## 1 Introduction  
Breast cancer is a significant health problem not only in the United States but globally and was the second leading cause of cancer-related death in the United States in 2018 [1]. Mammography, MRI (Magnetic Resonance Imaging), and B-mode ultrasound are the three most common imaging modalities used for breast cancer screening [2, 3]. However, each of these modalities has its own unique shortcomings. The sensitivity of mammography in detecting breast lesions decreases in women with high-density breast tissue, and high-density breasts are considered to be more at risk for developing breast cancer [3, 4]. In dense breasts, MRI can be used in conjunction with breast mammography to detect breast tumors [5, 6]. Nevertheless, the operational cost and availability of MRI imaging limit the accessibility of this modality. Conventional B-mode ultrasound (US) is a high-sensitivity, non-ionizing, and low-cost tool that is widely used for screening various types of human tissues [7,8]. However, false positives due to ultrasound screening result in many unnecessary biopsies [9,10]. Therefore, a more effective breast cancer screening tool is sought. Photoacoustic tomography (PAT) is an imaging methodology that uses light absorption by endogenous or exogenous chromophores, and subsequent US pressure wave generation for imaging. Photoacoustic (PA) imaging has been demonstrated to be useful for a variety of medical and biological diagnostic applications, including early cancer detection [11, 12, 13, 14]. Biomarkers such as vascularity and hypoxia have been shown to have diagnostic value in the differential diagnosis of various types of cancers including breast cancer [15, 16, 17]. In addition, when PA is augmented with nano-sized contrast agents, it can provide a reliable platform for the molecular imaging of cancer and its sub-types [18, 19, 20, 21]. In clinical applications, PA imaging has been shown to produce real-time molecular and functional information with high resolution at relevant depths [19, 22]. Several PAT imaging systems with different illumination and acquisition modes have been developed for breast cancer imaging. However, the observed limitations of these systems are in part due to the non-optimum acoustic signal acquisition or illumination methodologies used. Our presented system is meant to be non-invasive (i.e., both illumination and acquisition are external), with the illumination and measurement system external to the imaged tissue. Our method images a cross-section inside the cylindrical US transducer array by illuminating the targeted area using a ring beam. Therefore, the light has to only diffuse half the tissue diameter that is encountered when using side illumination. Point or diffuse illuminations are suitable for imaging cross-sections close to the point of light entry [11, 23, 24, 25, 26, 27], and the given fluence drops with light propagating through the tissue towards higher vertical depths as shown in Figure 1. This could make it difficult to access areas close to the chest well. Other PAT imaging methods, such as the PA mammography system [28], compress the tissue for better light penetration but can cause discomfort, or a loss of important PA biomarkers arises from the presence of blood by pushing the blood out of the tissue. One type of full-ring illumination system uses an acoustically penetrable optical reflector (APOR). However, APORs can only support low laser energies and US transmission through the reflector is highly angle-dependent [29, 30, 31]. Other illumination methods for deep tissue illumination include internal illuminations [32, 33]. However, internal illumination is difficult to develop for breast imaging applications. Therefore, it is vital to develop an alternative solution for improving the uniformity of energy distribution within the breast tissue for more accurate PAT imaging. Ultrasound tomography (UST) using a ring-shaped US transducer has shown promising results in breast cancer screening [34, 35, 36, 37, 38].