Effect of measurement on the ballistic–diffusive transition in turbid media

Abstract

The dependence of the transition between the ballistic and the diffusive regimes of turbid media on the experimental solid angle of the detection system is analyzed theoretically and experimentally. A simple model is developed which shows the significance of experimental conditions on the location of the ballistic-diffusive transition. It is demonstrated that decreasing the solid angle expands the ballistic regime; however, this benefit is bounded by the initial Gaussian beam diffraction. In addition, choosing the appropriate wavelength according to the model's principles provides another means of expanding the ballistic regime. Consequently, by optimizing the experimental conditions, it should be possible to extract the ballistic image of a tissue with a thickness of 1 cm.

Short wavelength infrared optical windows for evaluation of benign and malignant tissues

“…where μ 0 s ¼ μ s ð1 − gÞ is the reduced scattering coefficient, l tr ¼ 1∕μ 0 s is defined as the transport mean-free path, 20 and g ¼ hcos θi is the mean cosine of the scattering angle (anisotropy factor). 21 When the solid angle δΩ is small, the total transmitted light intensity I can be written as the sum of the number of ballistic photons (I b ) and of a fraction of the diffusive photons (I d ) 22…”

Study of a simple model for the transition between the ballistic and the diffusive regimes in diffusive media

“…[15][16][17][18] Recent experiments reveal that the transition length depends not only on the scattering coefficient but on the collecting angle as well. As was later demonstrated experimentally, 19,20 despite its simplicity, this model anticipated the transition from the ballistic regime to the diffusive one with high accuracy. 19,20 It should be stressed that the determination and classification of the transition point are not merely an academic issue.…”

“…This model was shown to predict the experimental results, 19,20,34 however, it was shown that there is a discrepancy of a factor of 2 to 4 in the prefactor of the diffusive term.…”

“…For biological tissues (of almost any kindskin, brain, liver, and so on) that are thicker than 2 mm, the ballistic component of the light [in the visible or near-infrared (IR) regimes] is negligible. 19,20 It should be stressed that the determination and classification of the transition point are not merely an academic issue. [8][9][10] Since the TMFP, 11,12 which is the reciprocal of the reduced scattering coefficient, is the diffusion length scale, it was assumed that the length of the transition from the ballistic regime to the diffusive one should also be equal approximately to this length scale.…”

Ballistic imaging of biological media with collimated illumination and focal plane detection

“…It has recently been shown 26 that by applying two simple and well-known modifications, it is possible to substantially extend the ballistic imaging depth of a diffusive medium. This method was based on previous research, 27 which demonstrated that the transition point between the ballistic and diffusive regimes depends not only on the scattering coefficient, but on the collection angle of the detection as well.…”