Workflow for modeling of generalized mid-spatial frequency errors in optical systems.

We propose a workflow for modeling generalized mid-spatial frequency (MSF) errors in optical imaging systems. This workflow enables the classification of MSF distributions, filtering of bandlimited signatures, propagation of MSF errors to the exit pupil, and performance predictions that differentiate performance impacts due to the MSF distributions. We demonstrate the workflow by modeling the performance impacts of MSF errors for both transmissive and reflective imaging systems with near-diffraction-limited performance.

Use of pupil-difference moments for predicting optical performance impacts of generalized mid-spatial frequency surface errors.

In this work, we present a methodology for predicting the optical performance impacts of random and structured MSF surface errors using pupil-difference probability distribution (PDPD) moments. In addition, we show that, for random mid-spatial frequency (MSF) surface errors, performance estimates from the PDPD moments converge to performance estimates that assume random statistics. Finally, we apply these methods to several MSF surface errors with different distributions and compare estimated optical performance values to predictions based on earlier methods assuming random error distributions.

Pupil-difference moments for estimating relative modulation from general mid-spatial frequency surface errors.

Standard surface specifications for mid-spatial frequency (MSF) errors do not capture complex surface topography and often lose critical information by making simplifying assumptions about surface distribution and statistics. As a result, it is challenging to link surface specifications with optical performance. In this work, we present use of the pupil-difference probability distribution (PDPD) moments to assess general MSF surface errors and show how the PDPD moments relate to the relative modulation.

Single-shot phase calibration of a spatial light modulator using geometric phase interferometry.

A vibration-insensitive, single-shot phase-calibration method for phase-only spatial light modulators (SLM) is reported. The proposed technique uses a geometric phase lens to form a phase-shifting radial shearing interferometer to enable common-path measurements. This configuration has several advantages: (a) unlike diffraction-based SLM calibration techniques, this technique is robust against intensity errors due to misalignment; (b) unlike two-beam interferometers, this technique offers a high environmental stability; and (c) unlike intensity-based methods, the phase-shifting capability provides a phase uncertainty routinely in the order of ${2}\pi /100$2π/100.

Precisely calibrated and spatially informed illumination for conventional fluorescence and improved PALM imaging applications.

Spatial light modulation using cost efficient digital micromirror devices (DMD) is finding broad applications in fluorescence microscopy due to the reduction of phototoxicity and bleaching and the ability to manipulate proteins in optogenetic experiments. However, precise illumination by DMDs and their application to single-molecule localization microscopy (SMLM) remained a challenge because of non-linear distortions between the DMD and camera coordinate systems caused by optical components in the excitation and emission path. Here we develop a fast and easy to implement calibration procedure that determines these distortions and matches the DMD and camera coordinate system with a precision below the optical diffraction limit.