Mie Scattering of Red Light Lasers

M. Carnohan, T. Brinsa

Department of Physics, College of Charleston, Charleston, SC

INTRODUCTION

Scattering is a phenomenon in which the direction, frequency, or polarization of a wave is changed when the wave encounters discontinuities in a medium, or interacts with material at the atomic or molecular level. Mie scattering is the scattering of an electromagnetic wave by particles or refractive index inhomogeneities of a size on the order of the wavelength of interest [3]. When discussing light scattering, the importance of the size of the particle is clear when one understands the interaction to be related to other forms of electromagetic behavior on a macroscopic level, such as the incident reflectivity of light in a mirror. If visible light is to be reflected specularly, then the reflecting surface must not contain flaws approaching the size of the wavelengths. A form of scattering in which the largest component of light is scattered isotropically, called Rayleigh Scattering, occurs when EM waves interact with particles with size less than the wavelengths. When this occurs, a mirror-like effect of back scattering takes place because the wavelengths are larger than the size of the particles. A molecular mirror is created where the particles act as the flaws did in the mirror example. Mie scattering takes place when particles are roughly the size of the waves. Most of the light passes through the medium in a forward direction; because true interaction and not simple reflectance occurs.

Scattering behavior is modeled several different ways in the sciences. Use of the radiative transport equation alllows for modeling of intereactions of light with tissues by assuming homogeny of tissue constituents. The relevance of this research to medical applications is that the mechanism of scattering in certain instances in the tissue may follow a Mie-like behavior, in which a far greater amount of laser light is preserved in a near collimated form than can be estimated solely by the radiative transport equation.

METHODS

Solution Preparation

The polystyrene solution is a homogenous solution which contains 10% by volume 2.04m m diameter spheres. The solution is diluted 1:1000 in a water. As illustrated in Figure 1, the diluted solution is placed in a Pyrex test tube which is suspended within a beaker containing an index matching medium. Finding a medium with a similar index of refraction to that of Pyrex is done to eliminate reflection off of the tube (B). Matching the index helps avoid strong reflectance which would appear incorrectly in data as back scattering from the solution. The use of Wesson oil™, as an index matching medium, eliminates the difference in the two refractive indices.

Equipment

FIGURE 1 A photometer (D) measures the intensity of laser light on discrete angles around the solution (B). The photometer is maintained 12.45 cm from the solution and has aperture width of 0.78 cm.(A) Diode laser at 670nm, and a HeNe laser at 632.8 nm. The solution is suspended in a beaker (C) filled with the index matching medium. The test tube containing the solution is clamped in place on a ring stand. The beam emitted from the laser is radial to the concentric containers (B and C).

Accurate measurements cannot be taken from 170° >q >-170° because of a physical limitation: eclipsing the beam of the laser with the detector. Intensity measurements are taken every 10° by careful transport of the photometer around the solution. For results to remain accurate, the beam of the laser is positioned to bisect the center of the solution perpendicular to the test tube in which the solution is suspended. Prior to actual exposure to the solution, the laser is centered in the aperture of the photometer. The laser is leveled using height measurements conducted at several points around the equipment.

RESULTS

Raw Data

Measurements demonstrate scattering is primarily in the forward direction (q between —80° and 80° ). Limited back scattering is observable to be slightly constant (q between —180 and —105 and q between +105 and +180). The Henyey-Greenstein function is used to compare the generated function to a theoretical.

(1)

The Henyey-Greenstein function is an analytical expression used to approximate Mie scattering. Paramenters which affect the b and ghg components of the function are the wavelength of light, and the size and density of the solutes in a solution. The b in the expression represents a fractional component of isotopic scattering. While the g, the component of anisotropy, is a theoretically calculated number based on radius of express particle, wavelength of laser, index of refraction of the medium, imaginary index of refraction of specific solution and the density of solution. The g component represents the amount of light which scatters in a forward direction and is found by the use of the Mie Calculator on-line [2]. The g that is utilized in the expression is the average cosine of the phase function for all phase angles. Defined in terms of ghg and b, ghg = (1-b)g.

FIGURE 3 The phase function of a HeNe laser overlaid by the fitted H-G function where: b=0.43, hg=0.9245614, and g = 0.527.

DISCUSSION

As measurements involving the photometer were sensitive to position as well as light intensity, error from imprecise placement and extraneous light have a place in data assessment. Light present, not expressly from the source, may be a near constant which may not affect relative data. But the strong dependence on angular position of the detector most likely will impact the resulting phase measurements. Repeated measuring is the only way to avoid function shifting and insure proper symmetric output. Wesson oil™ as an index matching medium eliminated most of the non-scattering reflectance, but was not perfect- so allows for a source of some error in data for some backscattered values of q - which is the reason these values where not considered in the final data set.

Relative diffrence, calculated between g and ghg, is given by g/ghg and provides a general means of error analysis for our entire procedure. For the HeNe laser data, the relative error was found to be 57% while the Diode laser had a higher error of 69%. While the relative error seems high, it is important to note that the g generated by Prahl's Mie calculator comes from extremely controlled experimentation and compared conservatively to ggh found by a best-fit method. There is a clear demonstration of Mie type scattering, closely fitted to the H-G function, observable in each phase function despite the g discrepancy. This demonstrates the importance of the b component of the equation- it's low comparative value to that of g (b=.3, g=.75 for the HeNe laser) shows the reach of the expression in handling many different component conditions. Use of low estimated (isotropic) b values allowed for a fit to the H-G function with actual deviation of less than a few percent.

CONCLUSION

The procedures and calculation methods of the experiment present a means to find the scattering coefficients and phase function for scattering interactions in a solution with solutes of size near that of the wavelength of red light lasers. Such solutes are also near in size to some molecular constituents in human tissues which are subjected to EMR from red light sources both naturally and in medical applications. The average cosine (where a cosine of 1 demonstrates all forward scattering) for each set of data was greater than .5 demonstrating largely forward scattring preset in each solution.

Acknowledgements

We thank Jeff Wragg for helpful discussion; Dr. Linda Jones for providing laboratory facilities and resources; Scott Prahl for use of the Mie Calculator.

References