12 
outputs of the computer are converted to eight 
analog voltages, corresponding to the desired x 
and y positions of the four tables. The pulse out 
puts from each optical measuring unit are accu 
mulated in a reversible counter; the state of the 
counter represents the instantaneous position of 
the corresponding table axis. To obtain the servo 
drive error signal, the counter state is converted 
to an analog voltage, which is then subtracted 
from the analog voltage representing the corre 
sponding computed table position. The servos, 
acting in response to the error signal, drive the 
appropriate table axis in a direction to make the 
actual table position equal the computed table 
position. 
Because analog servos are limited in speed, the 
accurately scaled servo error signal is also used 
to move the position of the scanning raster (or 
printout raster) in a direction to nullify the 
effects of any servo error. The response of the 
deflection system is about 1000 times faster than 
the analog servos; the area under investigation 
on the diapositive, or the printout area in the 
film plane, is therefore essentially free from 
delays and identical to the desired value. The 
measuring elements provide counting pulses at 
two-micron intervals, so that approximately 2 18 
pulses are required for the 20 inches (500,000 
microns) of table travel; hence, 18 bits are 
required to represent the position in the com 
puter. Because 18-bit digital/analog converters 
are prohibitive to implement, only the 11 least- 
significant bits of the table positions are trans 
ferred to the analog units ; once the table comes 
under control of the computer, the position error 
will be a very small part of the total range of con 
trol, and the larger bits would be redundant. The 
total range of the digital/analog converters is 
(2048) (2 microns) — 4096 microns (or 0.16384 
inch) of carriage motion. The servo system must 
keep the position error less than half this value 
to prevent ambiguity (as described later). 
The difference between the computed and actual 
table position is found by taking the difference 
between the d-c voltages appearing at the outputs 
of the two digital/analog converters. This is 
accomplished by a differential amplifier, whose 
output is the servo error signal. This output is 
later summed with the desired scan signal for the 
particular table to obtain the composite signal 
used to position the scanning spot. 
The servo error signal is also used in compen 
sating for a problem caused by dropping the larg 
est bits from the positioning unit. The division of 
the table position into 11-bit units, in effect, sets 
up a periodic measuring system in which the 
digital/analog converters change over their full 
range in each period. This is illustrated by scale 
SI in Figure 13, where the numbers represent 
digital/analog outputs for the given table posi 
tion. Suppose that at time A the command posi 
tion is at 6 and the table position at 4; then there 
is a two-unit error signal forcing the table to the 
right. At a later time B, the command position, 
e c , will have exceeded the full count of the digital 
to analog converters. Then the output is, say, 0.3 
instead of 10.3, while the actual position, e t , is 
8.3; the difference signal would be minus 8 
instead of 2. 
This situation is corrected by setting up a sec 
ond scale, S2, displaced from the first by half the 
periodic interval (i.e., an amount equivalent to 
the largest bit used). Conversion between the two 
scales is then obtained by complementing the 
largest bits in both digital/analog units (e c and 
e t ). When the excessive error is observed at B, 
the complementing would take place to shift the 
scale used to S2, where the readings (with the 
correct error difference of two units) would be 
5.3 and 3.3. 
As the system moves to the right, the problem 
recurs at C, where complementing would move the 
scale used back to SI. It is obvious that as long as 
the real error remains below half the interval (5 
units in the diagram), an observed error greater 
than half the interval must be corrected by the 
complementing technique. The periodic interval 
used in the equipment is 4096 microns; opera 
tional speeds and accelerations are limited to 
ranges yielding expected errors that are small 
with respect to the interval.