Sparse sampling of spectral components in Segmented Planar Imaging Detector for Electro-Optical Reconnaissance is an essential limiting factor to the imaging resolution. A dictionary learning method is proposed to improve the imaging quality. The images are segmented into patches, and data are extracted directly from small patches and taken as dictionary elements. By training high-and-low resolution image pairs, a coupled dictionary is obtained. The TV/L1 minimization and alternating direction multiplier method are used to restore high-resolution images. In this way, the quality metric RMSE of images is improved from 20.99 to 14.99, and PSNR from 21.69 dB to 24.62 dB.
The dual wavelength interferometry in digital holography can eliminate 2π ambiguities with a large synthetic wavelength, but the measurement error tends to be amplified. In this paper, a new numerical algorithm is proposed to reduce the amplification error, and further expand the measurement range. The wrapped phase map associated with one wavelength is used to assist unwrapping the phase map associated with the other wavelength. Since these two phase maps correspond to the same step height, an exhaustive searching method is applied. The measurement error will not be amplified linearly with the synthetic wavelength, but controlled at the same level with the single wavelength interferometry. In consideration of the measurement errors such as the environmental vibration, instability of wavelength and so on, a tolerance is set to guarantee the stability of the solution. The performance and feasibility of the proposed algorithm is verified by the numerical demonstration.
KEYWORDS: Reconstruction algorithms, Wavelets, Digital holography, Speckle, Holography, Wavelet transforms, Interferometry, Holograms, Signal to noise ratio
Digital holography is a promising measurement method in the fields of bio-medicine and micro-electronics. But the captured images of digital holography are severely polluted by the speckle noise because of optical scattering and diffraction. Via analyzing the properties of Fresnel diffraction and the topographies of micro-structures, a novel reconstruction method based on the dual-tree complex wavelet transform (DT-CWT) is proposed. This algorithm is shiftinvariant and capable of obtaining sparse representations for the diffracted signals of salient features, thus it is well suited for multiresolution processing of the interferometric holograms of directional morphologies. An explicit representation of orthogonal Fresnel DT-CWT bases and a specific filtering method are developed. This method can effectively remove the speckle noise without destroying the salient features. Finally, the proposed reconstruction method is compared with the conventional Fresnel diffraction integration and Fresnel wavelet transform with compressive sensing methods to validate its remarkable superiority on the aspects of topography reconstruction and speckle removal.
As an important measuring technique, white light interferometry can realize fast and non-contact measurement, thus it is now widely used in the field of ultra-precision engineering. However, the traditional recovery algorithms of surface topographies have flaws and limits. In this paper, we propose a new algorithm to solve these problems. It is a combination of Fourier transform and improved polynomial fitting method. Because the white light interference signal is usually expressed as a cosine signal whose amplitude is modulated by a Gaussian function, its fringe visibility is not constant and varies with different scanning positions. The interference signal is processed first by Fourier transform, then the positive frequency part is selected and moved back to the center of the amplitude-frequency curve. In order to restore the surface morphology, a polynomial fitting method is used to fit the amplitude curve after inverse Fourier transform and obtain the corresponding topography information. The new method is then compared to the traditional algorithms. It is proved that the aforementioned drawbacks can be effectively overcome. The relative error is less than 0.8%.
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