduced by a surface that expands and recovers upon the heating from a modulated source. A new two lens design is presented that can be easily adapted to commercial infinite conjugate microscopes and the sensitivity to misalignment is analyzed. The way to determine the beam size by means of a focus scan and the use of that same scan to verify if a thermoreflectance signal is overlapping with the desired ThERM mechanism are discussed. Finally, a method to cancel the thermoreflectance signal by an adequate choice of a nanometric coating is presented.

Parallel analysis of thermal field in a layered DC cable part I

Purpose – The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables. Design/methodology/approach – Initial-boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two-stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously. Findings – A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non-linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model. Research limitations/implications – The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter. Practical implications – The time-spatial distribution of thermal field in the cross-section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system. Originality/value – A parallel algorithm of solving initial-boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed.

Aberration correction of zoom lenses using evolutionary programming

A systematic approach for the aberration correction of zoom systems is presented. It is assumed that the powers and movements of the components of the zoom systems are known. Each component is considered as a system of thin lenses in contact. An evolutionary algorithm is developed to explore the multivariate hyperspace of design variables formed by spherical aberration, central coma, and longitudinal chromatic aberration of each component for infinite conjugate. The primary aberrations for each component at any zoom position are deduced from three central aberration coefficients of the component for infinite conjugate using conjugate shift formulas. Overall system aberrations of the zoom systems are determined by using stop shift formulas. In most of the zoom lens systems it is important to achieve stability in the primary aberrations of the system over the zoom range. This is facilitated by proper formulation of the merit function for the optimization process. Investigations have been carried out on four-component zoom lenses, and an ab initio structure of a four-component zoom lens is presented.

BERTRAND CURVES IN NON-FLAT 3-DIMENSIONAL (RIEMANNIAN OR LORENTZIAN) SPACE FORMS

Let M 3(c) denote the 3-dimensional space form of index q = 0,1, and constant curvature c 6 0. A curveimmersed in M 3(c) is said to be a Bertrand curve if there exists another curveand a one-to-one correspondence betweenandsuch that both curves have common principal normal geodesics at corresponding points. We obtain charac- terizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non- null Bertrand curves in M3(c) correspond with curves for which there exist two constants � 6 0 and µ such that �� + µ� = 1, whereand � stand for the curvature and torsion of the curve. As a consequence, non-null helices in M 3(c) are the only twisted curves in M 3(c) having in- finite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.

Optical imaging with spectrum aberration correction using a filtering macrolens

A filtering macrolens was developed to simultaneously achieve macro-optical imaging and correct spectrum aberration. The macrolens was a doublet lens comprising a filtering lens and a close-up lens. The shape of the filtering lens was designed to eliminate the optical path differences between the light rays in the absorbing medium. The close-up lens was designed to decrease the effective focal length of an ordinary camera lens to provide high magnification capability and collimate the diverging beams through the filtering lens. Experimental results demonstrated that the spectrum uniformity of the macro-optical images was markedly improved by the filtering macrolens. This innovation may be used in finite conjugate optical systems.

Catadioptric null test of ultra-deep concave aspheric lens in wide-field optical system

To test the ultra-deep conic surface in wide-field optical systems, a catadioptric null test method is researched in this paper. Equations of infinite conjugate null test system are established and solved using optical path length. The numeric results of a self-aligning mirror's shapes are fitted by coefficients and validation is done in optical design software. The rms wavefront error is 0.0019λ (λ=632.8 nm) in the example fitted by five coefficients. Furthermore, by adjusting spherical aberration distributions, an all-spherical finite conjugate null test system is designed, whose rms wavefront error is 0.0309λ. The test methods in this paper have been proven to be adaptive to many other similar ultra-deep surfaces, even with higher orders.

Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations

The conjugate gradient method (CG) for solving linear systems of algebraic equations represents a highly nonlinear finite process. Since the original paper of Hestenes and Stiefel published in 1952, it has been linked with the Gauss-Christoffel quadrature approximation of Riemann-Stieltjes distribution functions determined by the data, i.e., with a simplified form of the Stieltjes moment problem. This link, developed further by Vorobyev, Brezinski, Golub, Meurant and others, indicates that a general description of the CG rate of convergence using an asymptotic convergence factor has principal limitations. Moreover, CG is computationally based on short recurrences. In finite precision arithmetic its behaviour is therefore affected by a possible loss of orthogonality among the computed direction vectors. Consequently, any consideration concerning the CG rate of convergence relevant to practical computations must include analysis of effects of rounding errors. Through the example of composite convergence bounds based on Chebyshev polynomials, this paper argues that the facts mentioned above should become a part of common considerations on the CG rate of convergence. It also explains that the spectrum composed of small number of well separated tight clusters of eigenvalues does not necessarily imply a fast convergence of CG or other Krylov subspace methods.

Design and error analysis for optical tweezers based on finite conjugate microscope

Optical tweezers are unique tools for studying biophysical properties of single molecules. Design and construction of optical tweezers are very important. The optical path, the radial manipulation equation and axial manipulation equation of optical tweezers based on a finite conjugate microscope system are calculated using matrix optics. The influences of axial position adjustment of the objective, the installation location error of the coupling lens, the installation location error of the laser beam control system, and the installation location error of the confocal system lens' on radial trap position manipulation accuracy and axial trap position manipulation accuracy are analyzed. The results show that axial position adjustment of objective introduces no error in radial and axial trap position manipulation. The misalignment of laser beam control system has no effect on the radial manipulation, nor on axial manipulation when the coupling lens maintains alignment. It is concluded that misalignment of components of optical tweezers based on a finite conjugate microscope system has a greater effect on trap position manipulation error than misalignment of components of optical tweezers based on a infinite conjugate microscope system. The radial trap position manipulation error is less than 5.9% and the axial trap position manipulation error is less than 11.4% when the coupling lens installation location error is less than 10 mm. It is shown that optical tweezers can be modified from a finite conjugate microscope system. The formulations provide the basis for theoretical analysis of experimental alignment and adjustment.

Bertrand curves in the three-dimensional sphere

A curve α immersed in the three-dimensional sphere S3 is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. The curves α and β are said to be a pair of Bertrand curves in S3. One of our main results is a sort of theorem for Bertrand curves in S3 which formally agrees with the classical one: “Bertrand curves in S3 correspond to curves for which there exist two constants λ≠0 and μ such that λκ+μτ=1”, where κ and τ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S3 as the only twisted curves in S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3 and (1,3)-Bertrand curves in R4.

Evanescent field shapes excitation profile under axial epi-illumination

Axial epi-illuminating light transmitting a >1.3-numerical-aperture microscope objective creates an excitation volume at focus with size and shape dictated by diffraction and due to refraction by the objective and by the coverslip interface separating a specimen in aqueous buffer from the oil immersion objective. The evanescent field on the coverslip aqueous side affects primarily the excitation volume axial dimension as the specimen in focus approaches the interface to within a few hundred nanometers. Following excitation, an excited stationary dipole moment emits fluorescence in a spatially varying pattern collected over the large objective aperture. Collected light propagates in parallel rays toward the tube lens that forms a real three-dimensional image that is decoded to identify dipole orientation. An integral representation of the excitation and emitted fields for infinity-corrected optics--including effects of finite conjugate illumination, fluorescence emission near an interface, emitter dipole orientation, spherical aberration, light transmission through a dichroic filter, and for real microscopic specifications--accurately models observed field intensities including the substantial excitation from the evanescent field. The goal is to develop and verify the practical depiction of excitation and emission in a real microscope for quantitative interpretation of the 3-D emission pattern.

Subdiffraction scattered light imaging of gold nanoparticles using structured illumination

A reflective light-scattering (RLS) microscope with structured illumination (SI) provides subdiffraction resolution and improves the image quality of gold nanoparticles in biological systems. The three-dimensional (3D)-structured pattern is rapidly and precisely controlled with a spatial light modulator and scrambled at the conjugate image plane to increase spatial incoherence. The reconstructed SI-RLS image of 100 nm gold nanoparticles reveals lateral and axial resolutions of approximately 117 and 428 nm. We present a high-resolution image of gold nanoparticles inside a HeLa cell, with improved contrast.

Exploiting chromatic aberration for image-based microscope autofocus

Autofocus is a critical aspect of any automated microscopy application. Here we report on the successful exploitation of chromatic aberration to speed autofocus for biological microscopy. Using pairs of lenses aligned nominally as infinite conjugates, the chromatic aberration produced by a microscope can be manipulated to achieve multiplanar imaging covering a wide range of spacings. Using both three-chip CCD and Bayer-array color cameras, chromatic aberration-based multiplanar imaging is used to reduce by a factor of 3 the number of mechanical movements of the biological sample necessary to determine best focus. Chromatic aberration-based autofocus is validated using a 20×0.75 NA objective while scanning over 6000 fields of National Institutes of Health 3T3 cells cultured on a coverglass. The combined precisions (standard deviations) of 23.7 nm for a three-chip CCD camera and 23.3 nm for a Bayer-array camera are obtained. These precisions are approximately 1/20th of the depth of field of the objective.

Rewritable groups

A group G is said to have the n-rewritable property Q n if for all elements g 1 , g 2 , … , g n ∈ G , there exist two distinct permutations σ , τ ∈ Sym n such that g σ ( 1 ) g σ ( 2 ) ⋯ g σ ( n ) = g τ ( 1 ) g τ ( 2 ) ⋯ g τ ( n ) . We show here that if G satisfies Q n , then G has a characteristic subgroup N such that | G : N | and | N ′ | are both finite and have sizes bounded by functions of n. This extends the result of Blyth (1988) in [3] which asserts that if G satisfies Q n and if Δ is the finite conjugate center of the group, then | G : Δ | and | Δ ′ | are both finite with | G : Δ | bounded by a function of n. As a consequence, any group with Q n satisfies the permutational property P m with m bounded by a function of n.

Mirror-lens model of an off-axis volume holographic element with isotropic shrinkage

A mirror-lens model of an off-axis volume holographic element in the form of a thin lens and a spherical mirror is suggested for both meridional and saggital planes. Formulas are derived that allow optimal positions of the conjugate object and image planes and coordinates of the point sources of reference and object waves to be computed.

Modelling the primary chromatic aberrations and secondary spectrum of conceptual thick-lens modules

A virtual thick-lens module comprising three air-spaced thin lenses is proposed, which is able to have the identical primary chromatic aberrations and secondary spectrum for just real thick lenses, or groups or components within any thick lens, hence it is capable of studying the chromatic aberration behaviours of conceptual lenses without their detailed structures. The three thin-lens powers are first evaluated to match the required first-order quantities. Then the chromatic aberration coefficients of each thin lens are solved to satisfy the given system aberrations associated with the reference optical configuration. When the incident rays are changed, each thin lens will induce new chromatic aberrations according to the thin-lens formulae. The new system aberrations are obtained by adding those individual thin-lens aberrations together. The module can be directly applied to finite and infinite conjugates, focal and afocal lenses, as well as telecentric and non-telecentric lenses. Evaluations of the chromatic aberration variations of three different types of lenses are demonstrated.

Conjugate Heat Transfer High-Heat-Flux Amplification Simulation

High-heat-flux (HHF) removal (HHFR) limits can be formidable technological barriers that prevent or limit the normal implementation or optimization of new and novel devices or processes. A conjugate heat transfer HHFR simulation methodology has been developed with excellent resulting accuracy (>98.0% accurate) for predicting HHF amplification (peaking factors) and the peak flow channel inside wall temperature. The methodology can be used directly or expanded to a correlation form. Although the simulation utilized axial and swirl water flows with single-phase fully developed turbulent and subcooled flow boiling in a single-side-heated circular inside flow channel with a rectangular outer boundary, the methodology appears to be fluid- and flow regime-independent (e.g., applicable to developing or jet impingement flows) so that other fluids (e.g., gases, dielectric liquids, liquid metals) and flow regimes can be employed possibly for HHFR applications requiring specialized fluids and/or flow conditions. However, more work is required to validate the applicability of this methodology (and the correlation) to other fluids, flow regimes, and channel materials. Further, the approach can be expanded possibly to include applications employing a hypervapotron for HHFR. For the prototypic simulation cases (≤38.0 MW/m2) considered, the circumferential inside flow channel heat transfer coefficient distribution [h([varphi])] was not known a priori, so, h([varphi]) was determined from the unknown local inside wall heat flux via iterative finite element conjugate heat transfer analyses for flow regimes ranging from fully developed turbulent subcooled flow boiling (at the top of the flow channel) to single-phase turbulent flow (at the bottom of the flow channel).

Using FEM and artificial networks to predict on elastic buckling load of perforated rectangular plates under linearly varying in-plane normal load

Elastic buckling load of perforated steel plates is typically predicted using the finite element or conjugate load/displacement methods. In this paper an artificial neural network (ANN)-based formula is presented for the prediction of the elastic buckling load of rectangular plates having a circular cutout. By using this formula, the elastic buckling load of perforated plates can be calculated easily without setting up an ANN platform. In this study, the center of a circular cutout was chosen at different locations along the longitudinal x-axis of plates subjected to linearly varying loading. The results of the finite element method (FEM) produced by the commercial software package ANSYS are used to train and test the network. The accuracy of the proposed formula based on the trained ANN model is evaluated by comparing with the results of different researchers. The results show that the presented ANN-based formula is practical in predicting the elastic buckling load of perforated plates without the need of an ANN platform.

Boundary Pointwise Control for Diffusion Hopfield Neural Network

For a close to practical neural network in biology field, in this paper the author address the diffusion Hopfield neural network (HNN) with boundary pointwise control. In the framework of variational method at Hilbert space, the theoretical study finds and characterizes the boundary optimal control solution. Furthermore, with the numerical approach consist of finite element method (FEM) and conjugate gradient method (CGM), computational demonstration is performed for three neurons in two dimensions case. This approach adequately interpreted the effectiveness and feasibility of the control process in a realistic sense.