We design and implement a novel imaging technique that integrates bimodal phase and 3D fluorescence capabilities through aperture segmentation. This approach involves capturing four distinct fluorescence images, mirroring the principles of the Fourier light field microscope and the multi-view reflector microscope, enabling accurate 3D sample reconstruction. Additionally, four brightfield images are acquired for quantitative phase and amplitude reconstruction based on the Kramers-Kronig relations. By combining the strengths of phase imaging, such as digital refocusing, extended depth of field, and non-invasiveness, with the specificity of fluorescence imaging, this method offers a unique imaging solution. Imaging maize roots highlights its exceptional depth of field extension, while imaging a mixture of bacterial cells with and without fluorescent protein tags demonstrates its unique bimodal capabilities.
Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the CRB matrix from above; VUB overestimates the mean CRB by ~34%. However, compared to directly calculating the mean CRB over orientation space, we are able to calculate VUB ~1000 times faster.
Various methods exist for measuring molecular orientation, thereby providing insight into biochemical activities at nanoscale. Since fluorescence intensity and not electric field is detected, these methods are limited to measuring even-order moments of molecular orientation. However, any measurement noise, for example photon shot noise, will result in nonzero measurements of any of these even-order moments, thereby causing rotationally-free molecules to appear to be partially constrained. Here, we build a model to quantify measurement errors in rotational mobility. Our theoretical framework enables scientists to choose the optimal single-molecule orientation measurement technique for any desired measurement accuracy and photon budget.
We present a method to measure the molecular orientation and rotational mobility of single-molecule emitters by designing and implementing a Tri-spot point spread function. It can measure all degrees of freedom related to molecular orientation and rotational mobility. Its design is optimized by maximizing the theoretical limit of its measurement precision. We evaluate the precision and accuracy of the Tri-spot PSF by measuring the orientation and effective rotational mobility of single fluorescent molecules embedded in a polymer matrix.
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