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In this study, we propose a method for generating an angular spectrum using array radar and physiological component analysis. We develop physiological component analysis to separate radar echoes from multiple body positions, where echoes are phase-modulated by propagating pulse waves. Assuming that the pulse wave displacements at multiple body positions are constant multiples of a time-shifted waveform, the method estimates echoes using a simplified mathematical model. We exploit the mainlobe and nulls of the directional patterns of the physiological component analysis to form an angular spectrum. We applied the proposed method to simulated data to demonstrate that it can generate a super-resolution angular spectrum.

Purpose The aim was to quantitatively validate the hybrid angular spectrum (HAS) algorithm, a rapid wave propagation technique for heterogeneous media, with both pressure and temperature measurements. Methods Heterogeneous tissue-mimicking phantoms were used to evaluate the accuracy of the HAS acoustic modeling algorithm in predicting pressure and thermal patterns. Acoustic properties of the phantom components were measured by a through-transmission technique while thermal properties were measured with a commercial probe. Numerical models of each heterogeneous phantom were segmented from 3D MR images. Cylindrical phantoms 30-mm thick were placed in the pre-focal field of a focused ultrasound beam and 2D pressure measurements obtained with a scanning hydrophone. Peak pressure, full width at half maximum, and normalized root mean squared difference (RMSDn) between the measured and simulated patterns were compared. MR-guided sonications were performed on 150-mm phantoms to obtain MR temperature measurements. Using HAS-predicted power density patterns, temperature simulations were performed. Experimental and simulated temperature patterns were directly compared using peak and mean temperature plots, RMSDn metrics, and accuracy of heating localization. Results The average difference between simulated and hydrophone-measured peak pressures was 9.0% with an RMSDn of 11.4%. Comparison of the experimental MRI-derived and simulated temperature patterns showed RMSDn values of 10.2% and 11.1% and distance differences between the centers of thermal mass of 2.0 and 2.2 mm. Conclusions These results show that the computationally rapid hybrid angular spectrum method can predict pressure and temperature patterns in heterogeneous models, including uncertainties in property values and other parameters, to within approximately 10%.

The influence of the numerical aperture of a light beam that probes a layered object on the magnitude of the quantity measured with a confocal interference microscope upon determining the object thickness has been studied theoretically and experimentally for the case in which the signal is significantly affected by the spherical aberration arising in the probing beam as it passes through the object. The dependence of the quantity to be measured on the numerical aperture is obtained taking into account the influence of the spherical aberration on the signal. The criterion of the “nonaberrational” propagation of the beam probing the object is determined and the condition under which the influence of the spherical aberration on the signal of the confocal microscope can be neglected is found. An approximate analytical expression is obtained, which makes it possible to determine the “nonaberrational” width of the angular spectrum of the light beam probing the object, taking into account an empirical correction factor. The applicability limits of the analytical dependence of the quantity to be measured on the numerical aperture, which has been previously obtained for the case of a negligibly weak influence of the spherical aberration on the signal from the confocal microscope, have been determined.

To improve the detection sensitivity of porous silicon microcavity biosensors, CdSe/ZnS quantum dots are used to label complementary DNA molecules for the refractive index amplification and angular spectrum method for detection. In this method, the TE mode laser is used as the detection light and the light source is changed into a parallel beam by collimating and expanding the beam, which illuminates the PSM surface and receives the reflected light from the PSM surface through the detector. The angle corresponding to the weakest reflected light intensity before and after the biological reaction between probe DNA and complementary DNA of different concentrations labeled by quantum dots was measured by the detector, and the relationship between the angle change before and after the biological reaction and the complementary DNA concentration labeled by quantum dots was obtained. The experimental results show that the angle change increases linearly with increasing complementary DNA concentration. The detection limit of the experiment, as determined by fitting, is approximately 36 pM. The detection limit of this method is approximately 1/300 of that without quantum dot labeling. Our method has a low cost because it does not require the use of a reflectance spectrometer, and it also demonstrates high sensitivity.

In the angular-spectrum method-based computer-generated hologram, the zero-padding method is used to convert circular convolution into linear convolution. However, it will increase the calculation time and memory usage significantly. Therefore, a fast and simple method is proposed to solve the issue of the numerical convolution in the process of hologram generation by using the intermediate angular-spectrum method in this paper. Through replacing numerical Fourier transform by optical Fourier transform in the hologram generation, the calculation speed is approximately 6 times faster than that of the zero-padding method. And due to the scaling factors introduced by the Fourier lens and without the cropping operation, the reconstruction quality of the proposed method is improved significantly compared with the zero-padding method. Moreover, the optical reconstruction system is more compact than the 4-f filter system in the on-axis holographic reconstruction. Both numerical simulations and optical experiments have validated the effectiveness of the proposed method.

Accurate reconstruction of digital holograms that are large in the x direction and small in the y direction, known as horizontal parallax only digital hologram (HPO-DH), must be carried out by non-paraxial propagation approaches such as the classical angular spectrum (AS) method. However, the required space–bandwidth product (SBP) for reconstruction of HPO-DHs requires billions of pixels, which is computationally intensive. Moreover, application of zero-padding for removing aliasing components would generate an unbearable computational burden. In this work, a novel AS technique that reconstructs non-paraxial HPO-DHs with low SBP is proposed. The proposed technique first employs the multi-Fourier transform plane propagation method, which avoids the increase of size in the vertical direction of the HPO-DH to be processed. The second ingredient for field calculation is coherent superposition of vertical tiles formed from the multi-Fourier transform calculations. The described methodology enables reconstruction of HPO-DHs with the AS method and reduced SBP. Efficient managing of the SBP allows implementing zero-padding strategies in the x direction. It is shown that the padding strategies can be implemented in the frequency, space, and space–frequency domains. Hence, suppression of aliased components and increase of the spatial resolution is possible at the same time. Finally, the accuracy and utility of the developed technique is proved by both numerical simulations and experiments.

Holographic near-eye displays present true three-dimensional images with full monocular depth cues. In this paper, we propose a technique to expand the eyebox of the holographic near-eye displays. The base eyebox of the holographic near-eye displays is determined by the space bandwidth product of a spatial light modulator. The proposed technique replicates and stitches the base eyebox by the combined use of a holographic optical element and high order diffractions of the spatial light modulator, achieving horizontally and vertically expanded eyebox. An angular spectrum wrapping technique is also applied to alleviate image distortions observed at the boundaries between the replicated base eyeboxes.

The situation we will consider in this chapter can be summarized as follows. Suppose that we know the electric field at a given plane z = 0. We are now asking the following questions. How does the field E(x, y, z) evolve when we move away from the plane? How does it behave in the far-field zone? And what happens when we focus the far-fields through a lens or a system of lenses? To answer these questions, we will introduce a few novel concepts that play an important role in the field of nano optics. In the angular spectrum representation we decompose the field into its Fourier components, which can be easily propagated away from z = 0 by adding appropriate phase factors. To compute the electromagnetic fields far away from the plane z = 0, we introduce the concept of the stationary phase approximation. We will find that in the far-field the propagating fields are closely related to specific Fourier components. In experiments the focusing of fields in order to retrieve an image is achieved by optical lenses. In theoretical nano optics one can introduce a transformation for the far-fields in order to mimic the lens performance.

Terahertz digital holography (THz-DH) has the potential to be used for non-destructive inspection of visibly opaque soft materials due to its good immunity to optical scattering and absorption. Although previous research on full-field off-axis THz-DH has usually been performed using Fresnel diffraction reconstruction, its minimum reconstruction distance occasionally prevents a sample from being placed near a THz imager to increase the signal-to-noise ratio in the hologram. In this article, we apply the angular spectrum method (ASM) for wavefront reconstruction in full-filed off-axis THz-DH because ASM is more accurate at short reconstruction distances. We demonstrate real-time phase imaging of a visibly opaque plastic sample with a phase resolution power of λ/49 at a frame rate of 3.5 Hz in addition to real-time amplitude imaging. We also perform digital focusing of the amplitude image for the same object with a depth selectivity of 447 μm. Furthermore, 3D imaging of visibly opaque silicon objects was achieved with a depth precision of 1.7 μm. The demonstrated results indicate the high potential of the proposed method for in-line or in-process non-destructive inspection of soft materials.

Digital holographic microscopy (DHM) is a future three-dimensional (3D) microscopy due to its high-resolution and high-precision 3D images. Thus, it is getting attention in bioinformatics, semiconductor defect detection, etc. However, some limitations still exist. Especially, high-speed holographic imaging requires high-power lasers, which are difficult to image on highly absorbent or light-sensitive samples. To overcome these issues, we propose a new, to the best of our knowledge, digital hologram recovery algorithm called angular spectrum matching (ASM), which achieves hologram imitation to recover holograms in digital holography at low light intensities. The hologram used for the background phase comparison is recorded without objects; thus, no power limitation is required. The ASM utilizes this background hologram to recover dark holograms. We present experimental results showing improved DHM numerical reconstructions and recovered holograms under extremely low light conditions.

A stepwise angular spectrum method (SASM) for curved interfaces is presented to calculate the wave propagation in planar lens-like integrated optical structures based on photonic slab waveguides. The method is derived and illustrated for an effective 2D setup first and then for 3D slab waveguide lenses. We employ slab waveguides of different thicknesses connected by curved surfaces to realize a lens-like structure. To simulate the wave propagation in 3D including reflection and scattering losses, the stepwise angular spectrum method is combined with full vectorial finite element computations for subproblems with lower complexity. Our SASM results show excellent agreement with rigorous numerical simulations of the full structures with a substantially lower computational effort and can be utilized for the simulation-based design and optimization of complex and large scale setups.

There are many pure phase methods for designing acoustical holography structures in the known literature. Different methods may have different characteristics and lead to different results, but few researchers put these methods together for comparison. So we have no idea which method should be taken when dealing with a specific optimization case. This paper investigated the characteristics of three different PM methods, one is the direct search method taking suitable objective function and another two are the conventional IASA methods but with different restricts in image plane, one called ISREL relaxes the whole background pressure constraints and one called ISRES restricts the whole background pressure to zero. We find that DS is a balanced method in terms of various metrics evaluating target pattern and background noise. Finally, the ability of particle manipulation of DS was verified experimentally by designing a holography structure projecting a circle with a non-uniform phase gradient. In a word, it provides a specific comparison between the two mainstream methods DS and IASA by two optimization cases. On one hand, it gives us a clear view of the characteristics of these methods in designing acoustic holography; On the other hand, we know that DS may be a preferred algoritm for most optimization cases owing to its balanced characteristic regardless of time costs.

Computer-generated hologram (CGH) is the method of making holograms with computer. A CGH can be made without preparing and instructing the exclusive optical tool. Therefore, we can make holograms easily and economically compared to the optical method. There are several calculating methods for a CGH such as Fourier transform, Fresnel diffraction and etc. In this study, we discuss on the angular spectrum method which is not limited by the diffraction distance. The Kirchhoff integral has the advantage of making reconstructions similar to optical experiment. However, the angular spectrum method has the disadvantage of accruing an error without proper conditions. These conditions are related to the transfer phase function. Moreover, the transfer phase function is related to the sampling interval and the number of sampling points. Therefore, it is necessary to investigate the relationship about these conditions and reconstruction errors. This study reports on the reconstruction using the angular spectrum method under different conditions about the transfer phase function. Simulation results will be shown on the relationship under these conditions.

A time-division multiplexing method for computer-generated holograms (CGHs) is proposed to solve the problem of the limited space-bandwidth product. A three-dimensional (3-D) scene is divided into multiple layers at different depths. The CGH corresponding to each layer is calculated by an angular-spectrum algorithm that is effective at a wide range of propagation distances. All of the CGHs are combined into several group-CGHs. These group-CGHs are sequentially uploaded onto one spatial light modulator at a high frame rate. The space-bandwidth product can be benefited by the time-division processing of the CGHs. The proposed method provides a new approach to achieve high quality 3-D display with a fast and accurate CGH computation.

Quasi-non-diffracting beams are attractive for various applications, including optical manipulation, super-resolution microscopes, and materials processing. However, it is a great challenge to design and generate super-long quasi-non-diffracting beams with sub-diffraction and sub-wavelength size. In this paper, a method based on the idea of compressing a normalized angular spectrum is developed, which makes it possible and provides a practical tool for the design of a quasi-non-diffracting beam with super-oscillatory sub-wavelength transverse size. It also presents a clear physical picture of the formation of super-oscillatory quasi-non-diffracting beams. Based on concepts of a local grating and super-oscillation, a lens was designed and fabricated for a working wavelength of λ = 632.8 nm. The validity of the idea of normalized angular spectrum compression was confirmed by both numerical investigations and experimental studies. An optical hollow needle with a length of more than 100λ was experimentally demonstrated, in which an optical hollow needle was observed with a sub-diffraction and sub-wavelength transverse size within a non-diffracting propagation distance of 94λ. Longer non-diffracting propagation distance is expected for a lens with larger radius and shorter effective wavelength.

We have been investigating the angular spectrum method for analysis of single-mode and multimode optical fibers. The justification is simple because the approach requires less computational time than other methods because it is heavily dependent on the fast Fourier transform. This method should become much more important as new approaches are being studied for higher data rate transmission. We examine two basic components in the application of this technique to propagation of light in optical fibers – an absorbing layer at the outer radius and design of the interface between the cord and cladding of the optical fiber.

The image performance of acoustic and ultrasound sensors depends on several fundamental parameters such as depth of focus or spatial resolution. There are currently two different type of acoustic diffractive lenses: those which form a diffraction-limited spot with a shallow depth of focus (zone plates) and lenses which form an extended focus (quasi-Bessel beams). In this paper, we investigate a pupil-masked Soret zone plate which allows the tunability of a normalized angular spectrum. It is shown that the depth of focus and the spatial resolution can be modified, without changing the lens structure, by choosing the size of the amplitude pupil mask. This effect is based on the transformation of spherically converging waves into quasi-conical waves, due to the apodization of the central part of the zone plate. The theoretical analysis is verified with both numerical simulations and experimental measurements. A Soret zone plate immersed in water with D/2F=2.5 and F=4.5$\lambda$, changes its depth of focus from 2.84$\lambda$ to 5.9$\lambda$ and the spatial resolution increases from 0.81$\lambda$ to 0.64$\lambda$ at a frequency of 250 kHz, by modifying the pupil mask dimensions of the Soret zone plate.

We examine single-mode optical fiber transmission using the angular spectrum method. We find excellent agreement with the theoretical solutions for the cylindrical single-mode optical fiber. Next, we examine fiber coupler configurations with 1×2, 1×3, and 1×5 designs. The input within the central fiber core is broadcast equally into the surrounding fiber cores and then returns with propagation distances as expected. Then we examine supermode theory for the 1×3 case. The initial energy is sent into different combinations of fiber cores where their phase relationship governs the output. Surprisingly, we find evidence of an unexpected mode in some of the multicore designs. We expect these results might be useful for exploration of more complicated fiber core arrays. However, computational times are short using this algorithm.

We calculate the forces of a single-beam optical trap, also known as an "optical tweezers," on micron-sized dielectric spheres based on the wave optics regime. These forces have previously been calculated using a geometrical ray optics approach by Ashkin. The relatively simple approach proposed by Ashkin is based on tracing a set of equal intensity rays from a uniformly sampled microscope objective lens aperture, all passing through a single point in space, the focal point of the lens. This model does not take into account the wave nature of light and is, therefore, it cannot account for the effects of diffraction Here we propose the use of the angular spectrum method, based on the fast Fourier transform algorithm, to calculate the scalar wavefield on the surface of a microsphere, from which ray amplitudes and directions can be estimated. This allows for the Ashkin’s method to calculate forces on trapped spherical particle to be amended to account for the effects of diffraction. Numerical results are presented for a laser power of 10mW and a microscope objective with a numerical aperture of 1.25, and compared with those obtained using the traditional geometrical approach.

We propose a method that eliminates speckle artifact in the reconstruction of triangular mesh based computer generated holograms. The proposed method generates a number of holograms with different sets of interleaved plane carrier waves. The generated holograms are displayed sequentially with time-multiplexing, achieving speckle-free reconstruction without sacrificing the viewing angle or depth of focus. The proposed method is verified experimentally using viewing-window type holographic display setup. The experimental results indicate that the proposed method can achieve speckle-free reconstruction with smaller number of the time-multiplexing than conventional temporal speckle averaging techniques.

Since many optical imaging systems suffer from a limited depth of focus, three-dimensional (3D) objects, or even flat objects tilted with respect to the optical axis, are imaged with only a portion of them in focus. Typically, to overcome this problem, in-focus areas are extracted from different images taken at different depths. The in-focus regions are thus merged together to build the extended focus image (EFI). In this work, we propose a quasi-automatic method for the EFI construction of tilted objects, extracted at once by 3D output of the Angular Spectrum Method (ASM) from a single digitally recorded hologram. Results show that our method can be effectively used for the correction of the anamorphism due to the reconstruction on a tilted plane with respect to the hologram one. (C) 2013 Elsevier Ltd. All rights reserved.

Occlusion handling in computer-generated holography is of vast importance as it enhances depth information by presenting correct motion parallax of the 3D scene within the viewing angle. In this paper, we propose a computationally efficient occlusion handling technique based on a fully analytic mesh based computer generated holography. The proposed technique uses angular spectrum convolution that renders exact occlusion while preserving all other aspects of the fully analytic mesh based computer generated holography. The proposed method is computationally efficient as only a single convolution operation is required for each mesh without numerical propagation between the meshes. The proposed method is also exact as it performs the occlusion processing in the tilted mesh plane, being free from artifacts coming from orthographic spatial masking. The proposed method can be applied to the self and the mutual occlusions between the objects in the 3D scene. The computer simulated results show the feasibility of the proposed method.

Multimode optical fibers are gaining increased interest for higher data rate transmissions. In this work, we examine the propagation of beams in multimode optical fibers using the angular spectrum method for several values for the propagation constant V. We prepare a sequence of 4096 images over 200,000 steps, each representing a wavelength within the fiber. We perform a one-dimensional Fourier transform of these data and obtain the propagation constant for each transmitted mode. We then obtain the electric field profile for each transmitted mode. We find excellent agreement with weakly guided mode theory. This work represents another step in the use of this algorithm for analyzing more complicated optical fiber structures.

An efficient computing simulation routine has been implemented to model explicitly several types of Fresnel zone plate taking advantage of the circular symmetry. This code was used to evaluate an optimized approach for stacking of two high-resolution Fresnel zone plates., A computing simulation routine to model any type of circularly symmetric diffractive X-ray element has been implemented. The wavefield transmitted beyond the diffractive structures is numerically computed by the angular spectrum propagation method to an arbitrary propagation distance. Cylindrical symmetry is exploited to reduce the computation and memory requirements while preserving the accuracy of the numerical calculation through a quasi-discrete Hankel transform algorithm, an approach described by Guizar-Sicairos & Gutierrez-Vega [J. Opt. Soc. Am. A, (2004 ▶), 21, 53–58]. In particular, the code has been used to investigate the requirements for the stacking of two high-resolution Fresnel zone plates with an outermost zone width of 20 nm.

We propose a method to obtain a computer-generated hologram that renders reflectance distributions of individual mesh surfaces of three-dimensional objects. Unlike previous methods which find phase distribution inside each mesh, the proposed method performs convolution of angular spectrum of the mesh to obtain desired reflectance distribution. Manipulation in the angular spectrum domain enables its application to fully-analytic mesh based computer generated hologram, removing the necessity for resampling of the spatial frequency grid. It is also computationally inexpensive as the convolution can be performed efficiently using Fourier transform. In this paper, we present principle, error analysis, simulation, and experimental verification results of the proposed method. (C) 2016 Optical Society of America

The “perfect” vortex is a new class of optical vortex beam having ring radius independent of its topological charge (order). One of the simplest techniques to generate such beams is the Fourier transformation of the Bessel-Gauss beams. The variation in ring radius of such vortices require Fourier lenses of different focal lengths and or complicated imaging setup. Here we report a novel experimental scheme to generate perfect vortex of any ring radius using a convex lens and an axicon. As a proof of principle, using a lens of focal length f = 200 mm, we have varied the radius of the vortex beam across 0.3–1.18 mm simply by adjusting the separation between the lens and axicon. This is also a simple scheme to measure the apex angle of an axicon with ease. Using such vortices we have studied non-collinear interaction of photons having orbital angular momentum (OAM) in spontaneous parametric down-conversion (SPDC) process and observed that the angular spectrum of the SPDC photons are independent of OAM of the pump photons rather depends on spatial profile of the pump beam. In the presence of spatial walk-off effect in nonlinear crystals, the SPDC photons have asymmetric angular spectrum with reducing asymmetry at increasing vortex radius.

We will present an interactive computer-generated hologram technique using spherical angular spectrum. The spherical angular spectrum consists of the frequency spectrum of the object wave in all-around directions. The spherical angular spectrum is computed by a formula of the Fourier coefficients of point light source. Given a spherical angular spectrum, one can generate a planar hologram at a high speed for any given direction. We also present an interactive computer-generated hologram example using a hand-recognition sensor.

The features of the anisotropic acousto-optic Bragg diffraction in paratellurite related to the measurement and control of the angular spectrum of monochromatic optical radiation are analyzed. We consider the diffraction configuration in which a narrow angular component whose position is determined by the frequency of acoustic wave is deflected from the divergent optical beam. The angular spectrum of optical radiation can be measured using variations in the acoustic frequency. It is demonstrated that such a configuration can be used for the measurement of the angular spectrum of light and for the formation of the desired angular distribution.

We present a scheme using depth information to generate computer-generated hologram by angular spectrum method us. Any depth map can be used for calculating computer-generated hologram(CGH). The proposed method generates a polygon model through simplified process and generate the polygon-based CGH for more realistic 3D object.

The effects of the decoherence of a narrow-band optical field with a broad angular spectrum upon propagation through a plate of a transparent medium placed in one of the arms of the Michelson interferometer are established.

A novel angular spectrum method was proposed to numerically analyze off-axis free-space light propagation on a translated plane to an arbitrary angle. Utilizing a shifted angular spectrum method based on an oblique incident plane wave assumption, a generalized light propagation formulation was obtained in a wide range of both tilt angles and sampling intervals, which overcame the limitations of prior attempts. A detailed comparison of the proposed angular spectrum method with prior methods is numerically presented for diffractive optics and computer-generated holograms. The validity of the proposed method was confirmed experimentally by reconstructing a digital holographic image using a spatial light modulator.

The determination of numerical reconstruction distance is key to recover the wavefront at focal plane in digital holography. In this paper, we propose a new autofocus method based on angular spectrum method (ASM). The proposed method takes successive Fourier transform after 1st order spectrum selection, and then calculates the summation. It saves operations compared to classic autofocus functions. When an exhaustive z-axis search is performed, the proposed method obtains unimodality coincided with the results from four classic autofocus functions. Moreover, the proposed method is more time-effective, which is the optimal one for ASM. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Published version

An automatic angular-spectrum filtering for the phase reconstruction of dual-wavelength digital holograms in a common-path configuration is presented. The major procedure of this automatic angular-spectrum filtering consists of excluding the zero-order region of Fourier spectrums and locating the center of order +1 region of the angular spectrums for two individual wavelengths. The phase map of the object is retrieved with the automatic angular spectrum-filtering algorithm in dual-wavelength digital holographic system, which demonstrates that the automatic angular spectrum-filtering algorithm is feasible and effective. It provides an efficient solution for angular-spectrum filtering in real time dual wavelength digital holographic microscopy.

The application of digital holographic interferometry on the quantitative measurement of the domain inversion in a RuO2:LiNbO3 crystal wafer is presented. The recorded holograms are reconstructed by the angular spectrum method. From the reconstructed phase distribution we can clearly observe the boundary between the inverted and un-inverted domain regions. Comparisons with the results reconstructed by use of the Fresnel transform method are given. Factors that influence the measurement include the spectrum filter size and the spectrum movement are discussed. The spectrum filter size has an effect on the measurement of the details. Although the spectrum movement affects every single reconstructed image, it has no influence on the final measurement.

A layer-based angular spectrum method is proposed for computer-generated hologram. Experimental results demonstrate the feasibility of reconstructing three dimensional objects by using a phase-only spatial light modulator.

A method for the calculation of the impulse response of annular-sectorial (also called annular-segmented) pistons embedded in an infinite rigid baffle is presented. Our calculations are grounded on the Angular Spectrum method following the main features of the theoretical development presented by Guyomar and Powers. Unlike in the original method, the mathematical formulation of the problem is expressed in polar coordinates, leading to the use of n th-order Hankel transform instead of the most frequently used 2D-FFT. The request of a new method arises from the fact that circular boundaries of a radiator must be approximated, when using rectangular grids. This approximation allows the occurrence of a significant error. In order to test the proposed method, numerical results of the impulse response of annular-sectorial pistons were compared with those obtained by means of the original algorithm, and also with the well known, currently used Stepanishen’s method.

The thick film photoresist lithography is a much more complicated process compared to the thin film photoresist lithography. In this paper, we have developed a new model for lithography of thick film photoresist by using the angular spectrum theory. The thick film photoresist is divided into many homogeneous layers, and the diffractive optical imaging distribution in photoresist is regarded as superposition of different spectrum plane waves. Propagation of each plane wave is determined by the optical transfer function, and the propagation direction, amplitude and phase are dominated by reflection and transmission between each interface of the sub-layers. The fast Fourier transform (FFT) has been converted into a convolution calculation to keep the computation accurate and reduce computation cost. Numerical calculation results show that optical intensity in cross-sect of thick film resist is strongly affected by reflection, transmission on interface and variation of dielectric permittivity along direction of depth, and therefore these factors should be considered while analyzing diffractive imaging field in thick film photoresist.

In this paper the optical distribution in the near-field region of solid immersion lens (SIL) is investigated from the viewpoint of angular spectrum. Because of the big numeric aperture (NA) of objective in SIL storage system, the polarization of incident laser is also considered. Based on this investigation, a kind of high-pass angular spectrum filter method is proposed to decrease the optical spot size. The effect of filter in SIL system is analyzed in detail. Our theoretical analysis shows that this kind of filter can decrease the spot size by nearly 40% and light intensity loss by around 11%.

Bifurcation phenomenon in the energy-angular correlation spectrum of the vacuum laser acceleration has been observed with computer simulation. Concerning a focused laser pulse, the classical single-valued energy-angular correlation spectrum for a plane wave is, besides broadened to a band, bifurcated with the classical value in between the two branches. Analytic expression to describe the correlation has been derived and physical explanations based on the ponderomotive potential model and Lorentz-Newton force analyses are presented. The theoretical results are supported by numerical simulations which have been compared with the experimental results. This study is helpful in designing vacuum laser acceleration experiments.

In this letter, we demonstrate sectional image reconstruction and three-dimensional microscopy of small particles. We demonstrate sectional image reconstruction and holographic methods to obtain 2D and 3D images of small particles. A single hologram is sufficient to obtain a section containing only the focused parts of the reconstructed image. One can obtain images of different plane sections of a specimen in addition to its 3D display. The reconstruction of a digital hologram is based on the plane-wave expansion of the diffracted wave fields using Fourier optics (this method is also known as the angular spectrum method). With this method, the object-to-hologram distance can be quite small because the minimum-distance requirement does not apply. Furthermore, numerical reconstruction of transparent objects by this method may be interesting for micro-structure measurement.

Single beam optical tweezers hold particles behind the focal plane due to the highly focused laser beam. However, even moderately focused beams may stably con ne particles of high refractive index contrast and sizes up to half wavelength. This is caused by the fact that the light structure near focus is complex even for such moderately focused beams. The intensity pro le consists of several axial oscillations as well as off-axis lobes or rings which enhance trapping. Moreover, side lobes provide another multiple trapping sites for small sized particles. The properties of these traps will be analyzed theoretically by means of Generalized Lorenz-Mie Scattering theory.

The angular spectrum (AS) method is a popular solution to the Helmholtz equation without the use of approximations. Modified band-limited AS methods are of particular interest for the cases of high-off-axis and large distance propagation problems, because conventional AS methods are impractical due to requirements regarding memory and computational effort. However, these techniques make use of rectangular-shaped filters that introduce ringing artifacts in the calculated field that are related to the Gibbs phenomenon. This work proposes AS algorithms based on a smooth band-limiting filter for accurate field computation as well as techniques that evaluate only nonzero components of the field. This enables accurate field calculations with an acceptable level of computational effort that cannot be offered by current AS methods reported in the scientific literature.

Diffractive optical elements (DOE) are used for various purposes, such as a beam shaper, beam splitter and so on. In order to design DOEs, iterative Fourier transform algorithm (IFTA) is widely used. IFTA is fast and effective optimization method and can handle large size data. In the IFTA, propagation in the far field and near field is described by Fourier transform and Fresnel transform, respectively. Iterative angular spectrum approach (IASA) is one of iterative methods based on angular spectrum technique. IASA adopt angular spectrum technique as expression of propagation in near field instead of Fresnel transform. Angular spectrum technique is based on scalar diffraction theory and satisfies Helmholtz equation; therefore angular spectrum technique is the accurate method for the calculation of diffraction. We designed a DOE by using IASA and evaluated its diffraction characteristics based on vector diffraction theory. In this paper, we report on the outcome.

We present a technique that involves tailoring the angular spectrum in optical microscopy of silicon integrated circuits, with a solid immersion lens. Spatial light modulation to select only supercritical light at the substrate/dielectric interface, yields only evanescent and scattered light in the interconnect layers. We demonstrated the technique in optical excitation microscopy of 65nm silicon-on-insulator circuits, which enabled localization of a fault during microprocessor development. Acquiring images with and without angular spectrum tailoring allowed longitudinal localization of the electrical response to optical excitation. Lateral registration of electrical response and confocal reflection images to the circuit layout was also significantly improved.

The angular spectrum of spontaneous emission in a two-dimensional undulator free-electron laser is analyzed theoretically. Numerical calculation shows that thes-th harmonic spontaneous emission power density can be greatly enhanced by using a two-dimensional undulator, for whichl=s, so the harmonic number can be selected by selectingl. Therefore, the higher harmonic operation of a free-electron laser can be realized selectively.

A numerical reconstruction technique of digital holography based on angular spectrum diffraction by means of the ridge of Gabor wavelet transform (GWT) is presented. Appling the GWT, the object wave can be reconstructed by calculating the wavelet coefficients of the hologram at the ridge of the GWT automatically even if the spectrum of the virtual image is disturbed by the other spectrum. It provides a way to eliminate the effect of the zero-order and the twin-image terms without the spatial filtering. In particular, based on the angular spectrum theory, GWT is applied to the digital holographic phase-contrast microscopy on biological specimens. The theory, the results of a simulation and an experiment of an onion specimen are shown.