Multibeam continuous axial scanning two-photon microscopy for in vivo volumetric imaging in mouse brain

This study presents an alternative approach for two-photon volumetric imaging that combines multibeam lateral scanning with continuous axial scanning using a confocal spinning-disk scanner and an electrically focus tunable lens. Using this proposed system, the brain of a living mouse could be imaged at a penetration depth of over 450 μm from the surface. In vivo volumetric Ca2+ imaging at a volume rate of 1.5 Hz within a depth range of 130–200 μm, was segmented with an axial pitch of approximately 5-µm and revealed spontaneous activity of neurons with their 3D positions. This study offers a practical microscope design equipped with compact scanners, a simple control system, and readily adjustable imaging parameters, which is crucial for the widespread adoption of two-photon volumetric imaging.

Multibeam continuous axial scanning twophoton microscopy for in vivo volumetric imaging in mouse brain: supplemental document 1. Optimal drive waveform for continuous axial scanning A periodic waveform to drive the ETL was selected from three waveforms: sine, triangular, and sawtooth (Figure S1).First, the sine waveform causes the nonuniform motion of the focal points; therefore, the axial pitches of each captured frame must differ, and many frames are captured near the edges of the axial range.Second, the sine and triangular waveforms cause bidirectional scanning; thus, such drive waveforms update axial positions twice in a short time near the edges, and the update rate for each axial position becomes heterogeneous.Meanwhile, the sawtooth waveform is advantageous for the aforementioned problems; therefore, it is adapted as the drive waveform of the ETL.Uniform motion and unidirectionality are essential features of the drive waveform for continuous axial scanning with a fixed exposure time.

Device control for volumetric imaging
To control the proposed imaging system using analog voltage signals with sub-millisecond time resolution, an sCMOS camera (ORCA Fusion BT, Hamamatsu Photonics K.K.) and an ETL were connected to their respective DAQ boards, and 1 output channel per DAQ was used to control each device independently.The camera input terminal received rectangular waveform signals (0 or 3.3 V) as external readout triggers that end the last frame and begin the next exposure.The ETL was driven by a computer-generated periodic waveform through a USB-connected lens driver.The current range of the ETL, corresponding to the desired axial range, was mapped in the range of 0-5 V with 10-bit precision in the lens driver; i.e., the lens driver converted the signal from voltage to current.The analog voltage signals that independently output from the DAQ boards to the camera and ETL were routed to the input terminals of the DAQ and simultaneously recorded with timing information.
The custom imaging software that controlled the devices (camera, ETL, focus drive motor, and spinning-disk scanner) was coded by C# (Microsoft).This software allowed for xy, xyz, and xyz-t recording with a graphical user interface.To configure the ETL and camera parameters, C# source codes provided by Optotune Switzerland AG and Hamamatsu Photonics K.K. were, respectively, used in the software.

Transformation of the ETL focal length into the axial position and FOV change
To perform volumetric imaging with axial scanning by ETL, a conversion between axial shifts and the ETL current was established based on the measured data (Figure S2a).The axial shifts for various ETL currents were measured using a 1-µm bead phantom.First, at an ETL current of 0 mA, a single bead located near the coverslip was selected as a guide star.
Next, to measure the axial shift caused by each ETL current, the focal plane was refocused on the guide star bead using a mechanical focus drive motor (96A404, Ludl Electronic Products, Ltd.) after applying the different ETL currents.The measured axial shifts were fitted by a quadratic function (Figure S2a).As a result, the relational expression between the desired axial shifts z (µm) and the ETL current  (mA) under the 25× 1.05 NA objective lens is given as follows: For the measurement of FOV change as a function of ETL current, guide star beads were observed as described above.To search for the optimal scaling factors for each ETL current, images captured at an ETL current of other than 0-mA were resized and then compared with the image captured at an ETL current of 0-mA based on cross-correlation.The scaling factors with the highest cross-correlation for each ETL current were approximated by a quadratic function (Figure S2b) as follows: where I denotes the ETL current [mA].
Based on these relational expressions (Eq.(S1) and (S2)), scaling in xy-images as a function of axial shifts, M(z), was derived (Figure S2c) and can be written as follows: where z denotes axial shifts.a and b, given by −1.2×10 −3 and −1.2, respectively, were derived from Eq.(S1).

Figure S1 .
Figure S1.Optimal drive waveform for continuous axial scanning.(a) ETL drive waveforms (sine, triangular, sawtooth) that control the axial position (z(t)).The DAQ board outputs voltage signals (E(t)) as a periodic drive waveform and are converted to the ETL current (I(t)) by the lens driver.(b) Characteristics of waveforms for continuous axial scanning.Uniform motion of the focal plane results in frames with a consistent z pitch .Unidirectional scanning ensures a constant update rate for each axial position.(c) Image acquisition positions (200 frames) during continuous axial scanning for each drive waveform.

Figure S2 .
Figure S2.Relationship between ETL drive current, axial displacement, and FOV change.(a) Axial shifts as a function of the ETL current.Black dots represent the mean value (n = 2).Gray line represents the approximation by a quadratic function (R 2 > 0.99).(b) Scaling in xy-images as a function of the ETL current.Scaling values indicate the magnification to be applied to xyimages for correcting the image size.Black dots represent the mean value (n = 2).Gray line represents the approximation by a quadratic function (R 2 > 0.99).(c) Scaling in xy-images as a function of axial shifts, derived from (a) and (b).