The authors have no acknowledgements.

1. Acquisition of Gain Data for a Galvanometer Mirror
<ol>
	<li>Fix the galvanometer mirror such that it is stabilized to protect it from damage while oscillating. Not only the galvanometer mirror, but also the body of the galvanometer mirror, moves if not fixed in place using a custom-made metal jig with a circular hole for the galvanometer mirror. Fix the jig onto an optical carrier and an optical bench.</li>
	<li>Connect BNC cables from the AD/DA board through a terminal block to the input and position sockets in the servo driver of the galvanometer mirror.</li>
	<li>Program the sine-wave function generator as a graphical user interface (GUI) using the SDK of the AD/DA board with C++, which is able to set an arbitrary frequency, amplitude, and duration, as shown in Figure 3. 
	NOTE: This customized function generator contributes to cutting the temporal cost for continuous trials in step 1.5, since the trial is conducted many times.</li>
	<li>Set the frequency to vary from 100 Hz to 500 Hz in 100-Hz intervals, and set the amplitude to vary from 10 mV to 500 mV in 10-mV intervals in the GUI. Overall, 250 combinations exist. To test 250 combinations, a double loop is efficient to implement. The first loop is for frequencies from 100 Hz to 500 Hz, which is implemented 50 times. The second loop is for amplitudes from 10 mV to 500 mV, which is implemented for 50 times.</li>
	<li>Add the sine-wave path signal into the AD/DA board for 2,000 samplings as duration in the GUI. Simultaneously record the position signal of the galvanometer mirror to read the analogue value of the AD/DA board. In C++ coding using a library of AD/DA board, use the same thread for writing and reading in programming. Calculate the current angle of galvanometer mirror &#952; (writing information) by this equation 
	<img alt="Equation 2" src="/files/ftp_upload/55431/55431eq2.jpg" /> 
	where t is time, <img alt="Equation 3" src="/files/ftp_upload/55431/55431eq3.jpg" /> is amplitude, &#402; is frequency.</li>
	<li>Save the position signal data as a .csv file and include the value of the frequency and amplitude in its filename.</li>
	<li>Repeat steps 1.4 - 1.6 for 250 iterations.</li>
</ol>
2. Calculation to Get Pre-emphasis Coefficients
<ol>
	<li>Apply a median filter for the csv files (recorded signals) to avoid noise effects. The spatial size of the median filter is 5.</li>
	<li>Run the script to calculate the peak-to-peak value (corresponding with the amplitude multiplied by 2), using MATLAB for each of the csv files, as shown in Figure 4 (the graph represents the data of the sine-wave path).</li>
	<li>Plot the peak-to-peak data on a graph to determine the linearity at each frequency, and limit the usage region of the input amplitude when the plots are nonlinear, as shown in Figure 5. 
	NOTE: The nonlinear part of the graph represents saturation of the PID control; hence, it is advisable to avoid using them to secure the limitation of specification of control.</li>
	<li>Execute linear regression for peak-to-peak data in a spreadsheet to obtain the linear interpolation coefficients of each frequency. In this process, five sets of slopes and intercepts are obtained. They correspond with the frequencies from 100 Hz to 500 Hz at each 100 Hz. An approximation of the straight line of 300 Hz is displayed in Figure 5(A), and the linear interpolation coefficients of each frequency are shown in Table 1.</li>
	<li>Using quadratic multiple linear regression, execute quartic interpolation to obtain the quartic interpolation coefficients (pre-emphasis coefficients) in the spreadsheet for the linear interpolation coefficients of each frequency. The pre-emphasis coefficients are shown in Table 2. 
	NOTE: In this research, the linear interpolation coefficients vary in the form of a quadratic curve; however, other types of functions, such as quadratic and cubic equations, are applied if the error is minimal.</li>
</ol>
3. Online Signal Amplification Based on the Pre-emphasis Technique
<ol>
	<li>Execute the software that calculates the updated input amplitude value <img alt="Equation 5" src="/files/ftp_upload/55431/55431eq5.jpg" /> from the ideal input amplitude value <img alt="Equation 3" src="/files/ftp_upload/55431/55431eq3.jpg" /> and the frequency&#160;&#402; using the pre-emphasis coefficients.
	<ol>
		<li>Save the pre-emphasis coefficients as constant values in the C++ software. When the device is updated, these constant values are also updated.</li>
		<li>Program a function 
		<img alt="Equation 7" src="/files/ftp_upload/55431/55431eq7.jpg" /> 
		in the C++ software and obtain the linear interpolation coefficients. Substitute them for ai, bi, ci, di, and ei from the equation and Table 2.</li>
		<li>Program a function 
		<img alt="Equation 13" src="/files/ftp_upload/55431/55431eq13.jpg" /> 
		in the C++ software and obtain an updated input amplitude value <img alt="Equation 5" src="/files/ftp_upload/55431/55431eq5.jpg" /> to substitute for <img alt="Equation 3" src="/files/ftp_upload/55431/55431eq3.jpg" /> and the linear interpolation coefficients that were obtained in step 3.1.2.</li>
	</ol>
	</li>
	<li>Repeat steps 1.4 - 1.6 for arbitrary times with <img alt="Equation 5" src="/files/ftp_upload/55431/55431eq5.jpg" /> using the pre-emphasis technique in the GUI.NOTE: To avoid saturation of the region of PID control, set 400 mV for up to 200 Hz, 200 mV for up to 300 Hz, 100 mV for up to 400 Hz, and 50 mV for up to 500 Hz.</li>
	<li>Repeat step 2.2 and plot peak-to-peak data as a graph to view the improvement in the gain.</li>
</ol>
4. Experiment on Motion-blur Compensation
<ol>
	<li>Prepare a conveyor belt that can move at 30 km/h using a belt that can adhere to sticky textures. The custom-made conveyor belt is composed with a speed-control motor, an iron rubber belt, and so on. It can be replaced with ready-made conveyor belt which can control speed.</li>
	<li>Print a fine-texture pattern onto printable tape and paste it onto the conveyor belt. 
	NOTE: The pasted texture is shown in Figure 6. The stripes are programmed using a library &#34;ofxPDF&#34; in openFrameworks, and the photographic image is from a stock photo company.</li>
	<li>Set up optical devices such as a camera, a lens, and an illumination, as shown in Figure 2. Place the galvanometer mirror in front of the lens which is connected to the camera, and place the illumination to illuminate the conveyor belt.
	<ol>
		<li>Set the camera frequency to 333 Hz, the exposure time to 1 ms, and the number of pixels to 848 * 960 (width * height).</li>
	</ol>
	</li>
	<li>Synchronize the rotational timing of the galvanometer mirror and the exposure time of the camera. In the software, when the angle of the galvanometer mirror arrives the position where to start exposure, the program sends a software trigger into the camera. The timing of software trigger is illustrated in Figure 7.</li>
	<li>Input the speed of the conveyor belt vt (30 km/h) and the distance from the camera to the conveyor belt L(3.0 m) to calculate required angular velocity &#969;r of the galvanometer mirror in the GUI as in Figure 8.&#160;&#969;r is calculated as follows: 
	<img alt="Equation 18" src="/files/ftp_upload/55431/55431eq18.jpg" /></li>
	<li>Input the frequency &#402;(330.0 Hz) in the GUI as in Figure 8 to calculate original input amplitude <img alt="Equation 3" src="/files/ftp_upload/55431/55431eq3.jpg" />. Calculate&#160;<img alt="Equation 3" src="/files/ftp_upload/55431/55431eq3.jpg" /> as follows: 
	<img alt="Equation 19" src="/files/ftp_upload/55431/55431eq19.jpg" /></li>
	<li>Copy and paste <img alt="Equation 3" src="/files/ftp_upload/55431/55431eq3.jpg" /> into the source code, and rotate the galvanometer with the pre-emphasized control value&#160;&#952; for the galvanometer servo driver as follows: 
	<img alt="Equation 20" src="/files/ftp_upload/55431/55431eq20.jpg" /> 
	where t is time. Figure 7 illustrates how&#160;&#952; is calculated from A.</li>
	<li>Record images when the conveyor belt is moving at vt (30 km/h). 
	NOTE: Figure 9 illustrates the motion of the conveyor belt.</li>
</ol>

<ol>
	<li>Bass, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Handbook Of Optics. 3, (1995).</li><li>Marshall, G. F., Stutz, G. E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Handbook of optical and laser scanning. , (2011).</li><li>Aylward, R. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Advanced+galvanometer-based+optical+scanner+design.">Advanced galvanometer-based optical scanner design.</a> Sensor Rev. 23 (3), 216-222 (2003).</li><li>Duma, V., Rolland, J. P., Group, O., Vlaicu, A., Ave, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Advancements+on+galvanometer+scanners+for+high-end+applications.">Advancements on galvanometer scanners for high-end applications.</a> Proc SPIE. 8936, 1-12 (2014).</li><li>Duma, V. -. F., Lee, K., Meemon, P., Rolland, J. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Experimental+investigations+of+the+scanning+functions+of+galvanometer-based+scanners+with+applications+in+OCT.">Experimental investigations of the scanning functions of galvanometer-based scanners with applications in OCT.</a> Appl Opt. 50 (29), 5735-5749 (2011).</li><li>Wang, C., Shumyatsky, P., Zeng, F., Zevallos, M., Alfano, R. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Computer-controlled+optical+scanning+tile+microscope.">Computer-controlled optical scanning tile microscope.</a> Appl opt. 45 (6), 1148-1152 (2006).</li><li>Jofre, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Fast+beam+steering+with+full+polarization+control+using+a+galvanometric+optical+scanner+and+polarization+controller.">Fast beam steering with full polarization control using a galvanometric optical scanner and polarization controller.</a> Opt Exp. 20 (11), 12247-12260 (2012).</li><li>Liu, X., Cobb, M. J., Li, X. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rapid+scanning+all-reflective+optical+delay+line+for+real-time+optical+coherence+tomography.">Rapid scanning all-reflective optical delay line for real-time optical coherence tomography.</a> Opt lett. 29 (1), 80-82 (2004).</li><li>Li, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Laser+beam+scanning+by+rotary+mirrors.+II.+Conic-section+scan+patterns.">Laser beam scanning by rotary mirrors. II. Conic-section scan patterns.</a> Appl opt. 34 (28), 6417-6430 (1995).</li><li>Duma, V. I. L., Tankam, P. A., Huang, J. I., Won, J. U., Rolland, J. A. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optimization+of+galvanometer+scanning+for+optical+coherence+tomography.">Optimization of galvanometer scanning for optical coherence tomography.</a> Appl opt. 54 (17), 5495-5507 (2015).</li><li>Hayakawa, T., Watanabe, T., Ishikawa, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Real-time+high-speed+motion+blur+compensation+system+based+on+back-and-forth+motion+control+of+galvanometer+mirror.">Real-time high-speed motion blur compensation system based on back-and-forth motion control of galvanometer mirror.</a> Opt Exp. 23 (25), 31648-31661 (2015).</li><li>Hayakawa, T., Watanabe, T., Senoo, T., Masatoshi, I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Gain-compensated+sinusoidal+scanning+of+a+galvanometer+mirror+in+proportional-integral-+differential+control+using+the+pre-emphasis+technique+for+motion-blur+compensation.">Gain-compensated sinusoidal scanning of a galvanometer mirror in proportional-integral- differential control using the pre-emphasis technique for motion-blur compensation.</a> Appl opt. 55 (21), 5640-5646 (2016).</li><li>Visioli, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Practical PID Control. , (2006).</li><li>Vilanova, R., Visioli, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> PID Control in the Third Millennium. , (2012).</li><li>Ortega, R., Kelly, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=PID+Self-Tuners:+Some+Theoretical+and+Practical+Aspects.">PID Self-Tuners: Some Theoretical and Practical Aspects.</a> IEEE Transa Ind Electron. 31 (4), 332-338 (1984).</li><li>Mnerie, C., Preitl, S., Duma, V. -. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mathematical+model+of+a+galvanometer-based+scanner:+simulations+and+experiments.">Mathematical model of a galvanometer-based scanner: simulations and experiments.</a> Proc SPIE. 8789, 878915 (2013).</li><li>Mnerie, C. A., Preitl, S., Duma, V. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Performance+Enhancement+of+Galvanometer+Scanners+Using+Extended+Control+Structures.">Performance Enhancement of Galvanometer Scanners Using Extended Control Structures.</a> 8th IEEE International Symposium on Applied Computational Intelligence and Informatics. , 127-130 (2014).</li><li>Mnerie, C., Preitl, S., Duma, V. -. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Control+architectures+of+galvanometer-based+scanners+for+an+increased+precision+and+a+faster+response.">Control architectures of galvanometer-based scanners for an increased precision and a faster response.</a> Proc of SPIE. 8925, 892500 (2014).</li><li>Farjad-rad, R., Member, S., Yang, C. K., Horowitz, M. A., Lee, T. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+0.4-+m+CMOS+10-Gb/s+4-PAM+Pre-Emphasis+Serial+Link+Transmitter.">A 0.4- m CMOS 10-Gb/s 4-PAM Pre-Emphasis Serial Link Transmitter.</a> IEEE J Solid-State Circuits. 34 (5), 580-585 (1999).</li><li>Buckwalter, J. F., Meghelli, M., Friedman, D. J., Hajimiri, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Phase+and+amplitude+pre-emphasis+techniques+for+low-power+serial+links.">Phase and amplitude pre-emphasis techniques for low-power serial links.</a> IEEE Journal of Solid-State Circuits. 41 (6), 1391-1398 (2006).</li><li>Le, S., Blow, K., Turitsyn, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Power+pre-emphasis+for+suppression+of+FWM+in+coherent+optical+OFDM+transmission.">Power pre-emphasis for suppression of FWM in coherent optical OFDM transmission.</a> Opt exp. 22 (6), 7238-7248 (2014).</li></ol>

The authors have nothing to disclose.

This article presents a procedure capable of expanding the sine-wave frequency range to achieve high-accuracy trajectory tracking with PID control. Because the responsiveness of a galvanometer mirror is limited by its inertia, it is critical to use a galvanometer mirror when the control path is steep. However, in this research, we propose a method to improve the specification of control and then prove the method by obtaining experimental results.
In our procedure, step 2.5 is the most critical...

Various optical actuators and control methods suitable for various optical applications have been proposed and developed1,2. These optical actuators are able to control the optical path; galvanometer mirrors especially offer a good balance in terms of accuracy, speed, mobility, and cost3,4,5. Actually, the advantage offered by the speed and accuracy of galvanometer mirrors has led to the realization of a variety of optical applications, such as target tracking and drawing, scanning control, and motion-blur compensation6,7,8,9,10,11,12. However, in our previous motion-blur compensation system, a galvanometer mirror using a proportional-integral-differential (PID) controller provided a small gain; hence, it was difficult to achieve a higher frequency and a faster speed11.
On the other hand, PID control is a widely-used method, as it satisfies a certain level of tracking accuracy13. A variety of methods have been proposed to correct the gain in PID control. As a typical solution, PID control parameter tuning is conducted manually. However, it takes time and special skill to maintain. A more sophisticated method, an auto-tuning function to automatically determine the parameters, has been proposed and is widely used14. The tracking accuracy for high-speed operations is improved using the auto-tuning function when the proportional gain value P increases. However, this also increases the convergence time and noise in the low-speed range. Hence, the tracking accuracy is not necessarily improved. Although a self-tuning controller can be tuned to set suitable parameters for PID control, the tuning introduces a delay because of the need to obtain suitable parameters; therefore, it is difficult to adopt this method in real-time applications15. An extended PID controller16,17 and an extended predictive controller18 have been proposed to extend general PID control and to enhance the tracking performance of galvanometer mirrors for a variety of tracking paths, such as triangular waves, sawtooth waves, and sine waves. However, in those systems, the galvanometer system was regarded as a black box, whereas a model of the control system was required, and the control system was not regarded as a black box. Hence, those methods require that their model for each galvanometer mirror be updated. Moreover, although Mnerie et al. validated their method of focusing on a detailed output wave and phase, their research did not include the attenuation of the entire wave. In fact, in our previous research11, the gain was significantly decreased when the sinusoidal frequency was high, thereby indicating the necessity to compensate for the gain of the entire wave.
In this research, our procedure for gain compensation with PID control12 is based on the pre-emphasis technique19,20,21&#8212;a method to enhance the quality or speed of communication in communications engineering&#8212;which enables the construction of an experimental system using existing equipment. Figure 1 shows the flow structure. The pre-emphasis technique is able to obtain in advance the desired output value from an input value, where PID control is not effective, even if the galvanometer mirror and its controller are regarded as black boxes. This enables them to expand the frequency and amplitude range in which a gain of 0 dB can be obtained without tuning the PID control parameters.
When the gain is amplified, the response characteristics of the galvanometer mirror generally differ at different frequencies, and therefore, we need to amplify each frequency with amplification coefficients. Thus, a sine wave is suitable for the pre-emphasis technique, as there is only one frequency in each sine wave. In this research, because we apply gain compensation to accomplish motion-blur compensation, the control signal is limited to sine-wave scanning, and the sine-wave signal constitutes a single frequency, unlike other waves, such as triangular and sawtooth waves. Further, the input signal into the galvanometer mirror is updated immediately within the next cycle because of the open loop after the pre-emphasis coefficients are set. In other words, we need to know only the input-to-output ratio to regard the controller as a black box, and detailed modeling is not required. This simplicity allows our system to be easily embedded in applications.
The overall goal of this method is to establish an experimental procedure of motion-blur compensation as an application by gain compensation using the pre-emphasis technique. Multiple hardware devices are used in these procedures, such as a galvanometer mirror, a camera, a conveyor belt, illumination, and a lens. Central software user-developed programs written in C++ also constitute part of the system. Figure 2 shows a schematic of the experimental setup. The galvanometer mirror rotates with gain-compensated angular velocity, thereby making it possible to evaluate the amount of blur from the images.

<table><tbody><tr><td>Galvanometer mirror</td><td>Cambridge Technology</td><td>M3s X axis</td><td></td></tr><tr><td>Custom-made metal jig</td><td>ASKK</td><td>-</td><td>With circular hole for galvanometer mirror</td></tr><tr><td>Optical carrier</td><td>SIGMAKOKI</td><td>CAA-60L</td><td></td></tr><tr><td>Optical bench</td><td>SIGMAKOKI</td><td>OBT-1500LH</td><td></td></tr><tr><td>Oscilloscope</td><td>Tektronix</td><td>MSO 4054</td><td></td></tr><tr><td>AD/DA board</td><td>Interface</td><td>PCI-361216</td><td></td></tr><tr><td>PC</td><td>DELL</td><td>Precision T3600</td><td></td></tr><tr><td>Galvanometer mirror servo controller</td><td>Cambridge Technology</td><td>Minisax</td><td></td></tr><tr><td>Lens</td><td>Nikon</td><td>AF-S NIKKOR 200mm f/2G ED VR II&amp;nbsp;</td><td></td></tr><tr><td>High-speed camera</td><td>Mikrotron</td><td>Eosens MC4083</td><td>Discontinued, but sold as MC4087. The cable connection is different from MC4083</td></tr><tr><td>Conveyor belt</td><td>ASUKA</td><td>-</td><td>With a speed-control motor(BX5120A-A made by Oriental Motor), iron rubber belt(100-F20-800A-J made by NOK), and so on</td></tr><tr><td>Printable tape</td><td>A-one</td><td>F20A4-6</td><td></td></tr><tr><td>Photographic texture</td><td>Shutterstock, Inc.</td><td>231357754</td><td>Printed computer motherboard with microcircuit, close up</td></tr><tr><td>Terminal block</td><td>Interface</td><td>TNS-6851B</td><td></td></tr><tr><td>CoaXPress board</td><td>AVALDATA</td><td>APX-3664</td><td></td></tr><tr><td>MATLAB</td><td>mathworks</td><td>MATLAB R2015a</td><td></td></tr></tbody></table>

gain-compensation methodology for a sinusoidal scan of a galvanometer mirror in proportional-integral-differential control using pre-emphasis techniques

Galvanometer mirrors are used for optical applications such as target tracking, drawing, and scanning control because of their high speed and accuracy. However, the responsiveness of a galvanometer mirror is limited by its inertia; hence, the gain of a galvanometer mirror is reduced when the control path is steep. In this research, we propose a method to extend the corresponding frequency using a pre-emphasis technique to compensate for the gain reduction of galvanometer mirrors in sine-wave path tracking using proportional-integral-differential (PID) control. The pre-emphasis technique obtains an input value for a desired output value in advance. Applying this method to control the galvanometer mirror, the raw gain of a galvanometer mirror in each frequency and amplitude for sine-wave path tracking using a PID controller was calculated. Where PID control is not effective, maintaining a gain of 0 dB to improve the trajectory tracking accuracy, it is possible to expand the speed range in which a gain of 0 dB can be obtained without tuning the PID control parameters. However, if there is only one frequency, amplification is possible with a single pre-emphasis coefficient. Therefore, a sine wave is suitable for this technique, unlike triangular and sawtooth waves. Hence, we can adopt a pre-emphasis technique to configure the parameters in advance, and we need not prepare additional active control models and hardware. The parameters are updated immediately within the next cycle because of the open loop after the pre-emphasis coefficients are set. In other words, to regard the controller as a black box, we need to know only the input-to-output ratio, and detailed modeling is not required. This simplicity allows our system to be easily embedded in applications. Our method using the pre-emphasis technique for a motion-blur compensation system and the experiment conducted to evaluate the method are explained.

The results presented here were obtained using an AD/DA board and a camera. Figure 1 shows the procedure of the pre-emphasis technique; therefore, it is the core of this article. It is unnecessary to set the parameters of the PID control after the initialization state; hence, the online process is significantly simple.
Figure 10 shows the results obtained by applying the pre-emphasis technique t...

Watch this Scientific Journal Video about Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques at Jo

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

We propose a method to extend the corresponding frequency by using a pre-emphasis technique. This method compensates for the gain reduction of a galvanometer mirror in sine-wave path tracking using proportional-integral-differential control.

Galvanometer mirrors are used for optical applications such as target tracking, drawing, and scanning control because of their high speed and accuracy. ...

gain-compensation-methodology-for-sinusoidal-scan-galvanometer-mirror

Universidad San Sebastian

Research

Education

JoVE Journal

JoVE Core

Electrical Engineering

Physics

Engineering

Unit 1

Introduction to Signals and Systems

Direct-Current Circuits

SCIENTISTS IN ACTION

8.6K Views.  University of Tokyo. We propose a method to extend the corresponding frequency by using a pre-emphasis technique. This method compensates for the gain reduction of a galvanometer mirror in sine-wave path tracking using proportional-integral-differential control.

Video: Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces

The non-stationary nature and variability of neuronal signals is a fundamental problem in brain-machine interfacing. We developed a brain-machine interface to assess the robustness of different control-laws applied to a closed-loop image stabilization task. Taking advantage of the well-characterized fly visuomotor pathway we record the electrical activity from an identified, motion-sensitive neuron, H1, to control the yaw rotation of a two-wheeled robot. The robot is equipped with 2 high-speed video cameras providing visual motion input to a fly placed in front of 2 CRT computer monitors. The activity of the H1 neuron indicates the direction and relative speed of the robot's rotation. The neural activity is filtered and fed back into the steering system of the robot by means of proportional and proportional/adaptive control. Our goal is to test and optimize the performance of various control laws under closed-loop conditions for a broader application also in other brain machine interfaces.

We use a closed-loop fly-machine interface to investigate general principles in neuronal control.

The non-stationary nature and variability of neuronal signals is a fundamental problem in brain-machine interfacing. We developed a brain-machine ...

Neuroscience

Scanning-probe Single-electron Capacitance Spectroscopy

The integration of low-temperature scanning-probe techniques and single-electron capacitance spectroscopy represents a powerful tool to study the electronic quantum structure of small systems - including individual atomic dopants in semiconductors. Here we present a capacitance-based method, known as Subsurface Charge Accumulation (SCA) imaging, which is capable of resolving single-electron charging while achieving sufficient spatial resolution to image individual atomic dopants. The use of a capacitance technique enables observation of subsurface features, such as dopants buried many nanometers beneath the surface of a semiconductor material1,2,3. In principle, this technique can be applied to any system to resolve electron motion below an insulating surface.
As in other electric-field-sensitive scanned-probe techniques4, the lateral spatial resolution of the measurement depends in part on the radius of curvature of the probe tip. Using tips with a small radius of curvature can enable spatial resolution of a few tens of nanometers. This fine spatial resolution allows investigations of small numbers (down to one) of subsurface dopants1,2. The charge resolution depends greatly on the sensitivity of the charge detection circuitry; using high electron mobility transistors (HEMT) in such circuits at cryogenic temperatures enables a sensitivity of approximately 0.01 electrons/Hz&frac12; at 0.3 K 5.

Scanning-probe single-electron capacitance spectroscopy facilitates the study of single-electron motion in localized subsurface regions. A sensitive charge-detection circuit is incorporated into a cryogenic scanning probe microscope to investigate small systems of dopant atoms beneath the surface of semiconductor samples.

The integration of low-temperature scanning-probe techniques and single-electron capacitance spectroscopy represents a powerful tool to study the ...

Video-rate Scanning Confocal Microscopy and Microendoscopy

Confocal microscopy has become an invaluable tool in biology and the biomedical sciences, enabling rapid, high-sensitivity, and high-resolution optical sectioning of complex systems. Confocal microscopy is routinely used, for example, to study specific cellular targets1, monitor dynamics in living cells2-4, and visualize the three dimensional evolution of entire organisms5,6. Extensions of confocal imaging systems, such as confocal microendoscopes, allow for high-resolution imaging in vivo7 and are currently being applied to disease imaging and diagnosis in clinical settings8,9.
Confocal microscopy provides three-dimensional resolution by creating so-called "optical sections" using straightforward geometrical optics. In a standard wide-field microscope, fluorescence generated from a sample is collected by an objective lens and relayed directly to a detector. While acceptable for imaging thin samples, thick samples become blurred by fluorescence generated above and below the objective focal plane. In contrast, confocal microscopy enables virtual, optical sectioning of samples, rejecting out-of-focus light to build high resolution three-dimensional representations of samples.
Confocal microscopes achieve this feat by using a confocal aperture in the detection beam path. The fluorescence collected from a sample by the objective is relayed back through the scanning mirrors and through the primary dichroic mirror, a mirror carefully selected to reflect shorter wavelengths such as the laser excitation beam while passing the longer, Stokes-shifted fluorescence emission. This long-wavelength fluorescence signal is then passed to a pair of lenses on either side of a pinhole that is positioned at a plane exactly conjugate with the focal plane of the objective lens. Photons collected from the focal volume of the object are collimated by the objective lens and are focused by the confocal lenses through the pinhole. Fluorescence generated above or below the focal plane will therefore not be collimated properly, and will not pass through the confocal pinhole1, creating an optical section in which only light from the microscope focus is visible. (Fig 1). Thus the pinhole effectively acts as a virtual aperture in the focal plane, confining the detected emission to only one limited spatial location.
Modern commercial confocal microscopes offer users fully automated operation, making formerly complex imaging procedures relatively straightforward and accessible. Despite the flexibility and power of these systems, commercial confocal microscopes are not well suited for all confocal imaging tasks, such as many in vivo imaging applications. Without the ability to create customized imaging systems to meet their needs, important experiments can remain out of reach to many scientists.
In this article, we provide a step-by-step method for the complete construction of a custom, video-rate confocal imaging system from basic components. The upright microscope will be constructed using a resonant galvanometric mirror to provide the fast scanning axis, while a standard speed resonant galvanometric mirror will scan the slow axis. To create a precise scanned beam in the objective lens focus, these mirrors will be positioned at the so-called telecentric planes using four relay lenses. Confocal detection will be accomplished using a standard, off-the-shelf photomultiplier tube (PMT), and the images will be captured and displayed using a Matrox framegrabber card and the included software.

The complete construction of a custom, real-time confocal scanning imaging system is described. This system, which can be readily used for video-rate microscopy and microendoscopy, allows for an array of imaging geometries and applications not accessible using standard commercial confocal systems, at a fraction of the cost.

Confocal microscopy has become an invaluable tool in biology and the biomedical sciences, enabling rapid, high-sensitivity, and high-resolution optical ...

Bioengineering

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators

Mechanically underdamped electrostatic fringing-field MEMS actuators are well known for their fast switching operation in response to a unit step input bias voltage. However, the tradeoff for the improved switching performance is a relatively long settling time to reach each gap height in response to various applied voltages. Transient applied bias waveforms are employed to facilitate reduced switching times for electrostatic fringing-field MEMS actuators with high mechanical quality factors. Removing the underlying substrate of the fringing-field actuator creates the low mechanical damping environment necessary to effectively test the concept. The removal of the underlying substrate also a has substantial improvement on the reliability performance of the device in regards to failure due to stiction. Although DC-dynamic biasing is useful in improving settling time, the required slew rates for typical MEMS devices may place aggressive requirements on the charge pumps for fully-integrated on-chip designs. Additionally, there may be challenges integrating the substrate removal step into the back-end-of-line commercial CMOS processing steps. Experimental validation of fabricated actuators demonstrates an improvement of 50x in switching time when compared to conventional step biasing results. Compared to theoretical calculations, the experimental results are in good agreement.

The robust device design of fringing-field electrostatic MEMS actuators results in inherently low squeeze-film damping conditions and long settling times when performing switching operations using conventional step biasing. Real-time switching time improvement with DC-dynamic waveforms reduces the settling time of fringing-field MEMS actuators when transitioning between up-to-down and down-to-up states.

Mechanically underdamped electrostatic fringing-field MEMS actuators are well known for their fast switching operation in response to a unit step input ...

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Plasmonics, which are based on the collective oscillation of electrons due to light excitation, involve strongly enhanced local electric fields and thus have potential applications in nonlinear optics, which requires extraordinary optical intensity. One of the most studied nonlinearities in plasmonics is nonlinear absorption, including saturation and reverse saturation behaviors. Although scattering and absorption in nanoparticles are closely correlated by the Mie theory, there has been no report of nonlinearities in plasmonic scattering until very recently. 
Last year, not only saturation, but also reverse saturation of scattering in an isolated plasmonic particle was demonstrated for the first time. The results showed that saturable scattering exhibits clear wavelength dependence, which seems to be directly linked to the localized surface plasmon resonance (LSPR). Combined with the intensity-dependent measurements, the results suggest the possibility of a common mechanism underlying the nonlinear behaviors of scattering and absorption. These nonlinearities of scattering from a single gold nanosphere (GNS) are widely applicable, including in super-resolution microscopy and optical switches. 
In this paper, it is described in detail how to measure nonlinearity of scattering in a single GNP and how to employ the super-resolution technique to enhance the optical imaging resolution based on saturable scattering. This discovery features the first super-resolution microscopy based on nonlinear scattering, which is a novel non-bleaching contrast method that can achieve a resolution as low as l/8 and will potentially be useful in biomedicine and material studies.

Saturable and reverse saturable scattering were discovered in isolated plasmonic particles and adopted as a novel non-bleaching contrast method in super-resolution microscopy. Here the experimental procedures of detecting and extracting nonlinear scattering are explained in detail, as well as how to enhance resolution with the aid of saturated excitation microscopy.

Plasmonics, which are based on the collective oscillation of electrons due to light excitation, involve strongly enhanced local electric fields and thus ...

Implementation of a Nonlinear Microscope Based on Stimulated Raman Scattering

Stimulated Raman scattering (SRS) microscopy uses near-infrared excitation light; therefore, it shares many multi-photon microscopic imaging properties. SRS imaging modality can be obtained using commercial laser-scanning microscopes by equipping with a non-descanned forward detector with proper bandpass filters and lock-in amplifier (LIA) detection scheme. A schematic layout of a typical SRS microscope includes the following: two pulsed laser beams, (i.e., the pump and probe directed in a scanning microscope), which must be overlapped in both space and time at the image plane, then focused by a microscope objective into the sample through two scanning mirrors (SMs), which raster the focal spot across an x-y plane. After interaction with the sample, transmitted output pulses are collected by an upper objective and measured by a forward detection system inserted in an inverted microscope. Pump pulses are removed by a stack of optical filters, whereas the probe pulses that are the result of the SRS process occurring in the focal volume of the specimen are measured by a photodiode (PD). The readout of the PD is demodulated by the LIA to extract the modulation depth. A two-dimensional (2D) image is obtained by synchronizing the forward detection unit with the microscope scanning unit. In this paper, the implementation of an SRS microscope is described and successfully demonstrated, as well as the reporting of label-free images of polystyrene beads with diameters of 3 &#181;m. It is worth noting that SRS microscopes are not commercially available, so in order to take advantage of these characteristics, the homemade construction is the only option. Since SRS microscopy is becoming popular in many fields, it is believed that this careful description of the SRS microscope implementation can be very useful for the scientific community.

In this manuscript, the implementation of a stimulated Raman scattering (SRS) microscope, obtained by the integration of an SRS experimental set-up with a laser scanning microscope, is described. The SRS microscope is based on two femtosecond (fs) laser sources, a Ti-Sapphire (Ti:Sa) and synchronized optical parametric oscillator (OPO).

Stimulated Raman scattering (SRS) microscopy uses near-infrared excitation light; therefore, it shares many multi-photon microscopic imaging properties. ...

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Optical phased arrays (OPAs) can produce low-divergence laser beams and can be used to control the emission angle electronically without the need for moving mechanical parts. This technology is particularly useful for beam steering applications. Here, we focus on OPAs integrated into SiN photonic circuits for a wavelength in the near infrared. A characterization method of such circuits is presented, which allows the output beam of integrated OPAs to be shaped and steered. Furthermore, using a wafer-scale characterization setup, several devices can easily be tested across multiple dies on a wafer. In this way, fabrication variations can be studied, and high-performance devices identified. Typical images of OPA beams are shown, including beams emitted from OPAs with and without a uniform waveguide length, and with varying numbers of channels. In addition, the evolution of output beams during the phase optimization process and beam steering in two dimensions is presented. Finally, a study of the variation in the beam divergence of identical devices is performed with respect to their position on the wafer.

Here, we describe the operation of a SiN integrated photonic circuit containing optical phased arrays. The circuits are used to emit low divergence laser beams in the near infrared and steer them in two dimensions.

Optical phased arrays (OPAs) can produce low-divergence laser beams and can be used to control the emission angle electronically without the need for ...

Time-Domain Interpretation of PD Control

Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive error signal generates a rapidly rising positive motor torque. This surge in torque leads to significant output overshoot and oscillations, attributed to the high force and insufficient damping. The system&#39;s output exceeds the desired value, reflecting the proportional control&#39;s excessive initial correction and weak resistance.
In the second phase, a negative error signal produces negative motor torque, which decelerates the output, causing it to undershoot the target. This undershoot indicates the system&#39;s tendency to overcompensate in the opposite direction after the initial overshoot. The torque reduction in this phase slows down the output, but the absence of adequate damping results in oscillatory behavior.
During the final phase, positive motor torque reappears, reducing the undershoot from the previous phase. Each oscillation sees a diminishing error amplitude, progressively stabilizing the system&#39;s output. The high initial correction and weak resistance that caused the overshoot are counterbalanced by increased resistance and reduced corrective force in this phase.
PD control effectively addresses these issues by introducing anticipatory adjustments based on the slope of the error signal. This anticipatory mechanism allows the system to predict and correct its direction, mitigating excessive overshoot and reducing the amplitude of oscillations. By adjusting the system&#39;s response rate, PD control fine-tunes the initial correction force and enhances resistance, leading to smaller overshoots and undershoots. Consequently, the system achieves a more stable and controlled output.

Consider a motor system with only proportional control that exhibits high maximum overshoot and oscillation, reflected in the error signal and its rate of ...

Design of Control Systems

KEY TERMS AND CONCEPTS

PI Controller: Design

Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual steady-state errors not corrected by the proportional part.
In an operational amplifier (op-amp)-based PI controller, resistors and a capacitor process the error signal, generating a control signal. The proportional feedback is derived from a resistor, while the integral response comes from a capacitor. Two- and three-op-amp circuit designs exhibit unique transfer functions, with PI controller parameters intrinsically linked to their circuit characteristics. The three-op-amp configuration allows for independent adjustment of proportional and integral gains through specific circuit parameters. Notably, in both circuits, the integral gain is inversely proportional to the capacitor value, which may necessitate large capacitors for effective PI control designs.
The PI controller enhances system performance by modifying the forward-path transfer function through the addition of a zero and a pole. This adjustment boosts system performance and reduces the steady-state error by an order of magnitude. In scenarios where the steady-state error to a given input is constant, the PI controller can reduce this error to zero, provided the system remains stable after compensation.
By addressing both proportional and integral aspects, PI controllers provide a robust solution for steady-state error correction in various applications. Their design, involving specific resistor and capacitor configurations in op-amp circuits, ensures precise control and performance enhancement, making them indispensable in modern control systems.

In applications like automatic brightness adjustment on smartphones, Proportional Integral controllers effectively mitigate steady-state errors for ...

Time and frequency -Domain Interpretation of PI Control

Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller&#39;s transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system&#39;s response and extends settling times. This requires careful design to position the zero near the beginning, away from major poles, and with minimal proportional and integral gains.
The PI controller&#39;s transfer function can typically be depicted in a Bode plot. The visualization helps in understanding the effects of proportional and integral components on system performance. Insufficient proportional gain can lead to steady-state errors, while proper attenuation and stability management involve both proportional and integral aspects.
A critical design consideration is the controller&#39;s negative phase, which can adversely affect system stability. To mitigate this, the corner frequency should be positioned as far left as bandwidth requirements permit, preventing phase lag from reducing the system&#39;s phase margin. For optimal performance, the compensated transfer function should intersect the zero-decibel axis at the new gain crossover frequency, ensuring the desired phase margin.
Additionally, the ratio of integral to proportional gain should be set relative to a significantly lower frequency, balancing the system&#39;s responsiveness and stability.
Designing an effective PI controller involves meticulous selection of integral and proportional gains. This selection process aims to avoid the need for a large capacitor, which is a more significant challenge in PI controllers compared to PD controllers. The large capacitor, if required, can complicate the physical implementation of the controller due to increased size and cost.
Overall, the careful placement of the zero, strategic selection of gains, and consideration of phase margins are essential in designing a PI controller that enhances damping, minimizes steady-state error, and maintains system stability.

Everyday devices like thermostats utilize PI controllers. These can enhance system damping and reduce steady-state error when the controller transfer ...