原子力显微镜反馈参数的理解.doc

对于这两个gain值，在Instruction Manual Software中是这样描述的： 2.3.1. Proportional and Integral GainAn AnalogyTo better understand gains and how they control SPM probes, consider the analogy of a hot air balloon carrying three balloonists. Each rider controls a separate valve on the balloons gas burner. The valves are mounted in parallel, such that if any one valve is open, gas flows to the burners, causing the balloon to rise. Similarly, each balloonist may turn their burner off to reduce altitude. Mounted beneath the balloons gondola is a camera, which automatically takes a photograph of the ground below. The balloons objective is to obtain detailed photographs of the surface. To obtain the highest resolution images, the balloon must track the surface as closely as possible without crashing into it. This poses a dilemma to the balloonists: how to tightly control the balloons position relative to the ground. Because the balloon will drift slightly up and down due to the effects of wind and temperature, the balloonists must establish some minimum altitude as a safety zone.Let us call this the “setpoint” altitude, and let us assume that it is set at an altitude of 100 meters.1 When the terrain is flat, the problem is simplified. The balloonists need only ensure a constant supply of gas is supplied to the balloons burners to keep the balloon aloft. As the terrain becomes hilly, the task becomes more complex. If the terrain rises, the balloonists must respond by firing the burners to lift the balloon. As the balloon clears the hill and terrain drops away, the balloonists must turn the burnersoff to reduce height and continue tracking the terrain. The type and intensity of the balloonists responses to terrain can be modeled in terms of three types of feedback: proportional, integral and LookAhead.2.3.2. Proportional GainProportional gain means that something is done proportionally in response to something else. In the case of our first balloonist, Peter, this means producing hot air in proportion to the balloons altitude above the terrain: where the terrain rises sharply, Peter uses large amounts of gas to lift the balloon; where the terrain is relatively flat, Peter supplies a small, steady amount of gas to maintain the setpoint altitude above the surface. A simple feedback loop emerges in this analogy: let us say Peter uses a range finderevery 30 seconds to determine the distance between the balloon and ground. If the balloon is below its setpoint altitude, he fires the burners. If the balloon is above its setpoint altitude, he turns off the burners to lower the balloon. The higher the proportional gain, the more Peter reacts to changes in altitude. For example, at a proportional gain of 1, if the balloon is 25 meters too low, he opens his valve at 10 liters per second; if the balloon is 50 meters too low, he opens his valve at 20 liters per second. The proportional gain value serves as a multiplier such that at a proportional gain of 2, the gas flow rates are doubled from a proportional gain of 1, and so on. Although this sort of feedback gain works well for simple, linear models, it does not function as well for nonlinear models. There remains always some residualerror which causes the system to approach, but not quite reach, the target state. Assuming that the balloonists wants to get as close as possible without crashing, the response will depend upon, among other things, the balloons speed over the terrain. When the balloon is being carried swiftly, it is necessary to apply feedbackearlier to compensate. (That is, more gas must be used earlier.) On the other hand, if there is little or no wind, the balloon may achieve a closer tracking of the terrain. There may also be sufficient knowledge of the terrain to anticipate its rises andfalls. In order to compensate for these effects, integral and LookAhead gain feedbacks may also be employed. These are discussed next.2.3.3. Integral GainIntegral gain is used to correct the cumulative error between a system and its target state. In the case of the balloon, it is not enough to use only proportional gain. As we have seen, the balloon will maintain a constant error around the setpoint altitude if it relies on proportional gain alone. It is also necessary to consider whether the total error between the balloons actual altitude and its setpoint altitude is increasing or decreasing over some interval of time. To correct for cumulative error, our second balloonist, Irene, utilizes integral gain. Let us assume that Peter announces the balloons altitude every 30 seconds from his range finder. Irene uses a stopwatch and clipboard to record the amount of error ateach measuring interval, averaging the error over a preceding interval of time (e.g., 3 minutes). Irene fires the burners based upon her observations: if she notices that the running average error puts the balloon below the setpoint altitude, she fires theballoons burners, if she notices that the average error puts the balloon above the setpoint, she turns the burners off. The effect of integral gain feedback is to reduce total error by addressing error over a longer period of time. This tends to smooth out the short-term, fluctuating effects of proportional gain while narrowing the error closer to the setpoint value. Unfortunately, if the integral gain is set too high, there is a tendency to overshoot the setpoint. Therefore, integral gain is highly sensitive and must be used carefully.如何分析原子力显微镜的相位（phase）图？作为轻敲模式的一项重要的扩展技术，相位模式是通过检测驱动微悬臂探针振动的信号源的相位角与微悬臂探针实际振动的相位角之差（即两者的相移）的变化来成像。引起该相移的因素很多，如样品的组分、硬度、粘弹性质等。因此利用相位模式，可以在纳米尺度上获得样品表面局域性质的丰富信息。迄今相位模式已成为原子力显微镜的一种重要检测技术。值得注意的是，相移模式作为轻敲模式一项重要的扩展技术，虽然很有用。但单单是分析相位模式得到的图像是没有意义的，必须和形貌图相结合，比较分析两个图像才能得到你需要的信息。Phase Imaging: Beyond Topography Phase Imaging is a powerful extension of Tapping Mode Atomic Force Microscopy (AFM) that provides nanometer-scale information about surface structure often not revealed by other SPM techniques. By mapping the phase of the cantilever oscillation during the TappingMode scan, phase imaging goes beyond simple topographical mapping to detect variations in composition, adhesion, friction, viscoelasticity, and perhaps other properties. Applications include identification of contaminants, mapping of different components in composite materials, and differentiating regions of high and low surface adhesion or hardness. In many cases, phase imaging complements lateral force microscopy (LFM) and force modulation techniques, often providing additional information more rapidly and with higher resolution. Phase imaging is as fast and easy to use as TappingMode AFM - with all its benefits for imaging soft, adhesive, easily damaged or loosely bound samples - and is readily implemented on any MultiMode or Dimension Series SPM with NanoScope III controller equipped with an Extender Electronics Module.In TappingMode AFM, the cantilever is excited into resonance oscillation with a piezoelectric driver. The oscillation amplitude is used as a feedback signal to measure topographic variations of the sample. In phase imaging, the phase lag of the cantilever oscillation, relative to the signal sent to the cantilevers piezo driver, is simultaneously monitored by the Extender Electronics Module and recorded by the NanoScope III SPM controller. The phase lag is very sensitive to variations in material properties such as adhesion and viscoelasticity.Once the SPM is engaged in TappingMode, phase imaging is enabled simply by displaying a second image and selecting the Phase data type in the NanoScope software. Both the TappingMode topography and phase images are viewed side-by-side in real time. The resolution of phase imaging is comparable to the full resolution of TappingMode AFM. Phase imaging can also act as a real-time contrast enhancement technique. Because phase imaging highlights edges and is not affected by large-scale height differences, it pr