Thermal error is one of the main sources of machining error of machine tools. Being a key component of the machine tool, the spindle will generate a lot of heat in the machining process and thereby result in a thermal error of itself. Real-time measurement of thermal error will interrupt the machining process. Therefore, this paper presents a machine learning model to estimate the thermal error of the spindle from its feature temperature points. The authors adopt random forests and Gaussian process regression to model the thermal error of the spindle and Pearson correlation coefficients to select the feature temperature points. The result shows that random forests collocating with Pearson correlation coefficients is an efficient and accurate method for the thermal error modeling of the spindle. Its accuracy reaches to 90.49% based on only four feature temperature points—two points at the bearings and two points at the inner housing—and the spindle speed. If the accuracy requirement is not very onerous, one can select just the temperature points of the bearings, because the installation of temperature sensors at these positions is acceptable for the spindle or machine tool manufacture, while the other positions may interfere with the cooling pipeline of the spindle.

Structured illumination microscopy (SIM) was recently adapted to coherent imaging, named structured oblique-illumination microscopy (SOIM), to improve the contrast and resolution of a light-scattering image. Herein, we present high-resolution laterally isotropic SOIM imaging with 2D hexagonal illuminations. The SOIM is implemented in a SIM fluorescence system based on a spatial-light modulator (SLM). We design an SLM pattern to generate diffraction beams at 0° and ± 60.3° simultaneously to form a 2D hexagonal illumination, and undertake calculations to obtain optimal SLM shifts at 19 phases to yield a reconstructed image correctly. Beams of linear and circular polarizations are used to show the effect of polarization on the resolution improvement. We derive the distributions of the electric field of the resultant hexagonal patterns and work out the formulations of the corresponding coherent-scattering imaging for image reconstruction. The reconstructed images of gold nanoparticles (100 nm) confirm the two-fold improvement of resolution and reveal the effect of polarization on resolving adjacent nanoparticles. To demonstrate biological applications, we present the cellular structures of a label-free fixed HeLa cell with improved contrast and resolution. This work enables one to perform high-resolution dual-mode - fluorescence and light-scattering - imaging in a system, and is expected to broaden the applications of SOIM.