# Method for Measuring Absolute Optical Properties of Turbid Samples in a Standard Cuvette
## 1 Introduction
Therefore, for quantitative determination of a sample's chemical concentrations (through the \(\mu_{a}\) spectrum), samples must be non-scattering or transparent; either innately or through some chemical washing. Whenever this is not possible the measurement will be confounded by scattered light. This implies that the \(\mu_{a}\) will be overestimated and its spectral dependence distorted leading to errors in the estimation of a sample's chemical constituents. One such instrument that shines when samples are transparent and non-scattering is the Perkin Elmer LAMBDA 365+ (Waltham, MA, USA), this and instruments like it are the workhorses of many chemical and biological laboratories. However, when diffuse sample measurement is necessary (and quantitative measurement of properties sought), one of the aforementioned techniques capable of option 2 is required. One example is the Gigahertz Optik SphereSpectro 150H (Tuerkenfeld, Germany) (SphereSpectro), an instrument directly designed for spectroscopic measurement of both \(\mu_{a}\) and \(\mu_{s}^{\prime}\) via integrating sphere. Furthermore, integrating spheres may be purchased as attachments to traditional spectrometers, thus adding diffuse functionality. One such example of a spectrometer that has this option is the Perkin Elmer LAMBDA 1050+ (Waltham, MA, USA). However, we are not aware of any commercially available instrument that utilizes the FD in such applications. Because of the apparent gap in the market for instruments which complete diffuse measurement of \(\mu_{a}\) and \(\mu_{s}^{\prime}\), namely implementation with instruments that utilize FD NIRS like techniques, we will focus closer on FD. Measurements of \(\mu_{a}\) and \(\mu_{s}^{\prime}\) with temporally modulated light, such as FD NIRS, is actually rather common but typically only in the research setting (using the Imagent for example). However, we know of no FD instruments designed for the sample sizes and form factors of traditional spectrometers which accept a vuette. In-fact FD NIRS methods typically require large sample volumes on the scale of liters to implement simple diffusion theory solutions. Two examples of work that considered FD measurements in confined regions were that in the slab [21] or block [22](which utilized the same diffusion theory model implemented here [23]), however the geometries considered in these works were rather large compared to a cuvette. There are advantages of FD NIRS which would lead one to seek or design and manufacture such an instrument. For example, FD NIRS can leverage existing techniques which eliminate the need for instrumental calibration such as the Self-Calibrating (SC) method [24]. Additionally, despite FD typically being implemented at discrete \(\lambda\), methods exist to achieve broadband \(\mu_{a}\) measurement. This may be done by combining measurements at discrete \(\lambda\)s in FD (or TD) with measurements at broadband \(\lambda\)s with Continuous-Wave (CW) [25; 26; 27], implemented with SC and a method dubbed Dual-Slope (DS), respectively, [28; 29; 30]. This leverages the fact that SC and DS both rely on a difference type measurement which is capable of subtracting away instrumental confounds. We see an opportunity to develop a method which leverages the tools available in FD NIRS to measure absolute \(\mu_{a}\) and \(\mu_{s}^{\prime}\) in a standard cuvette with milliliter scale volume in an attempt to compete with the existing integrating sphere type devices. Therefore, in this work we present a method that utilizes FD NIRS in a small geometry the size of a standard cuvette (\(45\,\mathrm{mm}\times 10\,\mathrm{mm}\times 10\,\mathrm{mm}\)). Our proposal relies on the SC/DS method to remove a majority of the instrumental confounds. To our knowledge no work has yet leveraged SC/DS directly on the cuvette geometry as we propose here.