Use of the circular Dammann grating in angle measurement

We describe a novel method of angle measurement by borrowing the concept of the circular Dammann grating (CDG). A three-order CDG is employed in this experiment. The displacement of the tilted angle can be determined accurately by measuring the projection from the distorted CDG image. This method is controlled only by the initial radius of the image and the converging ratio of the lens. Compared with conventional techniques, this technique has the advantages of a simple design with superior resolution to within 1 degree, low cost, and compactness. A theoretical analysis together with experimental results is presented.     

Design of circular Dammann gratings by employing the circular spot rotation method

A new concept based on the theory of Dammann gratings is proposed for the generation of circular optical beams. This grating shows that it can achieve equal intensity and equal spacing with acceptable efficiency that is controlled by set of transition points. A numerical solution is also presented together with the fabrication of 4-order circular Dammann grating by e-beam lithography. Experimental results agree well with the scalar diffraction theory. This grating has the potential to be further developed into practical applications.     

Three-dimensional Dammann vortex array with tunable topological charge

We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.     

Polarization-dependent circular Dammann grating made of azo-dye-doped liquid crystals

A polarization-dependent circular Dammann grating (CDG) was generated from an azo-dye-doped liquid crystal (LC) cell. A simple multiexposure photo-alignment process was used to fabricate a binary phase LC CDG zone plane, which was composed of an odd zone with a twisted nematic LC structure and an even zone with a homogenous LC structure. A two-order CDG with equal-intensity rings was produced through a Fourier transform. The maximum zeroth and first diffraction orders of obtained CDG can be separately achieved by rotating the analyzer's polarization direction. The CDG using an azo-dye-doped LC cell can be used to generate diffractions by lasers in a broad wavelength range, hence expanding possible device applications.     

Circular Dammann grating under high numerical aperture focusing

Circular Dammann grating (CDG) under high numerical aperture (NA) focusing is described based on Richards-Wolf vectorial diffraction theory in this paper. Several CDGs are presented under the condition of NA=0.9 with the illumination of circularly polarized plane-wave laser beams. Numerical results show that the sizes of these circular patterns with equal-intensity are in the wavelength scale, and doughnut-shaped central spots and dark rings are in the subwavelength width. To verify this kind of CDG, a binary pure-phase three-order CDG is fabricated to produce a dark center pattern surrounded by three concentric bright rings. The corresponding intensity distribution of the pattern on the focal plane of a high-NA objective (NA=0.9) is measured, and the results agree well with theoretical simulations. This kind of CDG with annular patterns of equal-intensity in the wavelength scale should be highly interesting for its potential applications in optical trapping, stimulated emission depletion (STED) microscopy, and the study of singular optics, as well as annular array illumination.     

Three-dimensional Dammann array

We demonstrate a scheme that can produce a three-dimensional (3D) focus spot array in a 3D lattice structure, called a 3D Dammann array, in focal region of an objective. This 3D Dammann array is generated by using two separate micro-optical elements, a Dammann zone plate (DZP) that produces a series of coaxial focus spots and a conventional two-dimensional (2D) Dammann grating (DG). A simple, fast, and clear method is presented to design this binary pure-phase (0,π) DZP in vectorial Debye theory regime. Based on this kind of DZP, one can always obtain a 3D Dammann array both for low and high numerical aperture (NA) focusing objectives. For experimental demonstration, an arrangement combining a DZP, a 2D DG, and a pair of opposing lenses is proposed to generate a 5×5×5 Dammann array in focal region of an objective with NA=0.127 and another 6×6×7 Dammann array for an objective of NA=0.66. It is shown that this arrangement makes it possible to achieve 3D Dammann arrays with micrometer-sized focus spots and focus spacings of tens of micrometers for various practical applications, such as 3D parallel micro- and nanomachining, 3D simultaneous optical manipulation, 3D optical data storage, and multifocal fluorescence microscope, etc.     

Structured light spots projected by a Dammann grating with high power efficiency and uniformity for optical sorting

We report a method for microfluidic multiple trapping and continuous sorting of microparticles using an optical potential landscape projected by a Dammann grating, enabling a high power-efficient approach to forming a composite two-dimensional spots array with high uniformity. The Dammann grating is fabricated in a photoresist by optical lithography. It is employed to create an optical lattice for multiple optical trapping and sorting in a mixture of polymer particles (n = 1.59) and silica particles (n = 1.42) with the same diameters of 3.1 μm. In addition to the exponential selectivity by the projected optical landscapes, the proposed microfluidic sorting system has advantages in terms of high power efficiency and high uniformity due to the Dammann grating.     

Simple focal-length measurement technique with a circular Dammann grating

A novel technique for focal-length measurements with a circular Dammann grating is presented. In the back focal plane of the lens under test, a one-order circular Dammann grating with limited aperture will produce double-humped radial rings. The separation between the two lobes varies with the displacement of the observed plane from the focal plane of the lens. By searching for the position at which the separation is minimal, the focal point of the lens can be located and hence the back focal length can be determined. Experimental results demonstrated that this method is efficient and can be used effectively for a quick check of focal length.     

Generation of Bessel beam arrays through Dammann gratings

In this work we apply the Dammann grating concept to generate an equal-intensity square array of Bessel quasi-free diffraction beams that diverge from a common center. We generate a binary phase mask that combines the axicon phase with the phase of a Dammann grating. The procedure can be extended to include vortex spiral phases that generate an array of optical pipes. Experimental results are provided by means of a twisted nematic liquid crystal display operating as a binary π phase spatial light modulator.     

Depth extraction of three-dimensional objects in space by the computational integral imaging reconstruction technique

A novel approach to extract the depth data of 3D objects in space by using the computational integral imaging reconstruction (CIIR) technique is proposed. With elemental images of 3D objects captured by the CCD camera through a pinhole array, depth-dependent object images can be reconstructed on the output plane by the CIIR technique. Only the images reconstructed on the output planes where 3D objects were located are clearly focused; so the depth data of 3D objects in space can be extracted by discriminating these focused output images from the others by using an image separation technique. A feasibility test of the proposed CIIR-based depth extraction method is carried out, and its results are discussed as well.     

On-axis diffractional behavior of two-dimensional pupils

We show that, at any Fresnel number, a suitable one-dimensional Fourier transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precision focusing, axial hyperresolution, or high focal depth.     

3-D Contouring of Diffuse Objects by Talbot-projected Fringes

Abstract

Talbot fringe projection, a moiré technique, is applied to three-dimensional contouring of diffuse targets for absolute shape measurement. The basic system relies on depth coding the test target surface by projecting the Talbot image of a linear grating. A second grating, similar to that used for the Talbot image, is employed to obtain the moiré fringes. These fringes represent surface contours of equal depth. Using a phase measurement technique and digital image processing algorithms, the surface shape information is obtained from the contour maps. Experimental results, merits and limitations of the system are discussed.     

光学三维测量中结构光栅投影系统的开发

为解决结构光三维测量系统中的光栅投影质量问题,提出并实现了以物理光栅为核心的结构光栅投影系统。该系统以现代光栅制造技术制造的精密光栅元件为核心,基于幻灯投影原理实现高质量的光栅条纹投影,利用步进电机带动高精密滚轴丝杆进行平移实现投影光栅的切换。实验结果表明,基于该系统实现的光学三维测量系统的可以达到1：100以上的对比度,具有较大的光强和良好的景深,同时能获得连续的强度分布及较好的正弦性,测量误差小于0．04mm,测量精度约为0．03mm,满足工业应用的要求。     

Superresolution laser beam shaping

The superresolution technique is well known for its ability to compress the central diffractive spot that is smaller than the Airy diffractive spot. In this paper, we extend the superresolution technique for different laser beam shaping. A complete set of superresolution diffractive elements is developed for the flat-top beam shaping, the single-circle beam shaping, and the novel circular Dammann grating. Five phase plates, corresponding to each of its applications, have been made by use of micro-optics technology. Experiments that are presented are in good agreement with the theoretical results. The superresolution technique presented in this paper should be highly interesting for the wide applications of laser beam shaping.     

Photoablation and lens damage from fractional Talbot images of Dammann gratings

UV photoablation of materials is recorded for both the near and far fields after transmission through a Dammann grating. The fused silica Fourier lens used for far-field imaging was damaged by a near-field intensity pattern with the same periodicity as the Dammann grating. The lens was located inadvertently at one eighth of the Talbot distance Z (T) behind the Dammann grating. Patterns recorded in copper film at the even-fractional Talbot planes compare qualitatively with calculated intensities. On the basis of these findings, a near-field intensity pattern was used to ablate vias in copper and polyimide films. The pattern at a distance of Z(T)/8 was used for via ablation because it is the pattern with the most fluence per spot.     

Dynamic optical coupled system employing even-numbered dammann gratings

Dammann gratings are well known for their ability to generate arrays of uniform-intensity beams from an incoming monochromatic beam. We apply the even-numbered Dammann grating to achieve dynamic optical coupled technology. A 1 x N dynamic optical coupled system is developed by employing two complementary even-numbered Dammann gratings. With this system we can achieve a beam splitter and combiner as a switch between them according to the relative shift between the gratings. Also, this system is a preferable approach in integral packaging. More importantly, this device has the potential to be applied to the splitting of a large array, e.g., 8 x 16 array and 64 x 64 array, which is difficult to be realized with conventional splitting methods. We experimentally demonstrated a 1 x 8 coupler at the wavelength of 1550 nm. Furthermore we analyze the effects of the alignment errors between gratings and the wavelength-dependent error on efficiency and uniformity. The experimental results and the influence of alignment error and wavelength-dependent error are analyzed in detail.     

Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions

We assess the validity of an extended Nijboer-Zernike approach [J. Opt. Soc. Am. A 19, 849 (2002)], based on ecently found Bessel-series representations of diffraction integrals comprising an arbitrary aberration and a defocus part, for the computation of optical point-spread functions of circular, aberrated optical systems. These new series representations yield a flexible means to compute optical point-spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases of practical interest. Because of the analytical nature of the formulas, there are no discretization effects limiting the accuracy, as opposed to the more commonly used numerical packages based on strictly numerical integration methods. Instead, we have an easily managed criterion, expressed in the number of terms to be included in the Bessel-series representations, guaranteeing the desired accuracy. For this reason, the analytical method can also serve as a calibration tool for the numerically based methods. The analysis is not limited to pointlike objects but can also be used for extended objects under various illumination conditions. The calculation schemes are simple and permit one to trace the relative strength of the various interfering complex-amplitude terms that contribute to the final image intensity function.     

Creating three-dimensional lattice patterns using programmable Dammann gratings

We demonstrate the creation of a three dimensional (3D) lattice of focus spots using a 3D Dammann grating structure. Such a 3D lattice of focus spots can be used for probing 3D structures or for creating 3D photonic crystal structures in optically sensitive media. Experimental results are included where the patterns are encoded onto a programmable liquid crystal display. We demonstrate the generation of five planar arrays each having 6×6 points surrounding another set of four planar arrays each having 5×5 points with a single pattern.