Modified phase function model for kinoform lenses

A more computationally tractable model of the kinoform lenses in hybrid refractive-diffractive systems is proposed by taking into consideration the actual phase function of the kinoform lenses for every wavelength. The principle and outline of this modified model are explained. We compare the results of this approach with the more conventional single order calculation and with the standard diffraction-order expansion by using a practical hybrid optical system example.     

Diffractive-refractive correction units for plastic compact zoom lenses

A method of designing a plastic zoom lens with a diffractive-refractive hybrid corrector, comprising one diffractive lens and one refractive lens, is described. The efficiency of this method is demonstrated by designing a compact zoom lens for a mobile phone. This zoom design, incorporating lenses made only of two commercial optical plastics (polymethylmethacrylate and polycarbonate), provides high optical performance.     

Optimization of kinoform lenses with the Monte Carlo method

For the optimization of non-Fourier-type computer-generated phase holograms (kinoform lenses), a method based on the Monte Carlo procedure is suggested. This method can be regarded as analogous to the iterative Fourier transform algorithm method that is widely used for the optimization of Fourier-type computer-generated phase holograms (kinoforms).     

Small-feature-size fan-out kinoform etched in GaAs

A binary fan-out kinoform for focusing and splitting an incident beam into a 4 × 4 spot array, with a largest deflection angle of 28°, was designed, fabricated in GaAs, and evaluated. The kinoform was defined in resist with electron-beam lithography and etched into GaAs with chemically assisted ion-beam etching. Light at wavelength 0.98 μm from a single-mode fiber was used to illuminate the kinoform. The efficiency was measured to be 34%, and the uniformity error for the 4×4 spots was 29%. Although the typical feature size of the kinoform is only roughly two wavelengths, we found that the scalar theory of diffraction can be used. A first kinoform was designed with the customary Fresnel-diffraction theory, which was found to be too coarse, resulting in a fan-out exhibiting some distortion. A second kinoform was designed with the more rigorous Fresnel-Kirchhoff expression, and its fan-out shows no distortion.     

Diffraction calculation for an X-ray refractive kinoform lens

The influence of thickness jump in a kinoform X-ray lens on transmitted beam formation in the near and far field has been studied for the first time using a numerical diffraction model.     

Diffractive-refractive hybrid doublet to achromatize the human eye

Abstract

In this work, we show the design of a diffractive-refractive hybrid doublet to achromatize the human eye. It takes advantage of the achromatizing properties of diffractive elements combined with conventional optics. The performance of the doublet has been compared with conventional systems, which have more elements. The results show that it is a useful alternative to those systems.     

Extra-axial stigmatic imagery with a thick planar kinoform

A kinoform lens and its substrate are usually treated as two distinct components with a common interface. Thick kinoform lenses treat the relief profile and the substrate as an integrated component. An analytical approach for the design of higher-order thick kinoform lenses for stigmatic imaging between extra-axial conjugate points is presented. An illustrative example is given.     

Diffractive-refractive hybrid corrector for achro- and apochromatic corrections of optical systems

The possibility is shown of achro- and apochromatic correction of an optical system with any residual chromatism by completing the system with a diffractive-refractive hybrid corrector comprising one diffractive lens and one or two refractive lenses.     

Laser-machining experiment with an excimer laser and a kinoform

We have used a kinoform to increase the beam-power utilization in an excimer-laser-machining experiment. The kinoform creates the pattern to be machined. Thus less power is wasted on the blocking parts of a shadow mask. To achieve as smooth an intensity profile as possible, the kinoform was also used together with a microlens-array beam homogenizer. We discuss the intensity distributions of the patterns created by the kinoform with and without the beam homogenizer as well as the design of the kinoform and the homogenizer, with emphasis on the relation to the coherence properties of the laser beam.     

Fabrication and testing of sputtered-sliced kinoform style Fresnel zone plate

The Fresnel zone plate (FZP) is a type of lens for focusing X-rays. We have fabricated a kinoform style FZP with a 30-step structure composed of concentric multilayer of alternating Cu layer, Al layer, and 28 composite material (Cu, Al) layers. The multilayer was deposited using a magnetron sputtering apparatus with two DC-sputtering guns. The focusing characteristics were evaluated at the synchrotron radiation beamline of SPring-8, and the focused beam size measured by knife-edge scanning was 0.8 μm at 40 keV. The peak diffraction efficiencies measured using ion chambers for 1st- and 2nd-order diffraction were 42% and 12% at 40 keV and 20 keV, respectively. High-order X-ray diffraction was also examined using the data obtained from a CCD camera.     

Fabrication and testing of sputtered-sliced kinoform style Fresnel zone plate

The Fresnel zone plate (FZP) is a type of lens for focusing X-rays. We have fabricated a kinoform style FZP with a 30-step structure composed of concentric multilayer of alternating Cu layer, Al layer, and 28 composite material (Cu, Al) layers. The multilayer was deposited using a magnetron sputtering apparatus with two DC-sputtering guns. The focusing characteristics were evaluated at the synchrotron radiation beamline of SPring-8, and the focused beam size measured by knife-edge scanning was 0.8 μm at 40 keV. The peak diffraction efficiencies measured using ion chambers for 1st- and 2nd-order diffraction were 42% and 12% at 40 keV and 20 keV, respectively. High-order X-ray diffraction was also examined using the data obtained from a CCD camera.     

Midwave infrared optical zooming design and kinoform degrading evaluation methods

In this study, an optical zooming design method is constructed by ray tracing. The loci of each thin lens is determined utilizing algebraic relationships. A mechanical compensation structure is adapted to stabilize the position of the focal plane. The Gaussian design result is applied for the midwave infrared spectrum, and aberrations can be reduced by controlling the geometric parameters of the thick lens. One hybrid achromatic singlet is introduced utilizing a diffraction optical element. The kinoform surface relief is calculated being the same as its microfabrication process. The effects of the discontinuous zonal profile and the thermal degradation are evaluated.     

Quadrant kinoform: an approach to multiplane dynamic three-dimensional holographic trapping

Real-time dynamic holographic optical tweezers suffer from an intrinsic limitation. The diffractive optical element, which is the key to reconstruction, requires time for the calculation and physical constraints to be satisfied. In particular, when working in a volume these requirements become highly expensive. Quadrant kinoform represents an alternative to traditional 3D holograms. A spatial domain multiplexing combined with lens term phase profiles allow the independent addressing and control of different planes in the reconstruction volume. The bidimensional holograms used pose less severe physical constraints and the reduced size leads, at the cost of a lower reconstruction resolution, to a consistent speedup in the computation time thus improving real-time interactions.     

Error reduction of quantized kinoforms by means of increasing the kinoform size

There are two kinds of method that utilize the redundancy in kinoform domains for reducing the reconstruction errors of quantized kinoforms. One is the iterative-dummy area (IDA) method, which increases the kinoform size indirectly by the addition of a dummy area to the desired image. The other is the interlacing technique (IT), which increases the kinoform size directly by the interlacing of a number of subkinoforms whose sizes are the same as the desired image. We compare the error reduction of quantized kinoforms between these two methods. Simulation results show that reconstruction errors from the IT method can be reduced further and faster than those from the IDA method when the kinoform size is increased to larger than 4 x 4 times the size of the desired image.     

Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator

Random-phase distributions that are statistically independent individually are used for computing kinoforms. These uncorrelated kinoforms are recorded and read out sequentially by a phase-only liquid-crystal spatial light modulator, and reconstructed images with well-developed speckles are added. The fidelity of the resultant image to an original is improved as the number of additions increases. The dependence of the speckle contrast on the initial random phase and the influence of the liquid-crystal spatial light modulator's display performance on the image quality are discussed.     

Error dependence of quantized kinoform reconstruction on the position of the desired image

Two-dimensional Fourier transform kinoforms can be calculated by use of a discrete Fourier transform. It is well known that the off-axis reconstruction has lower reconstruction error than the on-axis one. Here we make what to our knowledge is a new analysis on the effect of phase quantization in the Fourier domain. We find that the kinoform reconstruction error changes periodically according to the position of the desired image when a large dummy area is added. The error dependence of quantized kinoform reconstruction is simulated on the position of the desired image by use of the iterative dummy area method and the iterative interlacing technique.     

Phase retrieval of recorded kinoform transmittance and estimation of the phase-recording curve characteristic

Methods are presented for recovering, by the use of the basic Gerchberg-Saxton algorithm, the complex-valued transmittance of a recorded kinoform and for estimating the phase-recording curve characteristic of a kinoform-fabrication system by comparison of the phase to be recorded with that actually recorded. Related issues considered here are the shift of the central sampling point from the optical axis in the Fourier-image domain, a kinoform phase sequence suitable for estimating the curve characteristic, the initial estimate of the iterative algorithm, and the influence of errors in the measurement of the kinoform or of the Fourier-image amplitude. Results of an optical experiment with a fabrication system including a photographic process are discussed and shown to confirm the effectiveness of the proposed methods.     

Spectrum leveling by an iterative algorithm with a dummy area for synthesizing the kinoform

This paper describes a new iterative algorithm for synthesizing the kinoform so that the Fourier spectrum of an object is leveled by adjusting the information of a dummy area introduced into the object's domain, spatially isolated from the signal area. Theoretical consideration of the effect of the dummy area derives the required size of the dummy area, and computer simulations prove it to be valid, although restricted to an object composed of binary numbers. Also, it is shown that highly efficient use of the incident light is possible to achieve. Experimental results verify the proposed scheme.     

Chromatic aberrations of radial gradient-index lenses. II. Selfoc lenses

Simple equations used for analyzing chromatic aberrations of Selfoc lenses were derived in terms of Buchdahl chromatic coordinates and Buchdahl dispersion constants. The equations that employ gradient-index chromatic constants Ψ(1) and Ψ(2) are used for selecting suitable ion-exchange pairs to design an achromatic Selfoc lens.