Objective Selecting an appropriate method to analyze images obtained with similar imaging systems and with similar image resolution values but clearly different image quality is challenging. Traditional resolution evaluation methods, such as Rayleigh criterion, Abbe criterion, and FWHM, are not sufficiently reproducible to evaluate the resolution of an actual image and are not universal among different systems. Theoretically, the point spread function (PSF) size of laser scanning confocal and two-photon microscopes is fixed; however, the actual imaging resolution is affected by many other factors. SRM systems, such as SIM, STED, PALM, and STORM, achieve super-resolution by PSF modulation technology or single molecule positioning technology. However, the theoretical resolution of these systems is only related to the limited experimental conditions that can be achieved in practice, such as photobleaching, phototoxicity, and molecular positioning accuracy. Thus, there is no fixed resolution. Therefore, traditional resolution evaluation methods cannot be applied to all systems simultaneously. Here, we adopt a resolution evaluation method based on sectioned Fourier shell correlation (sFSC) , which is an image-based method that does not require any a priori information and can be directly used to calculate the resolution of a given image. We expect that this method will be used to evaluate and compare the imaging capabilities of different imaging systems and can be applied to optimize image restoration. Methods We adopt a resolution evaluation method based on frequency domain correlation. First of all, we use the checkerboard method to divide the original image by pixel into two groups that have the same details but uncorrelated noise. Then, we apply a Fourier transform to obtain the spectrum diagram of all the images. After that, the corresponding strength values in the wedge shell selector are substituted to a correlation calculation formula until all frequency shells and azimuths are completed. In the next step, the cutoff frequency of each azimuth angle is calculated. Here, the cutoff frequency is defined as the frequency when the correlation value drops to 1 / 7 . Finally, the resolution result is calculated according to the reciprocal of the cutoff frequency under each azimuth angle. Then, the sFSC resolution curve, which is azimuth angle dependent, is plotted. In addition, for image restoration, 3D effective PSF can be modeled with the sFSC resolution result as the input to a deconvolution algorithm (Fig. 4). Results and Discussions As a resolution evaluation method, sFSC is very sensitive to the image signal-to-noise (SNR) as well as all sample and system dependent factors; consequently, sFSC can accurately calculate the actual imaging resolution of the system. Compared with the results of FWHM, a commonly used resolution measurement method, the resolution results calculated by the proposed sFSC method can better reflect the overall quality of the image input, not just the ROI quality (Fig. 3) . To obtain better microscopic image restoration, it is very important to accurately model the imaging PSF of the target system. Given the sensitivity of the sFSC method to image resolution, theoretically the PSF fitted according to its resolution results will be closer to the system imaging PSF. In Wiener filtering deconvolution image restoration, the lateral and the axial resolution of the reconstructed image are improved by 14. 5 yo and 33. 2 yo , respectively ( Fig. 5, Tables 2 and 3 ) . Compared with the PSF deconvolution results obtained by FWHM measurement and theoretical resolution calculation, the PSF based on sFSC fitting can better recover image details and improve image signal-to-noise ratio when used as the input to the deconvolution algorithm (Figs. 6 and 7) . According to the evaluation results of a blind image blur evaluation algorithm and the proposed sFSC method on a reconstructed image, we find that, compared with traditional PSF fitting methods, after sFSC-based deconvolution restoration both the image quality and resolution have improved (Tables 4 and 5) . Conclusions Considering a two-photon imaging system as an example, this paper verifies the effectiveness of the sFSC-based 3D image resolution evaluation method by comparing the results of the sFSC method with the theoretical calculation method and FWHM. Regarding image restoration, considering a confocal microscopic system as an example, the 3D PSF model obtained using sFSC results can be used for deconvolution image restoration. This restoration process can effectively retain the texture details and improve the 3D resolution. In Wiener filtering deconvolution image restoration, the lateral and the axial resolution of the reconstructed image are improved by 14 . 5%, and 33.2% , respectively.
