## 3 Results  
To test the feasibility of the proposed method, an optical system based on the Fizeau interferometer was built. Figure 4b presents a photo of the measuring device. The sketch of the actual optical path system is shown in Figure 4a. A Littman external cavity (TLB-6804, Newport Corporation, Irvine, USA) consisting of a grating and a cavity mirror was used as the light source. The beam from the laser was directed at the reference surface and the transparent plate to be tested. The beams are reflected from the reference surface, front surface, and rear surface propagate along the same direction and form interference fringes on the CCD camera (The Imaging Source, Bremen, Germany) with the resolution of \(1024\times 1024\) pixels. The sample is placed vertically on an adjusting machine, with an air-gap distance of H, which is approximately \(M\) times the length of the optical thickness of the transparent plate. The central wavelength \(\lambda_{0}\) of the tunable laser is 632.8 nm. The required laser wavelength is selected by tuning the inclination of the diffraction grating. Such a wavelength control can be executed both manually and automatically by using a computer coupled with the corresponding electro-mechanical unit. In our experiment, the wavelength was finely scanned from 632.67 nm to 632.97 nm and 36 interference images were recorded with an equal wavelength interval. The minimum fine-tuning resolution was 0.1 GHz, corresponding to \(\Delta\lambda\approx 0.5\times 10^{-4}\) nm for \(\lambda_{0}\approx 632.8\) nm. The stability of the light source wavelength was less than \(10^{-7}\) nm, which could reduce the error associated with the phase-shift during the recording time of 2 min. In the experimental setup, the expanded collimated laser beam was then projected onto the front-and-rear surfaces of the tested sample through a beam splitter and the reference plate as illustrate in Figure 4a. The light reflected from the reference plate and the interfaces of the tested transparent plate in projected through the beam splitter on the CCD, where the interference field is registered. The example of the field distribution captured by the CCD is shown in Figure 5a. The tested sample in the experiment was a transparent plate with a thickness approximately 5 mm. The transparent plate was made of JGS1 material and its refractive index was approximately 1.45 at a wavelength of 633 nm. The distance between the reference plate and the front surface \(H\) was adjusted to 72.5 mm (\(M=10\)) using a guide rail and adjusting part. In order to ensure the accuracy and stability of the experiment, the room temperature is stabilized to \(25\pm 0.2\)\({}^{\circ}\)C. In this paper, we set the phase-shift as \(\delta_{k}=\frac{\text{\text{\tiny{fe}}}\pi}{4}(k=1,2,3\cdots)\) in Equation (4). The diode laser coupled with the diffraction grating provided the interval of the wavelength change, \(\Delta\lambda=3.5\times 10^{-3}\) nm. The total wavelength-shift and phase-shift used in the experiment were 0.126 nm and 9\(\pi\), respectively. By applying the 36-step algorithm described in Section 2, the information of the front and rear surfaces and thickness variation could be extracted, respectively. The corresponding shapes of the front and rear surfaces of the optical component were calculated after the phase unwrapping had occurred. To remove the high-frequency noise, the phase map was filtered using the windowed Fourier transform (WFT) method [31; 32] as shown in Figure 5b-d.  
Figure 4: Experimental setup. (**a**) Schematic diagram of the interferometer used to measure the profiles of the front and rear surfaces; (**b**) laboratory photo of the measuring area of the transparent plate in a wavelength-tuning interferometer.