Fast objective coupled planar illumination microscopy

Among optical imaging techniques light sheet fluorescence microscopy is one of the most attractive for capturing high-speed biological dynamics unfolding in three dimensions. The technique is potentially millions of times faster than point-scanning techniques such as two-photon microscopy. However light sheet microscopes are limited by volume scanning rate and/or camera speed. We present speed-optimized Objective Coupled Planar Illumination (OCPI) microscopy, a fast light sheet technique that avoids compromising image quality or photon efficiency. Our fast scan system supports 40 Hz imaging of 700 μm-thick volumes if camera speed is sufficient. We also address the camera speed limitation by introducing Distributed Planar Imaging (DPI), a scaleable technique that parallelizes image acquisition across cameras. Finally, we demonstrate fast calcium imaging of the larval zebrafish brain and find a heartbeat-induced artifact, removable when the imaging rate exceeds 15 Hz. These advances extend the reach of fluorescence microscopy for monitoring fast processes in large volumes.

We analyze the effect on image quality when imaging outside of the native focal plane of an imaging system -referred to here as non-focal imaging. We begin by considering a conventional microscope imaging system configured to acquire an image of the native focal plane of the objective (diagrammed below, top). Modern microscopes are usually implemented with two lenses: an objective lens that faces the sample, and a tube lens that focuses light collected by the objective onto a camera sensor (or alternatively an eyepiece). The objective lens is designed to achieve diffraction-limited imaging of a single (native) object plane. Likewise a conventional tube lens forms a well-resolved image at a single image plane. Images of non-native object planes are also formed at non-native image planes (diagrammed in magenta) but in a conventional microscope these planes are not imaged because the camera sensor is coincident with the native plane.

Tube Lens
Some recently-developed microscopes bring these non-native planes into focus at the camera sensor by using a tube lens with a tuneable focal length (diagrammed below, bottom). Modern tuneable lenses can be adjusted very quickly, opening up the possibility of achieving high-speed 3D imaging simply 1 by scanning through a range of focal lengths. The drawback of this approach is that images of non-native planes suffer degraded image quality due to aberrations. Tuning the focal length of the tube lens corrects for the lowest order (defocus) aberration, but cannot correct for higher order aberrations (spherical, astigmatism, coma, etc). This is not due to imperfections in the tube lens: if the tube lens in isolation was fully aberration-corrected at each focal length in its range then the performance of the system would still be limited by the objective lens because it is not tuneable. Thus regardless of which tube lens is used, an objective lens that is not tuneable can only form an aberration-corrected image of a single object plane, as established by the Abbe sine condition.
Before reviewing the sine condition and exploring its implications for a nonfocal imaging system we note that if the tube lens could be tuned to correct not just defocus but all the aberrations of the combined tube lens/objective system, then one could indeed achieve diffraction-limited volume imaging. However such a system presents an extreme engineering challenge, especially considering the NA values and fields of view for modern microscope objectives. Current tuneable lenses are far from meeting this requirement. Thus in the analysis below we quantify the severity of spherical aberration when imaging in nonnative planes with a static objective lens and a tube lens that can be tuned to correct for system defocus. Since light is focused at infinity in the region between the two lenses, the distance between the lenses does not affect our analysis, and the system behaves as a single-lens system subject to the sine condition, diagrammed in the following page. Consider a point source along the optic axis separated by ∆z from the native object focal plane. Rays are emitted from this object over a range of angles and can be traced to the native image focal plane.
The sine condition states that in an aberration-corrected system each ray passing through the native object and image planes satisfies where n is the refractive index of the object immersion medium, n that of the imaging immersion medium (here taken to be 1 for air), M the local linear magnification near the axis, and θ, θ are the ray angles in the object and image space, respectively. For a ray of angle θ, let h denote the height of the strike position of each ray in the object focal plane, where h = ∆z tan θ. We can calculate the position ∆z θ where this intersects the optic axis: Note that the strike position is a function of θ, and therefore in general we do not have perfect focus. The only time the angle-dependence disappears (and thus aberrations are avoided) is when the ratio of square-roots cancels, which requires |M | = n. This is the condition derived more generally by the Maxwell perfect-imaging theorem. (We can also see that the longitudinal magnification is M 2 n .) When this condition does not hold, the fractional range of strike positions (up to the maximum angle consistent with the numerical aperture NA) is For M = 20 and water immersion, at NA 0.5 we get approximately 8%, and at NA 1 we get a 50% spread. The axial RMS spot radius offers a more informative summary of the imaging performance. This quantity is the square root of the mean squared error (MSE) in strike position for every ray within the collection cone of the objective lens. For a ray with angle θ emitted from a source at ∆z the squared error is For each angle θ an ideal point source at ∆z emits a circle of rays. It can easily be shown with trigonometry that the total light collected at angle θ is proportional to tan(θ). Therefore we scale the error at each angle θ accordingly to get the sum squared error and then divide to calculate MSE: The upper limit, θ is the maximum angle that the objective can collect as specified by the NA. Note that the above calculates the RMS spot radius in image space; in order to convert this to object space units divide by the axial magnification.   An arrow marks the intersection of the line with the sensor trace. The timing of this intersection sets the initial guess for the timing of image acquisition. The procedure illustrated in panels b-e is applied independently for each such plane that the user desires to image. (b) The initial guess at camera timing based on the piezo sensor is inaccurate for fast dynamic recordings. Two images of the same bead sample were acquired: one during dynamic operation with the timing guess described in (a), and a second image, which serves as ground truth, was acquired at the same location during a very slow scan. The overlay of the two images shows poor correspondence. Scalebar: 5 µm. (c) The initial timing guess is refined by acquiring dynamic images at various temporal offsets and choosing the offset that yields an image matching the static template. The timing offset that yielded an image with minimal dissimilarity (see methods) is marked with an asterisk. (d) When the images corresponding to the optimal timing from (c) are overlaid they show good axial alignment, but the dynamic image exhibits a lateral shift. (e) A lateral translation is sufficient to align the dynamic image from (d) with the template. This lateral transformation is recorded and applied to align each corresponding slice of each stack in a timeseries recording. (f) When the same procedure is applied to align each 5 µm-spaced slice in a stack, slices vary in their optimal timing offset. (g) Optimal timing offsets are shown for each slice in both the forward and reverse stacks of a bidirectional recording. Note that optimal timings cannot be predicted by the depth in the sample, as would be expected from a simple error in sensor gain. Multiple DPI modules can be chained together to split the image to more than two cameras. Shown is a diagram of an OCPI system with DPI scaled to four cameras. The fundamental repeating unit of the design is outlined in orange. Abbreviations are the same as in Figures 1a and 3a. (b) Each DPI module compounds losses to imperfections in the transmission and reflectivity of the relay lenses and the KEM, respectively. These losses are plotted separately as a function of the number of cameras in the system for relay lens transmission efficiencies ranging from 70% to 90%. (c) Same as (b) but KEM losses have been combined with transmission losses for each lens plotted. (d) As more cameras are added to the system less of the vertical extent of each sensor is utilized to acquire a full stitched image. As shown in Figure   1, the maximum framerate is inversely proportional the utilized vertical extent of the sensor. (e) The fraction of each image that contains redundant image information increases linearly with the number of cameras in the system. Thus the effective size of the field of view is reduced by a small amount when compared with a single-camera system. at the frequencies of the putative heartbeat signal are highly correlated across neurons, suggesting that the two frequencies are components of a single signal. For each of the 629 segmented neurons we measured the size of the peak in the PSD at each frequency. Peak amplitiude was measured by dividing the PSD amplitude at each frequency by the mean amplitude of the two surrounding frequency bins (thus peak size is not defined for the maximum and minimum frequency bins). Plotted is the correlation between peak sizes across frequencies. Correlations near the diagonal are expected to be strong because they are between similar frequencies.

Supplementary
However the strong correlation between the 7.5 Hz and 2.5 Hz peak size stands out. Correlation is also visible at 5.0 Hz (another harmonic of 2.5 Hz).  Figure 5). Putative heartbeat-related peaks are visible at 1.8 Hz and the 3.6 Hz harmonic (see methods for details of ROI selection). The difference in fundamental frequency (1.8 Hz) when compared to 2.5 Hz for the fish from Supplementary Figure 5 can be explained by individual variability in heart rate. Image registration diminishes the magnitude of the peaks but does not remove them. (b) The fish from (a) was imaged again after administering a heart-stopping dose of anesthetic (tricaine). The putative heartbeat-related peaks from (a) are fully attenuated, confirming that the signal originates from physiology rather than microscope hardware. (c) A power spectral analysis of the changing magnitudes of pixel translation vectors over time (translations found by registering video frames from (a) and (b)). Peaks in the pre-anesthetic power spectrum correspond with the image intensity peaks from (a), confirming that the artifact originates primarily from specimen motion. Note that peaks have magnitude less than 1, indicating that the artifact results from sub-pixel motion.