Galvanometer scanner

The QUAD beamscanner uses four mirror galvanometers, driven by analog voltages, to move the beam across the sample. The four mirrors are arranged in two pairs, each of which is utilized to deflect the beam along one of the two scan axes, ensuring that no offset in the back-focal plane is introduced across the full scan range [BREH11]. Therefore, the positioning of the two paired mirrors relative to each other and hence also the applied voltages are interdependent.

An exemplary snippet of the voltage courses over time applied to the scanner is displayed in figure 3.11 for all four mirrors under typical acquisition conditions. For a classical image scan, a triangular shaped signal is applied to the scanner’s mirrors. Studying exemplarily thex-axis, which is usually the fast scan axis corresponding to a line in the image, and in particularX1, the graph can be split in areas of rising and falling voltages with the latter being comparably short. Areas of continuously increasing voltage resemble the time of a line acquisition, with the signal collected by the detector during the scan being assigned to the corresponding pixel. The falling segments are used to move the scanner back to the starting position to acquire a new line. They-direction is handled accordingly with a much smaller slope for the voltage increase, corresponding to one scan cycle per image.

The dependence between X1 and X2 or Y1 and Y2 is of linear nature and is determined as U_X2 =−0.960·U_X1−0.463V,

U_Y2 =−0.960·U_Y1+ 0.07V.

In the following, the mirror X1 for the x-direction is studied exemplarily. The slope m_X1 on rising segments and the maximal voltage difference ∆UX1 are determined by the image parameters, i.e. the pixel size ∆x, pixel dwell time ∆t and total number of pixelsN_x as well as a unique calibration parameterγ for the specific setup, determined by imaging a reflective calibration grid with a known spacing. The slope of the applied voltage as well as the total voltage difference are given by

For measuring the scanner’s response, the voltage applied to the scanner driver as well as the monitoring voltage on the scanner driver’s output yielding the actual scan position are measured while acquiring an image of size 3µm×3µm with a pixel size of 20 nm×20 nm and pixel dwell time of 10µs. The results are displayed in figure 3.12(a), featuring the input and

- 4 - 2 0 2 4

(a)Voltage on inputs X1 and X2.

200 400 600 800 1000

(b)Voltage on inputs Y1 and Y2.

Figure 3.11:Voltage applied byImspectorto the driver of the QUAD scanner on the four inputs for a pixel size of 20 nm×20 nm, a pixel dwell time of 10µs and an image size of 3µm×3µm. Each pair of voltages is linearly dependent. Note the different time scales for the fast scan axis X and the slow scan axis Y.

output voltages as well as their difference. Due to the finite response time of the scanner, the monitored output voltage of the scanner driver has a temporal offset compared to its input, resulting in a voltage difference at fixed time points. This voltage difference, as displayed in figure 3.12(a), can be translated into a positioning error, giving the maximal deviation between nominal and actual scan position. The deviation is dependent on the chosen pixel dwell time, as shown in figure 3.12(b). The functional dependence can be explained by solving the differential equations for describing the motion of a galvanometer (cf. appendix A). For a constant slope of the input voltage, as it is the case during a line acquisition, the nominal and actual scan position have, in the limit of large times, a constant offsetT in time, assuming the system to be critically damped. This offsetT only depends on the characteristics of the galvanometer, but not on the acquisition parameters. Translating the actual scan position back into a voltage, as done for the monitoring output, yields a constant delay of the output voltage compared to the input voltage. The resulting voltage difference amounts to

∆U =m·T = 13.5 V 85µm ·∆x

∆t ·T

with the slope m as determined previously. Calculating the spatial deviation resulting from this voltage offset yields

∆d= ∆U

13.5 V·85µm =T ·∆x

∆t.

These considerations are supported by the hyperbolic fit shown in figure 3.12(b) alongside with the measured data.

Figure 3.12: Measurement of the scanner’s response as a function of the pixel dwell time. An image size of 3µm×3µm and a pixel size of 20 nm×20 nm are chosen as acquisition parameters. (a) Voltage applied to the scanner driver (input) and monitoring voltage on the scanner driver’s output (left axis) as well as their difference (right axis) for a pixel dwell time of 10µs. (b) Maximum spatial displacement between input and monitoring output as a function of the pixel dwell time.

As seen from figure 3.12(b), a spatial displacement of more than 2µm between nominal and monitored scan position occurs for a pixel dwell time of 1µs. Hence, for scanning techniques with different scan patterns, varying pixel dwell time or tracing possibilities there is the need for a scanning device with a faster response time, resulting in a lower displacement.

An overview of beam scanning techniques can be found in [MS04], featuring galvanometer scanners as well as acousto-optic and electro-optic scanners alongside less common scanning techniques. Most of them, like galvanometer scanners, do not meet the necessary requirements for speed and response time. Acousto-optic scanners are sufficiently fast, but the deflection is wavelength dependent and therefore not suitable for the presented experimental setup.

EODs as additional scanning devices fulfill all requirements presented beforehand, lacking only on the scan range which is, depending on the optical components thereafter, in the range of a few µm. Since they are driven by an analog voltage, yet have no mechanical parts, they can deflect the beam almost instantaneously. The deflection is a function of the index dispersion and is relatively constant over the wavelength range of operation. To realize a larger scan range, they are combined with the galvanometer scanner utilized so far, a similar architec-ture as described in [RB14]. The specific properties of the EODs employed herein for such a combination is discussed in the following.