Geometrical-optics approach to increase the accuracy in LED-based photometers for point-of-care testing

: A geometrical-optics approach is proposed to increase the accuracy in photometric measurements, using a point-of-care testing (POCT) LED-based sensor. Due to stray-light effects, the measurement accuracy depends on the dimension of the CMOS area, where the radiation is detected. We propose two image processing approaches and evaluate the influence of the sensor area. In addition, we demonstrate that with the same measurement, both absorption coefficient and refractive index can be determined, measuring the beam attenuation and the spot-size enlargement due to ray refraction.


Introduction
Healthcare is becoming more consumer-focused, and requires screening diagnostic tests, that are portable and easy to operate, to provide results in real time and at the site of patient care, far from traditional laboratories [1]. The point-of-care testing (POCT) market is estimated to have grown 9.3% between 2013 and 2018, and focuses on early detection, prevention and managing of chronic illnesses, as well as on environmental monitoring. A rapid screening of infectious diseases is critical in remote or resource-limited areas, where there is not an easy access to a clinical infrastructure, and a prompt treatment may prevent infections from spreading. Malaria and dengue fever diagnosis in remote locations are now possible with new POCTs [2,3], as well as blood typing [4], and water quality monitoring [5,6]. Many POCT devices are based on colorimetric o spectrophotometric analysis of a sample liquid, such as blood or saliva, using reagents to form a colored compound: the biomarker concentration is proportional to the color intensity [7]. Mobile phones are used for colorimetric tests, by taking a picture of the sample and estimating the substance concentration from the RGB pixel values in the image [8].
First photometers for clinical chemistry date back to 1930, and nowadays, they play a fundamental role in many biochemical, pharmaceutical and microbiological experiments that involve DNA, RNA, protein isolation, and enzyme kinetics [9][10][11]. Spectrophotometry is routinely used to quantify the hemoglobin concentration in blood [12], and in Enzyme-Linked Immunosorbent Assay (ELISA) tests, to measure proteins and antibodies for many diseases ranging from HIV to cancer [13].
Photometric and spectrophotometric sensors measure the number of photons absorbed after that a light beam passes through the sample [14], giving information on the absorption parameter α at different wavelengths. The transmittance T is related to the absorbance A, also known as optical density (OD), according to the Beer-Lambert law

Absorba
Figure 2 (c) s sensor (witho Fig. 2   (2)  . n m     a m profile y remains bsorption Therefore, water Φ i hat yields mm, that ssible, the onding to ension to diameter). effect and on on the tensity of aluated as rough the suring the e circular (4) ween the (5) In bo the i back The absor spectrophotom Figure 5 s (5), consideri both approach cases the accu is less than 2% Therefore (diameter N = included in th In addition an accuracy o We have other coloring

Refractiv
Using a singl refractive ind beam spot siz of liquid insid index n by the For sake o are quite negl evaluated as a oth cases, we intensity Φ dark kground dark no rbance measur meter BioPhoto shows the OD ng two sensor hes give satisfa uracy increases % using Eq. (5) , we can con = 350 pixels), i he evaluation of n, the image p of 2%, that is qu performed a la g dyes, obtainin 5 sorbance and t g the enlargeme n in Fig. 1    From these measurements, the corresponding refractive index is evaluated using Eqs. (6) and (7), and the results are reported in Fig. 6(b) and in Table 2.
Since θ 1 = 4.52 deg, we can use the small-angle approximation and evaluate the refractive index as n~tanδ/tanθ 1 ; in this case, the spot-size variation becomes that can be evaluated as a linear approximation about the point n 0 . For the central value n 0 = 1.4, the spot-size variation corresponds to −28.08 + 33.43/ R.I.U. (refractive index unit). Using the proposed optical architecture, we are able to analyze a broad range that goes from n = 1.2 to 1.6, but with a limited accuracy that depends on the slope of Eq. (8). If the refractive index range is reduced, the linear approximation furnishes more accurate values. The refractive index interval and measurement accuracy can be varied by changing the distance d of the LED source from the lens, i.e. the magnification parameter M (the cuvette width h = 10 mm is a standard parameter). A spot-size increase of at least 2 pixels can be detected, that corresponds to about Δw = 1% variation, with an average accuracy Δn = n 0 2 Δw (d-h)/h = 0.03 R.I.U.

Summary
Commercial spectrophotometers used in laboratories employ expensive lasers or monochromators and photodetectors. To reduce the costs, portable POCT for colorimetric analysis mount LED sources and CMOS image sensors; however, their accuracy is limited by diffraction and stray-light effects. We propose a geometrical optics approach to evaluate their accuracy and investigate the influence of the dimension of the image sensor area, where the transmitted intensity is detected. We refer to two different real-time image processing strategies, measuring the average intensity on the sensor area, or evaluating the absorbance by a pixel-by-pixel approach. Furthermore, with the same intensity measurements, we can also evaluate the liquid refractive index, measuring the beam spot-size enlargement and identify the liquid.