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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Cytometry A. Author manuscript; available in PMC Dec 1, 2010.
Published in final edited form as:
PMCID: PMC2838728
Exploration of Chromatic Aberration for Multiplanar Imaging: Proof of Concept with Implications for Fast, Efficient Autofocus
Martin Weinigel,¦ Albert L. Kellner, and Jeffrey H. Price§
Burnham Institute for Medical Research, 10901 North Torrey Pines Road, La Jolla, CA 92037
University of Applied Sciences Jena, Department of Medical Engineering, Carl-Zeiss-Promenade 2, 07745 Jena, Germany, + 49-3641- 20 56 00 (phone), + 49-3641- 20 56 01 (fax)
§Vala Sciences Inc., San Diego, CA
858.646.3162 (phone), 858.795.5298 (fax), jprice/at/, Lisa O’Brien, Assistant, 858.646.3100 x3270, akellner/at/
¦Current Contact, JenLab GmbH, Schillerstr. 1, 07745 Jena, martinweinigel/at/, 0049 15117851593 (phone)
Image-based autofocus determines focus directly from the specimen (as opposed to reflective surface positioning with an offset), but sequential acquisition of a stack of images to measure resolution/sharpness and find best focus is slower than reflective positioning. Simultaneous imaging of multiple focal planes, which is also useful for 3D imaging of live cells, is faster but requires complicated optics.
With color CCD cameras and white light sources common, we asked if axial chromatic aberration can be utilized to acquire multiple focal planes simultaneously, and if it can be controlled through a range sufficient for practical use. For proof of concept, we theoretically and experimentally explored the focal differences between three narrow wavelength bands on a 3-chip color CCD camera with and without glass inserts of various thicknesses and dispersions.
Ray tracing yielded changes in foci of 0.65–0.9 µm upon insertion of 12.5-mm thick glass samples for green (G, 522 nm) vs. blue (B, 462 nm) and green vs. red (G-R, 604 nm). On a microscope: 1) With no glass inserts, the differences in foci were 2.15 µm (G-B) and 0.43 µm (G-R); 2) With glass inserts, the maximum change in foci for G vs. B was 0.44 µm and for G vs. R was 0.26 µm; and 3) An 11.3-mm thick N-BK7 glass insert shifted the foci 0.9 µm (R), 0.6 µm (G), 0.35 µm (B), such that the B and R foci were farther apart (2.1 µm vs. 1.7 µm) and the R and G foci were closer together (0.25 µm vs. 0.45 µm). The slopes of the differences in foci were dependent on thickness, index of refraction and dispersion.
The measured differences in foci are comparable to the axial steps of 0.1–0.24 µm commonly used for autofocus, and focal plane separation can be altered by inserting optical elements of various dispersions and thicknesses. By enabling acquisition of multiple, axially offset images simultaneously, chromatic aberration, normally an imaging pariah, creates a possible mechanism for efficient multiplanar imaging of multiple spectral bands from white light illumination.
Key Terms: automated cytometry, 3D optical volume, simultaneous multiple focal planes, multifocal, on-the-fly autofocus
Automated microscopy and image analyses are revolutionizing biological research by: 1) adding objective quantification to classically subjective imaging, 2) turning months-long sequential trial-and-error slide-based experiments into days-long parallel multi-well plate experiments, and 3) enabling fast, large-scale image-based screens for active chemical compounds and genes (e.g., RNAi and cDNA) (116). Advances in automatic acquisition, measurement, comparison and pattern classification tools for cellular images continue (1729). Autofocus is a critical component of microscope automation and is most challenging to implement when using high numerical aperture objectives (NA ≥ 0.5), which exhibit high resolutions and small depths of field. Precise autofocus overcomes problems that include mechanical instability, movement of live specimens, variable thickness, drift (e.g., due to thermal expansion) and irregularities of biological substrates (e.g., slides and microtiter plates). Reflective positioning using laser-based methods (3032) can be faster but finding best focus by measuring the resolution of the images is more direct and can produce sharper images, especially with higher NA objectives.
Automated microscopes most commonly use incremental scanning, in which the stage is motionless while acquiring the image and then moved to the next field. At each field, a motorized stage moves the specimen (or objective) along the optical axis (z-direction) to collect a stack of images for measuring the position of sharpest focus (3335). The first field of each specimen can be focused manually (as is typical for manual loading of slides or microtiter plates) or automatically using a longer axial search range (as is typical in robotic slide/plate loading). Entire slides (with thousands of images) and hundreds of 384-well plates in a row (with millions of images) are routinely scanned automatically using autofocus. The axial positioning is performed by an objective positioner, or as for the experiments reported here, a motor on the fine focus knob of the microscope, or more recently, piezoelectric stage inserts (e.g., Mad City Labs, Madison, WI, and Physik Instrumente, Karlsruhe, Germany, Focus is moved through a specific number of steps (Δz) in the z-direction. Autofocus is performed by collecting and analyzing a sequence of images by applying various measures of resolution, acquired at different test object planes from different z-positions (3336). The highest relative focus measurement value corresponds to the best focused image. After finding best focus, the image is acquired and the stage is moved to the next field. In our experiments, maintaining focus in large scale scanning (thousands of fields) requires measuring focus on at least seven test focal planes (34,35). For incremental scanning, we demonstrated real-time focus measurements on a dedicated circuit board to perform autofocus in as fast as 0.25 s on adjacent fields of view for cells on coverslips; including stage motion, the fastest scanning rate was about 3 fields/s (34,35).
With vibrations blurring image acquisition for faster stage movements, we implemented parallel acquisition of multiple image planes with multiple real-time resolution-measurement circuits to achieve on-the-fly autofocus during continuous stage motion (3740). Time-delay-and-integration (TDI) scanning using large format area CCD cameras synchronized to the stage motion enables high sensitivity and high speed collection of long 2-D image strips. The combination of continuous stage motion with multiplanar image acquisition can increase the scanning speed four- to ten-fold, depending on the application. A “volume camera” is used to acquire multiple focal planes simultaneously, as shown in the cartoon in Fig. 1 (realized via imaging fiberoptic bundles or beamsplitters) (40).
Figure 1
Figure 1
A cartoon of simultaneous multiplanar image acquisition is shown.(40)
Multifocal imaging is also useful for 3D imaging of live specimens. Prabhat et al. utilized a 4-camera multi-focal-plane system to image fast events in living cells in 3D(4143), including a study of the sorting of endosomes to exocytosis at the plasma membrane by direct imaging (41). Mulitplanar imaging systems are somewhat complex, making them cumbersome, expensive and prone to additional aberrations.
Constructing a stack of images from the differences in foci produced by chromatic aberration on an RGB camera could create a simpler optical configuration in continuous-motion scanning and would speed conventional incremental scanning. Although microscope objectives are corrected for chromatic aberration, the correction is not perfect. In recent study where chromatic aberration correction with deconvolution was used to measure colocalization of sterols in lipid droplets in cells, 0.8–1.0 µm and 2.0 µm axial chromatic aberrations were reported for fluorescence emission wavelengths of 405 nm vs. 610 nm on multicolor 0.1 µm fluorescent beads using a 63X 1.4 NA oil objective on two different Leica microscopes (44). Each microscope objective should be assumed to have different aberrations (this may be true even comparing two objectives with the same part number), and objectives of increasing quality and cost have better aberration corrections than those of lower cost/quality. In addition to aberrations in the microscope optics themselves, the optics in a 3-chip camera may also contribute to the differences in foci at different wavelengths. Controlling differences in foci may only be practical with a mechanism for automatically adjusting chromatic aberration in a precalibrated manner for each objective/optical configuration.
The addition of a dispersive planar glass element in the diverging (or converging) beam path of the optical system produces chromatic aberration. It should thus be possible to control the amount of chromatic aberration (i.e. the separation of the focal planes acquired simultaneously on an RGB camera) by changing the thickness of the glass element and choosing glass with the appropriate refractive index and Abbe number (dispersion). To determine if the use of chromatic aberration might be practical for simultaneous acquisition of multiple focal planes we: 1) measured differences in focal planes with a 3-chip CCD camera and 2) explored insertion of different types of glass into the optical path to determine the potential for controlling the degree of chromatic aberration.
Modeling chromatic aberration
We used optical design software (Winlens, 4.4 LINOS Photonics GmbH, Goettingen, Germany, to model a reduced (simplified) version of a microscope system (see Fig. 3) and to determine the theoretical foci for various colors. The goal was to create a model of the basic optical components including a “glass sample” to adjust the axial differences between foci (Fig. 2) created by chromatic dispersion. We modeled a 3-chip CCD color digital camera using “red” (604 nm), “green” (522 nm) and “blue” (462 nm) wavelengths with the corresponding images acquired simultaneously. Inserting different glass samples into the path of light should enable control over the amount of chromatic aberration and thereby provide a method to adjust the differences between the respective object planes. In Fig. 2, a and b are the differences between best foci for the “blue” and “green”, and “green” and “red” wavelengths, respectively, and a' and b' are the differences between object planes after insertion of a glass sample.
Figure 3
Figure 3
Ray tracing was performed on this reduced version of the microscope imaging system.
Figure 2
Figure 2
These diagrams show chromatic aberration at red, green and blue wavelengths along with hypothetical differences in focus. The differences a and b are enlarged to a' and b' by adding a glass sample. The lower graphs show a schematic of the corresponding (more ...)
Ray tracing was used to calculate focal plane differences using the optical design Fig. 3, with “red” light of 604 nm, “green” light of 522 nm and “blue” light of 462 nm, hereafter referred to as ‘R’, ‘G’ and ‘B’. The CCD sensor defines the image plane where either the R, G, or B CCD of the 3-chip camera is placed. The glass sample next to the image plane is used to add chromatic aberration. The imaging lens on the right-hand of the glass sample has an effective focal length (EFL) of 24.54 mm and is fabricated with N-BK7 (Schott Technical Glass Solutions GmbH, Jena, Germany) glass. Our model of the microscope objective consists of three optical components: two achromats and one planar convex lens. Each achromat is composed of an N-SF2 (Schott Technical Glass Solutions GmbH, Jena, Germany) lens (biconvex) and an N-BK7 lens (plano-concave) and has an EFL of 38.11 mm. There was no cover glass. For medium resolution, a numerical aperture of 0.75 was chosen. The intermediate image plane is 140 mm in front of the first surface of the microscope objective. Without the glass sample, the overall magnification of the optical system is 20x.
During the experiment, the thickness of the glass sample was varied from 0 to 12 mm and image distance for paraxial rays was recorded for each wavelength. Experiments were carried out for three types of glasses: N-BK7, N-BASF64 and N-SF57 (Schott Technical Glass Solutions GmbH, Jena, Germany). Simulations using the model of Fig. 3 were carried out to match the dispersions of these glass samples.
Experiments measuring focal plane differences
The experiments were carried out on a Nikon Optiphot-I upright microscope, a Nikon CF Fluor DL 20X 0.75 NA objective with Phase 3 bright phase contrast and a Nikon 0.52 NA long working distance condenser, which were used in phase contrast illumination mode. An Osram 12V/50 W light source was used for transmitted light microscopy (bright field and phase contrast). The specimen was a Nikon 10 µm/division stage micrometer slide, which is thinner than the depth of field (by observation) and provides high contrast lines of known spacing for aiding determination of best focus.
During the experiments the objective was moved to change focus with a 100-µm range piezoelectric objective positioner (model P-720.00 PIFOC, Polytec PI, Costa Mesa, CA) and a closed-loop controller (model E-810.10, Polytec PI, Germany). The PIFOC was controlled by the digital-to-analog converter (DAC) on a National Instruments (Austin, TX) PCI-6031E data acquisition board with a digital resolution of 16 bits for a minimum digital step size of 1.5 nm, which likely exceeds the accuracy and precision (not measured) of the mechanical positioning. Images were acquired every 20.0 nm through a 4.0-µm range.
The images were magnified with a Nikon CCTV 0.9–2.25 zoom lens (Nikon, Japan) and imaged onto a Hitachi HV-F31F 3-CCD video camera (Hitachi, Japan) with a pixel size of 4.65×4.65 µm2, 1024(H) × 768(V) active picture elements and a horizontal frequency of 28.8 MHz. The camera has a built-in analog-to-digital converter (ADC). The image was recorded on a Dell Precision 380, P4 630 3.00GHz PC (Dell, TX) via the Open Host Controller Interface IEEE 1394 port of a PCI IEEE 1394 Firewire PCI-card. Camera acquisition and PIFOC movement were controlled with a program written in National Instruments Labview 7.1 that used the National Instruments IMAQ1394 driver.
The RGB wavelengths create three different resolutions or spatial cutoff frequencies. By observation, the best focus function curves (the narrowest and most unimodal) were recorded with a zoom of 0.975X, which resulted in a system magnification of 24.5X (as measured using the stage micrometer). With glass samples inserted in front of the CCD camera (Fig. 4), the largest observed change in magnification was to 24.3X. By the Rayleigh criterion (for bright field imaging with a condenser), the resolution d is given by d = 1.22λ0/(NAobj + NAcond), the R and G wavelengths were imaged at sampling multiples of 3.06X for R, 2.64X for G and 2.34X for B (or 1.53X, 1.32X and 1.17X oversampling relative to Nyquist sampling of 2X).
Figure 4
Figure 4
A schematic of the of the custom C-mount adapter at the top of the Nikon zoom lens is shown with a glass sample inserted.
To help narrow the depths of field, a Chroma 61000V2M triple bandpass filter (462 nm with 50% transmittance (T) at 457 nm and 467 nm; 522 nm with 50% T at 515 nm and 530 nm; and 604 nm with 50% T at 590 nm and 620 nm) was used (Chroma, VT). Some of the glass samples were small enough laterally to cause vignetting, which was removed by imaging a small region of interest (ROI) of 640×30 pixels2.
The sharpness measurements F were acquired as a function of the axial positions z as
equation M1
where h(x) is usually a high frequency bandpass finite impulse response (FIR) filter, i is the image, x, y and z are the pixel and axial positions, and n and m are the lateral dimensions of the image (3436). Fz is thus the sum of the squares of the high spatial frequency components divided by the square of the integrated intensity of the image to decrease fluctuations due to unstable illumination. For our experiments, we chose a 1-D 31-tap high frequency bandpass filter for h(x) that was previously shown to produce a unimodal focus function curve {0.00701; −0.00120; 0.00185; −0.01265; −0.01211; 0.08346; −0.04688; −0.18633; 0.27488; 0.13864; −0.58840; 0.22454; 0.66996; −0.74667; −0.30163; 1.00000; −0.30163; −0.74667; 0.66996; 0.22454; −0.58840; 0.13864; 0.27488; −0.18633; −0.04688; 0.08346; −0.01211; −0.01265; 0.00185; −0.00120; 0.00701} (36). Acquiring a set of z focus measurement values Fz from at a series of axial positions creates a focus function curve. As shown in Fig. 2, each wavelength is expected to produce a different focus function curve. To reduce the influence of multiple best foci in biological specimens and weight the choice of best focus toward the axial position at which the sample has the most high spatial frequency components, we use the power weighted average Wa
equation M2
to calculate best focus, where Fz, (the sharpness at each axial position z) is defined in Eq. 1 and α is chosen empirically. (35). The differences between the object planes produced by the RGB wavelengths were calculated from the differences in Wa of the three focal function curves. For use in autofocus, best focus measurements using Eqs. 1 and 2 were previously shown to be about an order of magnitude more precise (as measured by SD of repeated trials) than the depth of field of the objective (35) and are much more precise than the human eye for the small differences in focus we expected here.
The glass samples used to induce chromatic aberration are summarized in Table 1.The samples of N-BK7 were made from stacks of ~1.0-mm plain microscope slides that were assembled with Cargille non-drying immersion oil (code 1248; type B, n(e)=1.5180 +/− 0.0002) to maximize light transmission. The best focus with each glass sample in place was measured 20 times at each of the R, G and B wavelengths. The 20 best focus positions Wa were averaged and the differences between mean foci at the three wavelengths were calculated. The RGB optical path lengths within the CCD camera were not measured.
Table 1
Table 1
Glass samples used to induce chromatic aberration.
Inserting a thick glass sample is likely to also cause aberrations that reduce resolution. The resolutions were compared using a simple plot-based measurement of the “knife edge” (45) or edge spread function, which can also be used to calculate the line spread function and the modulation transfer function (MTF) (46). A 10-µm spacing micrometer slide was imaged with and without the N-SF57 12.2-mm thick glass sample, which was chosen with the expectation that the largest index of refraction and thickness would likely produce the greatest aberrations and reduction in resolution. The best focus position was determined using the method of Equations 1 and 2 with the 31-tap filter described above. The lateral differences in horizontal positions of the 10% and 90% points in 18 line plots (intensity as a function of pixel position) from randomly chosen positions along micrometer lines were measured for each condition and the median was used as the measure of resolution. The respective distances between pixels were measured directly from the micrometer images to normalize differences in magnification.
Chromatic Aberration Control in a Model Optical System
We first ray traced a simplified microscope optical system (see Fig. 3) to estimate the tractability of controlling the relative foci of R, G and B. Modern microscopes include sophisticated aberration corrections that this simple model doesn’t include. For our experiments reported in Fig. 5, we plotted the differences in foci for each glass sample referenced to an assumed baseline condition (no glass insert) of no chromatic aberrations (zero differences in R-G-B foci). For three 12.5-mm thick glass inserts of different indices of refraction (n), the estimated G-B differences in foci increased by up to 0.9 µm for n = 1.70824 and n = 1.85504 and 0.65 µm for n = 1.51872. For the same three 12.5-mm thick glass inserts, the G-R differences in foci increased to 0.9 µm for n = 1.70824 and n = 1.85504 and 0.70 µm for n = 1.51872. These differences in foci of up to 0.65–0.9 µm enable axial steps comparable to the 0.1–0.24 µm focus differences used in previous tests of autofocus precision performed on thousands of microscope fields using the same objective characteristics modeled here (20x, 0.75 NA) (34,35). That is, with G-B and G-R differences of 0.3 µm each, it would be possible to acquire nine planes spaced 0.1 µm apart by mechanically changing the objective position only three times. It isn’t necessary that the axial positions be evenly spaced; e.g., we previously reported axial sampling of 11 planes spaced 17, 10, 7, 6, 6, 6, 6, 7, 10, and 17 digital steps apart in a range of 2.196 µm (34).
Figure 5
Figure 5
Ray-traced focus differences are plotted as a function of the thicknesses of glass sample inserts with indices of refraction of n = 1.51872, n = 1.70824 and n = 1.85504.
Experimental Chromatic Aberration Control in a Microscope
With the ray tracing model having demonstrated appropriate control of chromatic aberrations for autofocus, we inserted three different types of glass samples into the optical path of a microscope and measured the changes in foci between R, G and B. Three different experiments of at least 100 measurements for each data point (all CVs < 5%) were carried out on different days, resulting in three different plots for each condition in Fig. 6. With no inserts, the differences in foci of ≥ 2.15 µm (G-B, left) and ≥ 0.43 µm (G-R, right) may be due to chromatic aberrations or axial misalignments (at these wavelengths) of the three CCD chips imaged through the trichroic prism inside the CCD camera.
Figure 6
Figure 6
Focus differences are plotted as a function of the thicknesses of glass samples inserted into the optical path. The indices of refraction are n = 1.51872, n = 1.70824 and n = 1.85504. The y-axes are truncated.
The G-B and G-R differences in foci in Fig. 6 are all dependent on thicknesses of the inserts. The slopes of the G-B differences in foci also increase with index of refraction and dispersion (nN-BK7 < nN-BASF64 < nN-SF57). The dependencies of the slopes of the G-R differences in foci on index of refraction and dispersion are less clear but the trends appear similar. The maximum change in the differences in foci for G-B (left) is ~0.44 µm. The maximum change in the differences in foci for G-R (right) is ~0.26 µm. Although less than the changes in differences in foci predicted by ray tracing, these differences again compare well to the axial steps of 0.1–0.24 µm used in previous tests of autofocus precision with the same objective (20x, 0.75 NA) (34,35).
Finally, in Fig. 7 we plotted the relative through-focus sharpness measurements, Fz (Eq. 1), with and without an 11.3-mm thick stack of N-BK7 microscope slides. The focus function curves in Fig. 7 with the glass sample inserted are wider than those without, with the differences in width greatest for blue and least for red. The side peaks are also larger for red and blue, which can be caused both by changes in sampling (magnification) and resolution. Since the change in magnification was small (the largest change was from 24.5x to 24.3x with the glass inserts), we measured the changes in resolution for each wavelength using the 12.2-mm thick N-SF57 glass sample (Table 1). The resolutions with and without the glass sample for R, G and B and the decreases in resolution are shown in Table 2. The decreases in resolution with the glass insert were greatest for B and R at 0.75 µm and 0.63 µm, respectively, and least for G at 0.40 µm. These differences are comparable to the differences measured between the wavelengths themselves without inserts (G-B difference of 0.71 µm, R-B difference of 0.28 µm and G-R difference of 0.43 µm), and are 2- to 3-fold greater than the differences in Rayleigh resolution (G-B and R-G). Since the focus function curves in Fig. 7 remained predominantly unimodal, these changes in resolution are unlikely to degrade autofocus performance. The differences in best foci as determined by Eq. 2 with α = 8 for each color are 0.35 µm (B), 0.9 µm (R), and 0.6 µm (G). With the shift in R focus greatest after insertion of the glass sample, the B and R foci are farther apart (2.1-µm vs. 1.7-µm) and the R and G foci are closer together (0.25-µm vs. 0.45-µm).
Figure 7
Figure 7
The focus function curves acquired without a glass sample (solid) and those with a 11.30 mm stack of N-BK7 glass sample (dashed) are plotted for direct comparison of the differences in best focus (marked by the vertical lines) as calculated by Eqs. 1 (more ...)
Table 2
Table 2
Resolutions Measured as Magnification-Normalized Knife-Edge-Gradients
This research shows that the differences in focus due to chromatic aberration can be controlled in the same range as that commonly used for axial sampling in image-based autofocus. Inserting coplanar glass samples into the light path of the microscope can be used to alter the amount of chromatic aberration and thus change the axial differences between the respective R-G-B focal planes. Such glass elements will also increase all of the Seidel aberrations, most particularly spherical aberration. If needed, the spherical aberration induced at each color can be controlled by using several planar elements placed in different positions in the optical system, with each element composed of a particular glass with different refractive indices and Abbe numbers. An element with parallel planar surfaces can act as an etalon and create interference patterns and ghost images, which can be reduced by using antireflection coatings or slight wedge angles (perhaps one to five degrees).
Taking advantage of chromatic aberration to obtain images from different foci depends on the presence of the expected wavelengths in the light coming from the specimen. With transmitted or reflected white light, the sample shouldn’t absorb a color to the point of compromising the sharpness measurement. Absorption will not be a problem for unstained samples (where image contrast is generated via phase contrast (34,35), DIC (47), or reflected epi-illumination). Tissues stained with absorbent color dyes (e.g., for immunohistochemistry) could alter the relative intensities of the chosen wavelengths. While the typically broad spectral absorbance curves of these dyes are unlikely to completely block any one wavelength, it may be useful to perform calibration to alter the relative camera gain or light source intensity for each wavelength. For fluorescence, the sample can be stained with the appropriate dyes or autofocus can first be performed using transmitted or reflected white light.
In the experiments with glass inserts, the B-R foci became farther apart and the R-G foci closer together with increasing insert thickness. This means that it may be useful to have alternative ways to control chromatic aberration. In this first set of experiments, we sought to answer if it is possible to control chromatic aberration and thus carried out the simplest set of experiments we could design. For our next goal – actually implementing autofocus based on the concept of chromatic aberration-induced multiplanar imaging – we note that the differences in foci also depend on the optical path lengths to the CCD chips inside the camera and the choices of wavelengths within the R, G and B color bands. Thus, it is likely that it won’t be necessary for the inserts to provide all of the needed axial sampling control. Other ways that might be used to control the differences in foci between the three images include: placing micropositioners on the CCD chips; changing the wavelengths by using filter wheels, tunable filters or tunable light sources; and adding lens elements. The differences in magnification and resolution should also be checked with any combination of these methods to ensure that the changes in the system transfer function that includes the high frequency band pass filter h(x) of Eq. 1 doesn’t overly compromise the image sharpness measurements. These methods could be used independently or together to achieve the needed differences in foci for each optical setup (e.g., after changing objectives). With multiple camera ports on each microscope and with, e.g., the Nikon dual-camera Multi-Image Module, it would be possible to use two RGB cameras to sample six foci, three cameras to sample nine foci, etc. The axial positions of the cameras themselves could also be controlled automatically. We thus conclude that chromatic aberration offers a potentially convenient method for simultaneously sampling the axial specimen space to speed autofocus.
We thank Ramses Agustin, Lam K. Nguyen, Rong Yang, Joseph Russo, David Charlot, and Michael Thieleking for their advice and help. This work was funded by NIH grants EB006200 and HG003916.
Conflict Disclosure: Jeff Price is CEO of and owns equity in Vala Sciences Inc.
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