## 1 Introduction  
Being an optical element, transparent plates play an essential role in a large variety of optical components and applications [1; 2]. The front and rear surface profiles together with the optical thickness are among the fundamental characteristics of a transparent plate. Precise control and monitoring of these characteristics by non-destructive and non-contact methods for samples with different sizes and thickness are often important from a technological point of view and are associated with the quality improvement of finished products. Several optical techniques have been developed for the determination of the thickness. Most of them are based on principles of ellipsometry and interferometry [3; 4]. For example, these include the excess fraction method, digital phase-measuringinterferometry [5], Fourier transform profilometry [6], random tilt phase-shifting [7], and 3D profilometry based on modulation measurement [8]. White-light interferometry and confocal microscopy have also been used for optical thickness and profile measurement of transparent plates [9; 10; 11; 12].  
Depending on the spectrum of the light source used, the methods applied to measure thickness variation can be classified as monochromatic or spectral. The experimental setups of some of those methods include both a monochromatic laser and a spectral halogen lamp [13]. One of the disadvantages of using confocal microscopy is the limitation in the diameter of an observing aperture.  
In addition, it is not suitable for measuring the distributions of the surface profiles and the thickness because this method is based on an assumption that a sample has a uniform thickness, it measures the sample on a point by point basis. White-light interferometry is time-consuming and involves a limited aperture. Moreover, the determination of large thicknesses requires a light source possessing a large coherence length.  
Wavelength tuning interferometry (WTI) [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25] is an effective method for application in surface metrology, which is primarily limited to front-surface reflected optical element measurements. WTI has also been exploited for separating overlapped interference signals formed by the reference surface of the interferometer used and both surfaces of the measured transparent plate in frequency domain. However, the WTI method [16] provides an air-gap length (the distance between the reference surface at Fizeau geometry to the front surface, Figure 1) which is less than the thickness of the sample. In order to facilitate its application in actual industrial measurements, the air-gap length must be large. In this case, it becomes difficult to measure a sample with a thickness less than 10 mm in an actual measurement process that uses Fizeau interferometer. Whereas a conventional phase-shifting interferometer [26] requires a stable phase detection method for only a single signal obtained from the surface to be tested. The challenge for a wavelength tuning interferometer is an extraction of information in several signal frequencies, when it is necessary to suppress the noise from the neighboring frequency signals.  
In this study, we report a developed interferometric phase-shifting method based on a 36-step algorithm to compensate for the phase-shift miscalibration and to suppress the signal contributions from other surfaces. Our algorithm for data processing realizes the separation of multi-surface superposition information. The method utilizes the spectral stretching of the Discrete Fourier Transform function and is meant to be used for measurements of transparent plates with arbitrary thicknesses. The experimental setup is based on the Fizeau interferometer with wavelength tuning.