Compensation accuracy

It is important to check how accurately the reference system compensates the position error. In order to do that, some positional error should be generated artificially and the final positions after completing the compensation o f this error should be compared to the initial positions.

6.7.1 Experiment

To achieve a step error close to the ideal case, a procedure was developed by the author. This procedure is explained with one experimental example (see Figure 6.22), in which the vertical step error was generated in a vertical flexure. The horizontal step error in a horizontal flexure was also generated in a similar way.

1. Start ~ ‘A ’: The closed loop system is operated with the two PZTs activated. The vertical MM is disabled by disconnection the power line. The horizontal and vertical positions in this situation are the target positions o f the QD.

2. ‘A ’: By the manual control o f the relay amplifier, the relay selects the MM instead o f the PZT. Since the vertical MM was disconnected, the positional error is not compensated by this MM.

3. ‘A ’ ~ ’B ’: The length o f the vertical PZT returns to the offset length (about 4 pm) and the vertical position is away from the original position.

4. ‘B ’: By the manual control o f the relay amplifier again, the relay selects the PZT. Now, the PZT starts to compensate the positional error.

5. ‘B ’ ~ end: After some oscillatory motion, positions are stabilised. These final positions are compared to the original positions to check the compensation accuracy.

The amount o f vertical step error can be adjusted by applying the isolated power to the vertical MM before the event ‘A ’. While the movement o f the MM is within the range o f the PZT compensation, the length o f PZT from the offset length can be varied and thus the amount o f vertical step error can be adjusted.

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Tim e (seconds)

Figure 6.22: The generation of step error function to the vertical flexure o f reference system. The vertical PZT loses control at point ‘A ’ and regains it at point ‘B ’ manually.

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Figure 6.23: The m agnified picture o f Figure 6.22 around event ‘B ’. T he d otted line is the original height value.

All experim ents about com pensation accuracy w ere carried out using a single p o lythene curtain, and w ith air bearing off, in order not to be disturbed by the air tu rb u len ce. The vertical and horizontal displacem ents o f the flexure w ere m easured by the vertical interferom eter and the eddy current sensor respectively. The air bearing w as placed 20 cm aw ay from the fibre tip, to reduce the effect o f the air turbulence.

6.7.2 Compensation accuracy

It w as show n in Figure 6.22 that the vertical and horizontal positions o f the Q D w ere precisely recovered w ithin 20 nm and 30 nm respectively, for 0.7 p m o f vertical step error. T his difference seem s to be related to the reference beam fluctuation, w h ich is explained in the previous section. Since the tim e gap betw een the events ‘A ’ and ‘B ’ is about 15 seconds, the reference beam position on the Q D m ay be different b etw een the tw o events due to the air turbulence, referring to Figure 6.20.

Figure 6.23 show s details o f the vertical displacem ent around event ‘B ’ in F igure 6.22. The am plitude o f the PZT overshooting w as 1.4 pm , 2 tim es the step error. A ctually, the am ount o f overshooting is reduced i f the capacitor in the PZ T am p lifier is

increased. For exam ple, it w as found experim entally that the overshooting w as reduced to 0.5 p m and oscillatory m otion w as also reduced, w hen a 25 p F w as used instead o f 5 pF . N evertheless, this characteristic does not seem to affect the com pensation accuracy. A lso, to use a low capacitance is advantageous in reducing the n um ber o f sw itches betw een the PZT and M M during the travel as explained in section 6.2.5. To reduce the effect o f the reference beam fluctuation during the com pensation accuracy test, the tim e gap betw een the events ‘A ’ and ‘B ’ w as set to 2 -3 seconds and the vertical displacem ents w ere m onitored. In this case, the am ount o f step errors w ere about 0.5 - 0 .6 pm . This process w as carried out thirteen tim es, and it took 70 seconds to finish the experim ent. T his experim ent is sim ilar to the repeatability test o f reference system .

F igure 6.24 show s the height differences o f each com pensation process. All differences w ere w ithin ±10 nm. The reason w hy there is m ore positive difference than negative is thought to be due to the reference beam fluctuation over a relatively long­ term scale. 0.012 0.0 1 0- 0.008 - 0.006-

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Figure 6.24: The difference betw een the original heights and final heights after the com pensation com pleted. The tim e interval betw een tw o events w as about 2 seconds, so that the am ount o f step error is about 0.5 pm .

Therefore, the compensation accuracy can be thought to be less than 10 nm. Also, this experiment proves that the residual hysteresis and cross-talk o f the flexure system after the modification is not a significant problem in the closed loop operation.