Expensive microscope objectives may be required in some microscopy imaging when cheaper objectives introduce optical aberrations that degrade the acquired image to an unacceptable level.

We are trying to create unaberrated images from images acquired with optical aberrations, starting with defocus and spherical aberration. We are using Fourier Optics to simulate the creation of the unaberrated and aberrated images.

We are currently using a phase diverse aberrated image set, which is generated by intentionally introducing known aberrations, as input to a variety of machine learning models to try and learn to do aberration correction. We also want to introduce domain knowledge about the optical imaging process and compare against naive machine learning models.

A fluorescent tag attached to a collagen monomer enables measurement of its location. Two tags could enable measurement of orientation.

However tags bind to locations other than the ends so their spacing is below the resolution of an optical microscope.

Structured illumination microscopy (SIM) utilizes multiple sinusoidal fringe patterns to produce a computed complex image where the phase is related to the tag location. Two orthogonal patterns could determine location of a tag in two dimensions. Surprisingly images of phase from two tags with only one direction of the pattern produce a symmetry pattern that exhibits a symmetry that is coupled to the direction of a line between the tags, even when the spacing of the tags is below the resolution limit of the microscope. Fourier and Radon transforms can be used to automate the process of determining monomer orientation in many cases for very small spacing of the tags.

Collagen monomers combine to form fibrils that are typically a few hundred nanometers in diameter. Measuring the diameter of these fibrils is important in the study of collagen growth and remodeling, but they are below the resolution of optical microscopes. Interference between scattering from the front and back surfaces will vary with diameter and wavelength.

The behavior is complicated by the effects of diffraction at these small dimensions, by the Gaussian illumination of the confocal microscope, and by the possibility of a fibril resting on the coverslip. Finite-Difference Time-Domain calculations can predict the confocal backscatter accurately. With multiple wavelengths the diameter can be inferred from confocal backscatter at multiple wavelengths.

Measuring rotation of objects is important in many fields such as Polarization fluorescence microscopy, biomotors, flow measurement, and bio-assembly. The scattering of light from most non-spherical objects will vary with their orientation, and will be periodic in time with period related to the rotation speed and the structure of the object.

Temporal correlation or spectral analysis can be used to understand the rotational dynamics.

For simple objects with a narrow range of rotation frequencies, spectral analysis is straightforward. In contrast when the rotation is driven by diffusion, analysis becomes more complicated. Further complications include interaction between translation and rotation such as in non-uniform flows, and the complicated motion of non-rigid bodies.