Husimi functions for coupled optical resonators.

Phase-space analysis has been widely used in the past for the study of optical resonant systems. While it is usually employed to analyze the far-field behavior of resonant systems, we focus here on its applicability to coupling problems. By looking at the phase-space description of both the resonant mode and the exciting source, it is possible to understand the coupling mechanisms as well as to gain insights and approximate the coupling behavior with reduced computational effort. In this work, we develop the framework for this idea and apply it to a system of an asymmetric dielectric resonator coupled to a waveguide.

Rotationally tunable multi-focal diffractive moiré lenses.

In this work, we show how the combination of cascaded multi-value phase diffractive optical elements can form a multi-focal moiré zone plate with tunable optical power in each diffraction order. The rotationally tunable moiré zone plate is capable of generating an array of equal intensity focal spots with a precisely adjustable axial distance along the propagation direction. Numerical simulations as well as experimental results verify that multiple focal spots are generated, and the distance between the generated uniform foci can be adjusted by a mutual rotation of one multi-value phase diffractive element with respect to the other.

Evaluation of quadratic phase hologram calculation algorithms in the Fourier regime.

The display of phase-only holograms with a spatial light modulator (SLM) has many applications due to its potential for dynamic three-dimensional projection of arbitrary patterns. We describe an innovative modification of the quadratic phase method for hologram calculation that uses error diffusion for initialization of an iterative phase retrieval algorithm. We compare the performance of our algorithm to other variations of hologram calculation approaches that use the quadratic phase method in the Fourier regime. Parameter variation is conducted for finding the differences and limits of the methods. Experiments with an SLM show the validity of the simulations.

Composite spiral multi-value zone plates.

We present composite spiral multi-value phase zone plates that are achieved by sectioning a spiral multi-value phase zone plate into several radial regions. Each region is composed of specially structured Fresnel zones with optimized phase values and an embedded basic topological charge. In numerical studies, it is shown that the proposed element is capable of producing equal intensity arrays of petal-like modes as well as dark optical ring lattice structures along the optical axis in multiple focal planes of the diffractive element. Additionally, it is demonstrated that the generated petal-like modes can be rotated in a controllable manner by implementing an angular frequency shift between the two composited spiral multi-value phase zone plates. We also illustrate that the rotation angle is independent of the diffraction order. Experimental results are included to verify the theoretical outcomes, where the phase pattern of the composite spiral multi-value zone plate is encoded onto a spatial light modulator.

Fabrication and characterization of deformed microdisk cavities in silicon dioxide with high Q-factor.

We demonstrate the excitation and characterization of whispering gallery modes in a deformed optical microcavity. To fabricate deformed microdisk microresonators we established a fabrication process relying on dry plasma etching tools for many degrees of freedom and a shape-accurate morphology. This approach allowed us to fabricate resonators of different sizes with a controlled sidewall angle and underetching in large quantities with reproducible properties such as a surface roughness RQ≤2nm. The excitation and characterization of these modes were achieved by using a state-of-the-art tapered fiber coupling setup with a narrow linewidth tunable laser source. The conducted measurements in shortegg resonators showed at least two modes within a spectral range of about 237 pm. The highest Q-factors measured were in the range of 105. Wave optical eigenmode and frequency domain simulations were conducted that could partially reproduce the observed behavior and therefore allow us to compare the experimental results.

Multifocal multi-value phase zone plate for 3D focusing.

We demonstrate a method for creating a three-dimensional (3D) array of focal spots by combination of a multi-focal diffractive lens and a two-dimensional multi-value phase grating. The multi-focal Fresnel-based lens is created by means of encoding special nonlinearities into the phase structure of a Fresnel zone plate and is represented as a mathematical superposition of this phase function with a refractive lens. The imposed nonlinearity type enables the creation of multiple focal spots with uniform intensity along the optical axis. We demonstrate the example of a 3D multi-value phase grating, which creates five focal planes with a $5 \times 5$5×5 transverse array of focal spots with equal energy distribution in each plane. Experimental results are included to verify the theoretical outcomes, where the phase pattern of a 3D multi-value phase grating is encoded onto a spatial light modulator.

Weighted spline based integration for reconstruction of freeform wavefront.

In the present work, a spline-based integration technique for the reconstruction of a freeform wavefront from the slope data has been implemented. The slope data of a freeform surface contain noise due to their machining process and that introduces reconstruction error. We have proposed a weighted cubic spline based least square integration method (WCSLI) for the faithful reconstruction of a wavefront from noisy slope data. In the proposed method, the measured slope data are fitted into a piecewise polynomial. The fitted coefficients are determined by using a smoothing cubic spline fitting method. The smoothing parameter locally assigns relative weight to the fitted slope data. The fitted slope data are then integrated using the standard least squares technique to reconstruct the freeform wavefront. Simulation studies show the improved result using the proposed technique as compared to the existing cubic spline-based integration (CSLI) and the Southwell methods. The proposed reconstruction method has been experimentally implemented to a subaperture stitching-based measurement of a freeform wavefront using a scanning Shack-Hartmann sensor. The boundary artifacts are minimal in WCSLI which improves the subaperture stitching accuracy and demonstrates an improved Shack-Hartmann sensor for freeform metrology application.

Scotoma Simulation in Healthy Subjects.

SIGNIFICANCE: This article shows a successful concept for simulating central scotoma, which is associated with age-related macular degeneration (AMD), in healthy subjects by an induced dark spot at the retina using occlusive contact lenses. The new concept includes a control mechanism to adjust the scotoma size through controlling pupil size without medication. Therefore, a miniaturized full-field adaptation device was used. PURPOSE: The aim of this study was to design a novel concept to simulate AMD scotoma in healthy subjects using occlusive contact lenses. METHODS: To define an optimal set of lens parameters, we constructed an optical model and considered both the anatomical pupil diameter and the opaque central zone diameter of the contact lens. To adjust the scotoma size, we built a miniaturized full-field adaptation device. We demonstrate the validity of this novel concept by functional measurements of visual fields using automated threshold perimetry. Finally, we conducted a perception study including two tasks, consisting of pictograms and letters. The stimuli were presented at different eccentricities and magnifications. RESULTS: The visual fields of all 10 volunteers exhibited absolute scotomas. The loss of contrast sensitivity ranged within 27 and 36 dB (P < .05), and the scotoma localizations were nearly centered to the macula (mean variation, 2.0 ± 4.8° horizontally; 3.5 ± 4.7° vertically). The eccentric perception of letters showed the largest numbers of correctly identified stimuli. The perception of pictograms showed significantly reduced numbers (P < .0001) and revealed a dependency on magnification. The results suggest that best perception is possible for magnified stimuli near the scotoma. CONCLUSIONS: We demonstrated that the creation of an absolute simulated AMD scotoma is possible using occlusive contact lenses combined with a miniaturized full-field adaptation device.

Modeling of light-emitting diode wavefronts for the optimization of transmission holograms.

The objective of applying transmission holograms in automotive headlamp systems requires the adaptation of holograms to divergent and polychromatic light sources like light-emitting diodes (LEDs). In this paper, four different options to describe the scalar light waves emitted by a typical automotive LED are regarded. This includes a new approach to determine the LED's wavefront from interferometric measurements. Computer-generated holograms are designed considering the different LED approximations and recorded into a photopolymer. The holograms are reconstructed with the LED and the resulting images are analyzed to evaluate the quality of the wave descriptions. In this paper, we show that our presented new approach leads to better results in comparison to other wave descriptions. The enhancement is evaluated by the correlation between reconstructed and ideal images. In contrast to the next best approximation, a spherical wave, the correlation coefficient increased by 0.18% at 532 nm, 1.69% at 590 nm, and 0.75% at 620 nm.

Efficient quantization of tunable helix phase plates.

Helix phase plates are used in a variety of applications from optical trapping to astronomy. Tunable helix phase plates based on the Alvarez-Lohmann principle allow variation of the topological charge of the helix by rotating the phase plates with respect to each other around the optical axis. Current designs generate an undesired inverse phase in the section determined by the rotation angle. We present tunable phase plates that use a special quantization to maintain a uniform phase over the tuning range, suppressing the undesired part. As one benefit, the efficiency of the elements is increased over the whole tuning range.

Aperture-coded confocal profilometry.

This Letter introduces a novel principle to the confocal profilometry for simultaneous measurement of surface position and tilt. The principle relies on an angle-dependent coding of the illumination of the surface-under-test, achieved by dividing the pupil into several subapertures. The reflected light is decoded to perform an angle-resolved analysis by measuring the intensity contributions of each individual subaperture. By comparing their contributions, additional information of surface tilt can be inferred. For our demonstration experiment the subapertures are encoded with specific spectral distribution, which may be called wavelength division encoding. Alternate coding procedures such as temporal or code division encoding are also feasible.

Fast and scalable algorithm for the simulation of multiple Mie scattering in optical systems.

The Monte Carlo simulation of light propagation in optical systems requires the processing of a large number of photons to achieve a satisfactory statistical accuracy. Based on classical Mie scattering, we experimentally show that the independence of photons propagating through a turbid medium imposes a postulate for a concurrent and scalable programming paradigm of general purpose graphics processing units. This ensures that, without rewriting code, increasingly complex optical systems can be simulated if more processors are available in the future.

Fresnel transform as a projection onto a Nijboer-Zernike basis set.

The Fresnel transform is widely used in optics to calculate the free-space propagation of paraxial fields. Generally, there is no analytical solution for the Fresnel transform; therefore, the numerical methods are used often. In this Letter, we propose a new semi-analytical method to calculate the Fresnel transform, which is based on an extended Nijboer-Zernike theory. We calculate two examples to investigate how the sampling rate and maximal number of Zernike polynomials affect the accuracy of our results, and then use this method to calculate the reconstruction of two different kinds of holograms. At the end, we discuss the advantages and disadvantages of our method.

Chromatic confocal matrix sensor with actuated pinhole arrays.

We present two versions of a chromatic confocal matrix sensor for the snapshot acquisition of three-dimensional objects. The first version contains separate illumination and detection pinhole arrays, while the second version uses a single pinhole array in double pass. The discrete lateral measurement points defined by the illumination and detection pinhole arrays are evaluated in parallel with a hyperspectral detection module. As this approach enables the spectrometric evaluation of all lateral channels, multilayer objects can be analyzed. To increase the lateral resolution the pinhole arrays are moved by micromechanical actuators. The paper includes a quantitative evaluation of the chromatic confocal module and proof-of-principle experiments with the full sensor system.

Subaperture stitching for measurement of freeform wavefront.

A method based on subaperture stitching for measurement of a freeform wavefront is proposed and applied to wavefronts calculated from the slope data acquired using a scanning Shack Hartmann sensor (SHS). The entire wavefront is divided into a number of subapertures with overlapping zones. Each subaperture is measured using the SHS, which is scanned over the entire wavefront. The slope values and thus the phase values of separately measured subapertures cannot be connected directly due to various misalignment errors during the scanning process. The errors lying in the vertical plane, i.e., piston, tilt, and power, are minimized by fitting them in the overlapping zone. The radial and rotational misalignment errors are minimized during registration in the global frame by using active numerical alignment before the stitching process. A mathematical model for a stitching algorithm is developed. Simulation studies are presented based on the mathematical model. The proposed mathematical model is experimentally verified on freeform surfaces of a cubic phase profile.

Wavefront-coding technique for inexpensive and robust retinal imaging.

We propose a hybrid optical-digital imaging system that can provide high-resolution retinal images without wavefront sensing or correction of the spatial and dynamic variations of eye aberrations. A methodology based on wavefront coding is implemented in a fundus camera in order to obtain a high-quality image of retinal detail. Wavefront-coded systems rely simply on the use of a cubic-phase plate in the pupil of the optical system. The phase element is intended to blur images in such a way that invariance to optical aberrations is achieved. The blur is then removed by image postprocessing. Thus, the system can provide high-resolution retinal images, avoiding all the optics needed to sense and correct ocular aberration, i.e., wavefront sensors and deformable mirrors.

Fast nonparaxial scalar focal field calculations.

An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first Rayleigh-Sommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately 800× in comparison to the normal angular spectrum method, while the memory requirements are reduced by more than 99%.

Numerical solution of nonparaxial scalar diffraction integrals for focused fields.

In this paper, we present sampling conditions for fast-Fourier-transform-based field propagations. The input field and the propagation kernel are analyzed in a combined manner to derive sampling criteria that guarantee accurate calculation results in the output plane. These sampling criteria are also applicable to the propagation of general fields. For focal field calculations, geometrical optics is used to obtain a priori knowledge about the input and output fields. This a priori knowledge is used to determine an optimum balance between computational load and calculation accuracy. In a numerical example, correct results are obtained even though both the input field and the propagation kernel are sampled below the Nyquist rate. Finally, we show how chirp z-transform-based zoom-algorithms may be analyzed using the same techniques.

Aberration analysis of optimized Alvarez-Lohmann lenses.

In this paper aberrations in Alvarez-Lohmann lenses are analyzed, and a semi-analytical strategy for compensation is derived. An x-y polynomial model is used to describe the aberrations and classify them into static and dynamic components. The lenses are enhanced by higher-order polynomials, and a numerical optimization process is used to determine the most influential coefficients. Two simulations of corrected systems are presented. The first one is optimized for on-axis imaging. The second system is optimized for multiple field points and shows the limitations of a single Alvarez-Lohmann lens. Two systems overcoming these limitations by introducing additional optical surfaces are presented, and their performance is analyzed in simulations.

Depth of focus analysis of optical systems using tunable aperture stops with a moderate level of absorption.

The size of the aperture stop of a lens is a major parameter to define, e.g., the depth of focus of an optical imaging system. In conventional systems, totally absorbing apertures are generally assumed. Their optical performance can be easily described by a geometric ray model. We propose an extended model to estimate the depth of focus with respect to a nontotally absorbing circular aperture, which may correspond to new concepts for tunable apertures, in particular for micro-optical systems. We present specifications to analyze and optimize the performance of those systems and verify the theoretical model by experimental depth of focus measurements with a partly transparent aperture.