Utilizing confocal microscopy to measure refractive index of articular cartilage


Thomas B. Kirk, Mechanical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia. Tel: +61-8-6488-3451; fax: +61-8-6488-1024; e-mail: Brett.Kirk@curtin.edu.au


This study proposes a method for measuring the refractive index of articular cartilage within a thin and small specimen slice. The cartilage specimen, with a thickness of about 50 μm, was put next to a thin film of immersion oil of similar thickness. Both the articular cartilage and immersion oil were scanned along the depth direction using a confocal microscope. The refractive index mismatch between the cartilage and the immersion oil induced a slight axial deformation in the confocal images of the cartilage specimen that was accurately measured by a subpixel edge-detection-based technique. A theoretical model was built to quantify the focal shift of confocal microscopy caused by the refractive index mismatch. With the quantitative deformations of cartilage images and the quantified function of focal shift, the refractive index of articular cartilage was accurately interpolated. At 561 nm, 0.1 MPa and 20 °C, the overall refractive index of the six cartilage plugs was 1.3975 ± 0.0156. The overall coefficient of variation of all cartilage specimens was 0.68%, which indicated the high repeatability of our method. The verification experiments using distilled water showed a minimal relative error of 0.02%.


Articular cartilage is a thin and hyaline tissue covering on the articulating ends of bones (Freeman, 1979). It is composed of chondrocytes embedded in the extracellular matrix. Functionally, the charged proteoglycans and collagens fibres in the extracellular matrix establish a dynamic meshwork to attenuate stresses, resist shear forces and maintain low friction (Mak et al., 1987). Structurally, there are four zones from the articular surface down to the subchondral bone: superficial, transitional, radial and calcified zones (Bhosale & Richardson, 2008). In each zone, the concentration of proteoglycans, the orientation of collagen fibres and the morphology of chondrocytes are different. These unique zonal features lead to diverse mechanical and optical properties along the depth of the cartilage.

There has been a long history of studying articular cartilage in both medicine and engineering (Benedek, 2006). Refractive index (RI) is a fundamental optical property of biological tissues (Tuchin, 2007). RI of articular cartilage has rarely been studied although it is important both for visualizing the cartilage microstructure and investigating the degenerative mechanism of articular cartilage.

As in most of biological tissues, variations in the RI of articular cartilage affect the degree of scattering nature, which is one of main difficulties in the development of effective 3D optical technologies for articular cartilage (Tuchin, 2007). In 3D imaging of articular cartilage, the RI mismatch at the interface between the cartilage specimen and another medium (such as an optical fibre, cover slip or immersion fluid) can induce artefacts along the optical axis. As these aberrations accumulate, all cartilage features depicted in the 3D images are deformed. Prior knowledge of the RI characteristics can help to calibrate these artefacts to more accurately locate defects in the clinical micrographs of articular cartilage, and therefore, improve the applications of optical devices to the diagnosis and treatment of cartilage-related diseases.

In addition to improving the quality of cartilage images, changes of the RI in articular cartilage could also help to understand the cartilage degeneration. Biochemical changes, such as the proportions of water or proteoglycans in the matrix, have been reported in cartilages of mammalian animals with natural osteoarthritis (McDevitt & Muir, 1976; Bhosale & Richardson, 2008). These changed compositions result in degraded mechanical performance (Meachim & Stockwell, 1979) as well as changes to the light propagation within the tissue (Tuchin, 2007). Furthermore, the microstructure variations in scale, shape and membrane thickness of chondrocytes or the disruption of the fibrous meshwork can all influence the RI of articular cartilage (Beuthan et al., 1996; Schmitt & Kumar, 1996). Thus, the RI could potentially be a useful tool to assess the cartilage degeneration and even support the clinical diagnosis of cartilage diseases such as osteoarthritis.

Several approaches for measuring the RI of various biological tissues have been developed, although these techniques have rarely been applied to articular cartilage. These approaches mainly utilized either internal reflection (Bolin et al., 1989; Li & Xie, 1996; Tsenova & Stoykova, 2003) or optical path shifting (Tearney et al., 1995; Knüttel & Boehlau-Godau, 2000; Wang et al., 2002; Dirckx et al., 2005; Binding et al., 2011). However, most of these existing methods require specially designed instruments and cannot easily to be applied within a small tissue region. Dirckx proposed a method using a standard confocal microscope to measure the RI of bovine muscle (Dirckx et al., 2005). This method avoids building specialized instruments and can assess small samples, but relies on the shape of profile curves crossing the sample. This principle decreases the reliability of the measured RI and makes it difficult to automatically process large-scale RI calculations due to the frequent manual interventions to the programs.

The RI of articular cartilage is generally taken to be approximately 1.50 in some studies, primarily because the proportion of water in normal articular cartilage is about 65–85% (Pan et al., 2003; Rogowska et al., 2003). To the best of our knowledge, the only previous experimental measurement of the RI of articular cartilage was based on a specially designed optical coherent tomography (OCT) (Wang et al., 2010). In Wang's study, cartilage samples harvested from bovine patellae were cut into three horizontal sections to investigate the depth dependency of the RI. However, due to the limited axial resolution of OCT, each cartilage section in Wang's study was about 0.5 mm thick. This section thickness is difficult to precisely describe the RI consistency with depth.

An ideal method for measuring the RI of articular cartilage should have the capacity to characterize both the lateral distribution and the depth dependency of the RI and should also consume only a small amount of cartilage. Confocal microscopy has been an imaging technique available in many biological laboratories and can scan samples within a very small 3D spot. Its particular configuration brings improved resolution and contrast compared to conventional optical microscopy and OCT (Hibbs, 2004). These advantages suggest that confocal microscopy has the potential to accurately measure the RI of articular cartilage.

In this study, we have developed an efficient method for determining the RI of articular cartilage with high precision and reliability utilizing a standard confocal microscope. This method is on the basis of the previous work of Dirckx et al. (2005), but with an alternative point spread function (PSF) model of the confocal microscope and a new technique based on subpixel edge detection for measuring the image deformations caused by RI mismatch.


Theoretical model and RI calculation

To improve resolution, immersion type objectives with a high numerical aperture (NA) were used in confocal microscopy. The immersion fluid and the cover slip were chosen to have very similar RI so that the optical distortion caused by any RI mismatch within the optical system could be minimized. Any RI mismatch between the specimen and the immersion fluid would cause the optical thickness of the specimen to be different from its physical thickness (Carlsson, 1991). Here, optical thickness is the thickness of an object measured from its optical images. This study measured the RI of articular cartilage on the basis of this mechanism.

Figure 1 shows the exaggerated optical path of an immersion-type objective. The objective delivers the illuminating light through the immersion fluid and cover slip (with the same RI n1) to a spot in the specimen with a RI of n2. If n1= n2, the light beam will be focused on point A (nominal focal position, NFP) following a straight optical path. If n1n2, the incident light will be refracted and the focus will be shifted to point A’ (actual focal position, AFP). If n1> n2, the refraction of incident light shifts the focus up (the dash–dotted line in Fig. 1). As each step size of the focal plane along z-axis decreases, the confocal microscope requires additional scanning planes to image the entire specimen, which means increased optical thickness. Conversely, if n1< n2, the focus will be moved to a deeper position and the optical thickness of the specimen will appear less than its physical thickness. The AFP and NFP together can describe the focal shift of a confocal microscope.

Figure 1.

Basic optical scheme demonstrating the focal shift caused by the RI mismatch between the specimen and immersion fluid. When the RI of the immersion fluid (n1) is greater than that of the specimen (n2), the objective lens actually focuses the incident light on point A’ rather than the nominal point A that is the expected focus for the matched RI.

It is difficult to directly quantify the focal shift. However, the 2D confocal image series can reflect the accumulation of the corresponding focal shift in different depths, which is caused by the mismatched RI of the specimens. Utilizing the accumulated effect of RI mismatch, a special specimen mount was designed in this study to measure the RI of articular cartilage. This mount can hold two specimens with identical physical thickness. One specimen is the articular cartilage to be measured. The other specimen, generally the immersion oil, works as the control specimen. Due to the RI mismatch, the optical thickness of the cartilage specimen is different from that of the control specimen. However, as the control specimen has a RI that matches the immersion fluid, its optical thickness will match to the physical thickness of the cartilage specimen. This arrangement allows the optical and physical thickness of the cartilage specimen to be measured simultaneously.

The optical thickness ratio (OTR) has been defined to express the diversity of optical thickness in the specimen mount. The relationship between OTR and focal shift can be briefly expressed as (Kuypers et al., 2005)


In Eq. (1), OTAC and OTOil are the optical thickness of the cartilage specimen and the immersion oil, respectively, whereas PTAC and PTOil denote the corresponding physical thicknesses. Δz is the step size of the objective along optical axis. Equation (1) indicates that the focal shift is positively related to the OTR. If a relationship between the RI mismatch and the corresponding OTR has been determined, the RI of articular cartilage could be calculated from the experimentally measured OTR using Eq. (1).

As the PSF model based on electromagnetic diffraction theory can approximate the light propagation within a confocal microscope, it has been used to estimate the focal shift caused by RI mismatch. Among the existing theoretical evaluations of the PSF model for confocal microscopes (Hell et al., 1993; Sheppard & Gu, 1993; Jacobsen et al., 1994; Sheppard & Török, 1997), the PSF model proposed by Sheppard & Török (1997) was adopted because it consumes much less computational resources but has required level of accuracy for this study.

The PSF of the whole confocal system consists of the PSF of illumination and the PSF of detection as below:


where λill and λflu denote the wavelengths of the illuminating laser and the fluorescence, respectively, nimm and nspm represent the RI of the immersion oil and the specimen to be measured and r is the displacement vector in the 3D space that the PSF describes. Due to the symmetrical arrangement of the objective lenses and the point detector in a confocal microscope, hill and hdet have same distributions (Hell & Stelzer, 1992; Sheppard & Gu, 1993).

In our study, the PSF model was built using the actual parameters of the confocal scan (nimm= 1.516, λill= 561 nm and λflu= 565 nm). The illumination profile at the exit pupil of the objective was modelled as a uniform distribution. Keeping these parameters constant in a specific experiment for articular cartilage, the left side of Eq. (2) can be simplified to h(r,nspm).

For a given nspm, once a specific NFP was input, the PSF model responded with a 3D distribution of the fluorescence intensity. However, only the PSF response along the z-axis, noted as hz(NFP(z), nspm), was used to quantify the focal shift. The peak of hz(NFP(z), nspm) indicates the actual focal point determined by the RI mismatch between nimm and nspm. The z coordinate of this simulated focal point is AFP(z). For each NFP varied within the range of 0–100 μm, the corresponding AFP was calculated as above. Finally, a linear fit of AFP versus NFP was performed. According to Eq. (1), the slope of this curve is OTR(nspm). In this way, one data point in the OTR vs. nspm curve was determined.

In healthy articular cartilage of an adult mammal, the water content is no less than 65% of the wet weight and can rise over 85% in the superficial zone (Lipshitz et al., 1976; Bhosale & Richardson, 2008). We therefore estimated that the possible range of the RI of articular cartilage is 1.30–1.51. By repeating the above procedure for varying nspm within this range, a series of points for the OTR vs. nspm curve were calculated and approximated by least square fitting. With this function, the corresponding RI of articular cartilage was easily calculated for each experimental OTR.

Specimen preparation and confocal scan

Within 2 h of slaughter, three femoral condyles were harvested from three lambs of about 1 week of age. Six cylindrical cartilage plugs (Ø 3 × 4 mm) were punched out from these condyles. Prior to frozen sectioning, the cartilage plugs were embedded in Tissue-Tek O.C.T. compound (Sakura Finetek USA, Inc., Torrance, CA, USA) and submerged in a metal tube filled with isopentane (2-methylbutane) for better thermal conductance. The metal tube was then immersed in liquid nitrogen for about 1 min to fast freeze the samples. This freezing procedure minimizes the histochemical alteration and morphological disruption to the cartilage samples. The cartilage plugs were horizontally cut into circular discs approximately 50 μm thick with a cyro-microtome (Leica cryostat CM3050S, Leica Microsystems, Wetzlar, Germany) at −20°C. For better comparability of the measured RI between different cartilage plugs, only the top six to seven layers of cartilage discs were selected for confocal microscopy.

The selected cartilage discs were stained with 0.03 g/L Rhodamine B for 1 min. After washing thoroughly, one disc was carefully placed on the slide with the assistance of a stereo microscope (SZH10 Research Stereo, Olympus, Tokyo, Japan). Adhesion microscope slides (SuperFrost® Plus, Menzel-Gläser, Braunschweig, Germany) were used to electrostatically attract the cartilage discs. The cartilage disc was examined in the stereo microscope to ensure that there were no bubbles existing below the cartilage. A drop of immersion oil (Type F, n= 1.516, Leica Microsystems, Wetzlar, Germany) that had been slightly stained with Rhodamine B was placed next to the cartilage disc as the control specimen, as shown in Fig. 2. The two specimens were covered by a cover slip to ensure that they had the same physical thickness. The edges of the cover slip were sealed to prevent the flow of immersion oil during the confocal scan.

Figure 2.

Schematic diagram of the specimen mount. The stained immersion oil is next to the cartilage specimen and the two specimens are covered by a cover slip to ensure that they have the same physical thickness.

Before the confocal scan, the RI of both the original immersion oil and the stained immersion oil had been measured using an Abbé refractometer (UHR-1R Universal type, Shibuya optical, Saitama, Japan), respectively, to estimate the potential deviation. The result showed that in our study, the relative deviation of RI induced by the small amount of fluorescent dye added was only 0.013%. Therefore, it was reasonable to treat the stained immersion oil as no mismatch of RI.

Using a standard confocal microscope system (Leica TCS SP2 AOBS, Leica Microsystems, Wetzlar, Germany) equipped with an oil immersion objective (Plan Apochromate, 63× and NA= 1.40) and a 561 nm wavelength laser, the interface between the cartilage disc and the stained immersion oil was scanned simultaneously from the top surface to the base with a step size of 0.73 μm. This step size was proper for the followed image processing and only induced reasonable time consumption. The size of each 2D image on the x–y plane was 512 × 512 pixels and four scanning frames were averaged for each layer to reduce random noise. The first image layer with fluorescence was examined to ensure the fluorescence of both specimens appeared simultaneously, which indicated the qualified preparation of the specimen mount.

Measurement of the optical thickness

In this study, optical thickness is a key factor for the accuracy of the measured RI. A typical intensity profile of the cartilage specimen obtained along the z-axis is shown in Fig. 3. Due to the mismatched RI and the signal attenuation of the imaging system, the intensity profile showed severe asymmetry. The complex structure of articular cartilage and the system noise together produce additional local fluctuations in the profile curve. These features make it difficult to correctly locate the cartilage surface and determine the optical thickness.

Figure 3.

Typical intensity profile crossing an articular cartilage slice. The curve is asymmetrical and fluctuating due to the features of confocal system. Both shoulders of the profile have transitional regions but the deeper shoulder is less defined, which increases the difficulty of determining the optical thickness.

To achieve a more accurate and reliable calculation of OTR, a subpixel edge-detection-based method was used to measure the optical thickness of the specimens. This method utilizes the intact edge information of the confocal slice rather than relies on several intensity profiles along the z-axis as previous studies have done (Tearney et al., 1995; Dirckx et al., 2005).

Subpixel edge detection can locate the object edges with high accuracy beyond the detector resolution (West & Clarke, 1990) and also provide a consistent and objective criterion for distinguishing changes in edge features. Tabatabai's grey level moment edge operator was adopted in this study because of its simple structure and low computational load (Tabatabai & Mitchell, 1984). The statistical characteristics of this edge operator can compensate for the negative impacts of system noise and local variation in images.

Before measuring the optical thickness of the specimens, a group of 2D confocal slices on the x–z plane were extracted from the 3D confocal image stack. A confocal image stack comprising m frames of 2D images (512 × 512 pixels on the x–y plane) was resliced into 512 frames of x–z slices with the size of 512 ×m pixels. Each of these confocal slices was smoothed using the self-adaptive median filter (Gonzalez & Woods, 1992) and enhanced by the histogram equalization. The traditional Canny operator (Canny, 1986) was then applied to the x–z slice to roughly locate the upper and lower surfaces of both specimens. The strong–weak double thresholds mechanism of the Canny edge operator is highly compatible with those images with severe noise and guarantees that even weakly represented edges can be detected (Canny, 1983).

Each confocal slice was divided into three regions (articular cartilage, transitional region and immersion oil, as shown in Fig. 4) for initial edge detection. As only the upper and lower surfaces of the specimens were of interest, all of the spurious edge pixels located in the inner area of the specimens were omitted. Subsequently, least square linear fit to the initial edge points gave an initial contour of the specimens (dashed lines in Fig. 4). Based on this initial contour, a series of columns along the z direction with relatively low noise and sharp edge profiles (short vertical solid lines in Fig. 4) were selected from the confocal slice, which were expected to contain the exact positions of the specimen surfaces. The length of each column depends on the grey level gradient of the detected edges. In our experiment, 4–6 pixels were sufficient to guarantee the coverage of the entire edge area.

Figure 4.

Schematic diagram of the procedure for measuring the optical thickness of specimens based on the subpixel edge detection. The solid dots denote the initial surfaces of the specimens detected by a Canny operator. The dashed lines are the linearly fitted initial contour from the solid dots. Several columns of data, shown as the short vertical solid lines, were extracted based on the initial contour. Each column represents the possible range containing the exact location of the surfaces. The crosses are the accurate surface located by 1D grey level moment edge operator. The solid horizontal lines are the final fitted surfaces for calculating the OTR.

The 1D grey level moment edge operator was applied to each of these selected vertical columns to calculate the exact surface positions of the specimens. These exact surfaces were again fitted by linear least square approximation (horizontal solid lines in Fig. 4). The optical thicknesses of the articular cartilage (OTAC) and immersion oil (OTOil) were determined from these fitted surfaces with subpixel accuracy. The experimental OTR of the cartilage and immersion oil specimens was then calculated using Eq. (1).

Statistical analysis and method verification

To minimize measuring error, a large number of measurements were performed. Each cartilage plug was cut into 6–7 discs and two to three scanning spots were selected from each cartilage disc. Depending on the image quality, about 350–500 confocal slices were selected from each scanning spot to run the measurement procedure described in sections ‘Theoretical model and RI calculation’, ‘Specimen preparation and confocal scan’ and ‘Measurement of the optical thickness’. The average RI calculated from all of these confocal slices was used as the RI of the current cartilage plug. For each plug, up to 4000–6000 RI calculations were executed to improve the reliability.

The coefficient of variation (CV) was used to estimate the reproducibility of the current method (Glüer et al., 1995). The single-factor anova (OriginPro 8 SR4, OriginLab, Northampton, MA, USA) was used to quantify the RI consistency among all of the cartilage plugs (Significance level α= 0.05).

Since the RI of distilled water has extensively been studied with numerous authoritative measurements reported in the literatures, the cartilage disc in the specimen mount was replaced by a drop of slightly stained distilled water to verify the accuracy of our method. The specimen mount was examined to avoid any bubbles between these two immiscible liquids. The sealed specimen mount formed two liquid films with the same thickness. The confocal scan and RI calculations applied to the distilled water were identical to those previously described in this study. Previous results of the RI of distilled water obtained using similar physical conditions to this study were utilized as the criterion to calculate the relative error of our method (Daimon & Masumura, 2007).


Theoretical simulation

The PSF model and OTR measurement were executed by a customized matlab program (matlab R2006a, Mathworks, Natick, MA). The z response of the PSF model for NFP= 20 μm is given in Fig. 5. When an RI mismatch between nimm= 1.516 and nspm= 1.330 was simulated, the AFP shifted from 20.00 up to 16.50 μm. Figure 5 confirms one point (16.50, 20.00) of the AFP versus NFP curve.

Figure 5.

Theoretical focal shift along the z-axis (normalized to its peak value) simulated by the PSF model of the confocal microscope. Due to the RI mismatch between nimm= 1.516 and nspm= 1.330, the focal point is shifted from NFP= 20.00 μm up to AFP= 16.50 μm.

The three examples in Fig. 6 illuminate the functional relationship between NFP and AFP for different RI mismatches. In the condition of nimm= 1.516, the RI of specimens were simulated as 1.330 (pure water), 1.410 (muscle) and 1.516 (immersion oil), respectively. For each case, the original data were fitted as a linear curve through the origin. The slopes of these three fitted curves were 1.1794, 1.1011 and 1.0000, respectively. For any given NFP, a greater RI mismatch leads to a greater focal shift. Correspondingly, the larger RI difference will give a greater OTR.

Figure 6.

Three examples of NFP as a function of AFP for different RI mismatches. For all three cases, the RI of the immersion system is nimm= 1.516 and the RI of the three specimens are nspm1= 1.330, nspm2= 1.410 and nspm3= 1.516, respectively. The slopes of the three fitted curves are 1.1794, 1.1011 and 1.000, respectively. The slope of 1.0000 indicates a matched RI.

For the case of nspm1= 1.330, the functional relationship between NFP and AFP is


Equation (3) suggests that if an OTR of 1.1794 was acquired experimentally, the RI of the cartilage sample would be close to 1.330. Other data points corresponding to different nspm are shown as circles in Fig. 7, which indicates good linearity (r2= 0.9994). The function of OTR versus nAC was approximated by linear regression as Eq. (4). Here, nAC is the RI of articular cartilage. The 95% confidence intervals of the slope and intercept are (−1.1266, −1.1003) and (2.6161, 2.6451), respectively

Figure 7.

RI as a function of OTR for the confocal microscope with an oil immersion type objective (NA= 1.40). The circles represent the original data from the PSF model and the solid line is the linear fitted result (r2= 0.9994). The RI ranges from 1.30 to 1.51 that covers most of biological tissues.

Experimental images and statistical results

Figure 8 shows some intermediate images from the procedure of optical thickness measurement. A typical confocal slice of the specimen mount has two parts, as shown in Fig. 8A. The bright part represents the cartilage specimen and the darker part is the immersion oil. This is because immersion oil was only slightly stained with tRhodamine B to avoid RI alteration. Compared with the immersion oil, the slice of articular cartilage appears thicker, which indicates a lower RI. The inner region of the cartilage is noticeably uneven due to its heterogeneous nature. The bright clumps on the cartilage side are caused by the fluorescence from chondrocytes.

Figure 8.

Brief procedure of the OTR measurement based on subpixel edge detection. (A) A confocal x–z slice. The left portion is the articular cartilage and the right portion is the stained immersion oil. (B) The enhanced confocal slice for edge detection. The transitional region was omitted from further processing. (C) The initial edges detected by the Canny operator with false edges still included. (D) The initial contour ready for subpixel edge detection. (E) The final result of subpixel edge detection. The solid dots denote the accurately positioned specimen surfaces that were linearly fitted as the solid horizontal line. The distances between the accurate upper and lower surfaces are the optical thicknesses of the specimens.

Figure 8B shows that the dynamic intensity range of the confocal slice was already expanded by the process of image enhancement. The Canny edge operator produced a large number of false edges on both sides of the image, as shown in Fig. 8C. These false edges were eliminated to improve the quality of the fitted initial contour, as shown in Fig. 8D. The dense dots in Fig. 8E are the edges detected with subpixel accuracy and the horizontal solid lines are the fitted accurate surfaces. The z-axis was partially broken to exaggerate the subpixel edges. The optical thickness of the specimen is the distance between the final upper and lower surfaces.

The average RI and the corresponding CV of each cartilage plug are listed in Table 1. The overall RI of all six plugs was 1.3975 ± 0.0156. The highest CV among the six plugs was only 1.04% and the overall CV was 0.68%, indicating that our method is highly reproducible (Glüer et al., 1995). The single-factor anova revealed no significant RI difference among the six cartilage plugs (P= 0.11> α= 0.05).

Table 1.  The RI and the corresponding CV of the cartilage plugs.
Cartilage plug indexCartilage discs No.RI (Mean ± SD)CV (%)
  1. The RI (mean ± SD) of each plug was calculated from all cartilage discs cut from it. The CV of each plug was based on the RMS average of the individual CV calculated from each cartilage disc. The overall means of the RI and CV for all cartilage plugs are listed in the bottom row.

161.3946 ± 0.01870.73
261.4068 ± 0.01560.56
361.4017 ± 0.01260.56
471.3916 ± 0.01400.51
561.3912 ± 0.00820.53
671.3994 ± 0.01581.04
Overall381.3975 ± 0.01560.68

In the verification experiment, the overall RI of the distilled water was measured as 1.3340 ± 0.0068 (0.1 MPa, 20°C and 561 nm), revealing no more than 0.02% of relative error compared to other measurements with the same conditions (n= 1.3343, 0.1 MPa, 20°C and 561 nm) (Daimon & Masumura, 2007).


Comparison of theoretical models

In this study, the theoretical model adopted to quantify the focal shift in confocal microscopy is a PSF model based on vectorial wave-optical theory. However, there is the other type of theoretical models using a geometrical approach to quantify the focal shift as (Carlsson, 1991; Visser, 1992)


where αinc is the incident angle of the marginal rays and αref is the corresponding angle of refraction. This definition assumes that the focal shift is only determined by the marginal rays of the aperture. For a small NA objective, Eq. (5) was simplified to (Wiersma & Visser, 1996)


Although Eqs (5) and (6) give simple relationships between the focal shift and the RI to be measured, questions regarding the accuracy and reliability of this geometrical approach still exist (Carlsson, 1991; Visser, 1992; Hell et al., 1993; Wan et al., 2000). To verify the accuracy of Eqs (5) and (6), the average OTR from our verification experiment of distilled water (1.1749 ± 0.0065) was substituted into these two equations, respectively. The corresponding RIs of distilled water were calculated as 1.6057 ± 0.0035 and 1.2904 ± 0.0071, respectively, which are not close to the reported value of 1.3343 (Daimon & Masumura, 2007). Therefore, neither of these two equations is capable of accurately interpreting the focal shift in confocal microscopy. Despite that the PSF model is more complicated, it provides accurate quantification of the focal shift caused by the RI mismatch.

To improve the practicability of the PSF model, we simplified two aspects of Sheppard's PSF model (Sheppard & Török, 1997). Firstly, the laser illumination profile at the exit pupil of the objective was modelled as a homogeneous distribution. Previous studies have shown that the actual illumination profile is close to a truncated Gaussian surface (Kuypers et al., 2004). However, the simulation of the sectioning profiles of specimens has demonstrated that this simplification mainly affects the intensity of the crossing profile rather than the extent (Kuypers et al., 2005). Therefore, this simplification induces little error and avoids the complex measurement of the actual illumination intensity of the confocal microscope. Secondly, the actual spectrum bandwidth of the fluorescence was replaced by the wavelength corresponding to the peak emission of Rhodamine B (565 nm). This simplification decreases the computational load remarkably with a tiny deviation in the simulated focal shift (Sheppard & Török, 1997).

Advantages of the current OTR measurement

Measuring the optical thickness of specimens is essential to the accuracy of the current method. Intuitively, optical thickness can be expressed as the span length of an intensity profiles across the entire specimen. The full width at half maximum (FWHM) is traditionally used to measure the width of an intensity profile. The advantages of FWHM are its simplicity and applicability especially for Gaussian-like symmetrical signals. However, for images acquired by confocal microscopy, the intensity continually decreases with depth, which induces severe asymmetry in the vertical profiles of the specimen slice. In addition, the scattering nature of biological tissues produces irregular local undulations in the intensity profiles (Fig. 3). All of these features indicate that FWHM is unsuitable for measuring the optical thickness of the biological specimens.

To overcome these problems, Kuypers proposed a method using a second-order derivative to locate both shoulders of the intensity profile (Kuypers et al., 2005). As the second-order derivative is very sensitive to the local fluctuations of signals, this method relies highly on the smoothness of the intensity profile. The profile curve needs to be well smoothed in advance, or as a compromise, only profile data with regular shapes should be selected. However, both profile manipulations reduce the measurement accuracy. Dirckx has suggested visually identifying the shoulders of the intensity profiles to determine the optical thickness of bovine muscle slices (Dirckx et al., 2005). This method introduces a subjective judgement, reducing both reliability and accuracy.

For articular cartilage, its unique microstructure and the uneven staining of different components can make the profile curves worse. In two typical examples shown in Fig. 9, either the unsharp lower edge (Fig. 9A) or the extra peak caused by over staining of the chondrocytes (Fig. 9B) would be difficult to process with existing methods.

Figure 9.

Two irregular intensity profiles of articular cartilage specimens. (A) A vertical profile without a sharp lower edge. (B) A vertical profile curve with extra peaks.

The main disadvantage of existing methods for measuring the optical thickness of specimens is their strong dependence on the shape of vertical intensity profiles. In this study, the optical thickness of the specimen was determined by the edge locations, which means existing highly developed edge detection techniques can be utilized. Our method avoids processing the irregular vertical profiles directly, and therefore, reduces measurement errors. As our method requires fewer manual interventions with the parameters, thousands of measurements for each cartilage plug could be executed automatically to enhance the reliability.

Measured RI of articular cartilage

In this study, the overall measured RI for the six cartilage plugs is about 1.39, which is consistent to the compositions of fresh mammalian articular cartilage (Mow et al., 1984). The small CV of each cartilage plug indicates that the method is repeatable and precise. The anova shows that there is no significant difference among the RIs of the individual cartilage plug. This result potentially suggests the little diversity of structure or composition among the cartilage specimens. The possible explanation could be the immaturity of the articular cartilage collected from healthy newborn lambs, in which the tissue differentiation was still not finished and the unique zonal structure was not finally formed. For a better horizontal comparison between cartilage plugs, only the first six to seven cartilage layers from the articular surface were measured as the RI of each cartilage plug, which further decreased the possible RI variation caused by the depth difference of cartilage. Therefore, the cartilage samples used in this study have less individual diversity and are suitable for assessing the method reliability. However, further study is still required to explore whether the growth and eventual degeneration of articular cartilage have measurable effects on its optical properties.

It is difficult to provide a comprehensive comparison of our results with other studies because experimental measurements for the RI of articular cartilage are rare. In Wang's study for bovine cartilage, an overall RI of 1.358 ± 0.022 was obtained (Wang et al., 2010). The difference between Wang's results and the current work could be caused either by the species differences or the differences in techniques. There was no verification experiment in Wang's study and no other experimental RI of articular cartilage could be found; therefore, potential errors and inconsistencies of the proposed method are difficult to be determined. However, the cartilage discs in our experiment spanned approximately 300–350 μm from the articular surface that corresponds to the first section (500 μm) in Wang's work. In this section, Wang reported a mean RI of 1.361 ± 0.032, which is more consistent with this study.

The confocal microscope recorded images within a spot of 0.24 × 0.24 mm2. In this small scanning spot, 512 confocal slices were obtained and the RI of each confocal slice was calculated separately. However, RI undulations were still found even in this small spot, as shown in Fig. 10. This is because articular cartilage is an optically heterogeneous tissue with diverse optical characteristics in different points. Furthermore, system noise of the confocal microscope has negative impacts on the measurement of optical thickness that increases the variability of the calculated RI. The system noise generally includes random noise and background noise. The random noise can be reduced by multiframe average. The background noise comes from electronic elements such as the detector, which is possible to be quantitatively estimated and offset from the confocal images.

Figure 10.

Fluctuations of RI within one confocal scanning spot.

In this study, to improve the reliability, the average RI of all confocal slices was used as the RI of the scanning spot. Thus, the measurement window of our method is 0.24 mm × 0.24 mm × 50 μm. This small window makes it possible to characterize the distribution of RI on the articular surface with a high accuracy. It also allows the study of RI gradient with depth using a sampling interval of only 50 μm, which is thin enough even for the degenerated adult articular cartilage with reduced thickness (Shepherd & Seedhom, 1999).

The accurate RI measured by our study also offers a method to determine the true size of an object in cartilage specimens. Substituting Eq. (1) into Eq. (4), we have


If there was a defect or a chondrocyte recorded in the cartilage image and its size was determined as OTAC, with an accurate RI measured in advance, the actual size of the object could be calculated directly. Equation (7) can only calculate the object size on the z-axis. However, as the focal shift is not severe on the other two dimensions, the object sizes on x-axis and y-axis could be closely approximated from the confocal images.


We have developed a method for the accurate measurement of the RI of articular cartilage utilizing a standard confocal microscope system. The overall RI of the six cartilage plugs harvested from lamb condyles was lower than the empirical values used previously (Herrmann et al., 1999; Pan et al., 2003) but quite close to the experimental values from Wang's study (Wang et al., 2010). This method is highly repeatable with a small relative error of 0.02%. The similar RI of the six cartilage plugs may also reveal that the structure and composition of articular cartilage changed little during the first week after birth. The current method can easily be implemented on a standard confocal microscope with an acceptable computing load. As only small and thin samples of articular cartilage are needed for this method, it is suitable for measuring the cartilage RI in any region of interest, such as the superficial zone.

Accurately determining the RI of articular cartilage and its distribution on the articular surface can help us better understand the mechanisms of joint loading and cartilage degradation. Potentially, the comparison of the RI between healthy and unhealthy articular cartilage could suggest an effective method to assess the cartilage status due to the changed compositions and structure. Furthermore, it might be developed as an assistant diagnosis technique for arthritis. Finally, using the measured RI of articular cartilage, the spherical aberrations caused by the RI mismatch in the optical imaging of articular cartilage can be calibrated to improve the image quality and locate the targets in cartilage more accurately.

However, the proposed method is not an in vivo measurement that limits its applications. For those potential applications described above, further studies are still required to thoroughly investigate the variation in RI of articular cartilage across a broad range of types and conditions.


The authors acknowledge the facilities, scientific and technical assistance of the Australian Microscopy & Microanalysis Research Facility at the Centre for Microscopy, Characterisation & Analysis, the University of Western Australia, a facility funded by the University, State and Commonwealth Governments. This work was posted in ‘Focus of Microscopy 2011’ and orally presented in the annual meeting of ANZORS 2011.