Electronics

The electronics for single-particle tracking consist primarily of servos for stabilizing the laser intensity, signal-processing electronics, tracking controllers, and high-voltage amplifiers for driving piezoelectric stage positioners. These are described below, and some of them are displayed in Fig. 6.3.

532 nm AOM Objective APD l/2 PBS l/4 Deflector Sample stage Fiber Dichroic Tube lens Achromat Filter Shutter CCD PD x w₀ Intensity Stabilizer Controller Lock-in Amp HV Amp y

Figure 6.3: Schematic diagram of the electronics for single-particle tracking.

Laser intensity servo Because of intensity and polarization drift in the optical fiber output, we need active servo control of the laser intensity at the sample. We do this in two ways, depending on experimental requirements. In the usual “noise-eater” configuration, we use the laser intensity monitor signal from the photodiode (PD) to electronically lock the intensity by feeding back to a VCA in order to adjust the rf power to the AOM (Fig. 6.3). However, in some of our experiments, we track particles with drastically different brightness. In these cases, we can switch the intensity servo monitor signal so that it locks the photon count rate. In practice, this means that when a bright particle enters the focus, the laser intensity is automatically reduced to maintain a constant fluorescence intensity.

Because the VCA operates exponentially, i.e., by providing a certain number of dB attenuation per volt, the gain of our intensity servo depends on its set point. If the lock point is in a very steep region of the attenuation curve, then small changes in intensity give a large amplitude feedback response, and similarly at shallow points of

the attenuation curve the servo is comparatively slow. We can therefore use neutral density filters to adjust the laser power at its source, so that at a given lock point, the intensity servo sits at different points of the attenuation curve and exhibits different gain and bandwidth. This is a convenient way to adjust the bandwidth of our in- tensity servos, which becomes a critical parameter for the fluorescence intensity lock. Although the VCA is quite fast, and we do not worry about driving it into instability, we have to keep the servo bandwidth low for locking the photon count rate or else we will feed photon counting shot noise into the system.

Lock-in amplifier We use a dual-phase digital lock-in amplifier (Stanford Research Systems, SRS850). The photon counter output is buffered by a digital fanout circuit and then fed directly onto the voltage sensing input of the lock-in. The reference is taken from the beam deflector drive signal. We typically use gain settings in the range 28–54 dB, filter time constants of 300 µs to 1 ms, and rolloff rates of 12 or 18 dB/oct.

Tracking controllers For tracking, we initially used a programable digital mi- crocontroller (Analog Devices, ADuC7024). Analog Devices supplied us with a test board and software (Keil µVision) that allowed us to program the microcontroller in C and download instructions onto the chip via USB interface. I wrote MATLAB software to convert arbitrary transfer functions into discrete time filters and load the coefficients onto the board. An example of one of the LQG control laws of Ch. 2 im- plemented using the microcontroller is shown in Fig. 6.4. It successfully implemented “arbitrary” transfer functions in this way, but with disappointingly low bandwidth and noise due to sampling and timing errors. Once loaded with even a second-order filter, the effective bandwidth of the microcontroller was barely 1 kHz. For higher- order filters, timing errors (missed samples and updates) accumulate and bandwidth continues to fall. Our original hope had been to implement the LQG filters designed in Ch. 2, but these were simply too high order to implement at sufficient bandwidth. For our first successful tracking experiments [25], we used a proportional-integral

101 102 103 -60 -40 -20 0 20 40 Amplitude (dB) 101 102 103 -200 -100 0 100 200 Frequency (Hz) Phas e ( o ) C P CP

Figure 6.4: Measured Bode plots of the response of our piezoelectric stage (P, green), a controller transfer function implemented on the microcontroller (C, blue), and the resulting open-loop transfer function CP (red). The microcontroller implemented one of the LQG control laws derived in Ch. 2 and does successfully cancel the piezo resonance near 400 Hz. Noise near the phase wrap point causes the jagged lines in CP. The transfer function displayed here is theaverageresponse, but timing errors in the microcontroller (which are magnified when the control law is implemented along two axes on the same chip) introduced too much noise for these control laws to be usable in the experiment.

(PI) control law implemented on this controller. For later experiments, however, we switched to analog integral controllers, using the microcontroller only to sense the position of the piezo stage and activate a recentering procedure when the stage reaches a boundary. In practice, the analog controllers have been quieter and easier to work with and have resulted in excellent tracking performance [27, 28]. On the other hand, with simple integral controllers, we cannot drive our piezo stage faster than about 40-60 Hz because of uncompensated phase accumulation.

High voltage amplifiers We use off-the-shelf high-voltage (HV) amplifiers sup- plied by Polytec, PI with their piezo stage. These amplifiers perform adequately, but they are slow (typically rolling off in the 100-300 Hz range). In addition, Polytec, PI provides highly accurate capacitive position sensors through the same amplifier

module, but these too have slow rolloffs at the same bandwidths. So although the amplifiers are nicely packaged and integrated, the experiment could benefit from an upgrade to faster electronics. However, all of the experimental results reported here used these amplifiers. On another note, on three separate occasions, we bought Poly- tec piezo stages with unstable position servo loops. (even unloaded and right out of the box). In all these cases, we simply locked these using Polytec’s position sensors and HV amps and a home-built controller circuit.

Dynamic signal analyzer We measure transfer functions using the swept sine response function of an SR785 dynamic signal analyzer (Stanford Research Systems). This instrument can measure response curves all the way down to DC.