Accurate and fiducial-marker-free correction for three-dimensional chromatic shift in biological fluorescence microscopy

Abstract

Correction of chromatic shift is necessary for precise registration of multicolor fluorescence images of biological specimens. New emerging technologies in fluorescence microscopy with increasing spatial resolution and penetration depth have prompted the need for more accurate methods to correct chromatic aberration. However, the amount of chromatic shift of the region of interest in biological samples often deviates from the theoretical prediction because of unknown dispersion in the biological samples. To measure and correct chromatic shift in biological samples, we developed a quadrisection phase correlation approach to computationally calculate translation, rotation, and magnification from reference images. Furthermore, to account for local chromatic shifts, images are split into smaller elements, for which the phase correlation between channels is measured individually and corrected accordingly. We implemented this method in an easy-to-use open-source software package, called Chromagnon, that is able to correct shifts with a 3D accuracy of approximately 15 nm. Applying this software, we quantified the level of uncertainty in chromatic shift correction, depending on the imaging modality used, and for different existing calibration methods, along with the proposed one. Finally, we provide guidelines to choose the optimal chromatic shift registration method for any given situation.

Figure 1

Registration methods to measure and correct chromatic shift using biological samples. Representative 3D-SIM images. (a) Actin filaments stained with dye-conjugated phalloidin. The same image is shown in the green (shown in green) and orange (shown in purple) emission ranges, detected simultaneously with different cameras. (b) The same image as in (a) after chromatic correction. (c) Nuclear DNA stained with DAPI excited at 405 nm. Images of normally discarded bleed-through signals in the green and orange emission ranges, detected simultaneously with different cameras. (d) The same image as in (c) after chromatic correction. (e) Nucleolar proteins, treacle and fibrillarin, stained with Alexa Fluor 488 and 568 in the same cell and shown at the same focus position as in (c). Images were acquired by sequential excitation with 488 and 561 nm, for detection in the green and orange emission channels, respectively. (f) The same image as in (e) after registration using the same parameters used to align (c). The boxed region was magnified and is shown in the inset. The scale bar is 2 µm for panels (a–f) and 0.5 µm for the inset in (f).

Figure 2

Comparison of the performances of the three calculation methods. (a) Comparison of registration performance using simulated data. An image stack of tubulin stained with CF405M was two-dimensionally shifted a known amount (see Methods or Supplementary Fig. S1a). Then, a maximum intensity projection was used to calculate the 2D registration error using each method. Deviation from the known registration parameters, i.e., the vector sum of the five parameters T_X, T_Y, M_X, M_Y, and R_Z, is shown. The bars indicate the standard errors of twelve repetitions of the simulation. ‘Quadrisection’ stands for quadrisection phase correlation (see Results and Fig. 3); ‘Log-polar’ stands for log-polar transformation combined with phase correlation; and ‘Simplex’ stands for an optimization method using the simplex algorithm. (b) The same data in (a) shown for the individual parameters: translation along the X and Y axes (T_X, T_Y), magnification along the X and Y axes (M_X, M_Y), and rotation around the Z axis (R_Z). (c) Comparison of noise-tolerance using simulated data. Both channels of the image created as explained in (a) were divided by constants ranging from 50 to 500, and either Gaussian or Poisson noise images with a standard deviation of 10 were added to both channels. The two datasets using Gaussian and Poisson noises were combined. Deviation from the known registration parameters is plotted as a function of average SNR (also see Supplementary Fig. S1). (d) Comparison of the time required for the calculations of 2D registration data of 508 × 508 pixels using eight cores of a Xeon E5-2623 v4 2.6 GHz processor. The bars indicate the standard error after 252 calculations.

Figure 3

Principles of quadrisection phase correlation and local phase correlation. (a) A 3D-SIM image of DAPI-stained cell nuclei acquired in two channels, where a 2D section is split into four regions (shown as cross lines). For each quadrisection, the phase correlation between the two channels is measured. (b) The resulting image has four identifiable correlation peaks (arrowheads) around the center (cross-marked by dotted lines). The shifts of each individual peak from the center of the quadrisection indicates the direction and magnitude of the necessary shift to align the two channels in each individual quadrisection image. Such shifts are shown as vectors (a–d) in (c). If we assume that the shifts consist only of affine parameters (translation, magnification, and rotation), then the vectors should be the sums of the vectors corresponding to translation, rotation, and magnification. Therefore, adding vectors (a and c) extracts the translation part of the vectors because the rotation and magnification parts of the vectors should have an opposing orientation with equal length and thus should cancel each other out. This way, by cancelling out the other components (rotation and magnification), two independent translation vectors (T_XY1 and T_XY2) are obtained, and are then averaged to obtain the total translation T_XY. Similar calculations yield the solutions for rotation and magnification. (d) A 2D section of the image shown in (a) after registration, where quadrisection phase correlation is split into windows of, for example, 128 × 128 pixels. For each window, the phase correlations between the two channels are measured, resulting in images as displayed in (e), where the shift of the individual peaks in each window indicate the direction and amount of shift necessary to align the two channels in each individual window. The local shifts were applied to the target images using a nonlinear elastic transformation. See Methods for more details. Scale bars are 5 µm.

Figure 4

Registration precision. (a) A 3D-SIM image of multicolor beads immobilized both on the coverslip and on the glass slide before (left) and after (right) registration. Maximum projections of the quarter field of view (20 × 20 × 8 µm) along the XY plane and the XZ plane are shown with a region magnified in the inset. The blue, green, and orange channels are indicated by their respective central emission wavelengths. Scale bars represent 5 µm for the larger field of view including the vertical (Z) axis and 1.25 µm for the inset. (b) Mean distances of individual bead localizations in the blue and orange channels relative to the green reference channel, applying the ‘global’ and ‘global + local’ registration methods. The 3D positions of 527 beads on two-layer multicolor bead samples were determined by 3D Gaussian fitting, and the 3D distances were averaged. Error bars indicate SD. (c) Plots of beads along the X coordinate. The Pearson correlation coefficient (r) is shown for each channel to show the correlation, if any, between deviation and position in the field of view.

Figure 5

Possible chromatic shifts in calibration slides. (a) Translation along the Z-axis (T_Z) measured for the different refractive indices of immersion oils using the blue channel as a reference. Two-layer multicolor bead slides were imaged by 3D-SIM using immersion oils with different refractive indices as indicated. Bars represent the standard deviation (SD) of 1–3 measurements at different positions of the two slides. The Abbe numbers (v_D) for these immersion oils are also shown in parenthesis. (b) The same data in (a) shown for each individual parameter. Larger values indicate greater fluctuation. (c) A single set of four two-layer blue bead slides (a–d) imaged with different objective lenses in the blue, green, and orange channels by deconvolution microscopy; the blue channel was used as a reference to measure T_Z. Bars represent SD from measurements taken at 5–6 positions of each coverslip. (d) Translation along the Z axis measured for three coverslips (numbered as 1, 2, and 3) from different companies. All coverslips were of standard thickness No. 1.5 (0.16–0.19 mm) except for Zeiss No. 1.5 H (0.170 ± 0.005 mm) and Fisher No. 1 (0.13–0.17 mm). Multicolor beads were imaged by 3D-SIM using a silicone immersion objective lens, except for coverslips from Ibidi, for which the results from deconvolution are shown since beam polarization (required for 3D-SIM) was affected by these plastic coverslips. Error bars represent SD from 3–7 acquisitions at different positions on each slide. (e) Translation of the orange channel position relative to the blue channel (detected on separate cameras) monitored over eight months. Error bars (horizontal lines) indicate the negligible SD of sample measurements within the same day. (f) T_Z measured for beads and biological samples using silicone immersion objective lens observed in the blue (442 nm) and green (525 nm) channels. “Cells” indicates fixed biological samples on the coverslip imaged by 3D-SIM at a mean observation depth of ~3 µm. Bars represent SD from at least three different slides.

Figure 6

Chromatic shift in illumination. (a) An illustration of the CLSM setup to measure chromatic shift only for illumination. When the pinhole was opened to its maximum size, almost all light goes into the detector (PMT). Therefore, the chromatic shift of emission light is negligible and only that of the illumination light is measured. (b) Fixed cells were stained with phalloidin conjugated with Alexa 488 and 594. The green channel, obtained by exciting with 488 nm, was aligned with respect to the red channel, obtained by exciting with 488 (“488” blue bars) or 561 (“488 + 561” green bars) nm using the global method. The vector sum of the seven global alignment parameters is shown. Different immersion oils were used to examine the influence of spherical aberration and dispersion. (c) An illustration of WFM and 3D-SIM illumination around the sample. (d) The same samples from (b) were imaged with WFM or 3D-SIM using the same objective lens. WFM images were deconvolved (WFM Decon) and 3D-SIM raw images were averaged to create pseudo-WFM images. The red channel excited with 488 nm and the green channel excited with 488 nm were aligned with respect to the red channel excited with 561 nm and the green channel excited with 488 nm. The vector sum of the seven alignment parameters is shown.

Figure 7

Chromatic shifts of replicates on the same coverslip. (a) Illustration of a chambered coverglass with numbers temporarily assigned to individual chambers. (b) Multispectral fluorescent beads and fixed cells stained with phalloidin conjugated with Alexa 488 and 594 were imaged with 3D-SIM. Then, the vector sum of the global alignment parameters for green and red was compared with chamber No. 1. (c) Mean difference of the vector sum of the global alignment parameters with chamber No. 1 (“Total”), neighboring chambers (“Neighbor”), and chambers with no contact (“No contact”).