Instruction manual

SPM Fundamentals for the MultiMode
Feedback Gains
Rev. B MultiMode SPM Instruction Manual 35
a similar trace of an irregular, random surface would reveal that each scan line bears little
resemblance to its adjacent line.
The entire purpose of LookAhead gain is to take full advantage of regular features by using every
line to anticipate the next one. In NanoScope software, the LookAhead gain value may be adjusted
between a range of 0 (off) to 16 (maximum). As values are adjusted upward from 0, the
LookAhead gain is weighted to apply more data from the adjacent (lagging) line. Although
LookAhead gain is relatively useless for random surfaces, it is a tremendous help on regular
surfaces.
When LookAhead gain is switched on (> 0), it is the first gain calculated in the feedback process
and is used to weight the integral gain as follows:
That is, the LookAhead-weighted integral gain, , is calculated by subtracting the adjacent
pixel’s Z-axis value from the one immediately next to it, then multiplying this difference by the
LookAhead gain value and summing the product with the current data value. A diagram of the
affected pixels appears as shown here:
Note: Although the LookAhead gain value can be set by the operator to values
between 0 and 1.0, these are not the values plugged into the equation. This is a
digital signal feedback process and the actual value multiplied varies between 0
and 2
24
. A similar rule holds also for both Integral and Proportional gain
At start-up, there is no information yet recorded from an adjacent scan line; therefore, the
LookAhead gain is effectively 0 until three lines have been scanned. This allows the system to
settle down and record data.
Integral Gain and Average Error
The second step in the feedback process uses integral gain to correct for error by averaging
(integrating) the total error. In the ballooning example, Irene kept a running average of the balloon’s
altitude error, then responded by firing the burners or turning them off to bring the balloon closer to
the setpoint altitude. Similarly, the SPM’s feedback process maintains a running average of the
error and responds to it. As we have seen, enabling the LookAhead gain by setting it > 0 conditions
the Integral gain entered by the operator. If LookAhead gain is turned off (= 0), integral gain
enters the feedback process unchanged. The integral gain is then used to calculate a running
average of error as follows:
G
LA
int
z
x
z
(x), (y-1)
z
x+1(),(y-1)
–()G
LA
+=
G
LA
int
Local scan line
Previous scan line
Direction of scan
z
x
z
(x),(y-1)
z
(x+1),(y-1)
Next scan line
z
acc
new
error G
LA
int
⋅ z
acc
old
+=