Method to quantify accuracy of position feedback signals of a three-dimensional two-photon laser-scanning microscope

Abstract

Two-photon laser-scanning microscopy enables to record neuronal network activity in three-dimensional space while maintaining single-cellular resolution. One of the proposed approaches combines galvanometric x-y scanning with piezo-driven objective movements and employs hardware feedback signals for position monitoring. However, readily applicable methods to quantify the accuracy of those feedback signals are currently lacking. Here we provide techniques based on contact-free laser reflection and laser triangulation for the quantification of positioning accuracy of each spatial axis. We found that the lateral feedback signals are sufficiently accurate (defined as <2.5 µm) for a wide range of scan trajectories and frequencies. We further show that axial positioning accuracy does not only depend on objective acceleration and mass but also its geometry. We conclude that the introduced methods allow a reliable quantification of position feedback signals in a cost-efficient, easy-to-install manner and should be applicable for a wide range of two-photon laser scanning microscopes.

Keywords: (170.0180) Microscopy; (170.2520) Fluorescence microscopy; (180.2520) Fluorescence microscopy; (180.4315) Nonlinear microscopy; (180.6900) Three-dimensional microscopy.

Fig. 1

Principle of measuring lateral positioning accuracy. (A) Experimental arrangement. Laser focus is dynamically deflected by one of two galvanometers and projected on a reflective grid of lines (distance: 10 ± 0.2 µm). Focus position at a specific time point depends on applied galvanometer command voltage u_Cx(t) (or u_Cy(t)). Position feedback signal u_Fx(t) (or u_Fy(t)) is continuously measured. Reflected laser beam intensity is simultaneously measured by a PMT and converted into voltage u_PMT(t). Inset shows relation between absolute focus position and grid tick marks. (B) Exemplified x-axis measurement. Top: Traces of u_Cx(t), u_Fx(t) and u_PMT(t). Gray box is scaled up and displayed below. Note that there is a significant phase shift between command signal u_C(t) and resulting mirror movement (u_F(t)). Peak detection indicates identified reflection maxima in u_PMT(t). Absolute positions p_Rx (or p_Ry) are calculated by discrete 10 µm distances of detected peaks. Note that calibrated position reverses after a change of galvanometer motion direction (gray highlighted, position 470 µm). Dashed lines indicate zero points (0 V). The dashed dotted line indicates position turning point.

Fig. 2

Principle of measuring axial positioning accuracy. (A) Experimental arrangement. Absolute position of objective dummy ’20x’ is simultaneously measured via capacitive piezo actuator feedback signal u_Fz(t) and laser triangulation p_Rz(t). Dummy position at a specific time point depends on applied command voltage u_Cz(t). ∆z – dummy elongation induced by the applied command voltage. CMOS – Complementary metal-oxide-semiconductor (resolution: 0.1 µm). µC – Microcontroller. (B) Exemplified measurement. Top: Traces of u_Cz(t), u_Fz(t) and p_Rz(t). Gray box is scaled up and displayed below. Note significant time lag between command and position signals (t_Fz and t_Rz). Dashed lines indicate base line levels (0 V).

Fig. 3

Change of bead intersection length as a measure of three-dimensional scan instability. (A) Three-dimensional projection of z-stack data (maximum intensity projections of z-stack intensities in XY, XZ and YZ plane) and spiral scan trajectory (white dashed line). Positions of intersected fluorescent beads, shown in B, are indicated by numbers (1 – 5). Cube dimensions: 500 × 500 × 200 µm³ (XYZ). (B) Examples of bead intensity profiles at different positions in spiral trajectory, scanned over 10 minutes. 10 pixels ≙ 10 µm. (C) Change of intersection length plotted versus time. The dotted line indicates no detected change. Note that no change in length not necessarily indicates position stability as the intersection of a sphere (bead) is not defined uniquely.

Fig. 4

Hardware time lag of measured position signals (t_Rx – x-axis reference, t_Fx – x-axis feedback, t_Ry – y-axis reference, t_Fy – y-axis feedback, t_Rz – z-axis reference, t_Fz – z-axis feedback) compared to command signals. (A) Lateral measurements. Data are pooled from sinusoidal movements (amplitude range: 62 – 248 µm, frequency range: 1 – 2000 Hz). x- and y-axis display different lag characteristics (Mann-Whitney U test: t_Rx – t_Ry, P < 0.001, n = 11 scan trials). Note additional constant lag between feedback and reference measurements (Wilcoxon signed rank tests: t_Rx – t_Fx and t_Ry – t_Fy, P < 0.001, n = 11 scan trials). (B) Axial measurements. Data is pooled from sinusoidal movements (command signal amplitude û_Cz: 0.625 – 5 V, frequency: 1 – 20 Hz). Note additional constant lag between feedback and reference measurements (two-sided students t-Test: t_Rz – t_Fz, P < 0.001, n = 20 scan trials). Each symbol represents lag derived from a single scan trial. *** P < 0.001.

Fig. 5

Position feedback calibration. Left: Calibration of feedback signals to reference positions (linear fit). Dashed lines indicate ideal fit. Insets: Magnification. Right: Deviations of feedback signals to reference position on the basis of linear fitted values. Dashed lines indicate zero deviation. Dotted lines indicate deviation threshold of ±2.5 µm. (A), (B) Discrete lateral position calibration (A: x-axis, B: y-axis). Each symbol represents a single analyzed discrete tick mark position. Note that data points are overlapping. (C) Continuous axial position calibration (z-axis). Right: Gray points represent single data points. Black curve represents moving average of data points (window size: 250 samples).

Fig. 6

Positioning accuracy of x-axis scan pattern is smaller than ±2.5 µm. (A) Examples of two different scan trials. Left: Triangular scan, 248 µm scan amplitude, 10 Hz scan frequency. Right: Damped sinusoidal scan, 248 µm scan amplitude, 10 Hz scan frequency. Note that the maximal absolute deviation of each scan trial was used for the threshold criteria in B (indicators 1 and 2). Dashed lines indicate zero deviation. Each symbol represents one analyzed discrete position. (B) Summarized results for each scan type. Each symbol represents maximal absolute deviation of a single scan trial. Numbers 1 and 2 represent examples from A. Note that data points are overlapping. Dotted lines indicate deviation threshold of ±2.5 µm.

Fig. 7

Positioning accuracy of y-axis scan pattern is smaller than ±2.5 µm. (A) Examples of two different scan trials. Left: Triangular scan, 248 µm scan amplitude, 20 Hz scan frequency. Right: Damped sinusoidal scan, 248 µm scan amplitude, 5 Hz scan frequency. Note that the maximal absolute deviation of each scan trial was used for the threshold criteria in B (indicators 1 and 2). Dashed lines indicate zero deviation. Each symbol represents one analyzed discrete position. (B) Summarized results for each scan type. Each symbol represents maximal absolute deviation of a single scan trial. Numbers 1 and 2 represent examples from A. Note that data points are overlapping. Dotted lines indicate deviation threshold of ±2.5 µm.

Fig. 8

Axial positioning accuracy depends on scan parameters and objective properties. (A) Position deviations of three single trials at different scan frequencies, but the same scan amplitude of 200 µm sinusoidal motion using regular objective dummy. A hysteresis occurs at a scan frequency of 20 Hz, whereas at 1 Hz and 5 Hz deviations for both motion directions are similar. Dashed lines indicate zero deviation. (B) Maximal absolute deviation of four different objective dummies at different scan amplitudes and frequencies (n = 13 trials). Dotted lines indicate deviation threshold of ±2.5 µm.

Fig. 9

Maximal absolute deviation of all four objective dummies at 20 Hz scan frequency and 200 µm scan amplitude sinusoidal motion. Each symbol represents a single scan trial. Maximal absolute deviation is dependent on objective mass and length (ANOVA: P < 0.001, n = 13 scan trials, post hoc Bonferroni pairwise comparisons: regular – none: P < 0.001; regular – short: P < 0.001; regular – long: P < 0.001). *** P < 0.001.