Computational adaptive optics for live three-dimensional biological imaging

Abstract

Light microscopy of thick biological samples, such as tissues, is often limited by aberrations caused by refractive index variations within the sample itself. This problem is particularly severe for live imaging, a field of great current excitement due to the development of inherently fluorescent proteins. We describe a method of removing such aberrations computationally by mapping the refractive index of the sample using differential interference contrast microscopy, modeling the aberrations by ray tracing through this index map, and using space-variant deconvolution to remove aberrations. This approach will open possibilities to study weakly labeled molecules in difficult-to-image live specimens.

Figure 1

The problem: Sample-induced optical aberration due to heterogeneous refractive index. (A) An example of a nonaberrated 3D image of 0.1-μm bead using high magnification (100×/NA1.3 objective) microscopy. In-focus and +/− 3 μm defocus images are shown. The subpanel A' is an xz section through the center of the 3D bead image. (B) A fluorescent bead imaged three-dimensionally (as in A) under a polytene nucleus in a Drosophila salivary gland cell, showing sample-induced distortions. B' is the corresponding xz section. (C) The image of a field of view containing several beads under a polytene nucleus, showing the spatial dependence of these distortions. The image is taken slightly out of focus to emphasize the different distortions. (D) DNA-specific dye Oli Green staining of polytene chromatin in a live cell. The optical section shown was processed by deconvolution using the symmetric unaberrated PSF. The familiar chromosome bands are almost entirely obscured by distortions for both the unprocessed or processed image. (Scale bars, 2 μm.)

Figure 2

The solution: A schematic outline. (A) Sample-induced aberration: The imaging situation is modified by variations in refractive index within the sample volume, resulting in highly distorted wavefront originating from the point source. For the presentation, three spheres with refractive index higher by 0.15 units above the medium were simulated in the sample volume. For viewing purposes, the in-focus image is 30 times attenuated with respect to the out-of-focus images shown (unaberrated cases would have 300 times the corresponding attenuation). (B) Evaluating the refractive index variations within the sample: The imaging conditions in A are observed with DIC optics (symbolically shown by the Wollaston prism), resulting in the 3D image consisting of a series of two dimensional gradient images of the refractive index of the sample. The three DIC images shown are at focal planes centered about the three spherical objects. They are processed by line integration (29) to yield a 3D map of the refractive index of the sampled volume. (C) Ray tracing through the sample: Light rays emerge isotropically from a point within the sample volume. Computerized ray tracing for the shown three spheres in the sample volume gives the distorted diverging wavefront at the entrance pupil of the microscope due to refraction of the ray directions and deviation of their optical paths from the ideal spherical wavefront (illustrated by extended ray ends). The Kirchhoff interference integral is applied to this wavefront to calculate the corresponding distorted point diffraction 3D image. (D) Deconvolution by using the distorted image reconstructs a point source.

Figure 3

Proof of principle: (A) Submicron beads on a slide were imaged under an oil droplet (18 μm in diameter). Distorted aberrated images were recorded. In the Inset, three optical sections for the bead 1 display a strong out-of-focus “flare” and highly asymmetric out-of-focus diffraction pattern (arcs instead of Airy rings). (B) The DIC images of this sample recorded three-dimensionally. Orthogonal section views are presented, with the superimposed projected positions of the beads. (C) PSFs computed by ray tracing through the oil droplet for the positions of the beads. The insert is three optical sections calculated for the bead 1. (Scale bars, 2 μm.)

Figure 4

Comparison of measured and calculated PSFs: A–D are defocused optical sections of bead 1 (as labeled in Fig. 3A) at 3.0 μm below focus and E–H are optical sections of bead 2 at 2.75 μm below focus. (A and E) A measured image of the 0.1 μm bead. (B and F) A computed 3D ray-traced PSF using a refractive index map from the line integrated oil drop DIC data. (C and G) A ray-traced PSF using simulation of an oil drop with uniform known refractive index. (D and H) A computed PSF in which the aberrated wavefront calculated by ray tracing through a simulated oil drop of uniform refractive index was applied to a measured, unaberrated PSF by using Eqs. 2a–2e. (Scale bars, 2 μm.)

Figure 5

Deconvolution results: (A) The beads shown in Fig. 3A were deconvolved with the ray-traced PSFs based on the refractive index map computed from Fig. 3B. The line profiles through the bead centers plot the logarithmic intensities down to the 10⁻⁴ noise level. (Scale bar, 2 μm.) (B) A quantitative comparison of the effect of various PSFs on the deconvolution process for bead 1 of Fig. 3A is shown as a function of the number of iterations. (Top) The peak integrated intensity. (Middle) The integrated intensity of the flare. (Bottom) The ratio of peak to flare intensity, a figure of merit for deconvolution effectiveness. Each plot has been normalized to the predeconvolution integrated intensity. The PSFs used to deconvolve bead 1 are: the image itself (Fig. 4A, solid line), a bead image taken under conditions of minimal distortions (Fig. 1A, dashed line), a ray-traced computed PSF based on the simulated refractive index map (Fig. 4C, dotted line), and a PSF calculated by applying the ray-traced wavefront distortions to a measured, unaberrated PSF using Eqs. 2a–2e (Fig. 4D, dash–dot line). After 15 deconvolution iterations, the signal (peak) intensity to nonsignal (flare) intensity ratio is improved 8-fold by using the ray-traced PSF and 15-fold by using the PSF modified by Eqs. 2a–2e, when compared with those using an unaberrated PSF.