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

Abstract

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 $2.19$ $μm$. 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 $3.60$ $μm$ ($1.33$ $μm$) is achieved in object space after the simple relay (adding a $5 \times$ microscope) over a field of approximately $1$ $μm$ $\times$ $1$ $μm$ ($200$ $μm$ $\times$ $200$ $μm$). The residual errors are likely dominated by diffraction artifacts in the features used for correction.

Figures (4)

• Figure 1: Layout of test setups produced using Zemax OpticStudio. Distance between the OAPs ($d_1$) is $\sim \qty{86}{\centi \meter}$ for setup 1 and $\sim \qty{66}{\centi \meter}$ for setup 2. Folding mirrors, used for alignment and for orienting OAP 3 under physical constraints, are not depicted. Components are not drawn to scale. OAP 1 is located $\qty{101.6}{\milli \meter}$ below OAP 2 in the optical tweezers system.
• Figure 2: (a) Image (flipped vertically) of the resolution target after the relay in setup 1, with groups 4 and 5 in the field of view. The camera has $640 \times 480$ pixels and a pixel size of $\qty{4.8}{\micro \meter} \times \qty{4.8}{\micro \meter}$. The two sets of points used for the correction, normalized so that they are aligned along the top and the left, are labeled in red and yellow. (b) Similarly labeled image of the same target after the $5 \times$ microscope. Only the smaller groups 6 and 7, at the center in (a), are in the field of view. A scale bar for both images is provided in the distortion-corrected Figure \ref{['fig:undistorted']}.
• Figure 3: Zemax simulations of setup 1 after the relay (both flipped vertically). (a) A $17 \times 17$ grid of paraxial image points are plotted using the Grid Distortion function, with quivers pointing to the corresponding real points. The color represents the distance between the two, normalized by field radius zemax2024. The goal of the distortion correction is to undistort the real points so that they overlap the paraxial points. (b) A digital image of the resolution target from thorlabs is propagated using the Image Simulation function and projected onto a $640 \times 480$ pixel grid to be compared to Figure \ref{['fig:distorted']}(a).
• Figure 4: Distortion-corrected images. (a) Image after the relay (corrected Figure \ref{['fig:distorted']}(a)). The yellow rectangles are overlaid on the edge of the groups to check that the distortion-corrected edges are straight. The squares with cross bars are overlaid on squares on the resolution target to check that the aspect ratio is as expected. (b) Image after the $5 \times$ microscope (corrected Figure \ref{['fig:distorted']}(b)), with the green rectangles and the squares similarly overlaid.