Bit rollover

The Delta Tau ACC-14D units have the ability to rollover bits from narrower bit width to larger bit width. That is, if one has an encoder that only provides 16 bits of output but which continues to go in a positive direction when changing from $2^{16}-1=65535$ to 0, this change can be interpreted as going from 65535 to 65536 in position. (Similarly a step from 0 to 65535 can be interpreted as a change from 0 to -1).

This capability is quite useful! For example, the travel range of the XPZT and YZPT piezos is 100 $\mu$m, and the laser interferometer gives a position increment of 632/2048=0.31 nm. As a result we would like to work at a dynamic range of 100:0.00031 or $3.2\times 10^{5}$ or about 18 bits during a scan at a particular (XSTG,YSTG) position. This large bit range is compounded by the fact that the (XSTG,YSTG) positions can be adjusted over a range of perhaps 5 mm, giving a complete range of adjustment of 5000:0.00031 or $1.6\times 10^{7}$:1 or 24 bits. Similarly, we would like to access the full 25 mm travel range of the ZSTG stepper with a resolution at least equal to its encoder step size of 0.074 $\mu$m, which requires a dynamic range of 25000:0.074 or $3.4\times 10^{5}$:1 or about 18 bits.