1. 高分辨照片的拍摄范围肯定很小，所以傅立叶变换所计算的范围也很小，而选区电子衍射一般都在小倍数拍摄。所以相对来说傅立叶变换是微区的精确信息，电子衍射一般是较大范围的平均信息。

2. FFT变换需要有HRTEM的照片，而SAED一般是在比较低的放大倍数下做，FFT变换的结果和用晶格相计算的结果是相同的。判断单晶需要SAED, FFT可以知道单晶的结晶性优劣

From muchong

Selected Area Electron Diffraction (SAED) and Fast Fourier Transform (FFT) are both used to analyze the structural information of materials at the nanoscale, but they differ in their origin, method of acquisition, and application, even when applied to the same High-Angle Annular Dark Field (HAADF) image.

1. SAED (Selected Area Electron Diffraction):

• Source: SAED is a diffraction technique based on direct electron diffraction in a transmission electron microscope (TEM). In SAED, a beam of electrons passes through a specific region of a sample, and the resulting diffraction pattern is obtained from the interactions between the electrons and the crystalline lattice of the sample.
• How it's acquired: SAED patterns are acquired by focusing the electron beam onto a small, selected area of the sample, usually by using an aperture to limit the region from which the diffraction pattern is collected.
• What it shows: The resulting pattern consists of bright spots or rings that represent the periodicity of atomic planes and give information about the crystal structure, orientation, and any imperfections such as dislocations.
• Key Information: It provides direct crystallographic information like lattice spacing, crystallographic orientation, and degree of crystallinity.

2. FFT (Fast Fourier Transform):

• Source: FFT is a mathematical transformation applied to the intensity contrast of an image (like a HAADF image) obtained in TEM or scanning TEM (STEM).
• How it's acquired: The FFT is computed from a real-space HAADF image, which is typically obtained through scanning a high-angle scattered electron beam over the sample. The HAADF image, rich in atomic contrast due to the Z-contrast (atomic number contrast), contains spatial frequency information, and applying FFT transforms this spatial domain into the frequency domain.
• What it shows: The FFT of an HAADF image highlights reciprocal space information, similar to a diffraction pattern, but derived from the image’s intensity variations rather than directly from the electron diffraction process.
• Key Information: FFTs are useful for analyzing periodic structures and lattice spacings in real-space images, and they can provide insights into lattice orientation, periodicities, and defects.

Key Differences:

• Data Origin:SAED comes from the direct diffraction of electrons passing through the crystal, which gives information about the crystal structure directly. FFT is a post-processing method of a real-space image (like HAADF), transforming spatial frequency data inherent in the image into reciprocal space.
• Acquisition Method:SAED requires physical selection of a region via an aperture during the diffraction experiment. FFT is generated computationally from a recorded image (like HAADF), meaning it can be applied to any region of an image post-acquisition.
• Nature of Information:SAED provides pure diffraction information (reciprocal space) about the sample’s crystal lattice. FFT provides reciprocal space information from an image that may have intensity variations influenced by both atomic number contrast and other real-space features.
• Use Case:SAED is generally used for precise crystallographic studies and identification of crystal phases. FFT is often used to quickly estimate periodicities, orientations, and defects from image data without needing to switch to diffraction mode.

In summary, while both SAED and FFT provide information about the crystalline structure of a material, SAED is obtained from direct electron diffraction, while FFT is a mathematical analysis of a HAADF image. Both can be useful depending on whether you're working directly with diffraction patterns or analyzing an image post-acquisition.