Direct time-of-flight (dToF) Lidar system based on single photon avalanche diode (SPAD) sensor plays a key role in the range finding applications because of its high sensitivity, low power consumption and high integrity. The travel time of photons backscattered from a distant target will be measured by the time-to digital-converters (TDC) to create a histogram whose peak location indicates the target distance. However, the bin width of histogram determined by the TDC’s time resolution (LSB) limits the precision of distance measurement. Therefore, sub-bin interpolation methods are introduced to facilitate super precision on-chip distance estimation. The balance between the performance and algorithm complexity must be kept very carefully, to maintain acceptable circuit area occupied, the power consumption and yet not to severely degrade performance. In this paper, we present the experimental results obtained from single point Lidar system composing of the Hangzhou Parity’s MPX102Q SPAD sensor as the receiver and a VCSEL pulse emitter as the transmitter. Several interpolation methods like the simple centroid or center-of-mass (CM) algorithm, and the gaussian mask centroid are applied to process raw histograms. The interpolation results of different algorithms are compared with the direct peak location method to examine their performance including distance resolution and ranging accuracy in different situations. Both sub-bin depth resolution, together with high precision and accuracy (mm level) covering a range up to 15m are achieved by this sensor containing integrated circuits for sub-bin interpolation, and this sensor is with potential to benefit the price-sensitive and power-constrained consumer products like sweeping robots.
Laser speckle has received extensive studies in its basic properties and wide applications. In the majority of research on speckle phenomena, these random optical fields have been treated as scalar optical fields, and the main interest has been in the statistical properties together with applications of the intensity distribution of the speckle patterns. In recent years, increasing attention has been paid to the statistical properties of random electric vector fields referred to as polarization speckle with spatially varying polarization state. Statistical phenomena of random electric vector fields with their close relevance to the theories of speckles, polarization and coherence theory have come to attract emerging interest due to their importance in a variety of areas for practical applications such as biomedical optics, remote sensing, astronomical observation and optical metrology. In this paper, we investigate the dynamic polarization speckle generated by a moving rough-surfaced retardation plate and present an exact analytical expression for the space-time lagged correlation for the stochastic fields within the framework of ABCD matrix theory (Canonical Transforms). General expressions are derived for the spot size, the mean polarization speckle size, the temporal coherence length, and the peak shift of the temporal correlation. Some interesting phenomena associated with dynamic polarization speckle have been predicted including polarization speckle boiling and polarization speckle translation. A general description of these phenomena has been given for arbitrary complex-valued ABCD optical systems.
In this paper, we review our recent work on the statistical properties of polarization speckle generated by a birefringent material with rough surface. After a short introduction of a less-known concept of polarization speckle with its unique properties of random polarization states fluctuating in space, we provide an intuitive explanation of the cause of polarization speckle by vector random walks in the complex plane for two components of the vectorial electric fields. The surface polarization scattering is investigated in terms of the coherence matrix, and a relationship between the statistical properties of the scattered light at the scattering surface and the micro-structure of the anisotropic media has been explored to understand the underlying mechanism. The coherence and polarization properties of the stochastic electric fields at the far field after propagation have been studied in order to describe their spatial structure and evolution. Furthermore, the dynamic properties of polarization speckle have also been investigated in order to investigate the simultaneous reduction of coherence and polarization of the scattered light for the first time.
Based on a rough-surfaced model for a birefringent material with a random interface between its surface and air, we explore the relationship between the correlation area and the spatial degree of polarization of the scattered electric field and the surface-height fluctuations. The statistical properties of the scattered light and the microstructure of the anisotropic material has been investigated based on the coherence matrix. It is shown that achieving depolarization is much more difficult than reducing the coherence for the scattered light introduced by the rough surface of the birefringent material.
Laser speckle has received extensive studies of its basic properties and associated applications. In the majority of research on speckle phenomena, the random optical field has been treated as a scalar optical field, and the main interest has been concentrated on their statistical properties and applications of its intensity distribution. Recently, statistical properties of random electric vector fields referred to as Polarization Speckle have come to attract new interest because of their importance in a variety of areas with practical applications such as biomedical optics and optical metrology. Statistical phenomena of random electric vector fields have close relevance to the theories of speckles, polarization and coherence theory.
In this paper, we investigate the correlation tensor for stochastic electromagnetic fields modulated by a depolarizer consisting of a rough-surfaced retardation plate. Under the assumption that the microstructure of the scattering surface on the depolarizer is as fine as to be unresolvable in our observation region, we have derived a relationship between the polarization matrix/coherency matrix for the modulated electric fields behind the rough-surfaced retardation plate and the coherence matrix under the free space geometry. This relation is regarded as entirely analogous to the van Cittert-Zernike theorem of classical coherence theory. Within the paraxial approximation as represented by the ABCD-matrix formalism, the three-dimensional structure of the generated polarization speckle is investigated based on the correlation tensor, indicating a typical carrot structure with a much longer axial dimension than the extent in its transverse dimension.
Recent research work on speckle patterns indicates a variation of the polarization state during propagation and its nonuniformly spatial distribution. The preliminary step for the investigation of this polarization speckle is the generation of the corresponding field. In this paper, a kind of special depolarizer: the random roughness birefringent screen (RRBS) is introduced to meet this requirement. The statistical properties of the field generated by the depolarizer is investigated and illustrated in terms of the 2x2 beam coherence and polarization matrix (BCPM) with the corresponding degree of coherence (DoC) η and degree of polarization (DoP) P . The changes of the coherence and polarization when the speckle field propagates through any optical system are analysed within the framework of the complex ABCD-matrix theory.
In this paper, a high-dimensional statistical signal processing is revisited with the aim of introducing the concept of vector signal representation derived from the Riesz transforms, which are the natural extension and generalization of the one-dimensional Hilbert transform. Under the new concepts of vector correlations proposed recently, the statistical properties of the vector signal representation for random signal are presented and some applications to speckle metrology developed recently are reviewed to demonstrate the unique capability of Riesz transforms.
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