## 1 Introduction  
During recent decades, whispering gallery mode optical cavities [1] have attracted substantial attention because of their benefits of high-quality factors, small mode volumes, and high energy density. They have been widely utilized in many fields, such as cavity quantum electrodynamics (CQED) [1], nonlinear optics [2], microcavity sensors [3; 4; 5; 6; 7], optomechanics [8], microcavity lasers [9], optical signal processing [10], and single molecule detection [3; 4; 5; 11]. Micro-bubble resonators (MBRs) [12] have become an especially important type of optical microcavities. These sensors facilitate optofluidic [6] and pressure sensing [13] due to their hollow structure. However, MBRs are asymmetrical ellipsoids in experiments, which causes their resonances to nondegenerate. As a consequence, a complicated dense spectrum is generated, and the resonances may overlap or couple with each other [14]. The two resonances have three relations in the dense spectrum according to the relationship between the coupling coefficient (\(g\)) and the critical coupling strength (\(\kappa_{\rm T}\)): overlap (\(g=0\)), weak coupling (\(g<\kappa_{\rm T}\), Fano resonance [15; 16] and electromagnetically induced transparency resonance [17; 18]), and strong coupling (\(g>\kappa_{\rm T}\), mode splitting [19]). A dense spectrum benefits cavity quantum electrodynamics [1] and nonlinear optics [2]. However, tracking and identifying the resonances in sensing applications are an essential task. Many efforts have been made, such as mode simplification [20; 21; 22; 23; 24] and the ab initiotheory of Fano resonances [25], to simplify and analyze the spectrum. However, mode simplification is unrepeatable, costly, and complex. The ab initio theory of Fano resonances only utilizes the amplitude of resonance, and can only discriminate simple resonances. Thus, analysis of the dense and complicated spectrum remains a challenge.  
In this work, we propose a new method based on the orthogonal demodulated Pound-Drever-Hall [26; 27] (OD-PDH) technique to analyze the dense and complicated spectrum directly. The Pound-Drever-Hall (PDH) technique can be used in laser frequency stabilization [26; 27] and highly sensitive sensing applications, e.g., nanoparticles [11], pressure [13], angular velocity [28], acceleration [29], and relativity applications [30]. The discriminating signal [27; 28] from the PDH system depends on an optical field rather than light intensity, so contains both amplitude and phase information of the resonance. The PDH system transforms the sharp imaginary information of the resonance and the slope information of the resonance into discriminating signals. Any tiny change of resonance will significantly influence the discriminating signals. Therefore, it can be used in highly sensitive resonance analysis. The OD-PDH technique [31; 32] is an improved PDH technique that can eliminate the phase difference between local oscillation and detection signal, and stabilize the discriminating signal. Using this method, the overlapping weak and strong coupling resonance parameters can be obtained accurately. Compared to other methods, this method is repeatable, simple, sensitive, and accurate. It can also increase the measurement range in differential resonance sensing, thus allowing differential sensing of overlapped resonances.