Rapid mapping of compound eye visual sampling parameters with FACETS, a highly automated wide-field goniometer

Abstract

A highly automated goniometer instrument (called FACETS) has been developed to facilitate rapid mapping of compound eye parameters for investigating regional visual field specializations. The instrument demonstrates the feasibility of analyzing the complete field of view of an insect eye in a fraction of the time required if using non-motorized, non-computerized methods. Faster eye mapping makes it practical for the first time to employ sample sizes appropriate for testing hypotheses about the visual significance of interspecific differences in regional specializations. Example maps of facet sizes are presented from four dipteran insects representing the Asilidae, Calliphoridae, and Stratiomyidae. These maps provide the first quantitative documentation of the frontal enlarged-facet zones (EFZs) that typify asilid eyes, which, together with the EFZs in male Calliphoridae, are likely to be correlated with high-spatial-resolution acute zones. The presence of EFZs contrasts sharply with the almost homogeneous distribution of facet sizes in the stratiomyid. Moreover, the shapes of EFZs differ among species, suggesting functional specializations that may reflect differences in visual ecology. Surveys of this nature can help identify species that should be targeted for additional studies, which will elucidate fundamental principles and constraints that govern visual field specializations and their evolution.

Appendix

Microscope

The microscope is a Nikon metallurgical model, mounted on a boom stand and focused by adjusting its position, while the subject remains stationary. It is equipped with five long-working-distance Nikon M-Plan objectives (2.5×, 5×, 10×, 20× and 40×), an epi-illumination attachment, and a camera tube with 1.0× relay lens. The Grasshopper Express video camera is configured to provide 920 × 760 pixel 8-bit grayscale images, with a frame rate of ~15 Hz. Axial epi-illumination is provided by a 50-W tungsten halogen lamp, with an intervening heat filter (Newport FSR-KG3), field and aperture diaphragms, and removable neutral density, spectral and polarization filters.

Goniometer alignment

Prior to making measurements from the eye, rotary axes A and B are carefully aligned to the fixed point (Fig. 2a, FP) to minimize the amount of repositioning and refocusing that are required to keep the eye in view. Rotary axis alignment (Fig. 4) is accomplished by viewing each axis when it is parallel to the optical axis of the microscope objective (Fig. 4, Axis M), or is made to appear so with a mirror. Axis A is aligned first, because it cannot be moved without altering the position of Axis B. The rotary stage angles are positioned at (0,0), a vertical translation stage (Fig. 2a, By) is used to move the eye temporarily below Axis M, and a small rail-mounted first-surface mirror, precisely oriented at a 45° angle, is moved into place to provide an overhead view of the eye and render Axis A virtually parallel to Axis M (Fig. 4a). A landmark on the eye is chosen near the center of the field of view, and as Axis A is rotated, the circular trajectory of the landmark reveals the location of Axis A at the center of the circle. Specific translation stages (Ax and Az; Fig. 2a) are used to move Axis A toward the center, and other stages (Bx and Bz; Fig. 2a) are used to recenter the landmark.

Fig. 4

Schematic overview of rotary Axis A and Axis B alignment procedures (see text for additional details). a To align axis A, the eye (e) is moved down below the objective axis (Axis M), and a 45º mirror (m) is moved into place to provide a view of the upper side of the eye. The position of Axis A in the (x,z) plane is determined by rotating the axis while viewing the eye, and using the appropriate translation stages to make Axis A coplanar with Axis M. b After removing the mirror, moving the eye up to bring the side of it back into view, and refocusing the microscope in the Z direction, the same procedure is used to adjust Axis B within the (x,y) plane until it coincides with Axis M. fp focal plane, ob microscope objective

After removing the mirror and bringing the side of the eye back into view (Fig. 4b), Axis B is aligned in the same way, now using stages Bx and By (Fig. 2a) to align Axis B, and stages x′ and y′ to recenter the eye. The accuracy of Axis A and B alignment is limited by the ca. 5 μm resolution of the micrometer adjustments on the corresponding translation stages (Ax and Az: Newport model 430; Bx and Bz: Melles Griot 2 × 2” stages; By: Oriel model 16611 vertical translation stage). The resolutions of motorized stages x′, y′, and z′ are well under 5 μm, as previously noted in the main text.

Autofocusing

Autofocusing is accomplished by obtaining a series of images across a focusing range, evaluating the quality of focus of each image by computing a “focus index,” and then moving the microscope to the best focus level. Since higher-magnification objectives have shallower depths of field, a different focusing range is used for each objective. The microscope is first moved from its current position (usually, the level that was previously in focus before the eye was rotated) to one limit of the focusing range. As the microscope is scanned through the focusing range, a series of digital snapshots is obtained, and the focus index is computed from a circular region of interest (ROI) at the center of the image. The software increases the minimum ROI diameter of 100 pixels when the facet diameters currently in view exceed a certain threshold. The focus index is defined as the variance of the pixel brightness values within the ROI:

$${\text{Focus index}}= \sum\limits_{i=1\; to\; N}(I_{i}-I_{m})^2 /N$$

where I _i is the intensity of the ith pixel, I _m is the mean pixel intensity, and N is the number of pixels in the ROI.

For a given scene that is viewed at several focus levels, the best-focused images tend to exhibit the highest variances, because local gradients in pixel brightness are steeper when edges and textures are in focus. The variance metric was chosen because previous tests of several alternative image-processing filters have shown this to be one of the most robust indicators of focusing quality (Sun et al. 2004), and preliminary tests of focusing on the surfaces of insect eyes demonstrated its effectiveness.

Each time the eye is rotated to a new orientation, focusing scans are used in two ways. First, a focusing scan is used to obtain information that will be used for recentering the eye. In this case (see “Recentering,” below), the image obtained at each focus level is divided into a grid of rectangular ROIs, and a local focus index is calculated from each ROI. Second, after recentering the eye, a final focusing scan and focusing adjustment is performed before acquiring the image that will actually be used to represent the view at the current orientation. For this purpose, only the central portion of the current view is of interest, so a single ROI is used at the center of the image, and for symmetry, this ROI is defined to be circular instead of rectangular. After the final focusing adjustment, three “live” video snapshots are averaged to reduce random noise in the images, and the mean image is saved to a file and also used for additional image processing (see “Image processing to measure ommatidial parameters,” below).

Recentering

After the eye has been rotated to a new orientation, its position within the vertical (“x,y”) focal plane is adjusted so as to center the portion of the eye that lies closest to the microscope objective. The purpose of this step is to ensure that distance and area measurements from the surface of the eye are made where its curved surface is most nearly normal to the microscope’s optical axis. This avoids measurement errors that could otherwise arise from viewing a tilted surface, and ensures that the eye surface is viewed in a consistent manner at each sampled orientation.

To identify the portion of the eye that lies closest to the microscope, the automated code first performs a focusing scan to bring the center of the current view into focus. Each image is divided into a grid of ROIs, and a focus index is calculated from each ROI. Next, the best-focused image level at each ROI location is used to construct a mosaic image in which each ROI is relatively well focused. Morphological image processing operations (see “Image processing to measure ommatidial parameters,” below) are then applied to exclude certain portions of the mosaic image that do not appear consistent with certain characteristics of compound eyes, as these parts of the image may represent locations outside of the boundaries of the eye. (Since the facetted surfaces of compound eyes are highly structured, they generally exhibit many edges. Thus, any ROI with a paucity of edges at its best focus level is excluded from further analysis.) The remaining ROI regions are used to create a 3-D topographic surface plot of eye “elevations” in the Z direction, and the eye is recentered, so as to position the maximum “elevation” at the center of the image. The final centering step is to identify the facet that is closest to the center of the image (see “Image processing to measure ommatidial parameters,” below) and position it precisely at the center.

Image processing to measure ommatidial parameters

Various image processing functions (many of which are provided in the MATLAB image processing toolbox) are used to enhance raw images and extract information about the sizes and locations of identifiable structures. Only the main steps are described here. After an eye sampling and image processing session, a separate MATLAB program is used to review the automated image processing results and correct any errors.

Using an averaged image from at least three snapshots, the image contrast is standardized by normalizing the range of pixel intensities to the full 8-bit gray scale, and a Gaussian smoothing operation is applied to minimize small bright or dark artifacts (Fig. 5a). A morphological “image opening” operation is applied to this image to help isolate the facets, but this operation should be scaled to the approximate sizes of the facets themselves. Therefore first, the bright white highlights on the convex surfaces of facets are used to provide a preliminary estimate of inter-facet distances. Due to the curvature of the eye surface, highlights and facet centers do not always coincide, but their spacing is similar. The grayscale image in Fig. 5a is converted to a thresholded binary (black and white) image (Fig. 5b), isolating the highlights as white spots on a uniform black background. The inter-highlight distance is then defined as the mean distance from the centroid of the most centrally located spot to the centroids of its four nearest neighbors (see Fig. 5b, blue lines). Returning to the previous grayscale image (Fig. 5a), an image opening step scaled to the inter-highlight distance renders each facet as a convex, relatively bright region surrounded by darker borders (Fig. 5c), and a “watershed” operation identifies individual facets as separate image regions with contiguous borders (Fig. 5c, yellow outlines). Finally, the local facet diameter is defined as the mean distance between the centroids of the most centrally located region and its four nearest neighbors (Fig. 5d, blue lines). To help the user visualize the facet lattice and evaluate the results of each processed image, the FACETS software marks the nine most centrally located centroids (Fig. 5d, yellow dots), and a Voronoi diagram, which depicts facet edges based on the centroid coordinates, is superimposed (Fig. 5d, yellow lines).

Fig. 5

Illustration of automated image processing steps that are used at each goniometer orientation to identify facets, locate facet centroid coordinates, and measure facet diameters. This view is from the anterior EFZ in Efferia (see Fig. 3b). a Grayscale image of the eye surface after averaging (N = 3), contrast enhancement and Gaussian smoothing. Regularly-spaced bright white spots are specular highlights reflected from the convex surfaces of cuticular corneas. b Binary (black and white) image from a, in which white spots correspond to the highlights. The mean inter-highlight distance is defined as the mean distance between the centroids of the most centrally located highlight and its four nearest neighbors (connected to the central highlight with blue lines). c Grayscale image from a, following an image “opening” step that has been scaled to the inter-highlight distance to emphasize facets, not highlights. Using the image in c, additional image processing steps identify individual facets (regions within yellow borders). d The final processing steps (here superimposed on the image from a) use the distances (blue lines) among the five most-central facet centroids (yellow dots) to measure the “local facet diameter” (see text for additional details). Arrows depict the overall flow of information during image processing. Scale bar in a = 50 µm

Using the mean of four inter-centroid distances as a proxy for facet diameters helps minimize possible errors due to image artifacts (e.g., from small specks of debris), which can distort the estimated dimensions of single facet regions. The distance measure also serves reasonably well regardless of the local geometry of the facet lattice. In eye regions where the facet lattice is hexagonal, inter-centroid distances correspond to the diameters of the nearly circular facets. In areas where the geometry is more square than hexagonal, the nearest four distances correspond to facet widths. Only the four nearest centroids are used, because in more-square regions, the distances to the fifth- and sixth- closest centroids would overestimate the desired measurement by as much as √2.