Lens Calibration in Systems for Increasing Resolution by Subpixel Shifts in Optical Microscopy

Optical microscope image quality is directly dependent on the objective lenses selected. In this paper we investigate a method of improving image quality by applying subpixel shifts, i.e. displacements smaller than the resolving power of the objective lens. The increase in spatial resolution is achieved by a mathematical calculation based on the expression of the spectrum of discrete signals, which uses the apparatus of generalized functions. To produce high-resolution elements, it is required to divide the Fourier spectrum generated from a few subpixel shifted images by a coefficient termed the aperture function. The aperture function depends on the kind of lens and can be its characteristic stated in the microscope passport. This paper presents a technique for calibrating a low-resolution lens based on the analysis of images taken with higher quality lenses. After determining the aperture function, you can apply a low-resolution lens to obtain higher quality images similar to the original. Structurally, as the resolution of a micro lens increases, its field of view decreases. At the same time, lenses with lower magnification provide a wider field of view. From a manufacturing point of view, lenses with lower resolution are easier to build, allowing them to exhibit higher metrological performance. The paper also discusses an analytical expression for the image spectrum that can be used for image reconstruction in the field of optical microscopy. Application of the inverse Fourier transform to this expression allows to reconstruct the original image with improved resolution.