時域聚焦多光子激發顯微術(temporal focusing multiphoton excitation microscopy，TFMPEM)可以數位微型反射鏡元件(digital micromirror device)來取代閃耀光柵(blazed grating)，其除了如時域聚焦具有軸向侷限大面積多光子激發外，並擁有圖案照明(patterned illumination)的能力；然TFMPEM因其物鏡後焦平面的孔徑沒有被填滿，造成其軸向激發侷限(axial excitation confinement)只有數個微米等級，無法達到繞射極限，使焦平面以外的螢光也一起被激發，上下層螢光互相干擾，導致拍到的影像受到離焦訊號的干擾，影響到影像的縱向解析度。近年來有許多去除離焦背景雜訊的方法被提出，其中包含光學切片結構光照明顯微術(optical section structured illumination microscopy)，然而為了重組一張影像，需要拍攝好幾張影像，如此TFMPEM原有之快速取像的優勢就喪失了。為了提升縱向解析度並保有原先快速取像的能力，可利用只需兩張影像(含一張結構式照射)的HiLo技術與TFMPEM結合，使其縱向解析能力進一步的提升。然而，HiLo的重建結果須依賴手動選擇的一組參數，造成HiLo影像較難自動重建。
本論文提出新的演算法來取代上述技術，首先藉由希爾伯特轉換(Hilbert transform，HT)消除離焦雜訊的方法，來解決影像較難自動重建的問題，此方法只需要兩張相同頻率不同相位的結構式照明影像，我們將兩張影像相減以消除離焦訊號，接著使用HT重建影像，但是由於兩張影像之間的背景有些許的變化，影像相減後會導致顯著的背景殘留，若使用HT將在重建影像產生寄生條紋。因此，進一步使用希爾伯特-黃轉換(Hilbert-Huang transform，HHT)演算法，在使用HT解調變以前，可用經驗模態分解(empirical mode decomposition)，將影像分解為多個本質模態函數(intrinsic mode functions)，然後去除背景殘留項，再對分量進行HT，影像重建後便不會有人造殘留物產生。目前利用HHT去除背景雜訊演算法，軸向解析度提升效果會因結構圖案的空間頻率(kp)高低所影響，空間頻率越高能去除的離焦訊號越多，能有更好的光學切片能力，目前影像軸向解析度分別由2.79 μm提升到1.37 μm在kp= 0.31 μm-1、1.22 μm在kp= 0.36 μm-1、1.08 μm在kp= 0.53 μm-1以及0.73 μm在kp= 1.06 μm-1等。

The temporal focusing multiphoton excitation microscopy (TFMPEM) replaces a blazed grating with a digital micromirror device (DMD). It can excite a large area, has high frame-rate capability and hold the advantage of two-photon excitation. However, the aperture of the back-focal plane of the objective lens is not filled up, so the TFMPEM axial confinement excitation (ACE) is limited to several micrometers. The fluorescence outside the focal plane is excited together, so the image is disturbed by the out-of-focus signal and the contrast of the image is reduced. The poor axial resolution limits many applications. In recent years, many methods have been proposed to increase axial resolution, including optical section structured illumination microscopy. However, we need several images to reconstruct an image, and the high frame-rate capability of TFMPEM is lost. In order to eliminate the background noise and scattering light of TFMPEM, the combination of HiLo algorithm and TFMPEM with only two images (including a structured illumination) is utilized. This method can improve the axial resolution and retain the high frame-rate capability. Nevertheless, the reconstruction result of HiLo strongly depends on a set of parameters that are manually selected by the operator. Because each layer of reconstructed images is subjectively assessed instead of a uniform quantitative standard, HiLo has the problem that is difficult to automatically reconstruct 3D images and measure the axial resolution.
In this thesis, a new algorithm to replace the HiLo technique has been proposed. It can solve the above problem by using Hilbert transform (HT) to eliminate out-of-focus noise. This method requires only two structural illumination images with the same spatial frequency but different phases. The two images are subtracted to remove the out of focus signal. Then we take the signal to Hilbert transform to obtain the signal in the focal plane. However, the background between the two structured illumination images may vary slightly. Subtraction of the image results in significant background residues. Using HT in this case will produce parasitic fringe in the reconstructed image. Therefore, we use Hilbert-Huang transform (HHT). Before we using HT reconstruction, we use enhanced fast empirical mode decomposition (EFEMD) to decompose the image into bidimensional intrinsic mode. After removing the background residue, there will be no artificial residue produced in the reconstructed image. The axial resolution improvement influenced by the spatial frequency. The higher the structure frequency (kp), the more out of focus signal can be removed. The axial resolution is gradually improved from 2.79 μm to 1.37 μm at kp = 0.31 μm-1, 1.22 μm at kp = 0.36 μm-1, 1.08 μm at kp = 0.53 μm-1, and 0.73 μm at kp = 1.06 μm-1.

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