Spatial Mode Decomposition Research Articles

Investigation of rotating instability characteristics in an axial compressor with different tip clearances

It is believed that the rotating instability phenomenon originating in the compressor tip region is due to leakage flow, which is closely associated with the blade tip clearance. In this work, we have studied the correlation between the dynamic characteristics of blade tip flow and the size of tip clearance for a single-stage low-speed compressor rotor, so as to unveil the mechanism of rotating instability. The full-passage numerical simulations were carried out to obtain the variations in frequency, circumferential mode, and spatial flow field associated with rotating instability. The results of spatial mode decomposition with open clearance show the number of predominate instability modes identified are 25 and 30, respectively. By diminishing the blade tip clearance, all these unstable modes greatly diminished. The formation and propagation of the tip leakage vortex were described in detail to show the development of rotating instability. Two flow field reduced-order methods, proper orthogonal decomposition and dynamic mode decomposition, were used to analyze the flow field, energy proportion, and stability of related modes under different tip clearances. The results show that the first several modes with strong stability account for a large proportion of energy and make a major contribution to flow unsteadiness. The energy proportion and stability of rotating instability decrease as the tip clearance becomes smaller. The blade-passing frequency and its multiples emerge as the main components of the flow field.

Superresolution Limits from Measurement Crosstalk.

Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. However, realistic measurement devices always introduce finite crosstalk in any such mode decomposition. Here, we show that any nonzero crosstalk leads to a breakdown of superresolution when the number N of detected photons is large. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and N. The scaling of the smallest distance that can be distinguished from noise changes from N^{-1/2} for an ideal measurement to N^{-1/4} in the presence of crosstalk.

Characteristics of fine-scale turbulence noise evaluated by modal analysis

Jet flows are common in daily life such as from high-speed hair dryers, they are also used extensively in industrial settings for drying and cleaning applications. Turbulence noise from jet flows consists of large-scale and fine-scale structures. Modal analysis method with experimental data has already been applied to study the properties of large-scale turbulence noise. In this paper, spatial mode decomposition is used to theoretically analyze fine-scale turbulence noise based on a modified Tam–Auriault (TA) model. This makes our analysis of fine-scale turbulence noise not subject to experimental constraints. Using the proposed method, similarities and differences between the two scales of turbulence noise can be observed. It is found that the zero-order mode of fine-scale turbulence noise depends mainly on the turbulence scale, whereas the non-zero modes depend mainly on the non-compactness of the source. We also calculate the dominant mode at each frequency, which allows a rapid yet accurate prediction of fine-scale turbulence noise to be made. This work helps in understanding the generation and radiation of fine-scale turbulence noise.

Decomposition of aberrated or turbulent wavefronts into a spatial mode spectrum using optical cavities.

It is shown that an aberrated wavefront incident upon a Fabry-Perot optical cavity excites higher order spatial modes in the cavity and that the spectral width and distribution of these modes is indicative of the type and magnitude of the aberration. The cavities are purely passive, and therefore frequency content is limited to that provided by the original light source. To illustrate this concept, spatial mode decomposition and transmission spectrum calculation are simulated on an example cavity; the effects of various phase delays, in the form of two basic Seidel aberrations and a composite of Zernike polynomial terms, are shown using both Laguerre-Gaussian and plane wave incident beams. The aggregate spectral width of the cavity modes excited by the aberrations is seen to widen as the magnitude of the aberrations' phase delay increases.

Measuring the complex orbital angular momentum spectrum and spatial mode decomposition of structured light beams

Light beams carrying orbital angular momentum are key resources in modern photonics. In many applications, the ability of measuring the complex spectrum of structured light beams in terms of these fundamental modes is crucial. Here we propose and experimentally validate a simple method that achieves this goal by digital analysis of the interference pattern formed by the light beam and a reference field. Our approach allows one to characterize the beam radial distribution also, hence retrieving the entire information contained in the optical field. Setup simplicity and reduced number of measurements could make this approach practical and convenient for the characterization of structured light fields.