Multi-lens System Research Articles

Dual-comb ranging method for simultaneously measuring the refractive index and surface spacing in a multi-lens system.

Precise determination of the refractive index and surface spacing in multi-lens system is essential for ultra-precision system performance, such as lithography objectives with strict requirements for each lens fabrication and assembly position. Generally, the nominal value of the refractive index at a given wavelength must be known before resolving the geometric thickness of multi-lens using conventional methods, which leads to inaccurate and inconvenient measurements. We propose a method to simultaneously measure the refractive index and surface spacing in multi-lens system based on dual-comb ranging method. The precision of the thickness measurement is better than 0.18 µm, and the refractive index is better than 1.6 × 10-4. This study provides a potential solution for realizing the real-time, fast, and precise measurement of the geometric thickness and assembly position of multi-lens in lithography objectives.

AUTOMATED DESIGN OF THE OPTICAL SYSTEM OF THE ZOOM RIFLESCOPE

It is proposed to perform an automated design of a multi-lens optical system of a zoom riflescope by using one of modern global optimization algorithms, namely the adaptive Cauchy differential evolution method. The optical system considered here provides the magnification 4-16× and the angular field of view in the object space from 5.15° to 1.32°. It has the entrance pupil diameter of 42 mm, the exit pupil distance within 85...90 mm, and the maximum system length of 325 mm. The riflescope contains 14 lenses in 9 components made of glasses from the CDGM catalog. In all zoom configurations of the optical system, any ray vignetting is absent. To achieve the high image quality, the parametric synthesis of the riflescope has been carried out simultaneously for five intermediate configurations, corresponding to magnifications 16×, 13×, 10×, 7× and 4×. By using the developed specialized software, an experimental examination of the operability of this approach has been performed on the example of automated design of the optical system having the parameters similar those found in commercially available samples. The performed simulation showed that the time interval required for direct automated design of the riflescope’s optical system is about 25 hours. The total number of unknown parameters (variables) was up to 90. The root-mean-square values ​​of the angular aberrations of the axial beams in all (five) configurations of the synthesized zoom system do not exceed 1 arc minute in the whole spectral range. The obtained results indicate that the design algorithm implemented in the computer program can be considered an effective tool capable to perform automated parametric synthesis of complex zoom optical systems with high image quality. The algorithm enables to establish the prescription data of optical systems, taking into account the technical requirements and restrictions specified by the designer.

Hopkins procedure for tunable magnification: surgical spectacles

We analyze the use of two varifocal lenses, with fixed interlens separation, for achieving tunable magnification at a specific throw. Our discussion extends the Hopkins procedure circumscribed to the determination of fixed optical powers in a multilens system. We illustrate our results by presenting the Gaussian optics design of surgical spectacles, which have tunable magnification while generating virtual images with zero throw. We also report novel formulas describing this type of two-lens zoom system, which works without any mechanical compensation.

Oriented Gaussian beams for high-accuracy computation with accuracy control of X-ray propagation through a multi-lens system.

A highly accurate method for calculating X-ray propagation is developed. Within this approach, the propagating wave is represented as a superposition of oriented Gaussian beams. The direction of wave propagation in each Gaussian beam agrees with the local direction of propagation of the X-ray wavefront. When calculating the propagation of X-ray waves through lenses, the thin lens approximation is applied. In this approximation, the wave parameters change discontinuously when the wave passes through a lens; the corresponding explicit formulae are derived. The theory is applied to highly accurate calculation of the focusing of X-rays by a system of many beryllium lenses. Fine structure of the wave electric field on the focal plane is revealed and studied. The fine structure is formed due to the diffraction of waves at the edges of the lens apertures. Tools for controlling the calculation accuracy are proposed. The amplitude of the electric field on the focal plane and the focal spot width are shown to be very sensitive to the quality of the calculation, while the best focus position can be obtained even from simple calculations.

Path Integral Formulation for Wave Effect in Multilens System

A formula to investigate the wave effect in a multi-lens system is presented on the basis of a path integral formalism by generalizing the work by Nakamura and Deguchi (1999). The wave effect of a system with two lenses is investigated in an analytic way as a simple application to demonstrate usefulness of the formula and variety of wave effect in multi-lens system.

Effect of spatial distribution of partial information on the accurate recovery of optical wave fields

We consider the problem of recovering a signal from partial and redundant information distributed over two fractional Fourier domains. This corresponds to recovering a wave field from two planes perpendicular to the direction of propagation in a quadratic-phase multilens system. The distribution of the known information over the two planes has a significant effect on our ability to accurately recover the field. We observe that distributing the known samples more equally between the two planes, or increasing the distance between the planes in free space, generally makes the recovery more difficult. Spreading the known information uniformly over the planes, or acquiring additional samples to compensate for the redundant information, helps to improve the accuracy of the recovery. These results shed light onto redundancy and information relations among the given data for a broad class of systems of practical interest, and provide a deeper insight into the underlying mathematical problem.

A high-accuracy complex-phase method of simulating X-ray propagation through a multi-lenssystem.

The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X-ray waves through a multi-lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi-lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi-lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi-lens system.

Achromatic and athermal lens design by redistributing the element powers on an athermal glass map.

We propose a new graphical method for selecting a pair of optical and housing materials to simultaneously achromatize and athermalize a multilens system. To obtain the material combination using an athermal glass map, the material suitable for housing is graphically selected, and then the powers of elements constituting an equivalent single lens are redistributed. Although a material combination does not exist, we can continuously change the power of each element. Thus, we can reasonably identify a pair of optical and housing materials that simultaneously satisfies achromatic and athermal conditions. By applying this method to design a Tessar lens, the chromatic and thermal defocuses are reduced to less than the depth of focus, over the specified waveband and temperature ranges.

Graphical Selection of Optical Materials Using an Expanded Athermal Glass Map and Considering the Housing Material for an Athermal and Achromatic Design

This paper presents a new graphical method for selecting a pair of optical glass and housing materials to simultaneously achromatize and athermalize a multilens system composed of many elements. To take into account the lens spacing and housing, we quantify the lens power, chromatic power, and thermal power by weighting the ratio of the paraxial ray height at each lens to them. In addition, we introduce the equivalent single lens and the expanded athermal glass map including a housing material. Even though a lens system is composed of many elements, we can simply identify a pair of glass and housing materials that satisfies the athermal and achromatic conditions. Applying this method to design a black box camera lens equipped with a 1/4-inch image sensor having a pixel width of $2{\mu}m$ , the chromatic and thermal defocusings are reduced to less than the depth of focus, over the specified ranges in temperature and frequency.

Simple Graphical Selection of Optical Materials for an Athermal and Achromatic Design Using Equivalent Abbe Number and Thermal Glass Constant

This paper presents a new graphical method for selecting a pair of optical glasses to simultaneously achromatize and athermalize an imaging lens made of materials in contact. An athermal glass map that plots thermal glass constant versus inverse Abbe number is derived through analysis of optical glasses and plastic materials in visible light. By introducing the equivalent Abbe number and equivalent thermal glass constant, although it is a multi-lens system, we have a simple way to visually identify possible optical materials. Applying this method to design a phone camera lens equipped with quarter inch image sensor having 8-mega pixels, the thermal defocuses over $-20^{\circ}C$ to $+60^{\circ}C$ are reduced to be much less than the depth of focus of the system.

Daylight enhancement using laser cut panels integrated with a profiled Fresnel collector

Performance of conventional vertical light pipes with acrylic domes is highly dependent on the solar altitude since for lower solar elevation the acceptance angle is limited due to the small inlet aperture. A profiled Fresnel collector with a multi-lens system is useful in enhancing light in a light pipe at low solar altitudes but suffers losses due to multiple reflections during transmission. In this paper we show that further enhancement of light during the morning and evening hours is possible by using a profiled Fresnel collector integrated with graded laser cut panels, i.e. laser cut panels with bands of varying depth to width ratio that can redirect low altitude sun rays axially down the light pipe. The effect of various depths to width ratios of the laser cut panel with respect to variation in incident light on the performance of a light pipe is also presented in this paper. The graded laser cut panel performed better than other laser cut panels. Optimum tilts of the laser cut panel at which maximum light is deflected for various incident angles of the source were identified. Maximum light output for the graded laser cut panel was for lower incidence of solar altitude angle. The graded/profiled laser cut panel was integrated with Fresnel north and south facing collectors and the performance was assessed in daylight. Good redirection of light was observed for the Fresnel collector in the morning and evening hours when compared to a light pipe with an acrylic dome or a Fresnel collector without a laser cut panel. The light is redirected more parallel to the axis of the pipe thus minimizing the reflections on the internal lining and thereby increasing the performance of the light pipe.

Conceptual design and assessment of a profiled Fresnel lens daylight collector

This paper describes design of daylight collectors using multiple Fresnel lenses, each facing the sun for a particular period of time in a day. The influence of solar movement on flat Fresnel lens was studied. The influence of groove density of the lens was also determined by which the suitable Fresnel lens was selected. Passive and profiled north-facing and south-facing collectors with multi-lens system have been designed based on the solar altitude and azimuth angle of a geographical location. Performance of the north- and south-facing collector at different times of a day with an acrylic dome indicated better efficiency and uniformity of lighting throughout the day time for the proposed profiled Fresnel collectors.

Multi-lens pier scour monitoring and scour depth prediction

Severe pier scour is usually the major cause of bridge failures. It is therefore crucial to develop various scour monitoring techniques and prediction models for real-time warning of bridge safety. In the present study, a multi-lens monitoring system for pier scour under laboratory conditions has been developed. By utilising a plurality of lenses, this system is capable of tracking scour images and obtaining real-time scour-depth variation through a series of image recognition processes. Laboratory experiments under unsteady flow conditions were carried out to validate the proposed monitoring method. Then, three time-dependent scour prediction models were employed for simulation and comparison with the measured data. In order to improve the scour prediction results, with the real-time scour monitoring data, a data assimilation scheme is proposed and applied to the scour model under clear-water scour conditions. The result shows that the accuracy of scour prediction for a lead time of 3 h can be improved significantly.

Chromatic aberration control for tunable all-silicone membrane microlenses

Tunable multi-chamber microfluidic membrane microlenses with achromaticity over a given focal length range are demonstrated. In analogy to a fixed-focus achromatic doublet lens, the multi-lens system is based on a stack of microfluidic cavities filled with optically optimized liquids with precisely defined refractive index and Abbe number, and these are independently pneumatically actuated. The membranes separating the cavities form the refractive optical surfaces, and the curvatures as a function of pressure are calculated using a mechanical model for deformation of flexible plates. The results are combined with optical ray tracing simulations of the multi-lens system to yield chromatic aberration behavior, which is verified experimentally. A focal length tuning range of 5-40 mm and reduction in chromatic aberration of over 30% is demonstrated, limited by the availability of optical fluids.

Optical quality of high-power fiber laser beams propagating through collimating systems

Within the framework of the ray optics theory, the effects of heating effect and geometric aberration on optical quality of fiber laser beam are calculated and analyzed. An analytical expression for the beam quality parameter M2 of fiber laser beam propagating through a multilens optical system is derived as a function of the system parameter. The optical quality of high-power laser beam propagating through a collimating system is investigated. It is shown that a best optical quality can be found as the laser power increases and the corresponding laser power depends on the collimating system parameter. The investigation presents a reference for the design of high-energy fiber laser collimating systems.

100% Fill-Factor Aspheric Microlens Arrays (AMLA) With Sub-20-nm Precision

Substitution of a single aspheric microlens (array) for a complex multilens system results in not only smaller size, lighter weight, compacter geometry, and even possibly lower cost of an optical system, but also significant improvement of its optical performance such as better imaging quality. However, fabrication of aspheric microlens or microlens array is technically challenging because conventional technologies used for macro-sized aspheres like single-point diamond milling, and those for spherical microlens like thermal reflow, are not capable of defining a complicated lens profile in an area as small as several to tens of micrometers. Here we solve the problem by using femtosecond laser micro-nanofabrication via two photon polymerization. Not only well-defined single lens, but also 100% filling ratio aspheric microlens array were readily produced. The average error of the lens profile is only 17.3 nm deviated from the theoretical model, the smallest error reported so far.

Expansion of an athermal chart into a multilens system with thick lenses spaced apart

Expansion of an athermal chart into a multilens system with thick lenses spaced apart

Multilens system design with an athermal chart

We have introduced an athermal chart that plots chromatic dispersive power and thermal dispersive power on a Cartesian coordinate, and we give the design method of a multilens system in contact that satisfies achromatism and athermalization. The advantages of this chart are (1) that the condition of achromatism and athermalization is clear and (2) that the approximate power of the lenses that compose the multilens system is easily found on the chart. Design indices are given through a few design examples with an athermal chart.

Compensation of Flexure in Instruments with any Number of Lenses

Formulas are derived for the image movement caused by small decentrations of a multilens system. It is shown that for a given decentration there exist nodal and principal points. A new axis can be defined in such a way that the usual projective paraxial laws still hold. Formulas are included for the case where the object is at infinity.