## 1 Introduction  
Rheumatoid arthritis (RA) is a chronic, progressive, systemic, inflammatory autoimmune disorder that causes chronic inflammation of the synovial membrane of small and large joints [1, 2]. Thus, people with RA can suffer from severe pain, joint stiffness, swelling of multiple joints, and lack of joint mobility. When untreated, these symptoms can lead to self-limiting arthritis or rapidly progressing multi-system inflammation with significant morbidity and mortality (including cardiac, neurological, and hematological complications). Studies show that up to 14 million people around the world [3] and approximately 1.5 million people in the US [4] are affected by RA and up to 10% of individuals suffering from RA can experience total disability [5]. In the US alone, RA leads to 9 million physician visits per year [6]. Despite recent advances in therapeutic intervention including biological therapies [7, 8], there is currently no cure for RA [9]. The early treatment of RA, however, has been shown to significantly improve clinical outcomes and management of the disease. It is, therefore, important to diagnose a subject with RA as early as possible. Early diagnosis of RA has been attempted using various imaging modalities such as X-ray, ultrasound (US), or MRI scans. X-ray imaging has the best-established role in the assessment of the severity of RA [10]. Radiography can document bone damage (erosion) that results from RA and visualize the narrowing of cartilage spaces. However, radiography is insensitive to the early manifestations of RA, namely, effusion and hypertrophy of the synovial membrane. US is more sensitive than radiography at assessing erosion and synovitis, which allows clinicians to provide early diagnostic imaging at the point of care. However, a main disadvantage of US is a high level of operator dependence for obtaining quality images [11]. MRI is most useful in assessing soft tissue problems, avascular necrosis, the degree of cartilage erosion, osteonecrosis, and carpal tunnel syndrome [12]. The study showed that contrast-enhanced MRI could achieve a sensitivity and specificity of 70 and 64% [13], respectively (82.5 and 84.5% in another study [14]) for the detection of RA. However, long data-acquisition times during which the subject needs to be immobilized, large costs, and the need for contrast agents (e.g., gadolinium to detect increased blood volume caused by neovascularization in the hypertrophic synovial membrane that can be toxic for RA patients with critical renal failure) have prevented MRI from becoming a widely used imaging modality for detection of RA. Thus, there is no single ideal modality for imaging RA diagnosis, i.e., X-ray, US, and MRI are complementary with their own strengths and drawbacks. Optical imaging techniques [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36] for the diagnosis of RA have also been extensively studied using a continuous wave (CW) system in early works [23; 26], and later a frequency domain (FD) system [34; 36], combined X-ray and photoacoustic tomography [29], and furthermore, molecular imaging approaches such as bioluminescence and fluorescence tomography [16; 21; 22]. The basis for optical methods is that in the early stages of RA, optical properties such as absorption and scattering are expected to increase in the synovium and the synovial fluid as the inflammatory process starts in this region. These studies were mostly based on the diffusion equation (DE) as a model of light propagation in tissue. More recently, a deep learning technique has also emerged as a viable tool for the diagnosis of RA [18]. Our research team has explored the potential of DOT imaging for detecting and characterizing RA by using the CW-ERT [25; 26] and the FD-ERT [32; 33; 34; 35; 36]. We reported that the CW-ERT-based DOT images yielded a sensitivity and specificity of 78 and 76%, respectively [25], and the FD-ERT based DOT images achieved a sensitivity and specificity of 85% and higher [34].