Laser confocal microscope with wavelet-profiled point spread function

We report a laser-scanning confocal reflectance microscope with a wavelet-profiled point spread function (PSF) for rapid multi-resolution extraction and analysis of microscopic object features. The PSF is generated via holography by encoding a π-phase shifting disk unto a collimated laser beam via a phase-only spatial light modulator (SLM) that is positioned at the pupil plane of the focusing objective lens. Scaling of the transverse PSF distribution is achieved by selecting a suitable ratio of the π-phase shifting disk radius and the pupil aperture radius. With one and the same objective lens and one SLM to control the phase profile of the pupil function, we produce amplitude PSF distributions that are accurate scaled representations of the circularly-symmetric Mexican hat mother wavelet.     

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates.Based on the stationary phase method,the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function.Finally,a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.     

高密度光盘径向倾斜对DPD循轨误差信号影响分析

根据高密度光盘参数 ,计算了聚焦光斑在光盘表面扫描过程中每个位置的光瞳光强分布 ,得到DPD(Differ entialPhaseDetection)循轨误差信号。考虑盘片的径向倾斜 ,在光瞳光强分布方程中引入盘片的径向倾斜角度参数 ,计算了高密度盘片产生径向倾斜时DPD循轨误差信号的变化 ,进而分析了盘片的径向倾斜引入的循轨伺服误差及其对循轨伺服的负面影响。结果表明 ,高密度盘片产生 0 .5°的径向倾斜相当于引入了 0 .0 12 μm的循轨误差     

Phase retrieval for high-numerical-aperture optical systems

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functionsreproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.     

一种基于OTF稳定性的波前编码相位板优化方法

提出了一种简单的可用于光学系统中子午弧矢方向白光OTF稳定性评价的波前编码相位板参量优化方法.该方法仅以标准偏差来评价OTF在目标景深范围内的稳定性,并且结合自适应模拟退火算法在参量空间内优化得到相位板的最佳参量.使用该方法优化得到的相位板参量,可以大幅度提高光学系统的景深,并且可以获得更为清晰、稳定的成像.对应用波前编码技术前后光学系统的成像性能作了比较,并且考察了优化参量的容差性.     

Polarization shifting interferometric profilometer

A phase sensitive Michelson interferometer based on interference microscope configuration with a polarization adjustment approach is proposed to determine the two-dimensional (2-D) surface profile of optical grating with real time capability. In the proposed method, nonlinear behavior of a PZT phase shifter is avoided by use of polarization stepping and a phase map is developed with the four-bucket algorithm. The phase map is unwrapped to give the true surface profile of the sample. A close agreement of measurements is found between the measured result determined by the proposed method and that determined by an atomic force microscope (AFM). We also analyzed the estimated uncertainty of measurement in the nanometer range for the random fluctuations of the experimental parameters.     

Amplitude point-spread function measurement of high-NA microscope objectives by digital holographic microscopy

We present here a three-dimensional evaluation of the amplitude point-spread function (APSF) of a microscope objective (MO), based on a single holographic acquisition of its pupil wavefront. The aberration function is extracted from this pupil measurements and then inserted in a scalar model of diffraction, allowing one to calculate the distribution of the complex wavefront propagated around the focal point. The accuracy of the results is compared with a direct measurement of the APSF with a second holographic system located in the image plane of the MO. Measurements on a 100 x 1.3 NA MO are presented.     

Fractional Gouy phase

In general, the total Gouy phase shift has the form n pi, where n need not be an integer. As a result of the Fourier transforming property of a lens, the Gouy phase is found to be related to the types of discontinuities at the upper or lower range of the pupil function Q(c) resulting from the asymptotic order of the Fourier transform. The sign of the Gouy phase is also related to the slope of the pupil function. The oscillations of the Gouy phase shift arise from the strength of the nondominant discontinuity.     

Two dimensional image scanning of movies using surface acousto-optic interaction

The scanning of two-dimensional black and white movies is described by using the interaction of light with surface acoustic waves. The modulation transfer function for the image scanner is derived. Further, it is shown that the spatial resolution is limited by the surface acoustic wave transducer bandwidth rather than the physical size of the exit pupil of the scanner.     

Resolution and contrast in confocal optical scanning microscopes

A theoretical study is made of a simple method of obstructing an amplitude pupil which results in improved microscope resolution with only a little degradation of the image contrast. Using a confocal scanning optical microscope the resultant point spread function is calculated, from which the image of a point object is deduced. The calculations are made for two different apertures — the first has four-fold symmetry and the second has eight-fold symmetry — and are compared with full circular and annular apertures.     

Melting of mesoscopic lattices of magnetic fluid thin film subjected to perpendicular fields

Applying a magnetic field on the magnetic fluid thin film perpendicularly, leads a phase separation that is concentrated in particles separating from a dilute phase. The concentrated phase forms cylindrical columns that construct two-dimensional lattices. This kind of artificial lattice is a novel mesoscopic system and has been explored with optical microscope, CCD, and digital imaging analysis. We explore the ordering evolution of the two-dimensional extraordinary lattice by varying the applied field. The ordering of these lattices is analyzed in terms of translational and bond-orientation correlation functions to address the two-dimensional melting.     

OTF synthesis: Low pass and band pass filters realized by periodic replication of the pupil function

We present a method which allows incoherent optical low and band pass filtering with high light efficiency. Our method is based on the principle of pupil function replication. The pupil functions are pure phase filters with discrete phase values. Experimental results are shown where the filters are simulated by computer generated holograms.     

On the relation between the wave aberration function and the phase transfer function for an incoherent imaging system with circular pupil

The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients to the Taylor expansion of the derived quadrature relation. Received 16 June 2001     

Polarization phase in aberration compensation

A phase/amplitude mask on the aperture of an imaging system results in a pupil function that is multiplicative with the lens function, resulting in a morphological transformation of the imaging wavefront. It was shown that such amplitude and phase functions can be implemented using polarization masks, with the advantage that the phase and amplitude can be controlled in real time and in some cases, independently of each other. The phase and amplitude variation over the mask can be controlled either by changing the polarization of the mask or by changing the input beam parameters. Wavefront tailoring using polarization-masked apertures is therefore feasible and may be utilized for focal shift and partial aberration compensation. For complete compensation of aberration, the phase distribution over the mask should be conjugate to that of the phase error of the aberrant wavefront, which necessitates the use of a continuously variable polarization mask. Since such a mask is difficult to implement, we have considered polarizing masks consisting of discrete polarized zones on the lens aperture, leading to polarization phase steps on the exit pupil of the imaging system. The simulation results presented in this paper show that effects of focal shift, partial compensation of primary spherical aberration and astigmatism can indeed be achieved by the proper use of polarization masked apertures.     

Structure and magnetic anisotropy of Co/Cu/Co films

The energy of the magnetic anisotropy of Co/Cu/Co polycrystalline ultradisperse films is investigated as a function of the thickness of copper and cobalt layers. The influence of the structure parameters (the size and distribution of defects, the period and amplitude of roughnesses) on the surface and volume components of the magnetic anisotropy is analyzed. The parameters of the structure inhomogeneities and their distribution over the film surface are determined from two-dimensional Fourier spectra and electron microscope images of the films.     

A new method of three-dimensional measurement by differential interference contrast microscope

Based on weak phase approximation and the partial coherence theory, we analyze the image characteristics of a phase object using a microscope. We show that the image of the phase object is formed by the interplay between the phase distribution and the defocus.Using this theory, we also show the image characteristics of a differential interference contrast (DIC) microscope.We develop a method for extracting the phase component from the DIC image using two images with different retardation to reconstruct the phase distribution of the object. We call our new microscope a “retardation-modulated DIC (RM-DIC) microscope”. We describe the RM-DIC microscope and confirm our method using grating samples with depths of 20 and 50 nm.To measure the three-dimensional (3D) figures of the microstructures on the object using a DIC microscope we need to extract the phase component from the DIC image and to deconvolute the phase component by means of the modulation transfer function (MTF) of the DIC microscope.We conclude that our RM-DIC microscope can take quantitative measurements of the phase distribution, making it a very useful tool for 3D measurement of an object’s microstructures.     

Effect of fabrication errors on axial super-resolution property of a three-zone pupil filter

Two models have been established using the basic definitions of super-resolution characteristic parameters for normalized spot size G_A and Strehl ratio S_A, of a three-zone axial super-resolution pupil filter with fabrication errors, to quantitatively analyze the effect of these fabrication errors on the axial super-resolution property. These new models established to describe the analytic relationship of G_Ae and S_Ae of a pupil filter with its fabrication errors and its transmission function A(ρ), phase function φ(ρ) and structural parameters, directly relate the super-resolution parameters of a three-zone axial super-resolution pupil filter to its fabrication errors to make the quantitative analyses of the effect of fabrication errors easier, thereby providing a theoretical basis for the analysis, design and fabrication of a three-zone axial super-resolution pupil filter. The models established for G_Ae and S_Ae have been used to analyze the effect of the fabrication errors of a pupil filter on its super-resolution property, with a three-zone phase-only pupil filters as example.     

Simulation of a polarization pupil filter using magneto-optic lens under elliptically polarized illumination

An active lens made of magneto-optic glass element and placed before a linear polarizer is shown to simulate the pupil plane amplitude and phase filter due to thickness dependent Faraday rotation variation in radial direction. Changing the applied magnetic flux density can dynamically change the pupil characteristics. The variation of intensity point spread function (IPSF) and optical transfer function (OTF) with magnetic flux density for elliptically polarized input beam is studied.     

Sidelobe decline in single-photon 4Pi microscopy by Toraldo rings

We demonstrate theoretically the feasibility of single-photon 4Pi-confocal microscopy. By inserting a pair of properly designed multi-ring phase-only pupil filters in the illumination path of a 4Pi microscope the height of the sidelobes of the point spread function substantially reduced, so that there is no ambiguity in the 3D image. Then, an axial resolution up to four times higher than that of single-photon confocal microscope can be effectively achieved.     

Exact diagonalization study of 2D Hubbard model on honeycomb lattice: Semi-metal to insulator transition

Phase transition in a honeycomb lattice is studied by the means of the two-dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semi-metal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-site interaction are determined using renormalized Fermi velocity factor.