Large field-of-view, distortion-corrected off-axis parabolic mirror relay microscope

Off-axis parabolic mirrors (OAPs) are occasionally desirable for specialized applications, but are known to introduce field-dependent astigmatic aberrations. In an experiment where optical tweezers are formed by OAPs, another OAP is added to form a relay configuration with an optional microscope, resulting in near diffraction-limited performance, with a resolution of $2.19$ $\mu m$. The severe radially non-uniform distortion incurred by this configuration, with a long path length and a large field of view, requires software corrections for the microscopic image. To avoid overfitting given the limited features available for calibration at the tweezers focal plane, a distortion model with a reduced set of parameters is selected based on simulation data. Applying the model to experimental data, an average residual error of $3.60$ $\mu m$ ($1.33$ $\mu m$) is achieved in object space after the simple relay (adding a $5 \times$ microscope) over a field of approximately $1$ $\mu m$ $\times$ $1$ $\mu m$ ($200$ $\mu m$ $\times$ $200$ $\mu m$). The residual errors are likely dominated by diffraction artifacts in the features used for correction.