In the field of optics, the miniaturization and integration of optical systems and optical chips are inevitable trends. Micro lenses, as core devices, are widely used in optical imaging, homogenizing lighting, and optical communication. The accuracy of the surface shape determines the optical properties of micro lenses, making the detection of surface shape errors crucial. During fabrication, the nonlinear effect of photoresist often leads to the appearance of convex or concave annular errors on the micro lens surface. These annular errors significantly impact the optical performance of micro lenses, necessitating the development of a method to quickly detect them. Compared with the traditional profiler, Hartmann wavefront detection, and interferometry methods, this method ensures a simpler test light path, easier operation, and improved test efficiency.
The study focused on the impact of surface shape errors on the distribution of light fields, based on the structure model of the banded error. The position of the boundary (R1) of the light spot formed by different banded errors was calculated following the principles of geometrical optics. Additionally, a method was proposed to determine the surface shape error of the band by analyzing the ratio of light intensity inside and outside the boundary. Through simulations of far-field light spots under different error models, the relationship between the ratio of light intensity inside and outside the boundary and the error value of the band was established. To validate the findings, micro lens arrays with various banded errors were fabricated using micro-nano machining technology. A test light path was then constructed to measure the spot energy distribution under different banded errors. The measured results were basically consistent with the simulated values.
Based on the 3D model structure of the girdle error, the peak to valley (PV) value of the girdle surface error of the micro lens obtained through optical software simulation and experimental testing, is found to be consistent with the interferometer test results. This confirms the validity of the theory of the girdle error, which involves dividing the region by the boundary line (R1) and determining the girdle error using the light intensity ratio inside and outside the region.
We examine the relationship between the PV value of the girdle surface error of the micro lens and the far-field spot. We present the principle of quickly determining the girdle error using the far-field spot and establish a structure model for the girdle error of the micro lens. The energy distribution of the micro lens spot is simulated under different error models, and the relationship between the light intensity ratio in specific regions and the girdle error value is determined. Furthermore, micro lens models with different banded error structures are fabricated using micro-nano machining technology. A test light path consistent with the simulation is constructed, demonstrating the feasibility of analyzing the far-field spot of the micro lens to obtain the girdle surface error. This method can guide the compensation of error values in the micro lens machining process, improve machining accuracy, and facilitate the screening of finished products.
