# Improvement of Fresnel Diffraction Convolution Algorithm
## 3 Experiments and Results
The beam on the reference side is reflected by reflecting mirror M1 and expanded by a 20-times microscope objective (MO1), then filtered into a spherical wave by a pinhole filter (PF1) with a diameter of 10 \(\upmu\)m, and passed through a Fourier lens (L1) with a focal length of 300 mm, where the beam is transformed into a plane wave. The plane wave then enters the microscope objective MO3 and is reflected to the CCD through the beam-splitter prism BS2. The objective side of the microscope objective MO3 has the same parameters as that of the microscope objective MO4 in order to compensate for the phase difference caused by MO4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Variable** & **Value** \\ \hline Wavelength & \(\lambda\) & 0.671 \(\upmu\)m \\ Magnification of microscope & M & 20\(\times\) \\ Pixel size & Pix & 3.45 \(\upmu\)m \\ Resolution of CCD & N’ & 1600 \(\times\) 1200 \\ Pixel number of hologram & N & 1600 \(\times\) 1600 \\ Diffraction distance & d’ & 246 mm \\ Reconstructed distance & d & 98.75 mm \\ Demarcation distance & d\({}_{t}\) & 28.4 mm \\ Radius of reconstructed light & R & 150.8 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of reconstruction of lung cancer section. Figure 7: Light path diagram of holographic microscopy experiment on lung cancer cells. The other light is used as the object light, passed through a beam spatial filter (SF2) with the same parameters as the SF on the reference light side, and then converted into a plane wave to irradiate the lung cancer cell sections. The object light carrying information about the lung cancer cells is imaged by a 20-times microscope objective (MO4) with a distance of 246 mm from the imaging plane to the CCD. During the experiment, a CCD is used to record the image plane amplitude information of the lung cancer cells passing through the microscopic objective MO3, and then the CCD is moved in the direction away from the lung cancer slice to take a Fresnel hologram of the magnified lung cancer cells. The experimental Fresnel holograms are reconstructed using the D-FFT algorithm, the T-FFT algorithm, and the D-FFT (Tukey) algorithm. The image amplitude of the lung cancer cells imaged by the microscopic objective MO4 is used as the reference image for the calculation of PSNR and SSIM, and the curves of PSNR and SSIM are shown in Figure 8. From this, the optimal value of \(\beta\) for this diffraction problem can be determined from the PSNR and SSIM curves. In Figure 8, the PSNR of the reconstructed amplitude obtained by the D-FFT algorithm is 9.5070, the PSNR of the reconstructed amplitude obtained by the T-FFT algorithm is 9.5351, and the PSNR of the reconstructed amplitude obtained by the D-FFT (Tukey) algorithm is 9.7277. The SSIM curves of the three algorithms have the same trend as the PSNR curves. The SSIM value of the D-FFT algorithm is 0.9902, the SSIM value of the T-FFT algorithm is 0.9906, and the SSIM value of the D-FFT (Tukey) algorithm is 0.9908. It can be seen that the PSNR and SSIM of the reconstruction results of the T-FFT algorithm are higher than those of the D-FFT algorithm, which means that the reconstructed intensity of the T-FFT algorithm is closer to the reference image than that of the D-FFT algorithm. The D-FFT algorithm has the lowest PSNR and SSIM, corresponding to the poorest reconstruction quality. This is consistent with theoretical knowledge and simulation results. With \(\beta\) increasing, the reconstruction quality of the D-FFT (Tukey) algorithm will exceed that of the T-FFT algorithm. According to Figure 8, the optimal \(\beta\) = 0.81 leads to the optimal reconstruction quality of the D-FFT (Tukey) algorithm. The results of the Fresnel holographic reproduction experiment under the optimal \(\beta\) are shown in Figure 9.  
As shown in Figure 9A-C, there are oscillations in the reconstruction amplitude of the D-FFT, T-FFT, and T-FFT (rect) algorithms.