2.1.

System Setup

The schematic setup for the LSM is shown in Fig. 1. A tunable femtosecond Ti:sapphire laser (720–950 nm, 80 MHz repetition rate, Chameleon, Coherent Inc., Santa Clara, California) provided excitation light. A polarizing beamsplitter cube deflected confocal reflectance light to the avalanche photodiode (APD) detector. A long-pass dichroic mirror (DM) directed the two-photon excited fluorescence (TPEF) signal to a photomultiplier tube (PMT). The microscopic objective (MO) (Olympus America Inc., Center Valley, Pennsylvania) was a $\times 40$ water immersion type. The optical scanner was a small beam diameter scanning galvanometer mirrors system (GVS202, Thorlabs, Newton, New Jersey). The motor had a maximum angular scanning range of 12.5 deg, a repeatability of $15\mu \mathrm{rad}$, and a step response time of $300\mu \mathrm{s}$. Within a small scan angle ($\pm 0.2\mathrm{deg}$), the maximum input frequency could go up to 1 KHz. The galvo driving board accepted external command input from a DAQ card. The driving board provided diagnostic pins with voltage signals proportional to the position of the scanner mirror. A multifunction DAQ card (NI USB-6363, National Instruments, Austin, Texas) drove the galvo, acquired APD and PMT output, and detected the galvo mirror position diagnostic signals.

Fig. 1

Schematic setup for the laser scanning microscopy (LSM).

2.2.

Galvo Driving Patterns and Image Reconstruction

Sinusoidal and triangular driving patterns with variable amplitude, frequency, and sampling rate were tested. The symmetry of both sinusoidal and triangular driving patterns allowed bidirectional scanning within each cycle, allowing better utilization of laser scanning time.¹¹ Only image lines belonging to the same scanning direction were used to reconstruct the image in order to minimize line shift distortion.¹⁰

2.3.

Computing Program and Software

A program was developed using LabVIEW (National Instruments, Austin, Texas). Synchronization of galvo driving signal and acquisition of detector and driving board diagnostic outputs were achieved by sharing the start trigger signal of the analog output. The voltage output from detectors was acquired as a linear array with a length equivalent to the total number of pixels. Once each cycle of the scan was completed, the linear array was folded into images with the correct dimensions. Raw image data were further analyzed in MATLAB® (Mathworks, Natick, Massachusetts).

2.4.

Resolution Target and Cell Culture

A positive combined resolution and distortion test target ($18\times 18\mathrm{mm}$, R1L1S1P, Thorlabs, Newton, New Jersey) was used. The concentric sector star pattern was scanned to detect image distortions and to verify the effectiveness of correction. Hut78 suspension T lymphoma cells cultured in RPMI-1640 medium (R0883, Sigma-Aldrich Canada, Oakville, Ontario) and stained with FM1-43 fluorescence dye were imaged. The cell culture was kept in the dark before imaging.

3.1.

Driving Pattern, Frequency, and Position Error

To find out the position error varying pattern versus the driving frequency, the galvo mirror driving signal frequency changed from 100 Hz to 1 KHz at an interval of 100 Hz. Sampling rates ranged from 100 to $500\mathrm{KS}/\mathrm{s}$. Results from the sinusoidal driving waveform showed that the position error varying pattern closely resembled the corresponding galvo mirror driving pattern, suggesting excellent linearity. The response time translated into a phase shift between commanded and actual movement patterns, thus it was possible to correct position error through phase compensation. The amplitudes for position error pattern with sinusoidal driving waveform were proportional to the sine values of the phase shift. The position errors for a triangular driving pattern were trapezoids. To find out the achievable minimum position error obviating the effect of response time ($\sim 300\mu \mathrm{s}$), a sequential step scan mode was implemented. Under this mode, the galvo scanner stayed for $500\mu \mathrm{s}$ after each position command, then the actual position voltage signal was measured. The resulting position error was a combination of position error and the readout error of the DAQ card ($\sim 0.15\mathrm{mV}$). Calculated from 200 readings, the achievable minimum position error had an average of 0.68 mV and a maximum of 2.2 mV.

3.2.

Position Error Correction

For a specific driving frequency and sampling rate combination, the phase shift remained fairly constant. Therefore, it was possible to counteract the phase shift effect by introducing an initial phase to the driving waveform. An advanced phase amount caused the galvo mirror to respond ahead of the commanded scanning position. Except for the initial starting period during which the galvo accelerated to follow the command voltage, the actual galvo mirror position eventually coincided with the commanded position after the galvo managed to synchronize with the input voltage. The initial phase shift is calculated using

The galvo mirror inertia also prevented the galvo from following abrupt changes when the scanning direction reversed. The consequence was a reduced duty cycle. To compensate for the reduced scanning range, the driving voltages could be amplified with a factor. For a sinusoidal driving pattern, the positional error for the galvo mirror could be effectively lowered to manageable levels that were comparable to that of the sequential step scan mode. The triangular driving pattern suffered from a reduced duty cycle more severely when compared to the sinusoidal waveform. As the driving frequency went up from 200 to 500 Hz, the duty cycle went down rapidly from 85.4% to 65.8%.

3.3.

UnderSampling of Driving Voltage Pattern

When galvo mirrors continuously scanned at a moderate rate, the position error suggested that precisely updating the command voltage at every scanning position did not necessarily translate into a more accurate galvo mirror position. Instead, it makes more sense to update the driving signal less frequently because the nonresonant galvo scanner has a rather limited bandwidth. For a resolution of $500\times 500\text{pixels}$, i.e., 500 command positions per image line, the sampling rates for the galvo driving signal were set at between $10\mathrm{KS}/\mathrm{s}$ and $1\mathrm{MS}/\mathrm{s}$ to find out whether lower sampling rates impacted position error significantly.

In Fig. 2, both the average and the maximum position errors did not significantly decrease once the sampling rate for the galvo driving voltage went beyond $50\mathrm{KS}/\mathrm{s}$, i.e., 50 voltage updates per image line. It was also evident that the triangular driving waveform generally resulted in a lower position error compared to the sinusoidal driving waveform. The average and maximum position errors for the triangular driving waveform were below 1.4 and 3.3 mV, respectively. The average and maximum position errors for the sinusoidal driving pattern were 2.3 and 5.8 mV, which almost doubled those of the triangular waveform. Therefore, the triangular driving waveform rendered a more accurate scanning position within the linear scanning range, which was important for spectral mapping.

Fig. 2

Maximum and average position error for sinusoidal and triangular waveform when updated with different sampling frequencies. Opened square: sinusoidal maximum; filled square: sinusoidal average; circle: triangular maximum; triangle: triangular average.

3.4.

Effect on Scanned Target Images

The scanned images of a sector star pattern in Fig. 3 demonstrate the phase shift effect and its correction. Essentially, the phase shift created a folding effect along the slow axis direction [Figs. 3(a) and 3(d)]. For a sinusoidal driving waveform, the effect created difficulty in subsequent image correction using a linearization technique.¹² The image in Fig. 3(b) was further distorted due to the varying scanning speed using a sinusoidal waveform. For a triangular driving waveform, the folding effect could be virtually eliminated after phase compensation [Fig. 3(e)]. However, there still existed a certain amount of image distortions, e.g., elongation, along the edges due to the reduced duty cycle. An effective way to compensate for the reduced duty cycle was to scan a wider range by increasing the driving pattern’s amplitude and the number of sampling points accordingly. After the image was acquired with 1.5 times scanning range along the fast axis, the image was cropped to exclude regions displaying significant geometrical distortion due to the reduced duty cycle [Fig. 3(f)]. The resulting image was distortion free and there was no need for image linearization. It is also important to note that the triangular scanning mode preserved image geometry with high fidelity, whereas image restoration in the sinusoidal scanning resulted in a noticeable sawtooth pattern along the straight edges [Fig. 3(c)].

Fig. 3

Distortion correction of a section star pattern image. For a sinusoidal driving waveform, image (a) without and (b) with phase shift corrected, (c) image corrected with pixel relocation algorithm. For a triangular driving waveform, image (d) without and (e) with phase shift corrected, (f) image acquired with increased scanning range showing the region of interest. (Image resolution $500\times 500$ acquired at 2 fps).

3.5.

Live Cell Imaging

Reflectance confocal and TPEF images of live T lymphoma cells were taken. The confocal images [Figs. 4(a) and 4(c)] clearly show the cell membrane and cytoplasm. In the TPEF images, the cell membrane and nucleus membrane stained with FM1-43 fluorescence dye could be clearly distinguished from the rest of cell by their strong fluorescence. Cell images without phase correction show a folding effect similar to that of the section star target. Without prior knowledge of the individual cell shapes and spatial arrangement in the culture medium, the distortions might be otherwise considered as cells with abnormal morphology, undergoing mitosis, or simply overlapping with each other.

Fig. 4

Imaging of live cells using confocal laser scanning microscopy (CLSM) and two-photon excited fluorescence (TPEF). (a) Confocal image without phase correction; (b) TPEF image without phase correction; (c) confocal image after correction; (d) TPEF image after phase correction.