Inverse matrix based phase estimation algorithm for structured illumination microscopy

Abstract

The fast imaging speed and low-intensity requirement of structured illumination microscopy (SIM) have made it one of the most widely used imaging tools in live cell imaging. In order to obtain a high fidelity reconstructed image, a precise estimation of the phase of the illumination pattern is required, especially in those structured illumination based techniques that rely on high-order harmonics to improve the resolution. This can be achieved in one of two fundamental ways. The first is to build a high-end control system capable of shifting a sinusoidal pattern with high precision, while the second is to apply estimation algorithms to determine how patterns shift during post-processing. The latter method is preferred in low-cost super-resolution imaging systems; however, existing algorithms are either time-consuming or fail due to noise and a low modulation depth. In this paper, we introduce additional matrixes into the phase estimation algorithm and propose an inverse matrix based phase estimation method with which analytical solutions of the phases can be determined without iteration. The proposed algorithm was validated via simulation and experiments using a home-made total internal reflection fluorescent SIM system (TIRF-SIM). When tested, the method obtained the true phase even when the modulation depth was low. The source code is now available for download by researchers and others.

Laser interference‐based technique for dynamic measurement of single cell deformation manipulated by optical tweezers

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“…After image processing and fringe center detection, the height of cell was calculated. The differences of refractive index were negligible for different cell parts [28,29], and ranged from 0.0339 to 0.0299 between cells and medium, which is one order of magnitude larger than the standard deviation of mean refractive index 0.002. In such situation, the mean value can be used to indicate the refractive index of whole cell.…”

“…These results indicate that Trypsin-EDTA does not affect the cell volume, as consistent with previous research. For instance, Cao et al used digital holographic microscopy to measure MLO-Y4 cell volume in the process of F-actin disruption, and found that the changes in F-actin distribution have no significant effect on cell volume [29].…”

Aberrations in Structured Illumination Microscopy: A Theoretical Analysis

“…Different numerical apertures (NA) were applied during the simulations, and the specific parameters in each simulation are presented in Table 1. Combining the excitation patterns and the PSFs of the detection path, the images of SIM were reconstructed using the inverse matrix-based phase estimation algorithm ( Figure 1E) [15], and the resolution was estimated using the parameter-free image resolution estimation method [25]. As what we expect, the comparisons between Figures 1C-G illustrate that using the objective with a larger NA generates a smaller PSF and a denser sinusoid pattern, thereby achieving a better resolution.…”

“…A series of images, when the sample is illuminated by the patterns with different phases and orientations, are acquired by a camera. Using the specific SIM reconstruction algorithms [12][13][14][15], the super-resolution image of the sample can be obtained.…”