Free-form surfaces have been applied in a wide range of modern optical systems. As a supporting technique for fabricating free-form surfaces, the interferometric null method for testing the surface figure error has very limited flexibility. In this Letter, we report a flexible interferometric null test method which can test free-form surfaces with a very broad departure varying range. In the presented flexible null method, a hybrid refractive and diffractive variable null (HRDVN) is utilized as the flexible null. The HRDVN has superb aberration types adaptability, amplitude adaptability, and moderate phase generating accuracy. A flexible interferometric null testing setup was established using the HRDVN. Its superb adaptive capacity and moderate test accuracy were successfully demonstrated by measuring a free-form surface with rotationally symmetric departure of $173.486\lambda$ ($\lambda =632.8\mathrm{nm}$) and non-rotationally symmetric departure of $23.786\lambda$.

Negative thermal expansion (NTE) lattices are widely used in aerospace engineering where the structures experience large temperature variation. However, the available range of NTE of the current lattices is quite narrow, which severely limits their engineering application. In this paper, we report an inverted trapezoid lattice (ITL) with large NTE. The NTE of the ITL is 2.6 times that of a typical triangular lattice with the same height and hypotenuse angle. Theoretically, with a pin-jointed assumption, the ITL can improve the NTE by order of magnitude if the length ratio of the composite rod is changed. In the presented ITL, a composite rod is utilized as the base of the ITL. The composite rod has large inner NTE. The inverted trapezoid structure converts the inner NTE to the vertical direction contraction and obtains an extra NTE. Finite element simulations and experimental verification by interferometric measurement were conducted to verify the large thermal expansion of the ITL.

Magnetorheological finishing (MRF) is a sub-aperture polishing process, which is often used to correct surface errors and remove sub-surface damage after grinding. A strong correlation exists between the material removal rate and surface roughness in MRF, but current theoretical models are incapable of predicting these two factors at the same time. In this paper, a theoretical model was developed to describe the material removal rate and surface quality after MRF in order to better understand the material removal mechanism of MRF and explain the relationship between surface roughness and material removal rate. Two modes of experiments (uniform polishing and fixed point polishing) were conducted on monocrystalline silicon to obtain the results of surface roughness and removal rate. The experimental results are highly consistent with the theoretical model calculated results. The theoretical model could be a reference for high-efficiency and ultra-smooth MRF process.

To improve the material removal efficiency and surface quality of single-crystal silicon after magnetorheological finishing, a novel green chemical-mechanical magnetorheological finishing (CMMRF) fluid was developed. The main components of the CMMRF fluid are nano-Fe₃O₄, H₂O₂, CH₃COOH, nanodiamond, carbonyl iron powder, and deionized water. The novel CMMRF fluid can simultaneously achieve Ra 0.32 nm (0.47 mm × 0.35 mm measurement area), Ra 0.22 nm (5 μm × 5 μm measurement area), and 1.91 × 10⁻² mm³/min material removal efficiency. Comprehensive studies utilizing a scanning electron microscope and a magnetic rheometer show that the CMMRF fluid has a high mechanical removal effect due to the well-dispersed nanodiamond and nano-Fe₃O₄ particles. The results of Fourier transform infrared spectra and Young’s modulus test reveal the mechanism of the chemical reaction and the mechanical characteristics deterioration of the modified layer. Under co-enhanced chemical and mechanical effects, an ultra-smooth and highly efficient MRF technology for single-crystal silicon is realized.

The profile and concentricity of hemispherical shells affect the frequency split and quality factor of hemispherical resonators. To compensate for machining errors caused by tool wear and tool setting, an on-machine measurement (OMM) method for the profile and concentricity of hemispherical shells in ultra-precision grinding was developed without the removal of workpieces from the machine tool. The OMM utilizes an inductive lever probe to test the inner and outer surfaces of the shell. A standard sphere is utilized to calibrate the relative position of the inductive lever probe at the two different work positions. To enhance the test accuracy of the OMM, a zero-position trigger-sampling method for the inductive lever probe was developed. It was verified to achieve a stable repeatability accuracy of 0.04 μm when using the OMM to realize a single-point sampling. Hemispherical shells were tested using the proposed OMM method. The concentricity test’s accuracy was verified to achieve accuracy better than 1 μm using a coordinate measuring machine and a standard sphere. The accuracy was 0.26 μm for testing the profiles of the hemispherical shell. The proposed OMM system was integrated with an ultra-precision machine tool. It is hoped that this method can help realize the integration function of machining-measurement-compensation.