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Contents | EBJ Home | Single molecule measurements and biological motors |
In all but the simplest optical tweezers devices, it is desirable to be able to move the optical trap around the field of view. Ideally this motion should be computer controlled, so that it is possible to perform manual manipulations (e.g., using a computer mouse) as well as automatic procedures (such as the application of waveforms to the trap position for calibration, stiffness measurements, etc.). In combination with a position sensor, it may also be desirable to apply feedback to the trap position.
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| Four independently steerable optical traps, produced using AODs. Note that the thermal motion of the trapped beads is much less than the freely diffusing beads. | ||
It is also often desirable to have two or more traps. For example, in experiments with molecular motors, it is often necessary to manipulate a cytoskeletal filament which is extended between two trapped beads. Dual traps may be produced by a number of means. Essentially there are two methods; the beam may be divided by a beamsplitter and the two parts steered independently and recombined; or the trap may be time-shared between two positions. If this is done rapidly enough (kHz) then the effect is similar to having two traps of half the intensity of the beam. The time sharing method has the greatest flexibility because it readily permits independent control of the two trap positions.
Methods of steering trapping lasers have been reviewed in (Svoboda and Block, 1994; Visscher et al., 1996). Essentially the only method which is fast and stable enough to produce multiple optical traps is the acousto-optic deflector or AOD (Molloy, 1998). These devices are solid state, reliable, stable and fast.
These devices essentially act as adjustable diffraction gratings. The incoming laser beam is diffracted to give a number of spots; the zeroth order spot corresponds to the undiffracted beam, and the other spots (first, second order etc.) are the diffracted beams. If the incident beam enters at the so-called Bragg angle, then up to 80% of the incident intensity will be in the first-order beam. The diffraction grating consists of a sinusoidal acoustic travelling wave in a crystal of a material such as tellurium oxide. The alternating compressions and rarefactions produce changes in the refractive index of the material which cause the diffraction effect. Changing the frequency of the input signal changes the spacing of the grating, and thereby changes the deflection of the first order spot. Changing the amplitude of the signal changes the efficiency of diffraction. In other words it becomes possible to control both the intensity and position of the optical trap.
The sound wave is produced by a piezoelectric transducer bonded to the AOD crystal. The input to this transducer is a radio-frequency (RF) voltage produced by a special driver unit. This driver unit can in turn be controlled by either an analogue voltage or a digital input – in either case, the system can be placed under computer control.
For optical trapping applications, position control in both x and y directions is generally required. This can be achieved by using two AODs in series with each other, mounted orthogonally to each other. AODs are generally provided in adjustable mounts which allow precise alignment with the incoming and outgoing beams. For example, the deflector angle can be adjusted to ensure that the input beam enters at the Bragg angle.
Because a pair of AODs will produce a number of spots, it may be necessary to exclude some of them with an adjustable rectangular aperture. This is particularly a concern if the laser is also being used fir position detection. For example, each deflector will produce beams of orders 0,1,2,3,… resulting in an array of spots (0,0), (0,1), (1,0), (1,1),…
The relatively low efficiency is one of the disadvantages of AODs, particularly when x-y deflection is required, when two scanners are needed, typically giving on overall efficiency of around sixty percent or less.
The accompanying figure illustrates the features of a typical acousto-optic deflector.
With these devices it is possible to chop at tens of kHz as opposed to the hundreds of Hz which are practical with galvanometer mirrors. (Chopping at higher frequencies gives more stable trapping because the trapped particles have less time to diffuse away when the laser is addressing the other trap position). The figure below shows an example circuit for producing two computer controlled traps by chopping.
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Circuit for "chopping" optical trap between
two positions. This schematic illustrates how a dual trap can be produced
using x and y AODs and analogue RF drivers. The alternation
of trap positions is controlled by timing signals generated by a timer integrated
circuit (555 - e.g.  LM555)
adjusted to give a 5 or 10 kHz TTL square wave with a duty ratio of
0.5. This signal is passed through a buffer and then an inverted waveform
is produced. These two waveforms control the timing of the “left” (L)
and “right” (R) traps respectively. This timing signal is also used,
if necessary, to demultiplex the position signal. The x and y
positions for the traps are stored in four pairs of latches (374)
(e.g. SN74LS374
or equivalent) whose outputs are alternated by the timing signals. The latches
are fed values from the computer’s data bus, each pair having a separate
address. The outputs of the latches are inputs to two 16-bit digital to
analogue converters (DAC) (e.g. Burr-Brown DAC712P).
The analogue voltage is transferred to the radio frequency drivers (RF)
by coaxial cable. The drivers’ RF output is then transferred by another
coaxial cable to the AOD itself. |
In addition to the AODs themselves, radio-frequency driver units are required. These units will usually be available from the AOD manufacturer, and are often tailored to particular AODs. Essentially these drivers fall into two types, with analogue and digital inputs respectively. The analogue types essentially consist of a voltage controlled oscillator (VCO) which produces a signal of the appropriate frequency (typically tens of MHz) which is then amplified by an RF power amplifier to give the appropriate power output (a few watts). The oscillator is controlled by an externally applied voltage. To interface this to a PC a digital to analogue converter (DAC) is needed (see figure).
The digital synthesiser type of driver has a number of advantages but is considerably more expensive. The signal to the driver is digital and therefore more resistant to noise; the output of the driver is also more stable and less noisy.
In addition to controlling the frequency of the AOD waveform, it is also useful to control the amplitude, as this determines the diffraction efficiency and thereby the laser power at the trap. This may be useful if the full power of the laser is not required, but the laser needs to be run at nominal power for the best stability. Analogue drivers typically have an input for an analogue voltage which will control the amplitude; this can be interfaced to a computer using another digital to analogue converter (an 8-bit device will probably be sufficient).
Manufacturers typically specify the response time of an AOD by the rise time (tr) for a change in position. This is simply given by the speed of sound in the material used (v) and the diameter of the laser beam (d): tr = d/v. In other words, the position of the first order spot will not change completely until the propagating wave has crossed the laser beam.
This is only a rule of thumb; the actual rise time also depends on the beam shape etc. For example, with a 1 mm diameter laser beam in a TeO2 AOD crystal, (acoustic velocity ~700 m·s-1) giving a rise time of approximately 1.4 μs. However, it is worth bearing in mind that matters are considerably more complex. For example, the electronics will also have a characteristic rise time, although this is likely to be of the order of the value above or less. When the beam diameter is small compared to the crystal dimensions, there will be a lag before the sound wave reaches the beam. For example, if the beam passes through the centre of a 10 mm TeO2 crystal, the sound wave will take about seven microseconds to travel the 5 mm before it reaches the centre of the beam.
A more significant issue is the form of acoustic termination or damping that is used at the far side of the crystal from the transducer. If some way of attenuating reflected sound waves is not achieved, then the reflected waves can have a severe effect on the performance of the AOD. For example, when a rapid change in beam position is desired (as when producing dual traps) then the frequency of the sound waves in the crystal must change. The response time is determined as given above. But any reflected sound waves will delay the settling of the AODs as there will be a mix of frequencies within the crystal. In other words, there will be spots at both positions. The time taken for the system to completely change to the new position will depend upon the number of reflections that are occurring. In our experience, this settling time can vary quite significantly between manufacturers.
In the previous example of a 10 mm TeO2 crystal, the first reflected wave would lead to a settling time of about 14 μs, the second would give 29 μs, and so on. If the chopping frequency is 10 kHz, then the dwell time at each spot position is only 50 μs, so that the settling time becomes a significant concern.
For many applications, this is not a major issue; for example, AODs are often used to scan beams, so that the small lag effect is much less noticeable. Even in dual trapping applications, this affect may not be significant, since it simply changes the time distribution of intensity at each position, and should not significantly affect trapping efficiency. However, it becomes a serious issue where the laser light is being used for position sensing, and it is necessary to separate the signals from the two traps. We have found that in practice it can take tens of microseconds for the system to settle, and care must be taken to ensure that the position signals are cleanly separated.
Other factors which should be considered when choosing AODs are
linearity – how linear is the response (deflection angle) to the input signal?
angle range – what is the useful range of angles which the deflector can achieve, and how much does the efficiency vary across this range?
anti-reflection coating - may be useful to improve efficiency
mounting design – particularly crucial for x-y pairs, where it is helpful if the deflectors are mounted as close together as possible. It should be easy to adjust – and lock - the angle to maximise efficiency. A large aperture is useful for ease of alignment.
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