Abstract
Super-resolution microscopy enables images to be obtained at a resolution higher than that imposed by the diffraction limit of light. Structured illumination microscopy (SIM) is among the fastest super-resolution microscopy techniques currently in use, and it has gained popularity in the field of cytobiology research owing to its low photo-toxicity and widefield modality. In typical SIM, a fluorescent sample is excited by sinusoidal patterns by employing a linear strategy to reconstruct super-resolution images. However, this strategy fails in cases where non-sinusoidal illumination patterns are used. In this study, we propose the least-squares SIM (LSQ-SIM) approach, which is an efficient super-resolution reconstruction algorithm in the framework of least-squares regression that can process raw SIM data under both sinusoidal and non-sinusoidal illuminations. The results obtained in this study indicate the potential of LSQ-SIM for use in structured illumination microscopy and its various application fields.
Highlights
The resolution of a fluorescence microscope is limited by the optical diffraction effect, which can be described by Abbe’s Equation [1]
structured illumination microscopy (SIM) employs sinusoidal illumination patterns with different directions and initial phases to downshift the high-frequency component of the fluorescence signals of a specimen into the scope of the optical transfer function (OTF), which is otherwise filtered in conventional microscopic optics, leading to resolution loss
Where kx and ky denote frequency coordinates corresponding to spatial coordinates x and y, respectively, and u and v are integration variables. This implies that a high-frequency component is coded into the frequency domain within the range of the OTF weighted by the spectrum of the illumination pattern
Summary
The resolution of a fluorescence microscope is limited by the optical diffraction effect, which can be described by Abbe’s Equation [1]. The high- and low-frequency components are unmixed using the solution of a set of linear equations and shifted to their correct positions in the reciprocal domain With this expanded spectrum, the resulting resolution is almost twice that of widefield fluorescence microscopy. In super-resolution reconstruction of SIM data, the parameters of sinusoidal illumination patterns (e.g., the frequency vectors and initial phases) must be precisely known. This knowledge is difficult and even impossible to obtain if the illumination patterns are distorted due to aberrations caused by the observed specimen, especially in the case of thick biological tissue [10]. Section Results and Discussion describes the validation of our approach using open-access SIM data under sinusoidal and nonsinusoidal illumination
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