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.     

Surface profilometry with laser-diode optical feedback interferometer outside optical benches

A simple and robust interferometer with a laser diode subject to optical feedback from the interferometer is presented for surface testing of a spherical mirror. The fringe phase can be locked by the optical feedback within less than 0.2pi (peak-to-valley value) even when the interferometer is placed on a wooden table. The fringe locking is caused by the change of lasing wavelength that suppresses the net phase change to be much less than 2pi. The locked fringe pattern with spatial carriers can be analyzed by a fringe analyzer at a video rate, and the measurement results of the spherical mirror showed the same result as on an optical bench.     

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.     

An online triple-frequency color-encoded fringe projection profilometry for discontinuous object

Abstract

An online triple-frequency color-encoded fringe projection profilometry is proposed to measure the complex and discontinuous object at straight-line movement. N frames of color fringe patterns are specially designed. Three grayscale sinusoidal grating patterns with geometric progression frequency growth are encoded into red (R), green (G), and blue (B) channels separately to compose a color-encoded fringe pattern. If these three grayscale sinusoidal grating patterns are phase-shifted N steps with an equivalent shift phase of 2π/N, they can compose the corresponding N frames of color-encoded fringe patterns as above respectively. In order to avoid the movement’s interference to the phase shifting, position adjustment should be done to guarantee the phase-shifting direction to be perpendicular to the moving direction. While these N frames of specially designed color-encoded fringe patterns are projected onto the moving object one by one, the corresponding deformed color patterns are captured by a CCD camera in real time. By color separating, color crosstalk compensation, pixel matching, and phase calculation, three wrapped phase at different frequencies can be extracted. The unwrapped phase can be solved by a simplified algorithm based on temporal phase unwrapping method from the relationship of the three wrapped phase at the same pixel. Thus, it is very suitable to measure the online complex and discontinuous objects at straight-line movement. The experimental results show the feasibility and the validity of the proposed method.     

Acoustic grating fringe projector for high-speed and high-precision three-dimensional shape measurements

A new acoustic grating fringe projector (AGFP) was developed for high-speed and high-precision 3D measurement. A new acoustic grating fringe projection theory is also proposed to describe the optical system. The AGFP instrument can adjust the spatial phase and period of fringes with unprecedented speed and accuracy. Using rf power proportional-integral-derivative (PID) control and CCD synchronous control, we obtain fringes with fine sinusoidal characteristics and realize high-speed acquisition of image data. Using the device, we obtained a precise phase map for a 3D profile. In addition, the AGFP can work in running fringe mode, which could be applied in other measurement fields.     

Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator

Recent studies have demonstrated that the phase recovery from a single fringe pattern with closed fringes can be properly performed if the modulo 2pi fringe orientation is estimated. For example, the fringe pattern in quadrature can be efficiently obtained in terms of the orientational phase spatial operator using fast Fourier transformations and a spiral phase spectral operator in the Fourier space. The computation of the modulo 2pi fringe orientation, however, is by far the most difficult task in the global process of phase recovery. For this reason we propose the demodulation of fringe patterns with closed fringes through the computation of the modulo 2pi fringe orientation using an orientational vector-field-regularized estimator. As we will show, the phase recovery from a single pattern can be performed in an efficient manner using this estimator, provided that it requires one to solve locally in the fringe pattern a simple linear system to optimize a regularized cost function. We present simulated and real experiments applying the proposed methodology.     

Modulo 2pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.     

MEMS光栅光调制器阵列的控制系统设计

针对光栅光调制器阵列的显示控制,提出了一种控制系统设计方案。设计应用软件,产生显示数据源,由USB数据线发送到FPGA芯片,在FPGA芯片上实现格式转换、乒乓操作、脉宽调制等模块电路。实验结果表明,该控制系统操作灵活方便,为测试光栅光调制器的显示参数提供了有力的技术支持。     

Closed-loop phase stepping in a calibrated fiber-optic fringe projector for shape measurement

Active homodyne feedback control can be used to stabilize an interferometer against unwanted phase drifts introduced by, for example, temperature gradients. The technique is commonly used in fiber-optic sensors to maintain the fiber at its most sensitive (quadrature) position. We describe an extension of the technique to introduce stabilized, pi/2-rad phase steps in a full-field interferometer. The technique was implemented in a single-mode, fiber-optic interference fringe projector used for shape measurement and can be easily applied to other fiber- or bulk-optic interferometers, for example, speckle pattern and holographic interferometers. Fresnel reflections from the distal fiber ends undergo a double pass in the fibers and interfere at the fourth port of a directional coupler. The interference intensity (and hence phase) is maintained at quadrature by feedback control to a phase modulator in one of the fiber arms. Stepping between quadrature positions (separated by pi rad for light undergoing a double pass) introduces stabilized phase steps in the projected fringes (separated by pi/2 rad for a single pass). A root-mean-square phase stability of 0.61 mrad in a 50-Hz bandwidth and phase step accuracy of 1.17 mrad were measured.     

Two-wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator

A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-microm synthetic wavelength.     

Optical control of plasmonic Bloch modes on periodic nanostructures

We study and actively control the coherent properties of surface plasmon polaritons (SPPs) optically excited on a nanohole array. Amplitude and phase of the optical excitation are externally controlled via a digital spatial light modulator (SLM) and SPP interference fringe patterns are designed and observed with high contrast. Our interferometric observations reveal SPPs dressed with the Bloch modes of the periodic nanostructure. The momentum associated with these dressed plasmons (DP) is highly dependent on the grating period and fully matches our theoretical predictions. We show that the momentum of DP waves can, in principle, exceed the SPP momentum. Actively controlling DP waves via programmable phase patterns offers the potential for high field confinement applicable in lithography, surface enhanced Raman scattering, and plasmonic structured illumination microscopy.     

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.     

Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.     

Electronic speckle pattern shearing interferometer with a photopolymer holographic grating

A photopolymer holographic grating is used to produce the two sheared images in an electronic speckle pattern shearing interferometer. A ground glass screen following the grating eliminates unwanted diffraction orders and removes the requirement for the CCD camera to resolve the diffraction grating's pitch. The sheared images on the ground glass are further imaged onto the CCD camera. The fringe pattern contrast was estimated to be above 90%. A validation of the system was done by comparing the theoretical phase difference distribution with the experimental data from the three-point bending test.     

Light adaptation in motion direction judgments

We examined the time course of light adaptation in the visual motion system. Subjects judged the direction of a two-frame apparent-motion display, with the two frames separated by a 50-ms interstimulus interval of the same mean luminance. The phase of the first frame was randomly determined on each trial. The grating presented in the second frame was phase shifted either leftward or rightward by pi/2 with respect to the grating in the first frame. At some variable point during the first frame, the mean luminance of the pattern increased or decreased by 1-3 log units. Mean luminance levels varied from scotopic or low mesopic to photopic levels. We found that the perceived direction of motion depended jointly on the luminance level of the first frame grating and the time at which the shift in average luminance occurs. When the average luminance increases from scotopic or mesopic to photopic levels at least 0.5 s before the offset of the first frame, motion in the 3pi/2 direction is perceived. When average luminance decreases to low mesopic or scotopic levels, motion in the pi/2 direction is perceived if the change occurs 1.0 s or more before first frame offset, depending on the size of the luminance step. Thus light adaptation in the visual motion system is essentially complete within 1 s. This suggests a rapid change in the shape (biphasic or monophasic) of the temporal impulse response functions that feed into a first-order motion mechanism.     

Reflective acousto-optic modulation with surface acoustic waves

A reflective optical modulator based on acousto-optic modulation of light by a mirror corrugated with surface acoustic waves is presented. Modulation of optical amplitude, frequency, and phase is demonstrated at visible (633- and 488-nm) and deep UV (244-nm) wavelengths. The reflective modulator has eight channels and achieves a maximum first-order diffraction efficiency of 6.0%.     

Hook method: improvement and simplification of the experimental setup

The conventional experimental setup used to measure anomalous dispersion by the hook method has been modified by replacing the spectrograph by a single grating in combination with a camera. The grating is used for diffraction angles close to pi/2 rad, and the focal distance for projection of the hook spectrum is 4 m. The high dispersion thus obtained (typically 200 mm/nm) considerably facilitates the use of the hook method for diagnostic purposes. Further, it is demonstrated that, for such large diffraction angles, a focusing element after diffraction at the grating can be avoided without losing too much sharpness in the hook spectrum.     

基于改进Sierra 抖动算法的微离焦投影三维轮廓测量技术研究

通过分析传统频率调制的相位轮廓测量技术,提出基于蛇形扫描改进Sierra抖动算法,结合微离焦投影,可减小正弦光栅二值化的量化误差,同时抑制非对称纹理,能较大地改善离焦后光栅的正弦性。将该抖动算法生成的离焦光栅用于三维轮廓测量技术,与Bayer有序抖动算法、Sierra抖动算法和Floyd-steinberg误差扩散抖动算法进行了比较,实验结果表明:改进Sierra抖动算法具备更好的适应性,能够较大程度地降低相位误差,运算速度快,生成光栅准确度较高,改善了相位质量,适用于高精度三维轮廓测量。     

Amplitude modulation and beam-steering properties of active binary phase gratings with reconfigurable absorption areas

By combining a binary phase grating and materials with a controllable absorption, it is shown theoretically that it is possible to modulate the light in a zero-order diffraction beam and that a high contrast level for the beam modulation can be obtained. The intensity of higher diffraction orders also changes, but it is calculated that high contrasts cannot be achieved for these higher-order beams with the active gratings that we examine. This specific modulator design that we use can be applied both for transmitted and for reflected light. Using the same ideas, one may build a beam-deflection device by varying the period of the grating by selectively changing the absorption levels in the grating. The deflection efficiency of the device can be improved compared with other designs by use of a grating with a reduced intensity of the nondeflected zero-order beam.     

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。