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A reflectance confocal scanning laser microscope (rCSLM) operating at 488-nm wavelength imaged three types of optical phantoms: (1) 100-nm-dia. polystyrene microspheres in gel at 2% volume fraction, (2) solid polyurethane phantoms (INO BiomimicTM), and (3) common reflectance standards (SpectralonTM). The noninvasive method measured the exponential decay of reflected signal as the focus (zf) moved deeper into the material. The two experimental values, the attenuation coefficient μ and the pre-exponential factor ρ, were mapped into the material optical scattering properties, the scattering coefficient μs and the anisotropy of scattering g. Results show that μs varies as 58, 8–24, and 130–200 cm-1 for phantom types (1), (2) and (3), respectively. The g varies as 0.112, 0.53–0.67, and 0.003–0.26, respectively.
A variety of optical measurements can easily measure the absorption coefficient, μa [cm-1], and the reduced scattering coefficient, μs′ = μs(1–g) [cm-1], of a tissue sample. However, separation of μs′ into the two factors, the scattering coefficient, μs [cm-1], and the anisotropy of scattering, g [dimensionless], usually involves bench-top experiments with thin tissue slices. This paper describes a method that measures μs and g noninvasively on an intact tissue, which is therefore useful for in vivo measurements of tissue optical properties . This paper demonstrates the technique on some phantom tissues.
The method uses reflectance confocal scanning laser microscope (rCSLM), or alternatively optical coherence tomography (OCT), to scan into a sample material and observe the exponential decay of reflected signal as the focus is translated deeper into the sample. At deeper depths it is more difficult for photons to penetrate to the focus and scatter back out into the collection solid angle of the objective lens. Others have recognized that attenuation of an rCSLM or OCT signal could characterize tissues (see  for review). The key improvement of this proposed method is to incorporate scattering anisotropy into the treatment so as to separately specify μs and g.
The method has been used to study the scattering consequences of a single gene mutation in mouse skin , the scattering changes as cells remodel a collagen gel [4,5], and the scattering changes in mouse skin when soaked in glycerin to achieve optical clearing . In all cases, the distinction between μs and g could be discerned. The g value is of particular interest since it relates to the size of scatterers . The method has been used for enhanced image contrast in optical coherence tomography imaging of breast cancer lymph nodes [8,9].
The three types of phantoms tested were (1) polystyrene microspheres in a gel, (2) solid polyurethane phantoms, and (3) a well-known commercial reflectance standard.
The goal of this report is to illustrate the use of the rCSLM technique as applied to solid phantoms and to offer an initial characterization of the μs and g of the phantoms.
A set of five phantom materials were tested:
The confocal reflectance scanning laser microscope (rCSLM), built in our laboratory as an inverted microscope, has been used in previous studies [1–3,5,6]. An argon-ion laser delivered ~10 mW of 488-nm wavelength to the microscope objective lens. The objective lens (NA = 0.90, water-dripping lens, LUMPlanFL, Olympus America, Melville, New York) was water-coupled to the phantoms. For the microsphere gel, the microscope was water-coupled to the coverslip. Figure 2 shows the basic design. Lateral scanning was implemented by x- and y- galvo scanning mirrors (RS-15, Nutfield Technology Inc., Windham, New Hampshire), yielding 512 x 526 pixels of equal 0.312 μm size. Axial z-axis translation of the focus was achieved by translating the sample using a motorized scanning stage (LS50A, Applied Scientific Instrumentation, Eugene, Oregon), yielding 1-μm axial stepsizes in the axial region of interest. However, to achieve a broader axial range of imaging, the axial stepsizes were increased to 5 or 10 μm at positions above and below this central region of 1-μm stepsizes. The detection arm was a lens/pinhole/photomultiplier-tube assembly (PMT: 5773-01, Hamamatsu Photonics, Japan). Scanning and detection were controlled by a data acquisition board (6062E, National Instruments, Austin, TX) and custom software developed using LabviewTM. Image reconstruction and analysis were done using MATLAB (Mathworks Inc., Natick, Massachusetts).
Figure 3 shows examples of the raw images of reflectance for the phantoms, shown as log10(V(z,x)) where V is the detector voltage. The abcissa, x, is the lateral position of the phantom. The ordinate, z, is the apparent depth of the focal volume equal to the difference between the focal length (FL) and the distance (h) between the objective lens and the phantom surface.
Figure 4 shows the calibration of the system. The glass-water(gel) interface of the microsphere-water(gel) phantom was imaged to yield a peak voltage Vgw = 5.14 V. The expected reflectance from this interface was rgw = ((nwater-nglass)/(nwater+nglass))2 = 0.00427, where nglass = 1.522. Then a calibration factor was calculated: calib = rgw/Vgw = 1.204x10-4 [1/V]. Thereafter, any measurement V was multiplied by calib to yield the reflectance R, which is the fraction of light delivered by the microscope that is returned into the microscope for detection.
To check the calibration, the axial profile, R(zf), for the polystyrene microsphere gel phantom was analyzed to fit the expression
As the distance height (h) of the lens above the surface of the phantom was changed, the apparent depth position of the focus varied as z = FL – h, where FL is the focal length of the lens. When h = FL, the focus is at the phantom surface. As h was decreased, z moved into the tissue. However the true position of the focus, zf, increased as
where Dglass is the thickness of the glass coverslip if in place (if no glass, Dglass = 0). The parameter zf/z = tan(θ1)/tan(θ2), where θ1 = a sin(NA/nwater) and θ2 = a sin(NA/nphantom). The factor NA/nphantom is referred to here as the effective numerical aperture. For the aqueous gel, the value of zf/z was 1.00. For the polyurethane and SpectralonTM phantoms, the value of zf/z was 1.20, based on an assumed value of 1.49 for nphantom. Hence, the original data versus z was converted to data versus zf before subsequent analysis.
The behavior of R(zf) depends on the parameters ρ and μ, which are described as
where Δz is the standard axial resolution, Δz = 1.4λ/NA2, where NA = sin(θ1/2)nphantom with θ1/2 equal to the half angle of light delivery within the phantom and nphantom is the refractive index of the phantom [2,3]. The value of nphantom for the polyurethane and SpectralonTM phantoms was assumed to be 1.49.
In Eq. (2), μ refers to the attenuation of light as photons move to/from the focus. When scattering is very forward directed, it is possible for photons to still reach the focus despite multiple scattering. The function a(g) varies from 1 to 0 as g varies from 0 to 1, i.e., from isotropic scattering to forward-directed scattering. The function was determined by Monte Carlo simulations of focused light penetration to a focus at zf for varying values of μs at a given g. The change in fluence rate at the focus versus value of μs, or F(μs) at constant g, was fit by Eqs. (1)–(3) to specify the value of a. Repeating for different values of g yielded the function a(g), which can be described as [2,3]
The effect of absorption, μa, is negligible unless working with a very strongly absorbing material. The factor 2 accounts for the round-trip in/out path of collected photons. The factor G is a geometry factor that accounts for the extra pathlength of photons when a high NA objective lens is used. The value of G depends on the NA of the lens, and is approximated by
where value θ2 is the maximum half-angle of collection at the phantom surface, which depends on the NA of the lens. The factor EGaussian(θ) = exp(–(θ/θ2)2) is a Gaussian function that describes the angular dependence of light entering the phantom. The assumption here is that the ±1/e portion of the laser beam was filling the back pupil of the objective lens and reaching the phantom. This assumption is easily modified in Eq. (6) to match a particular experimental setup. The factor T(θ) is the transport to the focus from a surface entry point at an angle θ with respect to the central z axis. Attenuation of T(θ) by tissue scattering and absorption decreases the contribution from light at larger angles of entry, which slightly decreases the average pathlength, Gzf, of photons reaching the focus. Equation (6) is more fully discussed in . In this experiment, G = 1.132.
The function b(g) describes the fraction of photons scattered within the axial Δz extent of the focus which are scattered back into the solid angle of collection of the objective lens. The function b(g) is approximated by the integral over all angles of backscatter that are within the collection angle of the objective lens:
where the scattering function p(θ) indicates the deflection of photons from their incident forward direction, π is the direct backscatter angle in radians and θ2 is the maximum half-angle of collection by the lens in radians. The function p(θ) was approximated by the Henyey-Greenstein function:
For the conditions of this experiment, b(g) ≈ 0.203exp(-1.716g) - 0.077exp(-0.744g), which equals 0.132 at g = 0, drops by 50% at g = 0.262 and drops by 90% at g = 0.732. Using Mie theory to generate p(θ) yields a similar b(g) as the Henyey-Greenstein function, except when the spheres are large and scattering is very forward directed (not shown).
The effective solid angle of collection by the objective lens was also dependent on the refractive index of the phantom. The θ2 is the maximum angle of collection by the lens, and was used in the calculation of b(g) in Eq. (3).
The functions a(g), b(g) and G(NA,g) continue to be topics of ongoing investigation.
Figure 5 shows an example analysis. A superficial region (5-50 μm below the surface) was used for fitting, beyond the effects of the front surface reflectance and before diffuse light begins to contaminate the signal. The noise floor due to diffuse light reflectance escaping within the solid angle eventually collected by the detector pinhole becomes important when the focus is located at depths beyond the transport mean free path, 1/(μs(1–g)). Hence, useful measurements are restricted to the superficial layer.
Figure 6 plots the mean μ versus mean ρ from Fig. 5 on a log-log plot. Superimposed on this plot is a grid of iso-g lines and iso-μs lines, based on Eqs. (3) and (4). This grid allows interpretation of the μ and ρ data in terms of the optical properties μs and g. The experimental data point (red circle) indicates μs = 57.7 cm-1, g = 0.072, μ = 130 cm-1, ρ = 9.2x10-4. Also shown is the predicted data point using Mie theory (black diamond), which has values of μs.MIE = 58.2 cm-1, gMIE = 0.129, μMIE = 131 cm-1, ρMIE = 8.2x10-4. Work continues on testing the accuracy of the first-order theory (Eqs. (3), (4)) and on experimental methods for preparing microsphere gels for calibration.
The images of Fig. 3 show that the solid phantoms (polyurethane and SpectralonTM) presented a low density of TiO2 particles that strongly scattered light. These phantoms did not present a uniform attenuation R(zf) within the range of imaging that could be reliably analyzed using Eqs. (1)–(3). Nevertheless, the data was fit by Eq. (1) to yield μ and ρ experimental values.
Figure 7 shows axial profiles of 15 random x,y positions in the phantoms. The curves indicate a slow attenuation of signal as the focus is moved deeper into the tissue. Red lines indicate exponential fits to the attenuation of the R(zf) signal (bold lines indicate region of data fitted), and the slopes specify the values of μ. The fit is extrapolated (dashed lines) to the front surface of the phantom to specify the value of ρ (indicated by red symbol).
Figure 8 plots the μ and ρ values specified by the fits shown as red lines in Fig. 7, and superimposes a grid of iso-μs and iso-g lines to aid interpretation. The grid is drawn assuming the lens is water coupled to an aqueous gel (n = 1.336). There is agreement between the experimental measurement and Mie Theory for the microsphere gel. The grid slightly shifts downward when the lens is water coupled to the phantom polymer materials (n assumed to be ~1.49) (grid not shown since shift is very small; the grid’s μ and ρ drop ~3%, so data are properly deduced to be ~3% higher than values calculated with the water-coupled grid). The analysis considered this effect when computing the values summarized in Table 1 .
This pilot study of the optical properties of phantoms is intended to illustrate a noninvasive experimental approach toward specifying the optical scattering properties of a phantom, specifically the scattering coefficient (μs) and the anisotropy of scattering (g). The polyurethane phantoms (INO BiomimicTM) were shown to have a background optical properties along with a low density of dispersed strongly scattering TiO2 particles. The SpectralonTM phantoms were more dense in scattering, hence a higher μs than the polyurethane phantoms, and individual strongly scattering particles were present but less evident. The polystyrene microsphere gel phantom was the most uniform phantom, composed of a high concentration (2% volume fraction) of 100-nm-dia. spheres. Our experience with microsphere phantoms using larger spheres is that they also present as discrete strong scatterers. Therefore, we routinely use small 100-nm-dia. spheres when calibrating experiments.
Future work should explore the wavelength dependence of the μs and g values derived from axially scanned rCSLM signals. Comparison of the values against macroscopic measurements of the diffusion property μs′ = μs(1–g) should be made.
The method outlined in this paper can be used with any confocal microscope or OCT system operating in reflectance mode. The method has been used with a variety of systems, both custom built and commercial. The μ measurement is easily accomplished if the axial stepsize between successive x,y images is known. The ρ measurement requires calibration, however, such as the measurement of a glass/water interface, as in this paper. Alternatively, the measurement of a microsphere gel can be used to calibrate ρ. Since the anisotropy g is sensitive to ρ, the calibration is worthwhile if rCSLM or OCT is used to characterize the nanoarchitecture of a tissue.
We thank Jean-Pierre Bouchard from INO, Inc., Canada, for supplying the Hard BiomimicTM and Soft BiomimicTM phantoms. This work was funded in part by NIH R24-CA84587.