Polychromatic polarization: Boosting the capabilities of the good old petrographic microscope

Polychromatic polarizing microscopy (PPM) is a new optical technique that allows for the inspection of materials with low birefringence, which produces retardance between 1 nm and 300 nm. In this region, where minerals display interference colors in the near-black to gray scale and where observations by conventional microscopy are limited or hampered, PPM produces a full spectrum color palette in which the hue depends on orientation of the slow axis. We applied PPM to ordinary 30 µ m rock thin sections, with particular interest in the subtle birefringence of garnet due both to non-isotropic growth or to strain induced by external stresses or inclusions. The PPM produces striking, colorful images that highlight various types of microstructures that are virtually undetectable by conventional polarizing microscopy. PPM opens new avenues for microstructural analysis of geological materials. The direct detection and imaging of microstructures will provide a fast, non-destructive, and inexpensive alterna-tive (or complement) to time-consuming and more costly scanning electron microscope–based analyses such as electron backscatter diffraction. This powerful imaging method provides a quick and better texturally constrained basis for locating targets for cutting-edge applications such as focused ion beam-transmission electron microscopy or atom probe tomography.


INTRODUCTION
The polarizing microscope is the fundamental analytical tool for any first characterization of geological materials. Invented almost two centuries ago (Davidson, 2010), its fundamental structure and analytical capabilities have not changed much since. Due to such long, established use, geologists may not realize that polarizing microscopy suffers from one major limitation, which is namely the poor capability to resolve microstructures where minerals have low birefringence (<0.010) and display interference colors in the gray scale. This corresponds to the range of retardance from 0 to ∼300 nm. Many important rock-forming minerals (e.g., feldspars, silica polymorphs, hydrogarnets, andradite, leucite, and apatite) possess such low birefringence intrinsically (Deer at al., 2013). Others, originally cubic, may acquire subtle anisotropy and birefringence due to imposed deformation. One classic example is birefringence haloes around inclusions trapped in diamond (Howell et al., 2010) or garnet (Campomenosi et al., 2020). Techniques to highlight the optical effects of very low birefringence materials include using compensators such as the Bräce-Köhler or the lambda plate. As the retardance is a function of thickness, another way to enhance birefringence effects is to make thicker sections. Although in some cases thick (e.g., 100 µm), sections provide satisfactory results (Cesare et al., 2019), they are seldom used because of the great drop in transparency and sharpness of the subjects imaged.
The above shortcomings of conventional optical microscopy, until now accepted as intrinsic and unsolvable, are overcome by a technique called polychromatic polarizing microscopy (PPM). We show how PPM, implemented as a complementary accessory on petrographic microscopes, allows unprecedented imaging of microstructures in very low birefringence minerals using standard 30 µm thin sections. PPM not only produces a full palette of colors in areas normally dominated by gray, but it allows fast, qualitative determination of crystallographic and strain orientations.

POLYCHROMATIC POLARIZING MICROSCOPY
PPM was first presented as a means of imaging biological objects with birefringence down to a few nanometers. Details of various optical setups and theoretical bases of PPM are given by Shribak (2015Shribak ( , 2017 and provided in the Supplemental Material 1 . The polychromatic polscope is very similar to the petrographic microscope, but the polarizer is accompanied by a special spectral polarization state generator, and the analyzer is accompanied by an achromatic quarter-wave plate, which forms the circular analyzer (Shribak, 1986). This setup makes it easy to switch from PPM to plane-polarized light (PPL) to cross-polarized light (XPL) visualization. Even at very low retardance, PPM produces the full hue-saturation-brightness (HSB) color spectrum in birefringent materials. Unlike in conventional polarizing microscopy, where interference colors are a measure of the retardance according to the Michel-Levy chart, HSB hues in PPM depend on the orientation of the slow vibration direction with respect to a preset zero direction (conventionally oriented E-W). This implies that hues change continuously during the rotation of the stage, repeating every 180°, and that extinction is never observed. For some aspects, PPM recalls the "fabric analyzer" (Wilson et al., 2003), which also uses the orientation of the optical indicatrix to find crystal orientation but requires an ad hoc *E-mails: bernardo.cesare@unipd.it; mshribak@ mbl.edu instrument and has never been used on minerals with birefringence of < 0.009.
The functioning peculiarities and potentials of PPM are illustrated by the close-up views on the central part of a frustule of the diatom Arach-noidiscus spp. (Fig. 1). These siliceous skeletons are normally black to dark gray under XPL (Fig. 1B). PPM (Fig. 1C) uses colors to visualize the structure of the frustule. By taking a complementary image with the PPM rotated to 90° (Fig. 1D), a differential image can be computed (Fig. 1E), which suppresses the imperfections and provides better measurements of hues. The range and geometric distribution of hues in the inner costae of the diatom are virtually identical to those of the color scheme in Figure 1F, which displays the experimentally calibrated variation of hue as a function of the angle between the slow direction of the birefringent material and the zero position of PPM (E-W in Fig. 1F). Through such analogy, PPM allows us to infer that (1) each of the 28 inner costae (Ross and Sims, 1972) radiating around a central ring of the diatom is a single crystal; (2) costae may be crystalline and not amorphous as commonly thought (e.g., Javaheri et al., 2015;Aitken et al., 2016); (3) they are crystallographically oriented following a radial pattern; and (4) they are length-slow, as the slow vibration direction is parallel to the elongation of each costa (Fig. 1E). Obtaining such a wealth of information on the basis of two optical images alone highlights the exceptional added value of PPM as a novel imaging technique over conventional polarized microscopy.

NON-ISOTROPIC GARNET GROWTH
We tested PPM on common (Fe-Mg-Ca-Mn) tetragonal garnets, which were recently shown to be more common than previously thought (Cesare et al., 2019). They are easily overlooked due to their very low birefringence except when observed in thick (≥100 µm) sections.
On regular 30 µm thin sections of pelites from the eastern Alps, PPM produces striking differential images in areas where XPL would show nothing but apparent isotropy (Figs. 2A-2C). The garnet is unexpectedly optically anisotropic and shows beautiful optical sector zoning with pairs of opposed sectors characterized by similar hue and therefore by similar optical orientation. It should be kept in mind that PPM is a semiquantitative technique, as the direction of the slow vibration axis provided by the hue in PPM images is not absolute but is the direction of the projection of the axis onto the plane of the thin section regardless of the actual dip angle of the axis. The boundaries between adjacent sectors range from sharp and straight to diffuse or compenetrated. Owing to the 30 µm thickness of the samples, these microstructures are much better resolved than when thicker sections are used. PPM was applied (Fig. 2D) to an eclogite from Port Macquarie, Australia (Tamblyn et al. 2019(Tamblyn et al. , 2020, that contains garnet compositions in the range expected by Cesare et al. (2019) for non-isotropic garnets. PPM reveals that the garnet crystals are birefringent and beautifully sector-zoned, where different zones may represent growth twins. Being the only technique by which these microstructures can be visualized on regular thin sections, PPM would be a key tool for precisely locating the targets for a focused ion beam (FIB)-based, high-resolution transmission electron microscopy study of possible twinning and its origin. The differential PPM images of Figure 2 also demonstrate, as one would expect, that the optical orientation of sectors is not random. In fact, the fast vibration direction is normal to the growing faces (Fig. 2D).
Optical anisotropy of garnet is also manifested as striped (or mottled) areas of crystals, sometimes within each sector, which is therefore not a coherent optical entity. The parallel stripes or bands can be as thin as a few tens of micrometers and often form intersecting sets characterized by two prevailing optical orientations (Fig. 2E). Striped birefringence patterns are well-developed (Figs. 2F and 2G) in another eclogite sample from the central Tauern Window, Austria (Warren et al., 2012), where, conversely, sector zoning is not evident. Analysis of PPM hue distribution in one of these zones (Fig. 2G) shows that the optic axes of stripes are systematically arranged along two orientations at a high angle to each other.

STRESS-INDUCED BIREFRINGENCE IN GARNET
Another application of PPM concerns the very low birefringence induced by non-isotropic stress fields applied to optically isotropic crystals. Such stress fields may have led to permanent deformation (i.e., plasticity) in the past or may be the signal of an elastic residual stress that is still acting on a crystal at room conditions, for example around inclusions.
Garnet may display crystal plasticity when deformed at high temperature (Prior et al., 2000) and/or high differential stress (Austrheim et al., 2017). Distortion of the crystal lattice may determine an optical anisotropy that is seldom detectable under conventional XPL. Using PPM, we imaged (Figs. 3A-3E) a felsic mylonite from the Musgrave Ranges, central Australia, where garnet underwent both brittle and plastic deformation as determined by electron backscatter diffraction (EBSD) and focused ion beam-transmission electron microscope investigation (Hawemann et al., 2019). The PPM images demonstrate that the complex internal deformation of garnet can also be rendered optically. With diffuse microfracturing along subparallel sets, the variations of hue in the garnet portions bounded by fractures indicate that the entire crystal is affected by crystal plasticity (Fig. 3A). The distribution of hue in the close-up images (Figs. 3B-3D) suggests the presence of a patterned optical orientation of deformed garnet structures. Furthermore, analysis of hue distribution with image processing software like ImageJ (Schneider et al., 2012) highlights the presence of subdomains with sizes in the range of 2-5 µm that display distinct optical orientation with respect to surrounding domains (Fig. 3E). This texture is strikingly similar to that of the subgrains of garnet imaged by EBSD by Austrheim et al. (2017). At present, it is unclear if the hue distribution in these differential PPM images at high magnification may be affected by optical artifacts and therefore does not correspond to real optical inhomogeneities. Should it, conversely, be verified by further investigation, the possibility of imaging subgrains in garnet optically by PPM would represent a major breakthrough for microstructural analysis. Lattice strain and anomalous birefringence in optically isotropic minerals is also induced by inclusions trapped at high pressure-temperature during metamorphism due to the contrast of their thermoelastic properties with those of the surrounding host (e.g., Howell et al., 2010). The residual stresses and strains recorded by host-inclusion systems are central to elastic thermobarometry (e.g., Bonazzi et al., 2019). With cooling and exhumation, inclusions typically induce "birefringence halos" in the surrounding garnet host at ambient pressure-temperature conditions. Although these halos are visible under XPL in the form of a cross-shaped extinction pattern ( Fig. 3F; Campomenosi et al., 2020), their imaging by PPM reveals important additional features. First of all, the black cross, unavoidable but also of little utility, is not present anymore. Conversely, the entire spectrum of hues covering all possible slow axis orientations is observed around inclusions (Figs. 3G-3I). This provides, without the need to rotate the stage and sample, immediate visualization of the continuous change of orientation of optic axes in the garnet that is now locally anisotropic. Such qualitative visualization can be refined by inspection of hue distribution by which, for example, departures from a purely radial pattern due to the shape and intrinsic anisotropy of mineral inclusions can be detected and analyzed (Fig. S1 in the Supplemental Material).

PERSPECTIVES
Although we focused our attention on garnet, the applications of PPM in the geosciences extend to all materials that possess very low retardance. For example, the unprecedented visualization of microstructures of Arachnoidiscus spp. (Fig. 1) demonstrates the potential that PPM has for the study of siliceous microfossils. The best applications of PPM are probably yet to be discovered. We foresee that PPM will become a fundamental tool for studying microstructures in crystals that-from the view point of the optical properties-are nominally isotropic or intrinsically birefringent (Burnett et al., 2001) or show low birefringence such as, for example, leucite, feldspars, and silica polymorphs (Fig. 4).
The imaging capabilities of PPM, especially in differential mode, disclose a wealth of micro-structural features that until now were optically inaccessible. PPM can be accomplished using a standard petrographic microscope and conventional thin sections, thus making PPM a fast and extremely cost-effective technique. Among the newest and most important utilities of PPM is the easy identification of the optical orientation of a (portion of) crystal by means of its hue such as, for example, the chalcedony fibers in Figures 4C and 4D. Although this is a semiquantitative method that cannot replace quantitative approaches such as universal stage or EBSD, the applications on garnet described above show that PPM is the perfect tool, and far more precise than conventional polarizing microscopy, for identifying and localizing targets for advanced analyses like TEM or atom probe tomography.