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A new optical device to measure forward scattered light in a range of 3° to 20° has been developed and tested. The scattered light is focused on a plane where its axial position is proportional to the scattered angle θ. A motorized iris diaphragm located at this plane selects the scattered light between 0° and a variable angle θ. This light is collected by an integrating sphere and converted into an electrical signal by an APD. The device was tested with suspensions of polystyrene microspheres of 3 different sizes. The obtained results are in good agreement with the Mie theory.
©2007 Optical Society of America
1. Introduction
Optical properties of biological tissues, such as the absorption coefficient μa, the scattering coefficient μs and the anisotropy factor g, relate respectively to the chemical composition, to the structure of the tissue and the size of the scatterers. These properties are basically measured by acquiring the intensity of the scattered light I(θ,φ) as a function of the angle θ with respect to the optical axis and azimuthal angle φ. Many devices suitable for characterizing cell scattering are described in the literature [1, 2, 3, 4, 5, 6]. They can be divided into two different types: goniometric and non-goniometric systems. Note that if the sample is held between two glass slides, it reduces the range of angle θ due to total reflection, depending on the mismatch of refractive index between the medium within the sample holder and that between the sample and the detector.
Goniometric systems measure the scattered intensity I(θ,φ). The sample is usually illuminated by a laser beam and the scattered light is collected in a small solid angle dΩ = dθdφ defined by the effective size of the detector which is moved around the sample and its distance to the sample (Fig. 1). To overcome the reduced range of measured scattering angles θ as explained before, Jacques et al [2] placed the sample in a tank filled with saline solution and moved an optical fiber in the solution to collect the scattered light. Passos et al [7] solved this problem by using a cylindrical holder, so that there is no refraction between sample and detector. To measure the scattering behaviour of phytoplankton cells that predominantly scatter forward, MacCallum et al [4] developed a system which collects light by means of a fixed lens and a moveable detector placed at its Fourier plane. To measure single cell scattering Watson et al [6] used an optical trapping and illuminated the cells with another laser shining perpendicular to the trapping laser. A parabolic mirror images the scattered light at infinity so that each bundle of light emerging from the mirror corresponds to a given scattering angle (θ,φ). Roman et al [8] replaced the light source of a polarized light microscope in order to illuminate the sample at different angles θ. Goniometric measurements were performed by capturing the pictures through the microscope with a CCD. Norman et al [9] investigated scattering of small particles by capturing with a CCD the scattered light diffused by a screen placed after the sample along the optical axis of the illumination. To detect small signals within the dynamic range of the CCD, the unscattered beam (collimated transmission) was blocked before the screen with a central obscuration.
Table 1. Measuring ranges of the scattering angle θ and φ of described systems (1-defined by fiber; 2-defined by detector area; 3-defined by rotating aperture; 4-defined by NA of objective)
Non goniometric systems use integrating spheres [10]. In a typical set-up the sample is placed between two integrating spheres, the first collects and measures backscattered light and the second forward scattered light. Additionally, a third sphere can be used to measure the colli-mated transmission. Using these measurements an inverse Monte Carlo simulation calculates the optical parameters μs, μa and g. With this method Hammer et al [1] investigated the optical properties of the eye fundus tissue and Laufer et al [3] showed the temperature dependence of optical properties of human skin.
The newly developed system, which was strongly motivated by the work of MacCallum et al [4], combines both the goniometric idea and the integrating sphere. Instead of moving the detector in the focus plane, a motorized iris diaphragm and an integrating sphere collecting the light are used. Table 1 resumes the measuring ranges of the different systems.
2. Material and Methods
2.1. Optical principles
Briefly said, goniometric systems measure the intensity I(θ,φ) = L(θ,φ)dAcosθdθdφ at distinct angles (Fig. 1) with dAcosθ being the effective radiation area and L(θ,φ) the radiance of the sample.
Fig. 1. Goniometric measurements: The sample is located at the origin of the coordinate system and dΩ represents the small solid angle defined by the detector.
With the standard integrating sphere technique light is collected in a defined large solid angle (Fig. 2). The intensity measured is therefore
where θ0 is defined by the exit port of the first sphere for the backward scattered light or by the entrance port of the second sphere for the forward scattered light. θmax is close to 90° depending on the distance between the sample and the neighborhood sphere port.
Fig. 2. Non goniometric measurements: The scattered light is collected and measured for a large solid angle defined by θ0 and θmax.
In the proposed setup (Fig. 3) forward scattered light is imaged on the focal plane of an optical system. This means that all rays having an angle θ with respect to the optical axis will be focused to a thin annulus of radius r θ.
Fig. 3. Experimental setup to measure small angle scattering. Light scattered at an angle θ1 is blocked by the iris, whereas light scattered at θ2 is collected (θ1 > θ2).
Located in this plane, an iris diaphragm with an aperture radius ri allows scattered light with angles smaller than the corresponding radius r ≤ ri to pass. An integrating sphere collects that light and a detector measures the intensity
where θ0 is close to 0° and is defined by a tilted optical glass fiber that acts as a central obscuration (Fig. 3). C is an instrumental constant and D(θ) the background light. Finally, the intensity of the scattered light I(θi) (Fig. 4) is obtained by deriving I *(θi(ri)) as
where Si = πri 2 is the collected area defined by the iris.
2.2. Experimental setup
A Helium Neon laser (632.8nm, 5mW, JDS Uniphase) is used as light source. The beam is filtered by a spatial filter and expanded to obtain a gaussian waist of 2.75mm in diameter. A pellicle beam splitter reflects 8% of the light to a reference photo diode (opt101, Burr Brown), which measures the intensity fluctuation of the light source. The horizontal sample holder consists of a microscope slide with affixed cover slips (150μm). The dimensions of the sample are about 40×15×0.15mm. The optical system consists of two achromatic lenses (f 1 =35mm, f 2 =50mm, f overall =20.20mm, Thorlabs) which focus the scattered and unscattered light on the iris plane. The image curvature (larger than 1000mm) is neglected.
To improve the detection of low light level, the unscattered beam is blocked by a tilted optical glass fiber with a diameter of 1.3mm so that the reflected beam leaves the system. Additionally, due to a 45° polished surface at the tip of the fiber, the light is collected and guided with the fiber out of the system. This collected light can be used for further applications. The light passing the iris is collected by an integrating sphere (10cm diameter with a port of 2.5cm, coating Zenith, SphereOptics) and is measured by an APD (C5460-01, Hamamatsu).
Using a stepping motor, a mechanism opens and closes the iris stepwise, with a step dθ arbitrary set to 0.2°. One measurement ranging from 3° to 23° is composed of 100 steps.
Data acquisition and control of the iris were carried out by a dedicated LabVIEW program. The sampling frequency was set to 1kHz and for one step 200 points were acquired and averaged, leading to an acquisition time per step of 200ms and provides one data point. Moreover the time to move from one step to another takes 400ms.
The acquired data were then computed with MATLAB. The data processing includes a low-pass filter, a mean signal calculation based on 10 measurements and a normalization. Furthermore the background, which is measured without sample, is subtracted from the normalized signal. Then the differences ∆I * between two consecutive data points are calculated Eq. (3). Additionally data are corrected for the non-linearity between ri and θi and for the mismatching refracting indexes between the microspheres solution, the glass and the air. Finally the signal is normalized in respect to the area given by the change in aperture of the iris dAi.
To ensure single scattering in our experiment the mean free path length (MFP) has to be at least 5 times larger than the sample thickness l. Making the assumption that μa of polystyrene is 0 the MFP can be simplified as 1/μs. Given the definition of the scattering coefficient where c is the concentration of microspheres, d their diameter and Qs the scattering efficiency. This last coefficent was calculated using the program from Scott Prahl [11]. In respect of the condition above, c becomes
This system was tested with polystyrene microspheres (n 633nm = 1.5864) of 3 different diameters d 1 = 1.03μm (Polyscience, Inc.), d2 = 3μm (Kisker Biotech), d 3 = 6μm (Kisker Biotech) and a sample thickness l of 150μm.
3. Results and discussion
Because the 3μm, respectively 6μm, microspheres were not NIST certified, we measured their diameter with an electron microscope (leo 1525, Carl Zeiss SMT) and found 2.54μm ± 0.05 and 5.66μm ± 0.06 (mean ± SD), respectively.
Figures 5, 6 and 7 show the scattering intensity obtained with the different polystyrene micro-spheres. For each measurement the corresponding theoretical curve is added. The used MAT-LAB code for Mie simulation is provided by Dave Barnett [12].
Fig. 5. Normalized intensity versus angle of light scattered by polystyrene microspheres (d 1 = 1.03μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.5864, d = 1.03μm and unpolarized light
The optical fiber produces a thin rectangular shadow from the centre to the edge of the iris (Fig. 3). The cross-sectional area of the fiber tip determines the lowest measurable scattering angle θ0 to about 3°. Light scattered at angles θi larger than 23° are not collected by the integrating sphere. This is mainly due to three reasons. First the cumulated refracting indexes mismatching, second the limitation given by the optical system and third the diameter of the entrance port of the sphere. Moreover the usable angle is limited to 20° because of the stray light generated by the optical system and inner reflections at the boundaries of all involved parts like the gear.
The mismatch between theoretical and experimental maxima could be explained by the distribution of the spheres diameters and by the non-spherical shape of the spheres, possibilities previously mentioned by Mourant et al [5].
Fig. 6. Normalized intensity versus angle of light scattered by polystyrene microspheres (d 2 = 2.54μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.5864, d = 2.54μm and unpolarized light
The signal to noise ratio (SNR) depends on the angle and rises when θ increases, in contrast to other systems where the SNR usually falls when θ increases. At 4° and 20° the SNR for the 1.03μm spheres diameter is 2.7dB and 23.6dB respectively.
Finally measurements made with a concentration 5 times smaller Eq. (4) showed similar results. Therefore no multiple scattering effects were considered.
Fig. 7. Normalized intensity versus angle of light scattered by polystyrene microspheres (d 3 = 5.66μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.5864, r = 5.66μm and unpolarized light
The results obtained with this proposed device are reproducible (Fig. 8) and the measured sphere diameter agree with the data acquired by a standard goniometer (Fig. 9).
Fig. 8. Reproducibility of the measurements with the proposed device. Normalized intensity from 10 measurements versus angle of light scattered by polystyrene micro-spheres (, from top)
The angular resolution could be increased by a factor of 10 which corresponds to an angular step of 0.02° by changing the step size of the iris. A thinner iris would increase the maximum collected angle θmax by a few degrees. A better central obscuration would not significantly
Fig. 9. Results goniometer λ=532nm: Normalized intensity, dashed line with errorbars, versus angle of light scattered by polystyrene microspheres (d = 2.54μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.594, d = 2.54μm and parallel polarized light
decrease θ0. Also the data acquisition time, which is now about 1 minute for one measurement could be decreased by increasing the sampling rate or the speed of the stepping motor.
4. Conclusion
In conclusion, we have developed a new instrument to measure forward scattered light. Our results are in accordance with the Mie simulation and with measurements obtained from a traditional goniometer. Moreover our setup allows faster measurements than the traditional goniometer.
Acknowledgments
David Roßkamp, a student from the university of applied sciences Jena, was doing his diploma work at the Institut de Recherche en Ophtalmologie. His stay was granted by the Swiss ERASMUS program through the university of applied sciences of western Switzerland. The authors thank Daniel Zufferey at the university of applied sciences of western Switzerland for measuring the diameter of the microspheres with the electron microscope.
References
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