Quantitative spectrophotometry of scattering media via frequency-domain and constant-intensity measurements

Abstract

The attenuation of light by scattering and absorbing media is nonlinearly dependent upon the absorption coefficient, since detected light has experienced many different flight times. The frequency response of such a sample to modulated light is also nonlinear. We derive an expression for the attenuation that includes both the absorption coefficient and the modulation frequency. Its form is a power series whose coefficients are the cumulants of the temporal point-spread function (TPSF). Recasting this expression in terms of intensity leads to a similar expression with the cumulants replaced by the moments of the TPSF. A means of exploiting this relationship to produce estimates of the absolute concentration of the absorbing species is suggested.

Use of HSI to measure oxygen saturation in the lower limb and its correlation with healing of foot ulcers in diabetes

“…The present clinical study was planned to determine if it was possible to confirm that a relationship existed between oxygenation of the lower limb in patients with diabetes and foot ulcers as determined by HSI at presentation, and healing of those ulcers at 12 and 24 weeks. We used equipment developed in‐house, employing novel software which was based on curve fitting of data derived from equations for the relationship between the attenuation and light scattering . The results of HSI reflect, but are not direct measures of, the relative proportions of oxygenated haemoglobin and are expressed in arbitrary units from 0 to 100.…”

Reduction of Error in Spectrophotometry of Scattering Media Using Polarization Techniques

“…When l a ¼ 0 the intensity of detected light, I s , is defined by the integral of s(t), while with l a 6 ¼ 0 the detected intensity, I a , is given by the integral of h(t). Consequently, the overall attenuation of the sample, A, can be expressed as the sum of the attenuations due to scattering, A s , and absorption, A a : 16,17 A ¼ ln…”

“…Equation 4 shows how the overall attenuation can be split into two components as initially recognized by Twersky, 17 who suggested that A s is essentially a constant offset in attenuation with A a linearly dependent upon l a as in the Lambert-Beer law. Although it has been appreciated for some time that this is an approximation (recently formalized 16 ), it is nevertheless adequate for many applications, with the prime example being the estimation of oxygen saturation (the ratio of the amounts of oxyhaemoglobin and total haemoglobin present in blood in vivo). The introduction of this A s term can be seen in Fig.…”

Light path-length distributions within the retina

“…9 However, this is not the only effect of scattering and in reality, the range of path-lengths introduced results in the relationship between attenuation and absorption becoming nonlinear. 10,11 In retinal imaging, it is often assumed that images obtained in reflection geometry can be used to estimate transmission measurements through a blood vessel. 6 A proportion of the illuminating light is scattered by tissues underneath the vessel and then illuminates the vessel from the underside.…”