Greer, Cody J.

Holy, Timothy E.

English

Digital Commons@Becker

Supplementary information forFast Objective Coupled Planar Illumination MicroscopyCody J. Greer and Timothy E. Holy1Supplementary Note 1: Aberrations for non-focal imagingWe analyze the effect on image quality when imaging outside of the nativefocal plane of an imaging system – referred to here as non-focal imaging. Webegin by considering a conventional microscope imaging system configured toacquire an image of the native focal plane of the objective (diagrammed below,top). Modern microscopes are usually implemented with two lenses: an objec-tive lens that faces the sample, and a tube lens that focuses light collected bythe objective onto a camera sensor (or alternatively an eyepiece). The objectivelens is designed to achieve diffraction-limited imaging of a single (native) objectplane. Likewise a conventional tube lens forms a well-resolved image at a singleimage plane. Images of non-native object planes are also formed at non-nativeimage planes (diagrammed in magenta) but in a conventional microscope theseplanes are not imaged because the camera sensor is coincident with the nativeplane.native objectfocal planenative imagefocal planenon-native objectfocal plane non-native imagefocal planeObjectiveConventional ImagingcamerasensorftubeTubeLensnative objectfocal planenative imagefocal planenon-native objectfocal plane non-native imagefocal planeObjectiveNon-focal Imagingcamerasensorftube (variable)TubeLensSome recently-developed microscopes bring these non-native planes into fo-cus at the camera sensor by using a tube lens with a tuneable focal length(diagrammed below, bottom). Modern tuneable lenses can be adjusted veryquickly, opening up the possibility of achieving high-speed 3D imaging simply1by scanning through a range of focal lengths. The drawback of this approachis that images of non-native planes suffer degraded image quality due to aber-rations. 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 thetube lens in isolation was fully aberration-corrected at each focal length in itsrange then the performance of the system would still be limited by the objectivelens because it is not tuneable. Thus regardless of which tube lens is used, anobjective lens that is not tuneable can only form an aberration-corrected imageof a single object plane, as established by the Abbe sine condition.Before reviewing the sine condition and exploring its implications for a non-focal imaging system we note that if the tube lens could be tuned to correct notjust defocus but all the aberrations of the combined tube lens/objective system,then one could indeed achieve diffraction-limited volume imaging. Howeversuch a system presents an extreme engineering challenge, especially consideringthe NA values and fields of view for modern microscope objectives. Currenttuneable lenses are far from meeting this requirement. Thus in the analysisbelow we quantify the severity of spherical aberration when imaging in non-native planes with a static objective lens and a tube lens that can be tunedto correct for system defocus. Since light is focused at infinity in the regionbetween the two lenses, the distance between the lenses does not affect ouranalysis, and the system behaves as a single-lens system subject to the sinecondition, diagrammed in the following page.2native objectfocal planenative imagefocal planepointsourceΔzΔz'image ofpoint sourcenon-native objectfocal plane non-native imagefocal planeConsider a point source along the optic axis separated by ∆z from the nativeobject focal plane. Rays are emitted from this object over a range of angles andcan be traced to the native image focal plane.The sine condition states that in an aberration-corrected system each raypassing through the native object and image planes satisfiesn sin θ = Mn′ sin θ′, (1)where n is the refractive index of the object immersion medium, n′ that ofthe imaging immersion medium (here taken to be 1 for air), M the local linearmagnification near the axis, and θ, θ′ are the ray angles in the object and imagespace, respectively. For a ray of angle θ, let h denote the height of the strikeposition of each ray in the object focal plane, where h = ∆z tan θ. We cancalculate the position ∆z′θ where this intersects the optic axis:∆z′θ =h′tan θ′(2)=Mhsin θ′√1−sin2 θ′(3)=M∆z tan θ1M n sin θ√1− 1M2n2 sin2 θ(4)=M2n∆z√1− 1M2n2 sin2 θ√1− sin2 θ. (5)Note that the strike position is a function of θ, and therefore in general we donot have perfect focus. The only time the angle-dependence disappears (andthus aberrations are avoided) is when the ratio of square-roots cancels, whichrequires |M | = n. This is the condition derived more generally by the Maxwellperfect-imaging theorem. (We can also see that the longitudinal magnificationis M2n .)When this condition does not hold, the fractional range of strike positions3(up to the maximum angle consistent with the numerical aperture NA) is√1− NA2M2√1− NA2n2− 1 (6)For M = 20 and water immersion, at NA 0.5 we get approximately 8%, and atNA 1 we get a 50% spread.The axial RMS spot radius offers a more informative summary of the imagingperformance. 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(∆z′θ − z′0)2 =(∆z′θ −M2n∆z)2(7)For each angle θ an ideal point source at ∆z emits a circle of rays. It caneasily be shown with trigonometry that the total light collected at angle θ isproportional to tan(θ). Therefore we scale the error at each angle θ accordinglyto get the sum squared error and then divide to calculate MSE:MSE =∫ θ′0tan(θ)(∆z′θ − M2n ∆z)2dθ∫ θ′0tan(θ) dθ(8)=∫ θ′0tan(θ)(∆z′θ − M2n ∆z)2dθ− ln(cos(θ′)) (9)The upper limit, θ′ is the maximum angle that the objective can collect asspecified by the NA. Note that the above calculates the RMS spot radius inimage space; in order to convert this to object space units divide by the axialmagnification.4Supplementary Note 2: Microscope parts(ordered approximately from excitation to collection of emission)Number in diagram Part description Vendor Custom? Part number Price (USD) Countnot shown Laser system w/5 wavelengths, AOTF Spectral (now Andor) no Laser Merge Module (LMM) 90000 1 *discontinued, estimated price1 Pigtailed fiber collimator OZ Optics no LPC-01-405/640-3/125-P-1-6AC-40-3S-3-2 146.5 12 Pigtailed fiber collimator holder (machine shop) yes NA 13 Lightsheet lens module (“cigarette”) (machine shop) yes NAnot shown Lightsheet achromat lens Edmund Optics no 45-262 87.5 1not shown Lightsheet cylinder lens Tower Optical yes* 99 1not shown Lightsheet achromat lens (thin sheet) Edmund Optics no 45-207 59 1not shown Lightsheet cylinder lens (thin sheet) Edmund Optics yes** 48-373 375 14 Rotation collar (machine shop) NA 15 Clamp for lightsheet lens holder (machine shop) NA 1not shown 10x, 0.3 N.A. objective (UMPLFLN10X/W) Olympus no  1-U2M583 774.25 16 20x, 0.5 N.A. objective (UMPLFLN20X/W) Olympus no  1-U2M585 1464.64 1not shown 40x, 0.8 N.A. objective (LUMPLFLN 40X/W) Olympus no 2500 17 Objective holder (RMS) (machine shop) yes NA8 Mini-dovetail stage (2-axis) Lightspeed Technologies Inc. no MDE266 304 19 Mini-dovetail stage (3-axis) Lightspeed Technologies Inc. no MDE269 573 110 dovetail stabilizer (machine shop) yes NA 111 Front piezo plate (machine shop) yes NA 112 Piezo positioner, 800um range Piezosystem Jena no NanoSX800 11205 1not shown Piezo amplifier (digital control) Piezosystem Jena no 30DV300 5616 113 Rear piezo plate (machine shop) yes NAnot shown Precision broadband mirror Edmund Optics no 48-017 395 1not shown 200mm tube lens Thorlabs no ITL200 450 1not shown Knife edged mirror Thorlabs no MRAK25-G01 125.46 1not shown 50/50 beamsplitter (25 x 36 mm) Thorlabs no BSW10R 110 1not shown Filter cube w/insert Thorlabs no DFM 304 1not shown Extra filter cube insert Thorlabs no DFMT1 201 1not shown 0.9x telecentric relay lens Edmund Optics no 62-902 2265 2not shown CMOS camera PCO no Edge 4.2 16400 2not shown Stages for aligning cameras Thorlabs no DTS25 179.5 4not shown DAQ board (PCI-6259) National instruments no 779072-01 1592.1 1not shown Physiology stage surface Thorlabs no PHYS24BB 2500 1not shown Lab jack Newport no 281 999.94 1not shown Breadboard for connecting lab jack Thorlabs no MB1224 259 1not shown XY microscope translation stage Scientifica no N/A (Quote ref: QLS-30894) 4042.5 1not shown RAID hard drives Seagate no 4221403 78.19 20not shown Breadboard for vertical mounting of system Thorlabs no MB1824 400 1Price total: 164194.69*Cylindrical lens specifications **Cylindrical lens specifications (thin sheet)Diameter  3mm +0/-0.2mm Same as Edmund Optics 48-372, only diameter was reduced to 5mmCenter Thickness  1mm ±0.1mmEdge Thickness  1.37mmEffective Focal Length -6.25mmBack Focal Length  -6.91mmFocal Length Tol  ±3%Radius  -3.24mmSurface quality  60/40 both sidesCoating  MgF2view from rear left123 485679101211view from left12791368101112view from front21534610789111213FrontA A40.00150.06A	(center	section)0.501.504.8033.20Sample	side⌀6.00⌀3.50⌀3.25⌀2.70 Laser	side⌀5.10⌀4.70Supplementary Figure 10.02 0.04 0.06 0.08Time (s)50100150200250Position (μm)a50 100 150 200Cycle #0.02000.02250.02500.02750.03000.0325Median absolute difference from mean cycle (μm)d50 100 150 200Cycle #0.1000.1250.1500.1750.200Largest absolute difference from mean cycle (μm)c50 100 150 200Cycle #130.130130.135130.140130.145130.150Mean sample value (μm)bSupplementary Figure 1 Consistency of the piezo response (a) Overlay of 200 consecutive piezo scan cycles as measured by the capacitive sensor of the device (cycles during the first 20 s of operation are excluded).The command signal was a 10 Hz triangle wave. Samples were acquired at 100 kHz and downsampled to 10 kHz for plotting. (b) Closed-loop control of the piezo prevents drift (“creep”) in the mean piezo response measuredduring each cycle from (a). (c) Piezo response cycles are also consistent on a per-sample basis after an initial settling period. First a mean response cycle was created by averaging corresponding samples across the 200cycles. Plotted is the maximum absolute difference of any sampled value of each cycle from the corresponding value in the mean cycle. Before computing differences each cycle was lowpass filtered with a gaussian kernelof width 100 µs to reduce sampling noise. (d) Similar to (c), but the median difference between corresponding samples in each cycle is shown.bd e0.00 0.25 0.50 0.75 1.00Image timing offset (ms)0.20.40.60.8Mismatch with template image (arb. unit)f0 50 100 150Slice depth (μm)0.40.60.81.0Optimal image timing offset (ms)Forward stackReverse stackgStaticDynamicMergedStaticDynamicMergedStaticDynamicMergeda20 40 60 80 100Time (ms)0100200300Position (μm)Piezo sensorSupplementary Figure 20.00 0.25 0.50 0.75 1.00Image timing offset (ms)0.20.40.60.8Mismatch with template image (arb. unit)c*Supplementary Figure 2 Slice timing calibration (a) A single piezo response cycle as measured by the piezo’s built-in capacitive sensor. The dashed line marks a position at which the user desires to acquire and image.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 independentlyfor 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: oneduring 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 poorcorrespondence. 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 offsetthat 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 dynamicimage 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 atimeseries 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 andreverse 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.Supplementary Figure 350100150200Position (μm)0.0030.0040.0050.0060.007-1.0-0.50.00.51.0Acceleration (m/s²)-0.3-0.2-0.10.00.10.20.3Force (N)0.00 0.01 0.02 0.03Time (s)-6-5-4-3-2-1Sensor error (μm)Velocity (m/s)a-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Force (N)-6-5-4-3-2-1Sensor error (μm)bSupplementary Figure 3 Kinetic analysis of scan system (a) Error in the scanning position measurement is better predicted by the acceleration (or equivalently, force) of the scan system than by lower-order kinetics.Plotted are measured kinetic parameters of the piezo during the “forward” sweep of the cycle shown in Supplementary Figure 2a. Only the subset of timepoints corresponding with the timing of each image is plotted, and theraw piezo sensor trace was first lowpass filtered with a gaussian kernel of width 300 µs to reduce sampling noise. From top to bottom: position, velocity, acceleration. The third trace also shows estimated force based onlyon acceleration and the 264 g load of the piezo. The fourth and final trace shows for each image slice the difference between the measured position and the actual position of the focal plane as determined with the camerain the procedure described in Supplementary Figure 2. Note that this trace aligns better with the acceleration/force trace than with the other traces. (b) Scatter plot of points from the blue force trace in (a) showing that forceis predictive of axial displacement of the focal plane.Supplementary Figure 4aCMOSCamera4KEMCMOSCamera3RelayLensRelayLensTLEFOBJBMPCLLP Volume ScanKEMRelayLensCMOSCamera2KEMCMOSCamera1Camera 1Camera 2Camera 3Camera 4RelayLensRelayLensRelay LensStitched ImageDPI module3 6 9 12 15Number of cameras0500100015002000Sensor height utilization per camera (pixels)3 6 9 12 15Number of cameras012345Fraction of sensor for redundant image (%)3 6 9 12 15Number of cameras020406080100Transmission (%)Relay lens, T=0.7Relay lens, T=0.8Relay lens, T=0.9Knife-edged mirror, T=0.97b d e3 6 9 12 15Number of cameras020406080100Total transmission to camera (%)With relay lens T=0.7With relay lens T=0.8With relay lens T=0.9cSupplementary Figure 4 Scalability of DPI (a) 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. Thefundamental 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 relaylenses 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 losseshave 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 Figure1, 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 thesystem. Thus the effective size of the field of view is reduced by a small amount when compared with a single-camera system.Supplementary Figure 5a0 2 4 6 8Frequency (Hz)100102104106108ΔF Power (photons2 )/HzMean across neuronsHeartbeat frequency bandsNon-heartbeat bands100 200 300 400 500 600Neuron index100200300400500600Neuron index−1.00−0.75−0.50−0.250.000.250.500.751.00Correlation of neuronal ΔF100 200 300 400 500 600Neuron index2 4 6 8Frequency (Hz)2468Frequency (Hz)0.00.20.40.60.81.0Correlation of PSD peak size across neuronsbSupplementary Figure 5 Heartbeat-mediated correlations in the ∆F signal (a) Comparison of time-domain correlations in the isolated heartbeat frequency bands (left) and another nearby set of frequency bands. Theformer correlation matrix contains a much higher proportion of strong positive and negative correlations, as would be expected with a broadly distributed heartbeat-induced motion signal. (b) The sizes of spectral deviationsat 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 thesize 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 definedfor 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.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).Supplementary Figure 6a0 10 20 30Frequency (Hz)105106107108109Average ΔF Power (photons2 /Hz)Before anesthesia UnregisteredRegistered0 10 20 30Frequency (Hz)105.0105.5106.0106.5107.0Average ΔF Power (photons2 /Hz)After anesthesia UnregisteredRegistered0 10 20 30Frequency (Hz)1.8 Hz3.6 Hz10−510−410−310−210−1100Average Motion Power (pixels2/Hz)Before anesthesiaAfter anesthesia1.8 Hz3.6 Hz5.3 HzbcSupplementary Figure 6 Changes in power spectra due to anesthetic and image registration (a) Spectral power averaged across image ROIs during single-plane imaging of the larval zebrafish forebrain at 100 Hz (This isa different individual than the fish shown in Supplementary 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 fundamentalfrequency (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 removethem. (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 fromphysiology 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 thepre-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 theartifact results from sub-pixel motion.

Fast objective coupled planar illumination microscopy

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Fast objective coupled planar illumination microscopy

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