Configure Luria-Bertani (LB) liquid medium with a 30% concentration of heavy water (Sigma-Aldrich). The Klebsiella pneumoniae resistant strains and Klebsiella pneumoniae sensitive strains were cultured in a 30% heavy water medium, in which the antibiotic meropenem was added at a concentration of 8 µg/µL and cultured overnight at 37 °C. Staphylococcus aureus was cultured using LB medium and culture at 37 °C overnight.

① Take 1 mL each of Klebsiella pneumoniae and Staphylococcus aureus cultured overnight, and centrifuge at 9000 rpm for 2 min to collect the bacterial sediment, and then use sterile water to wash the bacterial sediment three times, each time at 9000 rpm for 2 min, and finally dissolve the bacterial sediment in 1 mL of sterile water, shake and mix well. Take 100 µL of two groups of samples and shake and mix to prepare a mixed sample. 2 µL of the pure samples of Klebsiella pneumoniae and Staphylococcus aureus and the mixed samples of the two groups were spotted on the Raman chip (Champion Optics, Changchun, Jilin, China), respectively, and air-dried for Raman detection.

② Take 1 mL each of Klebsiella pneumoniae resistant strains and Klebsiella pneumoniae sensitive strains cultured overnight, the treatment conditions are the same as above, and the mixed sample is prepared. 2 µL of the pure samples of Klebsiella pneumoniae resistant strains and Klebsiella pneumoniae sensitive strains and the mixed samples of the two groups were spotted on the Raman chip, respectively, and air-dried for Raman detection.

In order to automatically calculate the number of stitched images, image recognition is performed at the same time as the acquisition of small field of view images. The number of identified bacteria in the unoverlapped area of the acquired image is accumulated and compared with the number of bacteria that the user has set to be detected to determine whether to continue acquiring images. To ensure the number of bacteria after splicing, if the accumulated bacteria do not reach the user-set number after scanning a certain line, all bacteria in the next line will be directly scanned.

Filtering and binarization of the acquired small-field images, use the FindContours() function of the OpenCV library to roughly calculate the number of single cells based on the size of the contours found. $n_i$denotes the number of single cells identified in the unoverlapped area of the i-th small-field image acquired, $n$denotes the number of single cells that the user wants to detect. Stop capturing images when $\sum n_i\ge n$.

Finding the spatial mapping link between the pixels of one picture and the pixels of another image and aligning them spatially with the least amount of error is known as image registration. To determine the offset between each field of view, a phase-correlation method is used. The phase correlation technology is based on the Fourier transform search concept. The offset is determined using the cross-power spectrum when there is just a translation between the two pictures. The position of the largest peak in the cross-power spectrum is the relative translation of the two images [20, 21, 22, 23].

Let $f_1(x,y)$ and $f_2(x,y)$ be two images, they have offsets in both the x- and y-axes, as shown in Fig. 2A. $f_1$and $f_2$ are related by the following transformation:

(1)$$f_2(x,y)=f_1(x-x_0,y-y_0)$$

Taking the Fourier transform of both yields the following connection, according to the shift theorem:

(2)$${\mathrm{F}}_2(\mathrm{u},\mathrm{v})={\mathrm{F}}_1(\mathrm{u},\mathrm{v})*{\mathrm{e}}^{-\mathrm{i}*2\pi *\left({\mathrm{u}}^{*}{\mathrm{x}}_0+\mathrm{v}*{\mathrm{y}}_0\right)}$$

The following is the definition of the cross-power spectrum between $f_1$ and $f_2$:

(3)$$\mathrm{R}=\frac{{\mathrm{F}}_1(\mathrm{u},\mathrm{v})*{\mathrm{F}}_2^{*}(\mathrm{u},\mathrm{v})}{\left|{\mathrm{F}}_1(\mathrm{u},\mathrm{v})*{\mathrm{F}}_2^{*}(\mathrm{u},\mathrm{v})\right|}={\mathrm{e}}^{-\mathrm{i}*2\pi *\left(\mathrm{u}*{\mathrm{x}}_0+\mathrm{v}*{\mathrm{y}}_0\right)}$$

* Denotes complicated conjugation. Applying the inverse Fourier transform to formula (3) yields the Dirac function (impulse function) $r={\text{F}}^{-1}\{R\}$, as illustrated in Fig. 2B. This function has a clear, sharp peak at the offset point. This function has a clear, sharp peak at the offset point, while the value at other locations is very near zero. By checking for the pulse function’s peak coordinates, the offset may be discovered:

(4)$$(\mathrm{\Delta }x,\mathrm{\Delta }y)=\left(\frac{1}{2}\right)\mathrm{center}(x,y)-\underset{(x,y)}{\mathrm{argmax}}\{r\}$$

Fig. 2.

Schematic diagram of fusion of two images. (A) Input two images with overlapping areas. (B) The impulse function picture was computed from the two photographs. (C) Direct stitching. Stitching seams frequently show up in panoramic stitched photos because of the associated changes in ambient light and cameras. (D) Pixel-level blending. Following pixel-level fusion processing, the stitching seams can be efficiently eliminated.

Global optimization is necessary to filter out any paired registrations that do not fit into the remainder of the connection network, identify the consistency across all pairs, and decrease errors since there are inconsistencies between the computed image offsets [24]. Fit the displacement connection of the other fields of view concerning the reference field of view using the least squares approach [25]. There is a set of transformations P = (${\overrightarrow{P}}_{\text{MN}}$: M, N$\in$V) where V is the set of all tiles, and each tile ${\overrightarrow{P}}_{\text{MN}}$ translates tile M to overlapping tile N, increasing pairwise alignment quality to the greatest extent possible. Given that F$\in$V is the defined public reference horizon, the optimal configuration is defined as $Q_{\text{VF}}=\{{\overrightarrow{q}}_{\text{MF}}:M,F\in V\}$, which satisfies the following conditions:

(5)$$\arg \underset{{\mathrm{Q}}_{\mathrm{VF}}}{\min }{\sum }_{\mathrm{M}\in \mathrm{V}\backslash \{\mathrm{F}\}}\left({\sum }_{\mathrm{N}\in \mathrm{V}\backslash \{\mathrm{M}\}}{\parallel {\overrightarrow{\mathrm{q}}}_{\mathrm{NF}}-{\overrightarrow{\mathrm{q}}}_{\mathrm{MF}}-{\overrightarrow{\mathrm{P}}}_{\mathrm{MN}}\parallel }^2\right)$$

In general, the overlapping portions will exhibit variances in light and dark intensity and degree of distortion due to the difference in sample time and sampling angle between the two pictures, and there will unavoidably be seams along the edge of the stitching. Therefore, it is necessary to add an illumination compensation algorithm to remove dark corners from the image: divide an image into M $\times$ N small blocks, calculate the average gray level of each small block, obtain the brightness matrix A of the small block, subtract the average gray level of the image from A, and obtain the average gray level of the small block Brightness difference matrix B. Through interpolation, matrix B is interpolated to matrix C with the same size as the original image, and the corrected image is obtained after subtracting matrix C from the gray value of the original image [26].

Above all, it is required to apply a smooth transition fusion procedure to the image to make the spliced image appear to have no seams [24, 27, 28, 29]. Linear fusion of the pixels in the overlapped area is the fusion technique employed in this work (Fig. 2C). By using linear blending, the weight of the pixels in the overlapped region is determined using the contribution block $T_i$’s weighting factor at each point [30]. The closer the pixel $l_i$ in the overlapping region is to the image boundary, the less it contributes to the overall intensity, dim refers to the dimension, representing the horizontal direction and the vertical direction. $l_{i,dim}$means that the coordinates of the pixel are extracted into two components in the horizontal direction and the vertical direction. Similarly, $T_{i,dim}$represents the length and width of the image block as two components in the horizontal direction and vertical direction, so that the shortest distance between $l_i$ and the horizontal boundary and vertical boundary of the image can be calculated respectively. The final fusion effect is shown in Fig. 2D.

The following formula defines the separation between each pixel and the picture border:

(6)$$d_{i,dim}^{\min }=\min (l_{i,dim},\mathrm{size}\left(T_{i,dim}-l_{i,dim}\right))$$

$T_i$ is a block of images. This pixel is simultaneously located in the region where n fields of view overlap. Initial weighting factor $v(T_i)={\prod }_{dim}{d}_{i,dim}^{min}/{\sum }_i^n{\prod }_{dim}{d}_{i,dim}^{min}$, the following is the final weight $w(T_i)$formula, the parameter $\alpha$controls how the overlapping sections are blended:

(7)$$\mathrm{w}\left({\mathrm{T}}_{\mathrm{i}}\right)={\left({\sum }_{\mathrm{j}}\mathrm{v}\left({\mathrm{T}}_{\mathrm{j}}\right)-{\sum }_{\mathrm{k}\ne \mathrm{i}}\mathrm{v}\left({\mathrm{T}}_{\mathrm{k}}\right)\right)}^{\alpha }\text{and}{\sum }_{\mathrm{i}}\mathrm{w}\left({\mathrm{T}}_{\mathrm{i}}\right)=1$$