## 2 Experimental Configuration and Phase Reconstruction  
The proposed configuration for wavelength-tuning common-path DHM is shown in Figure 1. In this process, an adjustable wavelength laser (a NEW FOCUS TLB-6804 series diode-pumped solid-state laser with a central wavelength of 632.85 nm, a wavelength-tuning range of 632.73-632.98 nm, and a frequency stability of 2 pm over 12 h) was coupled with a single-mode fiber using a coupler device (GCX-C18 PC-A; Daheng New Epoch Technology, Inc.). The beam was collimated using a fiber collimator (Thorlabs F260 FC-B with a design wavelength of 633 nm and a beam diameter of 2.8 mm) prior to illuminating the sample. After passing through a transparent functional microstructure specimen and a 10\(\times\) microscope objective (NA of 0.25), the beam wave front was modulated by the specimen and separately reflected by the front and back surfaces of a parallel glass plate, producing two divergent beams. The beams were then focused through a lens (focal length, 150 mm) and onto a filter plane composed of two filter windows, as shown in Figure 2. In the figure, the lower window includes a round hole with a 5 mm diameter and the upper window contains a pinhole with a 50 \(\upmu\)m diameter. The beam was transmitted through the round hole when the focus point, which is formed by the front surface of the parallel glass plate, matches the lower window. As a result, the wave front exhibits no change and the object wave front is produced. The beam originating from a reflection on the back surface of the parallel glass plate (coated high reflective film) is then focused in front of the filter. This forms a circular spot when the beam reaches the filter plane, which covers the entire pinhole window. The beam then diffracts as an ideal spherical reference wave front. The two waves from the round hole and pin hole filters interfere with each other and form a digital hologram. The corresponding interferogram was recorded by a grayscale CMOS camera (Imaging Source DMK 42 AUC03, 1280 \(\times\) 960 pixels, with a pixel size of 3.75 \(\times\) 3.75 \(\upmu\)m, and an 8-bit dynamic range). The wave fronts reflected from the front and rear surfaces of the parallel glass plane interfere with each other at a fixed optical path difference \(\text{OPD}=2 nd/\sqrt{n^{2}-\sin^{2}\theta}\), which depends on the parallel glass plate thickness \(h\), the refractive index \(n\), and the incident angle \(\theta\), as shown in Figure 3. For \(h=20\) mm, \(n=1.46\), and \(\theta=45^{\circ}\), the optical path difference (OPD) was 45.72 mm. The resulting phase difference between the two interfering beams \(\varphi\) can then be expressed as:  
\[\varphi=\frac{2\pi}{\lambda}\text{OPD}=\frac{4n\pi h}{\lambda\sqrt{n^{2}-\sin ^{2}\theta}} \tag{1}\]  
where \(\lambda\) is the centroid wavelength. Figure 1: The experimental configuration for wavelength-tuning common-path digital holographic microscopy (DHM). Figure 2: The window filter design. The upper window is 50 μm and the lower window is 5 mm; the distance is 10 mm. The wavelength of the tuning laser can be adjusted linearly from, for example, 632.73 to 632.98 nm. The phase difference will then be an inversely proportional linear relationship relative to the centroid wavelength (\(\lambda\) = 632.85 nm):  
\[\varphi-\Delta\varphi=\frac{2\pi}{\lambda^{\prime}}\text{OPD}=\frac{4n\pi h}{ (\lambda+\Delta\lambda)\sqrt{n^{2}-\sin^{2}\theta}} \tag{2}\]  
The optical path difference between the two interfering beams can be adjusted by using the parallel plate, thus varying the thickness and refractive index. The adjustable phase difference range for the tuning laser will change in response and phase-shifting digital holograms can be captured by the CMOS camera. In addition, the system noise from uncommon path configurations can be theoretically eliminated as the object and reference wave fronts pass through the same point in the experimental setup.