Design of gradient-index microlenses for stacked planar optics

The refractive-index profiles of planar matrix microlenses that result from the Luneburg lens theory turn out to yield considerable aberrations. The presented modification of the design process enables satisfactory suppression of the focusing errors.     

Direct writing of microlenses in polycarbonate with excimer laser ablation

A method for fabricating microlenses in polycarbonate material is reported. Using a direct-write technique based on scanning excimer laser ablation with a circular beam, we can etch an arbitrary shape in the polymer material. The beam is obtained by imaging a circular aperture onto the polymer surface, and scanning is realized by the translation stage carrying the sample, which makes successive contours with well-chosen diameters and scan velocities. Afterward, to smooth the ablated surface and release it from debris, a large beam aperture covering the full lens area is used to ablate the lens deeper into the substrate. The fabrication process and the characterization method are described, including calculation of the contour set for a desired lens shape. The optical performance is evaluated by Mach-Zehnder interferometry, showing that aberrations below lambda/10 are possible for slow lenses.     

Implementation of multilens micro-optical systems with large numerical aperture by stacking of microlenses

In the field of micro-optics there is a demand for objectives with large numerical aperture (NA). One example is optical storage in which a NA greater than 0.5 is required. For planar microlenses the NA is determined by means of the maximal index difference and the degree of exchange and reaches typical values of 0.13-0.2. Thus stacking is needed to build high NA objectives from planar microlenses. An additional benefit of stacking lenses is the possibility to correct for different types of aberrations. We realized two stacked systems: an array of micro-objectives with a NA of 0.45 from three microlens arrays and a confocal sensor head from four microlens arrays and one pinhole array mask.     

Testing of refractive silicon microlenses by use of a lateral shearing interferometer in transmission

Wave aberrations of refractive photoresist microlenses and silicon microlenses were measured with a lateral shearing interferometer. Because of the silicon elements, a near-infrared working wavelength (lambda = 1.32 mum) was used. The wave front was evaluated by a phase step technique with four steps. Integration of the phase distributions was performed with a computationally efficient Fourier transformation algorithm. The influence of the detector vidicon nonlinearity on the measured wave front was calculated. The defocusing behavior of the interferometer was investigated by fitting the measured wave fronts with the help of Zernike circle polynomials. It is shown that the reproducibility can be kept below lambda/100 rms. Examples for the measured wave fronts of plano-convex silicon microlenses are discussed in detail.     

Combined Twyman-Green and Mach-Zehnder interferometer for microlens testing

A new interferometer design for microlens testing is presented. The phase-shifting system combines the advantages of a Twyman-Green and a Mach-Zehnder interferometer and permits full characterization of the aberrations of microlenses as well as radius of curvature and focal length measurements. The Twyman-Green system is applied to surface testing in reflection (single reflection), whereas the Mach-Zehnder system is used for lens testing in transmission (single pass). Both measurements are performed without removal of the test part, allowing for combination of the results without confusion of the actual lens and without an azimuthal orientation error. The interferometer setup is explained, the test procedure is described, and experimental results are given.     

Modulation transfer function measurements of microjetted microlenses

We measured the modulation transfer function for microjetted microlenses with diameters ranging between 109 and 400 mum and with focal lengths ranging between 135 and 540 mum. We found that single-drop 109-mum-diameter microlenses perform close to their theoretical cutoff frequency. However, the larger lenses made with multiple droplets have a cutoff frequency that is 35% of the theoretical value. We interpret this as an illustration of the rapid increase in spherical aberration as the diameter of a lens increases.     

Integrated acoustooptic circuits and applications

The recent development of titanium-indiffusion proton-exchange (TIPE) microlenses and lens arrays has made possible the construction of a variety of single- and multichannel integrated acoustooptic (AO) and acoustooptic-electrooptic (EO) circuits in LiNbO(3) channel-planar waveguides 0.1x1.0x2.0 cm(3) in size. These hybrid AO and AO-EO circuits can be fabricated through compatible and well-established technologies. The most recent realization of ion-milled microlenses and lens arrays together with the recent development of gigahertz AO Bragg modulators and EO Bragg modulator arrays have also paved the way for construction of similar but monolithic AO and AO-EO GaAs/GaAlAs waveguides of comparable size. Both types of integrated AO and AO-EO circuits suggest versatile applications in communications signal processing, and computing. Efficient and simultaneous excitation of the channel waveguide array using an ion-milled planar microlens array has facilitated the demonstration of some of these applications.     

Optical aberrations of intraocular lenses measured in vivo and in vitro

Corneal and ocular aberrations were measured in a group of eyes before and after cataract surgery with spherical intraocular lens (IOL) implantation by use of well-tested techniques developed in our laboratory. By subtraction of corneal from total aberration maps, we also estimated the optical quality of the intraocular lens in vivo. We found that aberrations in pseudophakic eyes are not significantly different from aberrations in eyes before cataract surgery or from previously reported aberrations in healthy eyes of the same age. However, aberrations in pseudophakic eyes are significantly higher than in young eyes. We found a slight increase of corneal aberrations after surgery. The aberrations of the IOL and the lack of balance of the corneal spherical aberrations by the spherical aberrations of the intraocular lens also degraded the optical quality in pseudophakic eyes. We also measured the aberrations of the IOL in vitro, using an eye cell model, and simulated the aberrations of the IOL on the basis of the IOL's physical parameters. We found a good agreement among in vivo, in vitro, and simulated measures of spherical aberration: Unlike the spherical aberration of the young crystalline lens, which tends to be negative, the spherical aberration of the IOL is positive and increases with lens power. Computer simulations and in vitro measurements show that tilts and decentrations might be contributors to the increased third-order aberrations in vivo in comparison with in vitro measurements.     

Application of the see-saw method to all refracting optical systems

The optical see-saw diagram is a method that describes image correction to third-order approximation over a finite field of view in rotationally symmetric systems that employ aspheric surfaces. The aim of this paper is to describe the correction of aberrations caused by plane surfaces in all refracting optical systems in terms of the see-saw diagram. A lens correction algorithm based on the see-saw method is described to correct analytically the Seidel aberrations, primary spherical aberration, coma, astigmatism, and distortion, in such systems. We then apply this lens correction algorithm to the design of equivalent configurations by aspherizing different surfaces of the system, and the high-order aberrations of the equivalent configurations are evaluated by means of transverse-ray-aberration plots. Results indicate that this method gives information on what the contribution must be to the third-order aberrations that each component should provide to the system to give a better balance of high-order aberrations. Examples of the lens correction algorithm applied to lenses with six refracting surfaces and working for both finite and infinite object conjugates are given.     

Patterning flood illumination with microlens arrays

We describe a convenient lithographic technique that can produce simple, repetitive micropatterns over large areas (several square centimeters). The technique uses an illuminated array of micrometer-scale lenses to generate an array of optical patterns in an image plane located within micrometer distances from the lens array. A layer of photoresist, placed in the image plane, records the patterns. Microlenses with different sizes, profiles, composition, and indices of refraction produce corresponding patterns in exposed and developed photoresist. Both spherical and nonspherical microlenses were examined. Several types of optical element containing arrays of microlenses were fabricated and used to demonstrate that this technique can generate uniform micropatterns over large areas (>4 cm2) in a single exposure. The smallest features produced had dimensions of approximately 100 nm.     

Realization and optimization of planar refracting microlenses by Ag-Na ion-exchange techniques

We report the fabrication of planar microlenses with numerical apertures (N.A.'s) of 0.2 by field-assisted Ag-Na ion exchange in glass. To measure the N.A. of microlenses, different definitions can be used. We discuss the issue of measuring the N.A. and suggest an additional definition based on diffraction-limited performance. According to a simple model, the N.A. of a spherical lens is limited by the maximum index difference. Owing to this model, the N.A. for Ag-Na ion exchange is limited to a value of ~0.1. From measurements of microlenses, fabricated by field-assisted ion exchange, we obtained N.A.'s as high as 0.2, providing for diffraction-limited performance within the whole aperture.     

Calculation of holograms from elemental images captured by integral photography

We describe a method in which holograms can be produced by calculation from images captured by integral photography (IP). We present a basic algorithm obtained by simulating IP reconstruction, in which conditions are set so as not to cause aliasing in the holograms after the calculations. To reduce the calculation load, we also propose a way to limit the range of calculation considering the distribution of light and a way to shift the optical field on the exit plane of microlenses in a lens array. Finally, by optical experiments, we confirm that three-dimensional images can be reconstructed from holograms calculated from an integral photograph of a real object captured with an IP camera.     

Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation

We present a procedure that compensates for phase aberrations in digital holographic microscopy by computing a polynomial phase mask directly from the hologram. The phase-mask parameters are computed automatically without knowledge of physical values such as wave vectors, focal lengths, or distances. This method enables one to reconstruct correct and accurate phase distributions, even in the presence of strong and high-order aberrations. Examples of applications are shown for microlens imaging and for compensating for the deformations associated with a tilted thick plate. Finally we show that this method allows compensation for the curvature of the specimen, revealing its surface defects and roughness. Examples of applications are shown for microlenses and metallic sphere imaging.     

Replicated arrays of hybrid elements for application in a low-cost micro-spectrometer array

Abstract

We report on the fabrication and characterization of replicated hybrid elements for low-cost micro-spectrometer array applications. An array of hybrid elements, where one surface combines the fairly large dimensions of refractive microlenses with the submicron features of a diffraction grating, was successfully replicated by hot embossing. The parameters are: lens diameter=990 μm, height=60 μm, grating period=1 μm, linewidth=300 nm and grating depth=2 μm. These replicated spectrometer elements showed a maximum resolution of 2.25 nm and a stray-light suppression better than 30 dB.     

Correction of chromatic aberrations in GRIN endoscopes

A gradient-index (GRIN) endoscope can be constructed by substituting for the usual objective and relay sections suitable cylindrical index-distribution rod lenses. Currently available GRIN lenses exhibit large amounts of chromatic aberration. Axial color arises mostly from the relay lens, while lateral color is due to the objective lens. A negative lens cemented to a shortened GRIN relay lens can simultaneously correct axial and lateral chromatic aberrations with commercially available components. This correction system reduces the requirements for mechanical centration better than do color correctors that are incorporated into the ocular design. Monochromatic aberrations are also considered.     

Analytical and Numerical Examination of the Quantitative Imaging Properties of Optical Diffraction Tomography

Abstract

The imaging properties of two-dimensional optical diffraction tomography are examined analytically and numerically. Taking into account lens aberrations in the optical system used to image the scattered light, we first derive an expression for the overall coherent transfer function. Then we use computer simulations to examine the influence of lens aberrations by comparing images obtained by a system with lens aberrations with images obtained by an aberration-free system. We also discuss the significance of systematic positioning errors in the set-up.     

Off-axis refractive mass-transported gallium-phosphide microlens array for the reduction of distortion in an optical interconnect system

Mass-transport smoothing has been used to fabricate an array of off-axis gallium-phosphide microlenses for use in an optical interconnection system employing a single macroscopic lens to image an array of vertical-cavity surface-emitting lasers (VCSEL's) onto a detector array. Steering the individual VCSEL beams through the center of the relay lens creates an optical system with low distortion.     

Implementation of a hybrid lens

Details are presented of the design, fabrication, and use of a hybrid lens employed to interconnect two-dimensional arrays of optical transceivers. The hybrid lens consists of a custom-designed, 42-mm focal length, ?/5 compound lens followed by an array of afocal telescope compound microlenses.     

Index-distributed planar microlenses for three-dimensional micro-optics fabricated by silver-sodium ion exchange in BGG35 substrates

Fabrication of planar microlens arrays by silver-sodium ion exchange is possible by using a new glass type, optimized for this technology. Because of its nonlinear diffusion response it is well suited to the fabrication of microlens arrays. We show that the diffusion coefficient can be described theoretically by an exponential concentration dependence. The parameters of the planar microlenses are measured interferometrically and by imaging experiments. Because of the specific index distribution, new evaluation techniques for the determination of lens parameters from interferometric measurements have been applied. We also present a simple model that relates the achievable lens parameters to the diffusion conditions.     

Fabrication of polymer-based reflowed microlenses on optical fibre with control of focal length using differential coating technique

Thermal reflow of polymer to generate spherical profile has been used to fabricate microlenses in this paper. A simple model based on the volume conservation (before and after reflow) and geometrical consideration of lens profile, shows that the focal length of the microlens produced by reflow technique is a function of the initial geometry of microcylinders, i.e. diameter and thickness. This relationship of focal length with diameter and thickness is used as a basis to control focal length. A simple spin coating technique on dual surface is used to achieve differential thickness, to control the focal length of microlenses produced on the same substrate. A biomedical application of such combination of microlenses is endoscopy where the lenses of varying diameter and equal focal length are needed on top of optical fibre bundles to provide independent function of illumination and imaging. This paper incorporates the differential thickness technique to show a micro fabrication process to produce the polymer reflowed microlenses, with a control of focal length based on thickness. The design also helps to integrate these microlenses on top an optical fibre with accurate alignment.