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Shape-From-Focus method (SFF method) is a method for recovering depth from an image series which are taken with different focus settings. For method presented in this paper, the series must be taken with an optical device (optical microscope, CCD or classic camera) with very small depth of focus, different images must be focussed to different planes and may be taken with inconsiderable angle of view. Proposed method is capable to registered images with different scaling, it makes possible to construct full sharpened 2D image and also the 3D model of scanned object. Accuracy of the method is tested by comparing with 3D models obtained by confocal microscope in hardware supported confocal mode. [ABSTRACT FROM AUTHOR]

The spectral crosstalk from neighboring peaks introduces phase ripple errors in Depth-Resolved Wavenumber-Scanning Interferometry (DRWSI), due to the sidelope of window functions of Fourier Transform (FT). To address such a problem, an algorithm, Scale-Frequency Transform (SFT), is proposed for data evaluation of DRWSI. The simulations show that the sidelope decreases from −12.2 dB to −25.5 dB after using SFT. The experimental results in four-surface interferometry as well as six-surface interferometry demonstrate that SFT can reduce the phase ripple errors effectively without spoiling the depth resolution of DRWSI. Therefore, SFT minimizes the effect of spectral crosstalk. It is practical to replace FT with SFT in DRWSI. [ABSTRACT FROM AUTHOR]

In this paper, we proposed an improved method for calculating the fringe width of Fraunhofer diffraction. Because the diffraction patterns are equidistant when the diffraction angle is small, the width of fringes can be determined through finding out the spatial frequency of the fringes using Fourier transform. To make the result more precise, the experimental data are compared with the theoretical values having the same range of the image in the frequency domain to get the modified frequency. We applied this method to calculate the diameters of some filaments by measuring their Fraunhofer diffraction fringes. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) step parallel confocal image processing algorithm for synthetic aperture imaging ladar (SAIL) is proposed. The feature of the algorithm is the collected data are confocal imaged in space domain by 2D Fourier transform. The collected data are first expressed by separation of variables and time-domain data are translated into a spatial coordinate expression suitable for space optical conversion, compensated with an azimuth quadratic phase and then imaged in space domain by 2D Fourier transform. Functions of the algorithm for SAIL with rectangular apertures is described and analyzed in terms of continuous variables and functions. Then the position of the imaging point is given. The technique is a new, one-step confocal imaging method for ladar echo signal. The confocal image processing is simplified and the imaging time is shortened. The requirement of a ladar image processing system is also reduced. It has a significant advantage in the data processing of synthetic-aperture ladar target echo confocal imaging. [ABSTRACT FROM AUTHOR]

A non-cube beam-splitter (NCBS) is proposed, by which an incident beam can be separated largely in a direction and then the lights from the test object and the lights from a reference surface placed adjacently to the test object can be combined to construct a simple electronic speckle pattern interferometry (ESPI) system. Two mainly useful quantitative ways, to calculate the phase change of the test object, the phase-shift and the fringe carrier method with Fourier transform, can be achieved in the ESPI system with the NCBS. Experiments with phase-shifting and fringe carrier method are completed. The experimental results show that the monolithic design of the proposed NCBS is effective in ESPI measurement and immunity to vibrations. [ABSTRACT FROM AUTHOR]

Abstract: An Iterative Fourier Transform Algorithm (IFTA) for digital hologram generation from a digital image using phase-only information is described in this paper. The algorithm is implemented in a Texas Instruments TMS320C64x fixed point digital signal processor (DSP). The holograms are reconstructed in real time using a liquid crystal display system and a He–Ne laser. The ideas described in this paper can be extended to digital hologram generation of three-dimensional objects and their reconstruction in real time using liquid crystal spatial light modulators, which could be a way for 3D-display systems. [Copyright &y& Elsevier]

Abstract: Phase-shifting interferometry is widely used for high-precision surface measurements, but has difficulty in dealing with parallel optical plates. In this paper, an advanced method is proposed to simultaneously measure surface distributions of parallel optical plates from multiple surface interference fringes. The basic theory behind the technique is by applying wavelength-modulated phase shifting interferometry (WMPSI) to get enough frames of multiple surface interference fringes. In the procession of wavelength-modulated phase shifting, the phase variation for one point of the surface is traced and is processed by Fourier transform, and then the frequency spectrum of every surface can be separated from each other. Therefore, it allows extraction of front surface, back surface and thickness variation from multiple surface interference fringes with high precision. [Copyright &y& Elsevier]

Abstract: A novel Fourier transform 3D shape measurement method based on color fringe projection is proposed in order to solve the spectrum overlapping and phase unwrapping problems existed in Fourier transform profilometry (FTP). The R and G components of the color fringe are set to two sinusoidal patterns with different frequencies and the B component is set to the average value of R or G component. Then this pattern is projected to the object and the deformed fringe image is captured. Three gray patterns are separated from the color fringe, the background and high frequency noise can be eliminated using our method and the accurate unwrapped phase can be got. Only one shot color pattern is projected to get the 3D information of the object. Experiment results show that the 3D information of an object can be obtained rapidly and accurately. [Copyright &y& Elsevier]

Abstract: The expression of gyrator transform (GT) is rewritten by using convolution operation, from which GT can be composed of phase-only filtering, Fourier transform and inverse Fourier transform. Therefore, fast Fourier transform (FFT) algorithm can be introduced into the calculation of convolution format of GT in the discrete case. Some simulations are presented in order to demonstrate the validity of the algorithm. [Copyright &y& Elsevier]

Abstract: A new kind of wavefront reconstruction algorithm is proposed in this paper, which can estimate the wavefront from its orthogonal gradients at different sample points. We model the gradients measured by wavefront sensor with the Fried geometry. Iterative discrete Fourier transforms and the correspondent Fried inverse filter in spatial frequency domain are introduced. No special boundary control is required to process the boundary condition in this algorithm. The stimulation and the experimental results show that the new algorithm has strong capability to fit the wavefront and it is more available if the sample points are few. [Copyright &y& Elsevier]

Time-of-flight (TOF) three-dimensional (3D) imaging is an effective means for remote sensing and target recognition. Fourier ghost imaging (GI) acquires the Fourier spectrum first, then applies an inverse Fourier transform (IFT) to retrieve the image of interest. The Fourier spectrum can be artificially processed when needed. The Fourier spectrum of some partially transmissive occluders is generally concentrated in high-frequency regions. These occluders can be removed by applying an IFT using the low-frequency spectrum coverage. This strategy is innovative in TOF 3D GI. In a TOF 3D GI system with DMDs, the high repetition rate and short-pulse laser is generally employed, which is mismatched with the lower modulation frequency of grayscale patterns. The grayscale Fourier patterns are decomposed into binary patterns. The detected intensities corresponding to the binary patterns are multiplied by the corresponding weighted coefficients, and are summed to form the Fourier spectrum slices at different distances. Then, an IFT is applied to retrieve the image cubes, furtherly to obtain the depth maps with the image cubes. Two 3D experiments are carried out to evaluate the proposed technique. The results indicate the reflectivity and depth maps can reveal the information of the 3D objects under 25 % spectrum coverage. From an imaging experiment through a partially transmissive occluder, we we find the reflectivity and the depth map obtained by the low-frequency Fourier spectral coverage are significantly better than those obtained reconstructions with complete spectral coverage. These preliminary results indicate TOF 3D Fourier GI has potential advantages in the removal of netting. [ABSTRACT FROM AUTHOR]