AFM 成像参数AFM imaging parameters

公式与适用条件Formulas and conditions

• p_x = L_x / N_x，p_y = L_y / N_y 像素尺寸 = 范围 ÷ 像素数（假设 N 个像素均分 L）。有的软件用 L/(N−1)，N = 512 时两者差约 0.2%。pixel size = scan size ÷ pixel count (N pixels share L equally). Some software uses L/(N−1); at N = 512 they differ by about 0.2%.
• v = 2·L_x·f （约定 ①，计入回扫）(convention ①, retrace counted) v = L_x·f （约定 ②，只数去程）：针尖相对样品的线速度（去程、回程速度相同；与 L_y 无关）。(convention ②, trace only): tip speed relative to the sample (same in trace and retrace; independent of L_y).
• t_px = 1/(2·f·N_x) ① 1/(f·N_x) ② 每个像素的停留时间 = 去程时间 ÷ 每行像素数。dwell time per pixel = trace time ÷ pixels per line.
• t_frame = N_y / f 整幅图采集时间（每行一个周期、只成一条去程线）。约定 ② 下这只含去程；同时给出“若回扫与去程等速：2N_y/f”。frame acquisition time (one cycle per line, one trace line per cycle). Under ② this counts trace only; “if retrace takes as long as trace: 2N_y/f” is also shown.
• N_min = ⌈2·L_x/d⌉ 奈奎斯特：每个最小特征宽度至少采 2 个像素。Nyquist: at least 2 pixels per smallest feature width.
• 采样提示（经验规则，不是定律）：q = max(p_x, p_y) / R。q > 1 欠采样；0.5 < q ≤ 1 接近临界；0.1 ≤ q ≤ 0.5 较合理；q < 0.1 过采样。阈值 0.1、0.5、1 没有标准出处，基于“每个最小特征至少 2 个像素”和“横向分辨率受针尖尺寸限制”。针尖半径通常是厂家给的标称或上限值，磨损后会变大；真实横向分辨率还取决于样品形貌、成像模式和力。
• Sampling hint (rule of thumb, not a law): q = max(p_x, p_y) / R. q > 1 undersampled; 0.5 < q ≤ 1 near critical; 0.1 ≤ q ≤ 0.5 reasonable; q < 0.1 oversampled. The thresholds 0.1, 0.5 and 1 have no standard source; they follow from “at least 2 pixels per smallest feature” and “lateral resolution is limited by tip size”. The tip radius is usually a nominal or upper-limit value and grows with wear; real lateral resolution also depends on sample topography, imaging mode and force.
• 假设：恒速（忽略折返处加减速和死时间，真实速度略高于上面的 v）；忽略压电蠕变/滞后和慢扫描方向的行间步进时间。本工具只做几何和时间的算术，不判断成像质量，也不给反馈参数建议。
• Assumptions: constant speed (turn-around acceleration and dead time are ignored, so real speed is slightly higher than v); piezo creep/hysteresis and slow-axis stepping time are ignored. Only geometry and timing arithmetic is done; no judgement of image quality and no feedback-parameter advice.

显示位数只是格式，结果准确度受输入精度和所用假设限制；本工具不做不确定度传递。Displayed digits are only formatting; accuracy is limited by your inputs and the assumptions used. No uncertainty propagation is done.