Increasingly, DAC's are a limiting factor in nanopositioning resolution, especially in the latest millimeter-travel stages. A newly patented technology adds up to 10 bits of resolution to virtually any OEM DAC and popular PC analog I/O boards without hardware modifications and with full compatibility with legacy software. Applications range from scanned-probe microscopy and nanofabrication to advanced lithographies and optical tweezers.
Most motion devices are fundamentally analog. Since today’s is a digital world, an analog drive command is usually generated by a digital-to-analog converter (DAC) chip someplace in the system (Figure 1). Besides being embedded in digital piezo controllers, DACs are commonly used to command analog servos, either from a card in the user’s PC or OEM tool, or embedded into the servo-controller so computer interfaces like RS-232 can be provided.
Figure 1. A Digital-to-Analog Converter generates the voltage which, when amplified, drives a nanopositioner.
DACs are nearly universal in nanopositioning applications. In fact, DAC capabilities are one of the most important parameters defining a nanopositioning system’s ultimate performance- and its limitations.
Operation of DACs is simple enough: a digital number goes in, and an analog voltage comes out. The maximum size of the incoming number defines how fine a voltage increment can be commanded. For example, economical 12-bit DAC cards popular for PC applications can accommodate an incoming integer between 0 and [212-1]: its voltage range is thus divided into 4,096 steps, meaning the resolution is [Range ÷ 4,096]. If the voltage range of the DAC matches the analog input range of the nanopositioning system, then the travel range of the motion device is similarly divided into 4,096 possible locations. A 16-bit DAC would divide the same Range into 65,536 steps, thereby providing sixteen times finer positioning resolution. (It is important to match the DAC Range to the analog input range of the piezo controller. If Range is -10V to +10V but the analog input accepts 0 to +10V, one bit of resolution is lost. The number of addressable positions is reduced by two.)
DAC bitness is thus a limitation to piezo nanopositioning system resolution, as shown in Figure 2. Other system characteristics such as amplifier noise also present resolution bottlenecks, but DAC resolution is probably the most frequently encountered limiter, particularly for longer-travel piezo devices.
Figure 2. DAC bitness limits fine position control.
Until now, a DAC’s limitations were permanent characteristics of the specific chip. A PC user might choose between 12- and 16-bit cards for their PC; higher-resolution cards are uncommon, and most users prefer to stick with popular and well-supported National Instruments I/O cards, which generally top out at 16 bits. Used with PI’s P-628.2CD or P- 625.1CD PIHera® stages, with 1,000 and 500μm travels respectively, this results in 15 and 8nm resolution. Many applications could use better resolution than that. An entry-level 12-bit card would provide only 0.23 and 0.12μm resolution with these stages-coarser than many motorized stages provide. OEM users might choose an 18-, 20- or 24-bit DAC for their custom circuit design, but many high-bitness DACs are optimized for audio use and can present drift issues or other drawbacks. (Well designed all-digital controllers like PI’s E-710 and E-750.CP put their DAC inside the servo loop, eliminating DAC drift issues.) And sometimes a new design is not economically practical, yet user demands for higher and higher resolution persist.
More Performance from Existing DACs
Missing in the discussion above is time. DACs are typically very fast compared to motion devices, even those as responsive as a piezo-driven mechanisms. A fast analog update rate is what allows DACs to generate smooth arbitrary waveforms. It also means there is unused analog-output bandwidth in a typical nanopositioning setup.
PI’s patented HyperBit™ technology leverages this under-utilized time-domain capacity, converting it into many additional bits of physical positioning resolution with no loss of system bandwidth, stability or accuracy. HyperBit™ uses highfrequency modulation of the least-significant bit(s) of a DAC to accomplish this. For example, the LSB can be dithered using pulse-width modulation at a frequency where the system is unresponsive, acting like a flywheel to provide smooth, stable motion with far higher resolution than the DAC’s native resolution (Figure 3).
Figure 3. (above) The desired triangle positioning command sequence from Figure 2 is limited by DAC bitness, corresponding to the red lines in Figure 2. (below) With HyperBit™, the desired positioning sequence is achieved, corresponding to the white dots in Figure 2.
HyperBit™ can be implemented in software or hardware. It is available for license by OEM designers, and is a cost-effective software option for research and OEM applications. Implementations and options have included HyperBit-enabled LabVIEW subVIs, a Windows DLL for programmers using C or other popular languages, and HDL for designers using FPGAs. Point-to-point and waveform actuation are supported, open- or closedloop. Since the time-domain capability of the DAC would otherwise go unused, there is no impact on system bandwidth, responsiveness or speed.
Theory and Application
The theory of HyperBit™ is straightforward (Equation 1):
- Available DAC rate varies from chip to chip, and with interface (e.g. slow PCMCIA vs. fast PCI)
- PWM frequency is chosen to lie in the region of sluggish plant responsiveness (e.g. well above Fres)
For example, when calling .DLL, .LIB or subVI forms of HyperBit™, the user need only input their DAC’s update-rate capability and choose a LSB PWM rate somewhere above their mechanical resonant frequency, Fres or at a pole in the system’s Bodé response. In principle, any clocked DAC with an update rate matching these criteria can benefit from HyperBit™. Figure 4 shows several examples.
Figure 4. Examples of additional bits of resolution provided by HyperBit™. Virtually any clocked DAC benefits.
Waveform Actuation Examples
HyperBit™ lends itself well to improving the resolution of waveform actuation in scanning, probing and dithering applications. Figure 5 and Figure 6 document real-time interferometric measurements of a piezo nanopositioning stage when actuated in a variety of waveforms.
Figure 5. HyperBit™ provides additional bits of resolution in waveform actuation, as in raster scanning and similar applications.
Figure 6. High-resolution interferometry of raster scan, of amplitude ~10 LSB. (left) Bitwise step activity of DAC can be seen. (right) HyperBit™ adds additional resolution, improving the dynamic accuracy of the scan.
In Figure 5, the amplitude of the commanded waveform is ~1·LSB. Without HyperBit™, the resulting motion understandably bears little resemblance to the desired sine, triangle or sawtooth waveforms. With HyperBit™, the desired wavefoms emerge, no longer limited by DAC bitness.
In the high-resolution interferometry shown in Figure 6, the waveform amplitude is ~10·LSB. Without HyperBit™, the waveform shows stepwise behavior characteristic of limited DAC resolution. With HyperBit™, the waveform is significantly improved. It is also interesting to note from Figure 6 that the elimination of DAC granularity will also eliminate the consequent unwanted modulation peaks in the Fourier spectrum for small or slowly-varying motions. This can be important in applications such as nanoindentation, rheology, viscosimetry and apodization, where delicate frequency-domain signatures can have profound import.
The preceding examples illustrate HyperBit™ adding additional bits of resolution to motion commands on the order of a few LSB. But HyperBit™ can allow you to achieve sub-LSB commands as well. Figure 7 shows the results of using HyperBit™ to command a sawtooth wave of amplitude ~1/12·LSB. Without HyperBit™, this would be equivalent to commanding DC.
Figure 7. A low-level look at the patented HyperBit™ technology: in this extreme real-time interferometric example (which tested the limits of the metrology used!), HyperBit™ clearly allows a sawtooth waveform to proceed even though its commanded amplitude is 1/12 the electronic resolution of the DAC. The additional resolution in this case is ~4½ bits. The bottom graphs show the desired waveform (red line) and the actual LSB PWM waveform executed by the DAC.
Applications beyond nanopositioning: Licensing Offered!
HyperBit™ is a fundamentally flexible technology which can benefit virtually any application where the DAC update rate exceeds the responsiveness of the rest of the system. It works equally well in open and closed-loop situations. In closed loop systems it can exist upstream or downstream from the servo.
PI USA is seeking non-competitive licensees in many fields. Some possibilities are listed in Table 1 below.
Table 1. Potential licensed applications for HyperBit™ outside of the field of nanopositioning. Possibilities include both new designs and upgrades to existing equipment.
- Test & Measurement
- Active optics, beam stabilization & pointing, galvanometers
- Electro-Optic devices
- Cavity tuning & Stabilization
- Liquid crystal elements
- Spatial and spectral modulators
- E-beam and ion beamdeflection
- AFMs, scanning microscopies, NSOM, nanomanipulation
- Facilitates large-area processing
- Reduces higher-order granularity-driven dynamics & artefacts
- MEMS actuation
- Electrostatic, thermal, electromagnetic
- Precision metering & forcers
- Motion control
- Microsteppers, voice coils
- Data storage microactuation
- Holographic random-address access
HyperBit™ is an exciting and easily-implemented advancement in digital control of analog processes. By converting unused time-domain DAC capability into enhanced system resolution, HyperBit™ extends the performance of even the best available DACs. At the same time, existing DAC-driven equipment can be upgraded inexpensively, without hardware redesign or changes. Consult with your PI sales and applications professional today for information on leveraging this technology in your application.