Optical phantoms for biomedical polarimetry: a review

Abstract.

Calibration, quantification, and standardization of the polarimetric instrumentation, as well as interpretation and understanding of the obtained data, require the development and use of well-calibrated phantoms and standards. We reviewed the status of tissue phantoms for a variety of applications in polarimetry; more than 500 papers are considered. We divided the phantoms into five groups according to their origin (biological/nonbiological) and fundamental polarimetric properties of retardation, depolarization, and diattenuation. We found that, while biological media are generally depolarizing, retarding, and diattenuating, only one of all the phantoms reviewed incorporated all these properties, and few considered at least combined retardation and depolarization. Samples derived from biological tissue, such as tendon and muscle, remain extremely popular to quickly ascertain a polarimetric system, but do not provide quantifiable results aside from relative direction of their principal optical axis. Microspheres suspensions are the most utilized phantoms for depolarization, and combined with theoretical models can offer true quantification of depolarization or degree of polarization. There is a real paucity of birefringent phantoms despite the retardance being one of the most interesting parameters measurable with polarization techniques. Therefore, future work should be directed at generating truly reliable and repeatable phantoms for this metric determination. Diattenuating phantoms are rare and application-specific. Given that diattenuation is considered to be low in most biological tissues, the lack of such phantoms is seen as less problematic. The heterogeneity of the phantoms reviewed points to a critical need for standardization in this field. Ultimately, all research groups involved in polarimetric studies and instruments development would benefit from sharing a limited set of standardized polarimetric phantoms, as is done earlier in the round robin investigations in ellipsometry.

1. Introduction

The use of polarized light in clinical and preclinical applications is expanding,¹ and several recent reviews by Tuchin,² Ghosh and Vitkin,³ Qi and Elson,⁴ de Boer et al.,⁵ and Baumann⁶ have illustrated the fast progress of this approach in the medical field.

As polarimetric techniques reach the clinical and commercial stage, there is a need to validate them with replicative systems that could serve as biological proxies and mimic the characteristic trends of typical biological observations. Over the past several decades, a variety of such systems—commonly referred to as phantoms—have been implemented for the use of general optical imaging and sensing; Pogue and Patterson⁷ illustrated these tools in an exhaustive review. Here, we focus uniquely on phantoms used for polarimetry in biomedicine; these phantoms were not included in previous reviews and are relevant for scientists and engineers working on polarimetric applications.

Three dominant mechanisms influence polarized light as it travels through a biological media: depolarization, retardation, and diattenuation.

Scattering is a primary contributor to the process of depolarization. Loss of polarization is mainly due to the disarrayed changes of amplitude and phase of the scattered electromagnetic field reaching a detector.⁸

Scattering is generally very high in biological media due to the high density and large variety of sub- and extracellular components (such as organelles, nuclei, collagen fiber bundles, cell membrane, to name a few). Different polarization states of incident radiation—linear, circular, or elliptical—depolarize at different rates. As for the mathematical representation of depolarization, its theoretical premise is generally supported by the Mueller matrix of an intrinsic (or diagonal) depolarizer [Eq. (1a)], satisfying the covariance conditions [Eq. (1b)]:⁹

$$\begin{array}{c}{\mathbf{M}}_{\mathrm{\Delta }}=d_0\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& a& 0& 0\\ 0& 0& b& 0\\ 0& 0& 0& c\end{array}\right),0<d_0<1,|a|\end{array},|b|,|c|\le 1,$$ (1a)

$$\begin{array}{c}-a-b-c\le 1,-a+b+c\le 1,a-b+c\le 1,a+b-c\le 1.\end{array}$$ (1b)

It follows from Eq. (1a) that $1-|a|$ and $1-|b|$ represent the linear depolarization power (horizontal-vertical and $\pm 45\mathrm{deg}$ frameworks). Similarly, $1-|c|$ specifies the power of circular depolarization.

From this, the total depolarization power $\mathrm{\Delta }$ can be calculated as

$$\begin{array}{c}\mathrm{\Delta }=1-\frac{|a|+|b|+|c|}{3}=1-\frac{|tr({\mathbf{M}}_{\mathrm{\Delta }})-1|}{3},0\le \mathrm{\Delta }\le 1.\end{array}$$ (2)

In birefringent media, light experiences changes in propagation speeds for its different polarization components, which leads to phase differences (also called retardation) between those components. Linear retardation is the phase shift between two orthogonal linear polarization states (e.g., 0 deg and 90 deg, or $+45\mathrm{deg}$ and $-45\mathrm{deg}$). Circular retardation (also referred to as optical rotation) is the difference in phase between the right and the left circular polarized components of light, which happens due to circular birefringence (optical activity). The Mueller matrix of a linear retarder [see Eq. (3)] depends on its phase difference parameter $\delta$ and on the azimuth $\theta$ of its fast axis:

$$R=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& {\cos }^2(2\theta )+{\sin }^2(2\theta )\cos \delta & \sin 2\theta \cos 2\theta (1-\cos \delta )& -\sin 2\theta \sin \delta \\ 0& \sin 2\theta \cos 2\theta (1-\cos \delta )& {\sin }^2(2\theta )+{\cos }^2(2\theta )\cos \delta & \cos 2\theta \sin \delta \\ 0& \sin 2\theta \sin \delta & -\cos 2\theta \sin \delta & \cos \delta \end{array}\right)$$ (3)

The retardation ($\delta$) property of a uniaxial medium is frequently expressed through its birefringence and can be written as shown in Eq. (4), where $n_e$ and $n_o$ are extraordinary and ordinary refractive indices of a birefringent material, respectively, $d$ is the distance traveled by light (wavelength ${\lambda }_0$) through the birefringent medium, $\mathrm{\Delta }n=n(\theta )-n_o$, where $n(\theta )$ is the refractive index seen by the photon propagating in the direction $\mathbf{u}(u_x,u_y,u_z)$. Angle $\theta$ is the angle between the direction $\mathbf{u}$ and extraordinary axis of birefringent material defined as $\mathit{e}(\cos \eta ,\sin \eta ,0)$:

$$\begin{array}{c}\delta =\frac{2\pi d\mathrm{\Delta }n}{\lambda },\end{array}$$ (4)

$$\begin{array}{c}n(\theta )=\frac{n_o{n}_e}{{(n_e^2{\cos }^2\theta +n_o^2{\sin }^2\theta )}^{0.5}},\end{array}$$ (5)

$$\begin{array}{c}\theta ={\cos }^{-1}\left[\frac{u_x\cos \eta +u_y\sin \eta }{{(u_x^2+u_y^2+u_z^2)}^{0.5}}\right].\end{array}$$ (6)

Birefringence itself can be divided into “intrinsic birefringence” and “form birefringence.”² Typically, biological tissues rich in extracellular matrix (ECM) fibers, for example, skin, cornea, sclera, tendon, uterine cervix, and cardiac tissue, exhibit retardation.

Mueller matrix polarimetry^2–4 and polarization-sensitive optical coherence tomography (PS-OCT)¹⁰ are techniques capable of quantifying many of the aforementioned parameters of interest. Calculation of the Mueller matrix requires the modulation of both light source and detector into a minimum of four different polarization states for a total of 16 measurements. Once the Mueller matrix is determined, it can be decomposed¹¹ as a sequence of elementary polarization components: a diattenuator, a retarder, and a depolarizer. PS-OCT is an extension of OCT, a technique based on low-coherence interferometry that can provide high-resolution cross-sectional imaging of biological tissue, and it too can be used to quantify birefringence, diattenuation, and depolarization index, a parameter related to depolarization.

Diattenuation, also called dichroism, is generally considered to have the smallest impact on polarized light propagating in biological media. Diattenuation arises from polarization-selective attenuation of the electrical field. Related to diattenuation is the property of optical activity, also known as circular birefringence, which is characterized by the rotation of the polarization plane of linearly polarized light about the axis of propagation.² This property is prevalent for chiral molecules such as glucose, proteins, and nucleic acids.³

The use of polarimetry in monitoring biological tissue often focuses on quantification of the tissue preferential azimuth (i.e., the orientation of optical axis of uniaxial birefringent medium) related to the arrangement of a collagenous ECM or other cellular assembly. Skeletal muscle and cardiac tissue are both strongly depolarizing and birefringent due to cellular components and layered structure.

Collagen, animal cornea, retina, and optic nerves have all been shown to have large birefringence and preferential alignment through PS-OCT and polarized light microscopy.^12–14 Several studies using PS-OCT imaging on articular cartilage, which is rich in oriented collagen fibers, have shown changes in collagen retardation in depth.^15–18 Nerves have also been shown to yield retardation with polarization-sensitive spectroscopy.¹⁹ Since birefringence is the most common source of retardation and signal for this modality, in general most retardance phantoms can be used as PS-OCT phantoms.

Microtubules made from extracted elements of the porcine brain and axonemes prepared from sea urchin have been examined using polarized light microscopy, where fibers can be visualized.²⁰ The ECM of the cervix is composed of about 70% collagen and, therefore, has shown to have a significant retardation. Chue-Sang et al.²¹ used Mueller matrix polarimetry to calculate retardance, depolarization, and collagen fiber azimuth of ex vivo porcine cervix samples (seen in Fig. 1). Pierangelo et al. used wide-field multiwavelength Mueller matrix polarimeters to image cervical neoplasia and colon cancer.^22–30

Fig. 1.

Mueller matrix-derived parameters (Lu–Chipman decomposition¹¹) of an ex vivo porcine cervix: (a) CCD image, (b) depolarization power, (c) scalar retardation, and (d) azimuth of optical axis. Darkened area in the center of the image is the cervical OS. Overlaid lines are calculated from the mean of subsections of the azimuth depicted by the false color.²¹ Mueller matrix-derived parameters (Lu–Chipman decomposition) of healthy human cervical specimen: (e) CCD image, (f) depolarization power, (g) scalar retardation, and (h) azimuth of optical axis.²²

Vitkin et al. used Mueller polarimetry to determine the local structural disorders of the bladder³¹ and myocardium.³² Enhancement of superficial structure by eliminating deep penetrating scattered photons is also a common use of polarimetry in medicine. Groner et al.³³ used cross-polarization to highlight superficial vascular contrast in intravital microscopy, applying this technique, among others, to study brain perfusion and pancreatic and hepatic microcirculation.^33–38

Polarized light imaging has been used extensively to enhance surface contrast for dermatologic applications.³⁹ Demarcation of margins of skin cancers, not visible to the naked eye, has been conducted by several researchers, starting with setups focusing on linear depolarization to other systems,^40–43 utilizing full Stokes vector polarimetry and out-of-plane approaches.^44–46 The skin stratum corneum has been shown to be highly scattering hence producing strong depolarization.^47,48 Changes in retardation have been associated with the presence of collagen in the dermis. For this reason, scars have a strong response to polarized light as collagen in wounds recombines in the direction of local forces.⁴⁶

2. Optical Phantoms

We have categorized all phantoms by their dominant polarization property—namely, depolarization, retardation, diattenuation, or optical activity. We have also introduced a separate table for biological tissues used as phantoms. Many phantoms exhibit more than one property; hence, they may appear in more than one table, these repeated phantoms are identified by an asterisk (*). The retardation phantoms table includes an induced retardation column. This column is included to differentiate phantoms which are inherently birefringent due to their structure from phantoms that are mechanically stressed, strained, or otherwise manipulated in order to change their birefringence. Many of the phantoms cited in this review have been used by the same investigators in multiple journals, for simplicity, we have not cited all the articles using the same phantoms and limited the review to the ones that were substantially different to each other.

2.1. Biological Phantoms

The construction of polarimetric phantoms is a complex process; hence, biological samples are commonly used in polarization-sensitive optical modalities (Table 1). Collagen-rich tissues, for example, tendons or rat tails, are the most commonly used in polarimetry. As most biological tissues, collagen scatters (and, consequently, depolarizes); more importantly, collagen introduces a phase shift between orthogonal polarization states of incident polarized light² due to its strong birefringence. Since many healthy collagen-rich tissues behave as uniaxial birefringent media, the azimuth of optical axis of linear retardation related to collagen alignment can often be measured.^{21,22,27,51,59,77,78}

Table 1.

Biological tissues used as polarization phantoms.

Tissue type	Preparation	Polarization property	Transmission/reflectance	Ref.
Axonemes (sea urchin)	Extraction from sea urchin sperm and purification steps	Retardation	R	20
Bladder (porcine)	Excised, fresh	Depolarization, retardation, diattenuation	R	49
Brain (porcine)	Phosphate-buffered saline solution (0.02 M)	Depolarization	R	50
Cartilage (animal)	Excised, fresh	Depolarization, retardation	R	15–18
Cartilage (porcine)	Excised, fresh	Retardation, depolarization, diattenuation	T	18
Cervix (porcine)	Fixed in 4% paraformaldehyde and embedded in paraffin	Depolarization, retardation	R	51
Eye (cornea)	Excised, fresh	Retardation	R	13 and 14
Eye (optic nerve)	Cryosectioned	Retardation	R	12
Eye (retina)	Excised, fresh	Retardation	R	14
Fibroblast (rat)	Suspension	Depolarization	R	52 and 53
Heart (myocardium)	Excised, fixed	Depolarization, retardation	R	32, 54, 55, and 56
Heart (porcine myocardium)	Phosphate-buffered saline solution (0.02 M)	Depolarization	R	50
Heart (rat myocardium)	10% formalin and cut into 1 mm slices	Retardation, diattenuation, depolarization	R	57
Heart (valve leaflet)	Excised, fresh	Depolarization, retardation	R	58 and 59
Heart (porcine valve)	Excised, fresh	Retardation	R	60 and 58
Heart (porcine aorta)	Excised, fresh	Retardation	R	61
Heart (bovine right ventricle)	Cut into $2\mathrm{cm}\times 2\mathrm{cm}\times 1\mathrm{cm}$ sections	Retardation, diattenuation	R	62
Heart (swine right ventricle)	Excised, fresh	Retardation	R	63
Heart (rabbit right ventricular wall)	3.7% formaldehyde for 1 day and 20% sucrose solution for an additional 2 days	Retardation	R	64
Kidney cortex	Phosphate-buffered saline solution (0.02 M)	Depolarization	R	50
Liver	Phosphate-buffered saline solution (0.02 M)	Depolarization	R	40 and 50
Melanin granules	Suspension	Depolarization, retardation	R	65
Microtubules	Extraction from porcine brain and purification steps	Retardation	R	20
Nerve (lobster leg)	Excised, fresh	Depolarization, retardation	R	19
Skeletal muscle	Excised, fresh	Depolarization, retardation	R	32, 40, 50, 54–56, 64, and 66–68
Skin	In vivo	Depolarization, retardation	R	47, 48, and 69
Skin (calf)	Excised, fresh	Retardation	T	70
Skin equivalent model	Fixed and cut into few $\mu \mathrm{m}$ slices	Depolarization, retardation	T	71
Tail (rat)	Frozen and thawed	Depolarization, retardation	R	72
Tendon	Excised, fresh	Depolarization, retardation	R	45, 50, 60, and 73–76
Yeast cells	Suspension	Depolarization	R	53

Chicken or cow tendons have been used by many groups^{45,50,60,73–76} to validate polarization-based optical instruments. Azimuth angle is calculated^{45,50,58,60,72–76,79–83} as well as an increase in scalar retardance due to birefringence. Similar to tendon, murine tails also contain collagen fibers which are strongly aligned. Since the azimuth of the collagen fibers preferential orientation can be directly observed, a typical validation test for polarimeters includes positioning a tendon or rat tail at predetermined angles and then measuring samples at different and well-known angular positions.^21,59,72

While muscle tissue can be used for the same purposes as collagen-based phantoms, the interpretation of the results is less straightforward due to the increased cellularity of these tissues.⁶¹ Studies of myocardium muscle^{32,40,50,54–56,64,66–68} have been conducted by several investigators showing loss of retardation and local order for infarcted tissue. For this reason, samples of myocardium have been used to validate different polarimetric systems. Ghosh et al.⁵⁷ used Mueller matrix decomposition to calculate depolarization, diattenuation, and retardance of fixed rat myocardial tissue.

Heart valve leaflets are another highly collagenous and anisotropic tissue that have been used as a depolarization and retardation phantom.⁶⁰ As in previous example, the azimuth of collagen fibers’ preferential orientation can be detected and used for instrument characterization. Changes in depolarization can also be observed by treating the sample with collagenase.^58,59

Artificial skin models grown from epidermal keratinocytes forming a multilayered epidermis on top of collagen I hydrogel with dermal fibroblasts have also been used to mimic the interaction of polarized light with the skin.⁷¹ Unstained cuts of fixed skin equivalents of varying thickness (range: 5 to $30\mu \mathrm{m}$) were measured in transmission with Mueller microscopy and the values of retardation and depolarization parameters were extracted using logarithmic decomposition⁸⁴ of the measured Mueller matrices. The measurements confirmed parabolic dependence of depolarization and linear dependence of retardation on thickness, as follows from differential Mueller matrix formalism.

2.2. Depolarizing Phantoms

Several authors have studied the effect of particle size, density, and index of refraction on the polarization of scattered light.^85,86 As suggested by the results of these studies, the main scatterers in biological tissues are nuclei, organelles, and bulk tissue structures that limit the photon penetration depth and depolarize light traveling through these media.⁵³ The cell nuclei and organelles are frequently modeled as spherical scattering particles⁸⁷ of refractive index varying between 1.33 and 1.47. The components of ECM, such as collagen and elastin, have been represented by spherical⁸⁸ or cylindrical²⁵ structures.

Work by MacKintosh et al.⁸⁹ showed that circular polarization was maintained for longer depths as compared to linearly polarized light in Mie scattering regime (scatterer size $\ge$ light wavelength in the medium). In one of the relevant studies, Monte Carlo simulations supported this finding by showing that mean penetration depth was $\sim 2$ mean free paths (MFP) for linearly and 10 MFP for circularly polarized light in Mie scattering regime.⁸⁶

Suspensions of microspheres and other small particles are commonly used to create phantoms with scattering properties (Table 2). The amount of scattering can be adjusted depending on the size and concentration of the microspheres based on the Mie scattering theory. On a smaller scale, nanoparticles have also been widely used to create scattering phantoms in Rayleigh scattering regime. These particles can also be embedded in solid host media, such as gels or polymers, to ensure scattering properties of those materials. In addition, India ink, hemoglobin, and dyes are commonly added to influence the absorbing characteristics.

Table 2.

Depolarizing phantoms. *Phantoms that were also tested for other polarization properties in corresponding reference paper.

Depolarizing agent	Embedding material	Tissue mimicking	Phantom thickness	Transmission/reflectance	Ref.
GNPs (50 nm)	Intralipid	Contrast agent	Semi-infinite	R	90
Intralipid*	Water, India ink	Bladder wall	Semi-infinite	R	49
Intralipid	Water	Turbid biological media	Semi-infinite	R	53, 69, and 91
Intralipid or polystyrene microspheres	Water, Naphthol green	Porcine liver	$1\mu \mathrm{m}$, $1.4\mu \mathrm{m}$	R	92
Kapton tape (stacked)*	Layered against a rigid base	Theoretical standard	Semi-infinite	R	93
Mylar (biaxially oriented polyethylene terephthalate)*	Laid against a plexiglass base	Theoretical standard	Semi-infinite	R	93
Polystyrene microspheres	Water	Turbid biological media	Semi-infinite	R	24, 40, 53, and 94–97
Polystyrene microspheres	Intralipid	Turbid biological media	Semi-infinite	R	53 and 2
Polystyrene microspheres	Polyacrylamide, sucrose	Turbid biological media	$1{\mathrm{cm}}^3$	T	3
Polystyrene microspheres ($0.5\mu \mathrm{m}$) and fiber glass*	Polyacrylamide	Anisotropic sample	$1\times 2\times 4{\mathrm{cm}}^3$	T	98
Polystyrene microspheres and silk fibers*	Water	Anisotropic sample	2.1 cm	R	88 and 99
Quartz plate (wedged)*	None	N/A	3 mm	T	100
Melanin granules*	Water	Retina/retinal pigment epithelium	Semi-infinite	R	65
Silicon phantom (extruded)	Air between layers	Anisotropic sample	2 mm	R	51
Silicon (amorphous)*	None	Theoretical polarization standard	Semi-infinite	R	93
Silicon (poly-)*	None	Theoretical standard	Semi-infinite	R	93
Silicon grating	Silicon wafer	Theoretical standard	Semi-infinite	R	101
${\mathrm{TiO}}_2$ nanoparticles (530 nm)	PVC-based transparent material	Biopsy samples	1 mm	T	23
${\mathrm{TiO}}_2$	Wax	Skin	2 and 5 mm	R	44
ZnO nanoparticles (340 nm)	PVCP stock solution	Human skin	0.2 –to 2 mm	T	102 and 103

Several studies, such as Antonelli, Rakovic et al., and Cote and Vitkin,^75,94,95 have used aqueous polystyrene microsphere suspensions as backscattering polarization phantoms. In order to measure the change in scattering (i.e., depolarization power) calculated for different suspensions, microsphere diameter was varied.^{24,40,53,94–96} This class of phantoms has also been shown to depolarize linear polarization less with smaller-diameter microspheres as compared to circular polarization, while, with an increase of the microsphere diameter, circular polarization has been reported to be better preserved as compared to linear polarization.⁹⁶

While purely aqueous monodispersed suspensions of microspheres are most commonly used in scattering experiments, intralipid has also been used to create depolarizing phantoms.^2,53 Intralipid is commonly used as a nutrition supplement and is an emulsion of fatty micelles; therefore, scattering is due to multidispersed spherical structures. Aqueous intralipid suspensions with different dilution factors starting at 1:500 to 1:1 have been used to test depolarization with reflectance polarimetry.^53,69,91 An example of such experiment can be seen in Fig. 2, where loss of elliptical polarization is measured as a function of depth in an intralipid suspension as reported by Sridhar and Da Silva.⁶⁹ While intralipid suspension exhibits monotonic dependence of depolarization on light wavelength, the use of gold nanoparticles (GNPs) suspended in intralipid creates more complicated depolarization behavior.⁹⁰

Fig. 2.

Image from Ref. 69. (a) Ruler placed obliquely in a tank containing Intralipid^® solution, (b) elliptical channel image at 45 deg after subtraction method 1, (c) elliptical channel image at 45 deg after subtraction method 2. (b) and (c) have a common colorbar represented at the right edge of the figure. Yellow-dotted line represents the Intralipid^®–air interface. Each graduation on the ruler (i.e., 1 mm) corresponds to 0.35 mm in actual depth. Wavelength: 633 nm. Text is from Ref. 69.

Titanium dioxide (${\mathrm{TiO}}_2$) is another material commonly used to produce scattering in optical phantoms. ${\mathrm{TiO}}_2$ particles have been used in solid host media, such as polydimethylsiloxane or polyurethane, where, before the curing process, these particles are mixed into the polymer. Adjusting the concentration of ${\mathrm{TiO}}_2$ particles makes it possible to change the amount of depolarization.^7,23 Zinc oxide (ZnO) particles are also commonly mixed into polymers.^102,103 Melanin suspensions of rising concentrations can be used to test depolarization with PS-OCT and model the same phenomenon in the retinal pigmented epithelium. As demonstrated by Baumann et al.,⁶⁵ the change in depolarization based on melanin concentration has a linear relationship with degree of polarization uniformity (DOPU).

2.3. Retarding Phantoms

Polymer-based materials are a common source of retardation. Due to their molecular structure or preparation process, many polymers possess intrinsic birefringence (i.e., behave as uniaxial crystals).¹⁰⁴ Others can be induced to become birefringent by applying mechanical stress to the material.^3,105 Many of these polymers are transparent; hence, scattering particles such as microspheres can be added to better simulate biological media. Electrospun polymer fibers, fabricated by charging droplets of polymer at high voltages which creates an interconnected network of small fibers,¹⁰⁶ were used by Goth et al.⁶⁰ to determine the degree of anisotropy of the overall structure. The anisotropic biological elements in the ECM (particularly collagen and elastin) have been simulated with several materials, including silk^88,99 and glass fibers.^98,107 An example of fibrous phantom is shown in Fig. 3. Here, the phantom is composed of polystyrene microspheres and well-aligned glass fibers embedded in polyacrylamide (glass fibers have a $10\text{-}\mu \mathrm{m}$ diameter and 1.547 refractive index).

Fig. 3.

Image from Ref. 107. (a) Cylinder model, (b) sphere-cylinder model, and (c) sphere-cylinder birefringence model.

Phantoms for PS-OCT require a strong backscattering to generate a high image contrast and have ideally well-defined layers with homogeneous yet different values of birefringence (Table 3). Accordingly, Liu et al. have used a phantom consisting of a long birefringent polymer band laid over four smaller bands of differing birefringence. The optical axes of bottom four bands were oriented at 45 deg with the optical axis of top layer allowing for a depth-dependent change in retardation.¹⁰⁸ An example of this retarding phantom is shown in Fig. 4.

Table 3.

Retardation phantoms. The “induced retardation” column is for differentiating between phantoms which inherently exhibit their birefringence due to their structure and phantoms that are mechanically stressed, strained, or otherwise manipulated in order to change their birefringence. *Phantoms that were also tested for other polarization properties in corresponding reference paper.

Retardation material	Embedded material	Induced retardation	Tissue mimicking	Phantom thickness	Transmission/reflectance	Ref.
Birefringent film	Intralipid, India ink	Structure	ECM	Semi-infinite	R	49
Electrospun fibers (0.6 to $1.0\mu \mathrm{m}$)	None	Structure	Heart valve leaflet	Semi-infinite	R	60
Human hair	None	Structure	Human hair	N/A	R	15
Kapton tape (stacked)	Layered against a rigid base	Structure (layers)	Theoretical standard	Semi-infinite	R	93
Mylar (biaxially oriented polyethylene terephthalate)	Laid against a plexiglass base	Structure	Theoretical standard	Semi-infinite	R	93
Plastic cap*	None	Structure	Theoretical standard	Semi-infinite	R	76
Polycarbonate	None	Longitudinal stretch (heating and cooling)	Turbid biological tissue	$250\mu \mathrm{m}$	R	108
Polyacrylamide polymer (elastic)	None	4 mm stretch	Turbid biological tissue	4 mm	R	109
Polyacrylamide gels	Polystyrene microspheres, 1 M sucrose	Stretching	Turbid biological tissue	$1\times 1\times 4{\mathrm{cm}}^3$	T	105
Polyacrylamide*	Sucrose, polystyrene microspheres	Stretching	Turbid biological tissue	$1\times 1\times 1{\mathrm{cm}}^3$	T	3
Polyacrylamide*	Polystyrene microspheres and well-aligned fiber glass	Stretching (1 to 5 mm), birefringence = 0 to ${10}^{-5}$	Turbid biological tissue	$1\times 2\times 4{\mathrm{cm}}^3$	T	98 and 107
Polyethylene (low density)	None	Bending (up to 2.5 MPa)	Turbid biological tissue	1 mm	R	110
Polystyrene sphere	None	Structure	Infarcted myocardium	8 mm diameter	T	111
Polystyrene microspheres	Water	Structure	Turbid biological media	Semi-infinite	R	75, 97, 112
Polyurethane	Particle filled polypropylene	Longitudinal stretch	Theoretical standard	1 mm	R	113
Silicon (extruded)	Air between layers	Structure	Theoretical standard	2 mm	R	51
Silicon (amorphous)	None	Structure	Theoretical standard	Semi-infinite	R	93
Silicon (poly-)	None	Structure	Theoretical standard	Semi-infinite	R	93
Silk fibers*	Water	Structure	Anisotropic sample	Semi-infinite	R	88 and 99

Fig. 4.

Image from Ref. 108. (a)–(c) Intensity, birefringence, and DOP images of the slab and (d and e) cylindrical phantoms. (a) Representative cross-sectional images of the birefringence phantom for galvanometer-scanning system. (b) and (c) En-face images at different depths as indicated by the dashed red lines in (a). Horizontal and vertical scale bars for (a)–(c): 2 mm and $250\mu \mathrm{m}$, respectively. (d) Representative images obtained from one rotational scan with the catheter. Scale bar: 1 mm. (e) Longitudinal sections obtained from a pull-back data set, with its corresponding location indicated by the dashed red line in (d). Radial and horizontal scale bars: $250\mu \mathrm{m}$ and 1 mm, respectively. (Text from Ref. 108.)

Ghosh et al. induced changes in retardation by stretching a polyacrylamide phantom. Moreover, changing birefringence, and mixing polystyrene microspheres and sucrose into the polymer, produced phantoms that could be used to characterize retardance, depolarization, and diattenuation.^3,98,109 Extruded silicon, silicon wafers with gratings, and other types of silicon (poly and amorphous), as well as different tapes (e.g., Kapton and Mylar) normally used in solar panels, have been used to create phantoms containing different combinations of diattenuation, depolarization, and retardation properties.^51,93,101 Figure 5 shows an example of an experimental setup used to induce birefringence in a polymer through mechanical strain by Wood et al.¹¹⁴

Fig. 5.

Image from Ref. 114. Apparatus to create birefringent phantoms.

In order to account for different geometries and extract geometry-independent metrics of anisotropy, retardance measurements have been taken using an 8-mm-diameter polystyrene sphere of known anisotropy axis azimuth.¹¹¹ Fan et al.⁷⁶ imaged a plastic cap to determine its retardation with PS-OCT.

2.4. Diattenuating Phantoms

The asymmetry of a molecule can result in selective transmission of an incident state of polarized light. Swami et al.¹¹⁵ measured diattenuation as a parameter to identify the general shape of GNPs (Table 4). Differently shaped GNPs displayed different spectroscopic diattenuation values. Chen et al.¹¹⁶ and Lung et al.¹¹⁷ used a quarter-wave plate and a polarizer to test the performance of an analytical model for low diattenuating optical components as they were rotated from 0 deg to 150 deg with a step of 30 deg. Moreover, these authors also used a polymer polarizer baked at 150°C as a sample with both diattenuating and birefringent properties. Chenault and Chipman¹¹⁸ used a rotating sample polarimeter to find linear diattenuation and retardance of the sample calculated from intensity modulation.

Table 4.

Diattenuation phantoms. *Phantoms that were also tested for other polarization properties in corresponding reference paper.

Diattenuation agent	Solvent/preparation	Tissue mimicking	Phantom thickness	Transmission/reflectance	Ref.
GNPs (nonspherical shapes)	CTAB-coated GNPs	Theoretical standard	Semi-infinite	T	115
Kapton tape (stacked)*	Layered against a rigid base	Theoretical standard	Semi-infinite	R	93
Mylar (biaxially oriented polyethylene terephthalate)*	Laid against a plexiglass base	Theoretical standard	Semi-infinite	R	93
Polarizer	None	Theoretical standard	21.59 mm	T	116 and 117
Polarizer (baked)	150°C for 80 min	Theoretical standard	N/A	T	116 and 117
Polarizer (rotating)	None	Theoretical standard	N/A	T	118
Quarter-wave plate	None	Theoretical standard	N/A	T	116 and 117
Silicon (amorphous)*	None	Theoretical standard	Semi-infinite	R	93
Silicon (poly-)*	None	Theoretical standard	Semi-infinite	R	93

2.5. Circular Retardation Phantoms

The effect of circular birefringence is frequently associated with the presence of chiral molecules,¹¹⁹ such as glucose. The aggregation of the presence chiral molecules in media causes the rotation of polarization plane of linearly polarized light as it travels through that volume. Manhas et al.,⁹⁷ Ortega-Quijano et al.,¹²⁰ and Ossikovski et al.¹¹² added glucose to a polystyrene microsphere mixture in order to induce chirality and provide optical activity properties to the phantom^, (Table 5).

Table 5.

Optical activity phantoms.

Optical activity agent	Solvent/preparation	Tissue mimicking	Phantom thickness	Transmission/reflectance	Ref.
Glucose (l-lysine)	Distilled water, $\beta$-alanine, intralipid suspension, trypan blue dye	Turbid biological media	Semi-infinite	R	121
Glucose (d-)	Water, $2\mu \mathrm{m}$ polystyrene microspheres, lipofundin, blood plasma, ${\mathrm{SiO}}_2$ nanoparticles	Turbid biological media	40 mm	R/T	70, 97, 112, 120, 122, and 123
Glucose	Water	Eye aqueous humor	Semi-infinite	R	124–126
Glucose	Water	Eye aqueous humor	$1\times 1{\mathrm{cm}}^2$	T	127
Honey	None	Turbid biological media	Semi-infinite	R	75
Sucrose	Polyacrylamide, polystyrene microspheres	Turbid biological tissue	$1\times 1\times 1{\mathrm{cm}}^3$	T	3
l-(+) –arabinose, M. racemic	Water and polystyrene microspheres	Turbid biological tissue	$1\times 1\times 1{\mathrm{cm}}^3$	Side T	119

Malik et al.¹²⁴ developed several ocular models to investigate the feasibility of measuring glucose in the eye aqueous humor with polarization-based techniques (Fig. 6). The model shown also accounts for the cornea birefringence utilizing a PMMA-based phantoms overlaying a chamber mimicking the aqueous humor. A similar approach was used by Rawer et al.¹²⁵

Fig. 6.

Optical phantom from Ref. 124. The custom-built ocular model. Glucose concentration in the anterior section is varied through the two infusion tubes.

Other intralipid suspension liquid phantoms can be made with absorbers, such as dye, and optically active molecules, such as glucose and l-lysine, to test optical activity in samples.^18,121 Antonelli⁷⁵ used honey to calculate the optical activity of the sample. Pham et al.⁷⁰ and Chang et al.¹⁸ studied the concentration of glucose by measuring the optical rotation angle of circular birefringence (optical activity) in human blood plasma and porcine cartilage samples.

3. Conclusions

Optical phantoms that can be used for the calibration and benchmarking of polarimetric techniques and for mimicking the optical response of tissues have been used by several investigators.

It is to be noted that polarimetric optical phantoms are often unique to each research group and, aside from tests conducted on depolarization with microspheres suspensions, no standardization has been attempted. To our knowledge, only one company offers birefringent phantoms for polarized microscopy (NBS 1963A Birefringent Resolution Target by Thorlabs). As the biomedical applications of polarimetric techniques move toward quantification of directionality and retardation, more standardized phantoms are necessary. The PS-OCT phantoms proposed by Liu et al.¹⁰⁸ are a good example of such approach. The measurements of PS-OCT’s two core parameters, namely, retardation and azimuth of optical axis can be easily reproduced, and different instruments can be benchmarked using such standardized phantoms. These mixed properties phantoms, particularly ones that include both depolarization and retardation, are needed for many applications. Phantoms that have birefringence of form rather than just intrinsic birefringence are also needed to simulate fibrous tissues, such as the cervix, cardiac tissue, or muscle. Nevertheless, the task of creating general use phantoms is complicated by the heterogeneity of tissues, the complexity of polarized light–tissue interaction, and the strong wavelength dependence of polarization-based techniques.

For these reasons, the use of biological tissue as measurement standards is very common in polarimetric applications, but unless these samples are well-known or measured with an alternative modality (e.g., PS-OCT or second harmonic generation), the scientific rigor of these experiments remains limited.

As new fabrication modalities, such as 3-D printing and lithography, are becoming available to researchers worldwide, we believe that a collaborative effort in the development of a standardized optical phantom for polarimetry could truly benefit the scientific community.

Biography

Biographies of the authors are not available.

Disclosures

The authors have no relevant financial interests in this article and no potential conflicts of interest to disclose.