Quantifying distortions in two-photon remote focussing microscope images using a volumetric calibration specimen

Abstract

Remote focussing microscopy allows sharp, in-focus images to be acquired at high speed from outside of the focal plane of an objective lens without any agitation of the specimen. However, without careful optical alignment, the advantages of remote focussing microscopy could be compromised by the introduction of depth-dependent scaling artifacts. To achieve an ideal alignment in a point-scanning remote focussing microscope, the lateral (XY) scan mirror pair must be imaged onto the back focal plane of both the reference and imaging objectives, in a telecentric arrangement. However, for many commercial objective lenses, it can be difficult to accurately locate the position of the back focal plane. This paper investigates the impact of this limitation on the fidelity of three-dimensional data sets of living cardiac tissue, specifically the introduction of distortions. These distortions limit the accuracy of sarcomere measurements taken directly from raw volumetric data. The origin of the distortion is first identified through simulation of a remote focussing microscope. Using a novel three-dimensional calibration specimen it was then possible to quantify experimentally the size of the distortion as a function of objective misalignment. Finally, by first approximating and then compensating the distortion in imaging data from whole heart rodent studies, the variance of sarcomere length (SL) measurements was reduced by almost 50%.

Keywords: cardiac imaging; distortion; remote focussing microscopy.

Figure 1

ZEMAX optical model of a simplified scanning microscope. The rays are color coded according to the off-axis tilt angle of the lateral (X) scan mirror; red = +2°, green = 0°, blue = −2°. Inset is shown the model of an imaging objective, composed of a triplet lens and a physical aperture. Numbers indicate focal lengths in millimeters. See text for full details.

Figure 2

Sketch showing the optical layout of the remote focussing microscope (see main text for details). Where shown, numbers indicate lens focal lengths in millimeters. BCU, beam conditioning unit; PBS, polarizing beam splitter; QWP, quarter wave plate; PMT, photomultiplier tube; P, gravity fed perfusion of the cardiac tissue.

Figure 3

Images showing the structure of the laser fabricated calibration specimen. (A) Macroscopic image of the plastic dye-doped substrate. The fabrication region is indicated by the red square. Schematics showing how points were fabricated on a 10 μm square grid (B) over a 500 × 500 μm area, and extended axially (C) over a depth of 200 μm.

Figure 4

(A) Example two-photon image of the fluorescent specimen. Flaws in the plastic substrate are shown encircled. (B) Inverted version of (A). A line profile through the image (inset) shows the signal to noise ratio of the fabricated features. (C) Processed version of (B). The white crosses indicate the centroids of the local maxima. The white diamond shows the center of the 512 × 512 image. The separation between the fabricated points is 10 μm.

Figure 5

The impact of lateral misalignment on specimen illumination. The top horizontal line shows the focal plane of the triplet (f = 12.5 mm) objective. The chief rays have been extended below the focal plane to highlight the change in direction when the objective is displaced 2 mm to the left (A), when it has zero lateral displacement (B) and when it is displaced 2 mm to the right (C). Gray regions indicate clipping of the scan mirror image by the physical aperture. A simulation of the effect of the lateral displacement in (C) on a volumetric image of the columnar specimen is shown in (D). See main text for full details.

Figure 6

ZEMAX drawings showing the change in the vergence of chief rays with objective misalignment. The top horizontal line shows the focal plane of the triplet (f = 12.5 mm) objective. The chief rays have been extended below the focal plane to highlight the change in vergence. The simulations show axial misalignment of 10 mm below focus (A), at focus (B), and 10 mm above focus (C). Gray regions indicate clipping of the scan mirror image by the back aperture. A simulation of the effect of the axial magnification in (C) on a volumetric image of the columnar specimen is shown in (D). See main text for full details.

Figure 7

Plots showing the change in apparent fabrication point separation as a function of depth for the objective locations (Z₀-values) indicated. The average lateral feature separation was calculated five times for each image, with the average and standard deviation value shown for each point. Positive values of depth indicate a displacement toward the objective.

Figure 8

Plot illustrating the apparent change in position of a static point located at the edge of a 450 μm field of view between the top and bottom of a 100 μm stack for each of the objective positions shown. The colors of the points correspond to Z₀-values of −7 mm (blue), 0 mm (red), 11 mm (purple), and 15 mm (green).

Figure 9

Images taken from three different stages of raw data processing to determine the average SL of cells at a given depth of living cardiac tissue. A two-photon XY image (close up shown in A) is used to identify several cardiomyocytes cells with clearly identifiable sarcomeres (red crosses in A). To aid interpretation of the images, the inset in (A) shows a model cell (red) with sarcomeres (dark red) inclined with respect to the focal plane (blue). 40 × 10 pixel sub-images (yellow boxes in A and close up in B) are taken from each of the identified cell candidates in the two-photon image. (C) A Fourier transform is used together with image metadata to identify the mean SL of each cell. The centroid of the Fourier space peak in (C) was calculated using a 5 × 5 pixel window centered on the peak. The centroid value was then used together with the real space image size (in μm) to determine the SL. See main text for full details.

Figure 10

Measurements of mean SL as a function of imaging depth. Measurements were made of at least three cells at each depth. Images were taken at three different sites across two different hearts; one SD and one SHR (red = SHR, green and blue = SD). The trend line shows a steep change in image magnification with imaging depth.

Figure 11

Measurements of the mean SL as a function of depth in SD rodent hearts before (red) and after (purple) correction for a 20% change in magnification with depth.

Figure 12

XZ sections of a two-photon 3D image stack. A single cardiomyocyte is shown highlighted both before (A) and after (B) a coarse distortion correction. The lower arrow indicates the direction of the cell axis, with the vertical arrows indicating the direction of the sarcomeres. The image contrast has been enhanced to highlight the sarcomere structure. Scale bar: 20 μm in the focal plane (located at half the height of the image).