经验丨讲一讲AFM中的两个gain值有何意义，如何分析原子力显微镜的相位（phase）图？
本帖最后由 小柒啊 于 2017-5-11 09:07 编辑对于这两个gain值，在Instruction Manual Software中是这样描述的：
2.3.1. Proportional and Integral Gain—An Analogy
To better understand gains andhow they control SPM probes, consider the analogy of a hot air balloon carryingthree balloonists. Each rider controls a separate valve on the balloon’s gasburner. 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, eachballoonist may turn their burner off to reduce altitude. Mounted beneath theballoon’s gondola is a camera, which automatically takes a photograph of theground below. The balloon’s objective is to obtain detailed photographs of thesurface. To obtain the highest resolution images, the balloon must track thesurface as closely as possible without crashing into it. This poses a dilemmato the balloonists: how to tightly control the balloon’s position relative tothe ground. Because the balloon will drift slightly up and down due to theeffects of wind and temperature, the balloonists must establish some minimumaltitude as a safety zone.
Let us call this the “setpoint” altitude, and let us assume that it is set atan altitude of 100 meters.1 When the terrain is flat, the problem issimplified. The balloonists need only ensure a constant supply of gas issupplied to the balloon’s burners to keep the balloon aloft. As the terrainbecomes hilly, the task becomes more complex. If the terrain rises, theballoonists must respond by firing the burners to lift the balloon. As theballoon clears the hill and terrain drops away, the balloonists must turn theburners off to reduce height and continue tracking the terrain. The type and intensityof the balloonists’responses to terrain can be modeled in terms of three typesof feedback: proportional, integral and LookAhead.
2.3.2. Proportional Gain
Proportional gain means that something is done proportionally in response tosomething else. In the case of our first balloonist, Peter, this meansproducing hot air in proportion to the balloon’s altitude above the terrain:where the terrain rises sharply, Peter uses large amounts of gas to lift theballoon; where the terrain is relatively flat, Peter supplies a small, steadyamount of gas to maintain the setpoint altitude above the surface. A simple feedbackloop emerges in this analogy: let us say Peter uses a range finder every 30 seconds to determine the distance between the balloon and ground. Ifthe balloon is below its setpoint altitude, he fires the burners. If theballoon is above its setpoint altitude, he turns off the burners to lower theballoon. The higher the proportional gain, the more Peter reacts to changes inaltitude. For example, at a proportional gain of 1, if the balloon is 25 meterstoo low, he opens his valve at 10 liters per second; if the balloon is 50meters too low, he opens his valve at 20 liters per second. The proportionalgain value serves as a multiplier such that at a proportional gain of 2, thegas flow rates are doubled from a proportional gain of 1, and so on. Although thissort of feedback gain works well for simple, linear models, it does notfunction as well for nonlinear models. There remains always some residual
error which causes the system to approach, but not quite reach, the targetstate. Assuming that the balloonists wants to get as close as possible withoutcrashing, the response will depend upon, among other things, the balloon’sspeed over the terrain. When the balloon is being carried swiftly, it isnecessary to apply feedback
earlier to compensate. (That is, more gas must be used earlier.) On the otherhand, if there is little or no wind, the balloon may achieve a closer trackingof the terrain. There may also be sufficient knowledge of the terrain toanticipate its rises and
falls. In order to compensate for these effects, integral and LookAhead gainfeedbacks may also be employed. These are discussed next.
P gain：
比例补偿 按比例反应系统的偏差，系统一旦出现了偏差，比例调节立即产生调节作用用以减少偏差。比例作用大，可以加快调节，减少误差，但是过大的比例，使系统的稳定性下降，甚至造成系统的不稳定。
2.3.3. Integral Gain
Integral gain is used to correct the cumulative error between a system and itstarget state. In the case of the balloon, it is not enough to use onlyproportional gain. As we have seen, the balloon will maintain a constant erroraround the setpoint altitude if it relies on proportional gain alone. It isalso necessary to consider whether the total error between the balloon’s actualaltitude and its setpoint altitude is increasing or decreasing over someinterval of time. To correct for cumulative error, our second balloonist,Irene, utilizes integral gain. Let us assume that Peter announces the balloon’saltitude every 30 seconds from his range finder. Irene uses a stopwatch andclipboard to record the amount of error at each measuring interval, averaging the error over a preceding interval of time(e.g., 3 minutes). Irene fires the burners based upon her observations: if shenotices that the running average error puts the balloon below the setpointaltitude, she fires the balloon’s burners, if she notices that the average error puts the balloon abovethe setpoint, she turns the burners off. The effect of integral gain feedbackis to reduce total error by addressing error over a longer period of time. Thistends to smooth out the short-term, fluctuating effects of proportional gainwhile narrowing the error closer to the setpoint value. Unfortunately, if theintegral gain is set too high, there is a tendency to overshoot the setpoint.Therefore, integral gain is highly sensitive and must be used carefully.
I gain：
积分补偿 使系统消除稳态误差，提高无差度。因为有误差，积分调节就进行，直至无差，积分调节停止，积分调节输出一常值。加入积分调节可使系统稳定性下降，动态响应变慢。
I gain 补偿一段时间里累积的误差
P gain 补偿当前误差I gain 比 P gain 更敏感。
P gain应小于I gain的1/2，一般为1/2
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
PhaseImaging is a powerful extension of Tapping Mode Atomic Force Microscopy (AFM)that provides nanometer-scale information about surface structure often notrevealed by other SPM techniques. By mapping the phase of the cantileveroscillation during the TappingMode scan, phase imaging goes beyond simpletopographical mapping to detect variations in composition, adhesion, friction,viscoelasticity, and perhaps other properties. Applications includeidentification of contaminants, mapping of different components in compositematerials, and differentiating regions of high and low surface adhesion orhardness. In many cases, phase imaging complements lateral force microscopy(LFM) and force modulation techniques, often providing additional informationmore rapidly and with higher resolution. Phase imaging is as fast and easy touse as TappingMode AFM -- with all its benefits for imaging soft, adhesive,easily damaged or loosely bound samples -- and is readily implemented on anyMultiMode or Dimension Series SPM with NanoScope III controller equipped withan Extender Electronics Module.
InTappingMode AFM, the cantilever is excited into resonance oscillation with apiezoelectric driver. The oscillation amplitude is used as a feedback signal tomeasure topographic variations of the sample. In phase imaging, the phase lagof the cantilever oscillation, relative to the signal sent to the cantilever'spiezo driver, is simultaneously monitored by the Extender Electronics Moduleand recorded by the NanoScope III SPM controller. The phase lag is verysensitive to variations in material properties such as adhesion andviscoelasticity.
Oncethe SPM is engaged in TappingMode, phase imaging is enabled simply bydisplaying a second image and selecting the Phase data type in the NanoScopesoftware. Both the TappingMode topography and phase images are viewed side-by-sidein real time. The resolution of phase imaging is comparable to the fullresolution of TappingMode AFM. Phase imaging can also act as a real-timecontrast enhancement technique. Because phase imaging highlights edges and isnot affected by large-scale height differences, it provides for clearerobservation of fine features, such as grain edges, which can be obscured byrough topography.
Phase imaging is a powerful tool formapping variations in sample properties at very high resolution. It can beturned on while using TappingMode AFM with no cost in speed or resolution, andall NanoScope users are encouraged to add it to their SPM repertoire. Phaseimaging can complement force modulation and LFM methods, often with superiorimage detail, and can in some cases provide information not revealed by theseor other SPM techniques. The rapidly growing list of phase imaging applicationsincludes characterizing the components of composite materials, mapping ofsurface friction and adhesion, and identification of surface contamination.Phase imaging promises to play an important role in the ongoing study ofmaterial properties at the nanometer scale.
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