## 2 Materials and Methods
### Quantitative Image Quality Evaluation  
The quantitative performance of the designed scheme for light microscopy images was evaluated in terms of visual assessment, coefficient of variation (COV), peak signal-to-noise ratio (PSNR), and edge preservation index (EPI) [50], which are defined as:  
\[COV=\frac{S_{I}}{M_{I}}, \tag{5}\]  
\[SNR=20 log_{10}(MAX_{I})-10 log_{10}(MSE)\text{ and } \tag{6}\] \[MSE=\frac{1}{m\pi}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}[R(i,j)-I(i,j)]^ {2},\] \[EPI=\frac{\Gamma(\mathcal{A}_{1}-\overline{\mathcal{A}}_{1},\mathcal{A}_{2}-\overline{\mathcal{A}}_{2})}{\sqrt{(\mathcal{A}_{1}- \overline{\mathcal{A}}_{1},\mathcal{A}_{1}-\overline{\mathcal{A}}_{1})^{ \dagger}}\Gamma(\mathcal{A}_{2}-\overline{\mathcal{A}}_{2},\mathcal{A}_{2}- \overline{\mathcal{A}}_{2})}}\text{ and }\] (7) \[\Gamma(a,b)=\sum_{i,j\in ROI}a(i,j)b(i,j)^{2},\]  
where \(S_{I}\) and \(M_{I}\) are the mean and standard deviation of the input image, respectively; \(MAX_{I}\) is the maximum value of the input data; \(R(i,j)\) is the reference value of \((i,j)\) index without in the reference image of the m\(\times\)n matrix; \(p_{1}\) and \(p_{2}\) are the reference and measured data, respectively; and \(\overline{\mathcal{A}}\overline{\mathcal{P}}\) is the implementation of Laplacian filtering in the region of interest (ROI). The ROI for evaluating COV was set based on the distribution of the simplest tissues.  
To evaluate the usefulness of the proposed algorithm for the blurring effect that appears when focusing on a desired point in each of the three areas, no-reference-based evaluation parameters were used. The no-reference-based evaluation parameters used in this study were the natural image quality evaluator (NIQE) [51] and blind/referenceless image spatial quality evaluator (BRISQUE) [52], which are commonly applied in the imaging field. BRISQUE and NIQE evaluate image quality based on generalized Gaussian distribution (GGD) and multivariate Gaussian (MVG) fitting, respectively, and are expressed as follows [51; 52]:  
\[\mathrm{f}_{GGD}\left(x;a,\sigma^{2}\right)=\frac{\alpha}{2\beta\Delta\left( \frac{1}{a}\right)}exp\left(-\left(\frac{|x|}{\beta}\right)^{\alpha}\right), \tag{8}\]  
\[\mathrm{D}_{MVG}(v_{1},v_{2},\Sigma_{1},\Sigma_{2})=\sqrt{\left(\left(v_{1}-v _{2}\right)^{\intercal}\left(\frac{\Sigma_{1}+\Sigma_{2}}{2}\right)^{-1} \left(v_{1}-v_{2}\right)\right)}, \tag{9}\]  
where \(a\) denotes the shape parameter that controls the distribution of \(\sigma^{2}\); \(\Delta\) is the gamma function; \(\beta=\sigma\sqrt{\frac{\Delta\left(\frac{1}{a}\right)}{\Delta\left(\frac{1}{a} \right)}}\); \(v_{1}\) and \(\Sigma_{1}\) denote the vector and covariance matrices of an ideal image, respectively; and \(v_{2}\) and \(\Sigma_{2}\) denote the vector and covariance matrices of the test image, respectively.  
The gradient magnitude (GM) calculated the magnitude of the slope of image and it determines variation of edges [53]. It can be expressed as follows:  
\[GM(i)=\sqrt{\left(J\bigotimes f_{h}\right)^{2}(i)+\left(J\bigotimes f_{v} \right)^{2}(i)}, \tag{10}\]  
where \(J\) is microscopy image, \(f_{h}\) and \(f_{v}\) are 3 \(\times\) 3 template gradient filter yields the horizontal and vertical direction, and \(\otimes\) operator used the convolution between \(J\) and gradient filter. The high value of gradient magnitude indicates that the sharpness has relatively higher.  
Quantitative evaluation was performed using a total of 20 light microscopic images, and the average value was derived.