Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors

In both temporal and spatial carrier phase shifting interferometry, the primary source of phase calculation error results from an error in the relative phase shift between sample points. In spatial carrier phase shifting interferometry, this phase shifting error is caused directly by the wavefront under test and is unavoidable. In order to minimize the phase shifting error, a pixelated spatial carrier phase shifting technique has been developed by 4D technologies. This new technique allows for the grouping of phase shifted pixels together around a single point in two dimensions, minimizing the phase shift change due to the spatial variation in the test wavefront. A formula for the phase calculation error in spatial carrier phase shifting interferometry is derived. The error associated with the use of linear N-point averaging algorithms is presented and compared with those of the pixelated spatial carrier technique.     

数字图像单个像元分形维数的特征与计算方法

通过分形理论把空间结构信息引入遥感分类中,必须解决分形维数计算的问题,为此提出了一种通过相邻像元间灰度值大小的变化计算数字图像单个像元分形维数的算法。选定计算窗口值 L 后,运用所编程序对 TM 遥感数据进行运算,并得到所需分维值数据。发现所得分维值随窗口值 L 增大而减小;大窗口值的分维值图像较抽象,但建议窗口值不超过 61;小窗口值的分维值图像较清晰,但窗口值不能小于 5。     

Ultraviolet and visible imaging and spectrographic imaging instrument

The Ultraviolet and Visible Imaging and Spectrographic Imaging experiment consists of five spectrographic imagers and four imagers. These nine sensors provide spectrographic and imaging capabilities from 110 to 900 nm. The spectrographic imagers share an off-axis design in which selectable slits alternate fields of view (1.00° × 0.10° or 1.00° × 0.05°) and spectral resolutions between 0.5 and 4 nm. Image planes of the spectrographic imager have a programmable spectral dimension with 68, 136, or 272 pixels across each individual spectral band, and a programmable spatial dimension with 5, 10, 20, or 40 pixels across the 1° slit length. A scan mirror sweeps the slit through a second spatial dimension to generate a 1° × 1° spectrographic image once every 5, 10, or 20 s, depending on the scan rate. The four imagers provide narrow-field (1.28° × 1.59°) and wide-field (10.5° × 13.1°) viewing. Each imager has a six-position filter wheel that selects various spectral regimes and neutral densities. The nine sensors ut lize intensified CCD detectors that have an intrascene dynamic range of ~ 10(3) and an interscene dynamic range of ~ 10(5); neutral-density filters provide an additional dynamic range of ~ 10(2-3). The detector uses an automatic gain control that permits the sensors to adjust to scenes of varying intensity. The sensors have common boresights and can operate separately, simultaneously, or synchronously. To be launched aboard the Midcourse Space Experiment spacecraft in the mid-1990's, the ultraviolet and visible imaging and spectrographic imaging instrument will investigate a multitude of celestial, atmospheric, and point sources during its planned 4-yr life.     

Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition

We propose a phase measurement technique to retrieve optical phase distributions coded in noisy temporal speckle pattern interferometry signals presenting regions of adjacent low-modulated pixels, which is based on the bidimensional empirical mode decomposition and the Hilbert transform. It is shown that this approach can effectively remove noise and minimize the influence of large sets of adjacent nonmodulated pixels located in the time series of speckle interferograms. The performance of the phase retrieval approach is analyzed using computer-simulated speckle interferograms modulated with a temporal carrier. The results are also compared with those given by a technique based on the one-dimensional empirical mode decomposition. The advantages and limitations of the proposed approach are finally discussed.     

Pulsed TV Holography Combined with Digital Speckle Photography Restores Lost Interference Phase

The measuring of situations with optical measuring methods is difficult when a deformation field must be determined while it is superposed to comparatively large rotating or translating object motion. Interferometric methods such as pulsed TV holography might be suitable to measure the small transient deformation, but the often-large bulk motion makes the phase information disappear. However, by a combination of digital speckle photography (DSP) (also called digital image correlation) with pulsed TV holography, such measuring problems can be mastered. A method to calculate the bulk in-plane motion by DSP from the usual pulsed TV holography recordings and then to use this information to restore the interference phase is proposed. This technique may be attractive in the study of transient vibrations overlaid on rotating or translating motions.     

Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier

We present an optical phase measurement method based on the Hilbert transform for the analysis of a time series of speckle interferograms modulated by a temporal carrier. We discuss the influence of nonmodulating pixels, modulation loss, and noise that affect the bias and modulation intensities of the interferometric signal and propose the application of the empirical mode decomposition method for its minimization. We also show the equivalence between the phase recovery approaches that are based on the Hilbert and the Fourier transforms. Finally, we present a numerical comparison between these methods using computer-simulated speckle interferograms modulated with a temporal carrier.     

Spatial amplitude and phase modulation using commercial twisted nematic LCDs

We present a method for full spatial phase and amplitude control of a laser beam using a twisted nematic LCD combined with a spatial filter. By spatial filtering we combine four neighboring pixels into one superpixel. At each superpixel we are able to independently modulate the phase and the amplitude of light. We experimentally demonstrate the independent phase and amplitude modulation using this novel technique. Our technique does not impose special requirements on the spatial light modulator and allows precise control of fields even with imperfect modulators.     

An electro-optic holography system with real-time arithmetic processing

This paper reports the use of a real-time arithmetic image processor in an electro-optic holography system. A speckle interferometer is used to combine an image of an object, lit by laser light, with a mutually coherent reference beam. A CCD TV camera detects the interference pattern, and the phase of the reference beam is advanced by 90° between frames. An image is generated from each set of four sequential TV frames by subtracting alternate frames, squaring, and adding the two results. The result is improved picture quality compared with the use of binary pixels and compared with electronic speckle pattern interferometry. Experimental results are shown.     

Transient Deformation Measurement by Double-Pulsed-Subtraction TV Holography and the Fourier Transform Method

We report the measurement of transient bending waves with double-pulsed-subtraction TV holography. The correlation fringe patterns are automatically quantitatively analyzed by the application of Fourier methods. A novel optical setup with two different object-beam optical paths is demonstrated for the generation of carrier fringes. The proposed system is highly immune to environmental disturbances because the optical setup imposes no lower limit on the time separation between laser pulses. One removes the linear phase distribution due to the spatial carrier in the spatial domain by subtracting the phase of the undeformed carrier fringes from the phase of the modulated fringes. Experimental results obtained with an aluminum plate excited by the impact of a piezoelectric translator are presented.     

Time average vibration fringe analysis using Hilbert transformation

Quantitative phase information from a single interferogram can be obtained using the Hilbert transform (HT). We have applied the HT method for quantitative evaluation of Bessel fringes obtained in time average TV holography. The method requires only one fringe pattern for the extraction of vibration amplitude and reduces the complexity in quantifying the data experienced in the time average reference bias modulation method, which uses multiple fringe frames. The technique is demonstrated for the measurement of out-of-plane vibration amplitude on a small scale specimen using a time average microscopic TV holography system.     

High-definition imaging system based on spatial light modulators with light-scattering mode

We have developed a prototype high-definition imaging system using polymer-dispersed liquid-crystal (PDLC) light valves, which can modulate unpolarized light with high spatial resolution and exhibit a high optical efficiency, based on the light-scattering effect. We fabricated high-definition light valves with a fine polymer-matrix structure in a PDLC film by controlling the curing conditions used during the photopolymerization-induced phase separation and formation process. This device has excellent characteristics, such as a high resolution, with 50 lp/mm for a limiting resolution and greater than 20 lp/mm at the 50% modulation transfer function point, and a reflectivity of greater than 60%. An optically addressable full-color projection display was designed, consisting of three PDLC light valves, a schlieren optical system based on shift-decentralization optics with a xenon lamp illumination and input-image sources with 1.5 million pixels, including electrical image compensation of the gamma characteristics. We succeeded in displaying pictures on a 110-inch screen with a resolution of 810 TV lines and a luminous flux of 1900-2100 American National Standards Institute lumens.     

Digital speckle pattern interferometry using spatial phase shifting: influence of intensity and phase gradients

Spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS) provides the phase information due to the object displacement from two images, one stored before and other after loading. The technique needs a carrier fringe system. The double aperture mask in front of the imaging system is one of the methods for introducing the spatial carrier frequency for phase evaluation. The size of the apertures and their separation are important criteria to obtain appropriate phase shift/column within the desired size of the speckle for phase retrieval. The assumptions of constant intensity and phase on adjacent pixels of the camera while calculating phase in spatial phase shifting (SPS) are not met as the speckled object wave contains intensity and phase gradients, resulting in distortions in the calculated phase profiles. In this paper we discuss a strategy to overcome these problems. The contrast of the correlation fringe obtained using this approach is much improved. It also eliminates the distortion in the unwrapped phase map like wave ripples. The experimental results on an edge clamped circular plate loaded at the center are presented.     

Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators

We present a novel method of producing arbitrarily valued binary phase-only modulation from a commercially available ferroelectric liquid-crystal spatial light modulator that is used in conjunction with simple polarization components. By cascading of such stages, modulators with four and eight equally spaced phase levels are constructed with 128 × 128 pixels. Near-diffraction-limited performance, when stopped down to 64 × 64 pixels, is reported in producing simple diffraction patterns and when used to generate asymmetric spot arrays in the Fourier plane of a lens.     

Pseudorandom phase-only encoding of real-time spatial light modulators

We previously proposed a method of mapping full-complex spatial modulations into phase-only modulations. The Fourier transform of the encoded modulations approximates that of the original complex modulations. The amplitude of each pixel is encoded by the property that the amplitude of a random-phasor sum is reduced corresponding to its standard deviation. Pseudorandom encoding is designed for phase-only spatial light modulators that produce 360° phase shifts. Because such devices are rare, experiments are performed with a 326°modulator composed of two In Focus model TVT6000 liquid-crystal displays. Qualitative agreement with theory is achieved despite several nonideal properties of the modulator.     

Phase-shifting interferometry with uncalibrated phase shifts

A computationally efficient algorithm for phase-shifting interferometry with imprecise phase shifts is developed. It permits the use of an uncalibrated phase shifter and is also insensitive to spatial intensity variations. The measurement has both spatial and temporal aspects. Comparisons are made between pixels within the same interferogram, and these comparisons are extended across a set of interferograms by a maximum-minimum procedure. A test experiment is performed and confirms the theoretical results. An additional advantage of the algorithm is that an error measure can be developed. This error measure is used to implement an error correction scheme.     

Performance of TES X-ray Microcalorimeters with AC Bias Read-Out at MHz Frequencies

At SRON we are developing Frequency Domain Multiplexing for the read-out of superconducting transition edge sensor microcalorimeters for future X-ray astrophysical missions. We will report on the performance of Goddard Space Flight Center pixels under AC bias in the MHz frequency range. Superconducting flux transformers are used to improve the impedance matching between the low ohmic TESs and the SQUID. We connected 5 pixels to the LC filters with resonant frequencies ranging between 1 and 5 MHz. For X-ray photons of 6 keV we measured a best X-ray energy resolution of 3.6 eV at 1.4 MHz, consistent with the integrated Noise Equivalent Power. In addition, we improved the electrical circuit by optimizing the coupling ratio of the impedance matching transformer. In addition, we improved electrical circuit for impedance matching; modified transformer coupling ratio. As a result, we got the integrated noise equivalent power resolution of 2.7 eV at 2.5 MHz. A characterization of the detector response as a function of the AC bias voltage, bias frequency and the applied magnetic field is presented.     

基于不同空间结构Hadamard融合的图像边缘提取算法

目的针对图像边缘提取算法中噪声对边缘的影响,易导致边缘定位精度不高,出现虚假边缘与漏检等不足,设计一种不同空间结构Hadamard融合的图像边缘提取方案。方法首先,通过计算像素与相邻点之间的方差来分析像素的结构,得到边缘点的最大概率分布矩阵(MPDM),利用MPDM来表示候选边缘集。其次,通过分析邻域点之间的亮度,计算像素与其4个相邻像素之间的最大和最小差值,得到相应的差异矩阵,并引入Logistic回归分析对2种矩阵归一化处理,得到一个权重矩阵(WM)。然后,通过Hadamard乘积模型将MPDM与WM进行融合,从而设计边缘分割阈值函数。最后,通过比较WM和分割阈值,去掉非边缘点,检测出真实图像边缘。结果实验表明,与当前边缘提取方法对比,文中方法能够有效抑制噪声,得到的边缘清晰、完整,边缘细化度与平滑度良好,在客观评价FOM与ROC中具有更大的优势。结论所提算法具有良好的边缘提取精度,在图像处理与包装条码领域具有良好的应用价值。     

Performance analysis of phase-code multiplexed holographic memory

For analysis of effective phase-code multiplexing in a holographic memory system four types of phase code are generated and used as a reference beam. In computer simulations the size of the address beam is fixed at 32 x 32 pixels, and 0%, 5%, 10%, 15%, 20%, and 25% phase-error rates in a pixel are purposely added to the real phase values for consideration of the nonlinear phase-modulation characteristics of a practical spatial light modulator. Cross talk and signal-to-noise ratios (SNR's) are comparatively analyzed for these phase codes by calculation of the autocorrelation and the cross correlation. The pseudorandom code (PSR) has the lowest cross-correlation mean value of 0.067 among the four types of phase code, which means that the SNR of the PSR is higher than with other phase codes. Also, the standard deviation of the PSR, indicating the degree of recalled data degradation, has the lowest value, at 0.0113.     

Spatial carrier phase-shifting algorithm based on least-squares iteration

An advanced spatial carrier phase-shifting (SCPS) algorithm based on least-squares iteration is proposed to extract the phase distribution from a single spatial carrier interferogram. The proposed algorithm divides the spatial carrier interferogram into four phase-shifted interferograms. By compensating for the effects of the variations of phase shifts between pixels and the variations of background and contrast, the proposed algorithm determines the local phase shifts and phase distribution simultaneously and accurately. Numerical simulations show that the accuracy of the proposed algorithm is obviously improved by compensating for the effects of background and contrast variations. The peak to valley of the residual phase error remains less than 0.002 rad when the magnitude of spatial carrier is in the range from pi/5 to pi/2 and the direction of the spatial carrier is in the range from 25 degrees to 65 degrees. Numerical simulations and experiments demonstrate that the proposed algorithm exhibits higher precision than the existing SCPS algorithms. The proposed algorithm is sensitive to random noise, but the error can be reduced by N times if N measurements are taken and averaged.     

Four-plane space-variant Fresnel-transform optical processor with a random phase encoder

We introduce a four-plane Fresnel-transform space-variant optical processor consisting of an input plane and two filter planes. One filter mask is programmable with a spatial light modulator. The second filter mask is a fixed random binary phase array with a known pseudorandom distribution of pixels. The order of the masks can be interchanged, giving different output characteristics. In one case the Horner efficiency of the correlator increases dramatically. In the other case the edge enhancement of the output image is removed. We discuss the theory for this general processor and its implementation with phase-only masks. We present experimental results when a binary magneto-optic spatial light modulator was used.