Analytical solution for single-pixel ptychography through linear modeling.

Amplitude-modulated single-pixel ptychography (SPP) enables non-interferometric complex-field imaging of objects. However, the conventional iterative and nondeterministic reconstruction methods, based on the ptychography algorithm, pose challenges in fully understanding the role of critical optical parameters. In response, this paper introduces an innovative analytical approach that establishes a theoretical foundation for the uniqueness of SPP reconstruction results. The proposed method conceptualizes SPP as a system of linear equations in the frequency domain, involving both object and modulated illumination. Solving this equation system reveals a determined solution for the complex object, providing an alternative to iterative and nondeterministic techniques. Through a series of simulations, this approach not only validates the uniqueness of SPP reconstruction, but also explores key properties influencing accuracy.

Microscopic three-dimensional inner stress measurement on laser induced damage.

A three-dimensional (3-D) residual stress detection technique is proposed to detect and evaluate the residual stress occurring in optical components due to repairs carried out at laser induced damage sites. It is possible with a cross-orthogonal reflective photo-elastic setup to obtain complete 3-D information of the residual shearing stress around the damage site. The damaged volume of the optical component is numerically sliced into multilayers for this purpose and reflected light intensity is recorded from each layer. The shearing stress from the reflected light intensity is then calculated based on photo-elasticity theory. The validity of the approach is also verified in experiments where it could measure 3-D residual stress with an axial resolution of 10 µm along the light path.