## 3 Experiment and Analysis  
The three-dimensional spatial localization of quantum dots in tumor cells is realized by using CdTe/CdS/ZnS as a fluorescent probe to label human osteosarcoma cells and a positioning light path with DH-PSF. The schematic diagram of the DH-PSF 4f positioning optical path system is shown in Figure 7. The laser transmitter generates a beam which triggers the quantum dots inside the cell to produce fluorescence. Then the fluorescence is amplified and captured by the microscope system. Subsequently, the imaging beam enters the 4f positioning light-path system and is modulated by a double-helix point spread function. A double-helix spot image is generated and received by the camera. Finally, it is transmitted to the computer system for further analysis.  
In the first place, tumor cells are labeled by CdTe/CdS/ZnS quantum dots, which were transfected by lipo2000 liposomes. The tumor cells used in this experiment were human osteosarcoma cells (HOS). The complete medium used for culturing cells was made from Dulbecco's modified eagle medium (DMEM) basic medium, 10% fetal bovine serum, and 1% double antibody solution. The tumor cell samples, labeled with CdTe/CdS/ZnS quantum dot probes, were captured and measured on the imaging system platform. The tumor cell samples which were labeled by the quantum dot probes were placed on the objective table of microscope and the excitation of the laser light source was irradiated to the sample through the lower objective lens. The corresponding image was captured by a fluorescence microscope (Olympus IX53, Tokyo, Japan).  
Finally, by adjusting the imaging field, both the bright field and the fluorescence images of a single tumor cell were obtained, as depicted in Figure 8.  
Figure 6: Before and after optimization, the double-helix spot simulation pattern at the focal plane: (**a**) The simulated double spot pattern and the corresponding intensity distribution curve before iterative optimization; (**b**) the simulated double spot pattern and the corresponding intensity distribution curve after iterative optimization.  
Two phase modulators were installed in the DH-PSF positioning light-path system. The first was made by using the optimized algorithm proposed in this paper, and the other was made by using the non-optimization algorithm. The actual images of quantum dots in tumor cells were obtained by modulating the fluorescence imaging of the cells, respectively.  
The image clarity index of the final imaging results was evaluated by the image information entropy [23], which is  
\[E(x,y)=-\sum_{x,y}h(x,y)\log[h(x,y)] \tag{10}\]  
With \(h(x,y)\) representing the acquired image matrix.  
According to [PERSON] et al. [23], the smaller the image information entropy is, the less information is required for image restoration, which means the image is clearer.  
Figure 9 shows the localization images of the quantum dots in the tumor cells with and without optimization, respectively. The calculation shows that the image information entropy with and without optimization was 2.65 and 4.22, respectively. It becomes apparent that the image definition is significantly improved by the optimization process, as the image information entropy is reduced by 37.20%. As a result, the findings of this study strongly  
Figure 8: The experiment of cell labeling: (**a**) the bright field image; (**b**) the fluorescence image.  
Figure 7: Schematic diagram of DH-PSF 4f positioning optical path system.  
suggest that the proposed iterative optimization algorithm significantly improves the main lobe energy concentration.