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Polariscopy is any method that uses polarized light to determine the distribution of retardation in a transparent material. Polarimetry is a method that derives quantitative information using polariscopic techniques. Polariscopy/polarimetry is commonly used to detect stress-induced birefringence in photoelastic stress analysis, for the

identification of gemstones, and in petrology. In the latter case, specially adapted microscopes (petrological or polarizing microscopes) are used to determine and analyze the birefringent properties of crystalline minerals in thin sections of rock. Polariscopy may be performed with light transmitted or back-reflected through a sample.

birefringent properties of the sample (e.g. to determine magnitude and direction of retardation).

The discipline of polariscopy has developed its own terminology. Thus the term ‘fringe’ is synonymous with isochrome and refers to the coloured lines in a birefringent sample as seen with the polariscope using white light. They represent lines of equal retardation and, in photoelastic terms, are lines which join points with equal maximum shear stress magnitude. Isoclinics may be equated to isogyres as previously defined and represent the locus of points of extinction i.e. optically isotropic areas of the sample when linear polarized light is transmitted without alteration and is negated

(extinguished) by a second orthogonal polarizing filter (analyzer). A focal area of isotropic trasmission is termed an isotrope. In photoelasticity, isoclinics identify the locus of points in the sample along which the principal stresses are in the same direction as the vibration directions of the polarizer/analyzer.

Polariscopy with reflected light is used in photoelastic stress analysis where a reflective prototype is coated in a photoelastic material. Careful interpretation of results is

required as a simple relationship between induced birefringence and stress only occurs with normal incidence illumination and reflection alters the state of polarization. The use of photoelastic terminology in the study of corneal birefringence is potentially confusing as it has been taken to imply that corneal birefringence is photoelastic. This assumption has misled a number of previous investigators (e.g. Mountford 1982; Ichihashi, Khin et al. 1995; Volkov, Malyshev et al. 1990). As stated in §2.4.1, photoelasticity is insignificant in corneal optics where retardation, and hence the fringes/isochromes and isoclinics/isogyres, results from form and crystalline

birefringence. The use of photoelastic terminology which might suggest otherwise will be avoided.

5.1.1 Ophthalmic polariscopy

The simplest polariscopic studies of whole cornea have been on isolated dissected specimens between crossed polarizers. This was the method of earlier investigators such as Schiötz, Valentine and later Naylor and Stanworth (cited in Bour 1991)) and from which the conflict regarding uniaxial or biaxial behaviour arose (§13.1). Polarization microscopy of histologically prepared corneal sections (e.g. Figure 2.3) significantly advanced understanding of corneal cross-sectional architecture (e.g. Tripathi and Tripathi 1984; Bron, Tripathi et al. 1997). What studies there are do not take full advantage of the rotational stage of the polarizing microscope and describe the polarization phenomena without reference to orientation of the sample relative to the planes of polarization of the polarizer/analyzer. Human ex vivo studies have also been

limited by small sample numbers and possible confounding factors such as post mortem changes and fixation artefact.

In vivo biomicroscopy of the human eye in white unpolarized light is a standard

technique used routinely in clinical practice, but gives little structural information about the stroma and its lamellar organisation. Biomicroscopy of the human cornea in vivo

using reflected linear polarized light was first described in some detail by Koeppe (1921), who identified an interweaving network of lines in the stroma. These findings were later confirmed by Mishima (Mishima 1958; Mishima 1960) who proposed that the observed effects were due to peripheral radial and central interlacing populations of collagen fibrils. It was suggested that linear polarization biomicroscopy might be a

useful technique for the evaluation of corneal stromal structure in health and disease. The 1950-70s saw pioneering investigations into corneal birefringence and polarization physiological optics, but thereafter interest declined apart from the key finding that established the biaxial model (Blokland and Verhelst 1987). Up to this time the principle driving force behind the research was to determine and understand normal physiology and anatomy. Clinical investigations were limited to unsuccessful attempts to use stress-induced birefringence to measure intraocular pressure (Nyquist and Cloud 1970) and to measure glucose concentration in the aqueous humour of the anterior chamber by determining optical rotation (Rabinovitch, March et al. 1982). Attempts to directly visualise stress birefringence induced in the living human cornea by surgical manipulation (Misson and Stevens 1990) did not progress.

Developments in ophthalmic polarimetry gained momentum with the advent of

scanning laser polarimetry (SLP) (Dreher, Reiter et al. 1992), a technique developed to analyse the retinal nerve fibre layer in order to diagnose and monitor glaucoma. The relatively weak retinal birefringence was dominated by that of the cornea and early SLP devices had a fixed retarder (60nm orientated slow 15° nasally downward) to

compensate for the corneal retardation (Dreher and Reiter 1992). Initial results from numerous studies (see Garway-Heath, Greaney et al. 2002 for summary) showed the technique to be inferior to others in its ability to discriminate normal from glaucomatous eyes and this was found to result from the naïve assumption about the constancy of the magnitude and azimuth of the corneal retardation. This assumption also probably accounted, at least in part, for the failure of the aqueous humour glucose measurements (Rabinovitch, March et al. 1982; Malik 2009). Further studies (Knighton and Huang 2002; Weinreb, Bowd et al. 2002) more accurately defined the extent and variability of

human central corneal retardation which led to the introduction of SLP with a variable retarder and a consequent increase in the accuracy of the technique (Tannenbaum, Hoffman et al. 2004) . Despite this, SLP has now largely been superseded by optical coherence tomography (OCT), an interferometric technique that measures the echo-time delay and magnitude of back-scattered or reflected light to construct a 2- and 3-

dimensional image of ocular cellular (e.g. retinal) components (Huang, Swanson et al. 1991).

Compensation of ocular birefringence remains important in OCT in that similar polarization states are required in the reference and sample beams to maximise

interference. A natural development of OCT is polarization-sensitive OCT which, at the time of writing, is not yet commercially available but promises to further extend the diagnostic facility of interferometric techniques by measuring retardation data as well as scatter/reflection (Pircher, Hitzenberger et al. 2011). Other extensions of OCT currently under development include dual-beam-scan Doppler optical coherence angiography (OCA) (Makita, Jaillon et al.) and polarization-sensitive swept-source OCT (Yamanari, Makita et al. 2011). All techniques that image birefringent structures within the eye and beyond the cornea require the initial compensation of corneal retardation, thus a clear understanding of magnitude, orientation and spatial distribution of retardation across the corneal surface is essential for the accuracy of these techniques.

Apart from the sophisticated techniques outlined above and biomicroscopy using simple semi-fixed linear polarizers, more complex experimental investigations into corneal retardation have been performed with methods such as phase stepping polarimetry (Jaronski and Kasprzak 1998) and liquid crystal polarimetric techniques (Bueno 2000). Mueller matrix polarimetry greatly advanced the understanding of the birefringent

properties of the human eye in vivo (Blokland and Verhelst 1987). To date, the phase

stepping techniques are of low resolution (c. 250μm), but confirm previous findings using simpler techniques. Scanning laser polarimetry has been effectively used to study corneal birefringence in a small number of subjects (Knighton, Huang et al. 2008). The recent methods have disadvantages of expense, complexity and inaccessibility.

Although linear polarization biomicroscopy is relatively easy to perform, a fundamental disadvantage is that only birefringent elements (collagen fibrils in the case of corneas) orientated with principle axes at or near 45º to the axes of polarization are visible. An additional practical disadvantage is the need for a specially modified slit-lamp

biomicroscope with two rotateable, but mutually orthogonal, polarizing filters placed in the illumination and observation light paths respectively.

A simple, inexpensive and accessible polariscopic technique using reflected ‘circular’ polarization was first used to demonstrate corneal isochromatic rings (Blokland and Verhelst 1987) and later used empirically in conjunction with a slit-lamp biomicroscope to detect possible stress birefringence in corneas that had undergone surgical

manipulation (Misson and Stevens 1990). This technique has potential for the qualitative and semi-quantitative examination of human corneas in vivo although the

basic principles of the technique and interpretation of results are yet to be detailed. The purpose of the present chapter it to determine the theoretical bases for the various types of polariscopy that can be used in vivo and which might have clinical use.

The basic principles of polarized light, retardation and interference are outlined in §15.3 together with an introduction to the computational methods using Stokes vectors and Mueller matrices.