## 1 Introduction  
In the semiconductor industry, high-purity and high-quality polished silicon wafers are the best and most widely used material for the manufacturing of integrated circuits (ICs). Silicon wafers will still be the most basic and important functional material of the IC industry for the next several decades. This kind of material has high quality characteristics; for example, the current passes the wafer more quickly than other conductors and has excellent mobility under high temperature. Therefore, silicon wafers have a broad range of uses not only in semiconductors but also in microlithography and micro-electromechanical systems, even in tire pressure sensor systems. One of the basic parameters for measuring the performance of a silicon wafer is the surface profile. Therefore, the surface profile must be accurately measured [1]. Generally, the surface shape measurement methods can be divided into non-optical methods and optical methods. Non-optical methods include inductance methods [2], capacitance methods [3], atomic force microscopy (AFM), scanning probe microscopy (SPM), and scanning electron microscopy (SEM), among others. For testing large aperture optical devices, the limitations of non-optical methods are their nonlinearity and narrow dynamic range; thus, they do not meet the requirements of surface shape measurement. Optical methods mainly include confocal microscopy [4], structured light microscopy [5], and optical interferometry [6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Optical interferometry outperforms other methods not only because it is a non-contact measurement method but because optical interferometry has a broad measurement range. Optical interferometry involves low-coherence interferometry [6; 7; 8; 9], monochromatic interferometry [10; 11; 12], and spectral interferometry [13; 14; 15]. Spectral interferometry includes spectrally resolved interferometry [13] and wavelength-tuning interferometry [14; 15]. There are many other interference approaches to shape measurements. [PERSON] et al. [16] utilized a non-incremental interferometer based on two mutually tilted interference fringe systems to realize precise distance measurement of fast-moving rough surfaces. By using the specialized imaging acousto-optical tunable filter, [PERSON] et al. [17] achieved spectral selection of light in the output arm of an interferometer. [PERSON] et al. [18] developed a no-scanning 3D measurement method with high-precision, wide-range, and ultrafast time-resolution. Wavelength-tuning Fizeau interferometry has demonstrated better performance in the measurement of the surface profile [19; 20; 21; 22; 23] than other optical interferometry methods because of its ability for separating overlapped interference signals in frequency space. In the measurement process of using a wavelength-tuning Fizeau interferometer, the phase difference between the sample surface and the reference surface is changed step by step, the interferograms are captured by the CCD (Charge Coupled Device) camera at each step, and the phase distribution can then be obtained. When measuring the surface profile of silicon wafers with a wavelength-tuning phase-shifting interferometer, several kinds of errors may be generated:  
* phase shift errors, produced during phase shift;
* harmonics, resulting from high reflectivity; and
* coupling errors, generated between harmonics and phase shift error. Except for the phase shift error and harmonics, the coupling errors must be considered in order to obtain high measurement accuracy [24]. A well-designed phase-shifting algorithm can strongly improve the accuracy of the measurement. Therefore, various algorithms [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39] have been developed with the ability to compensate for the systematic errors in the measurement. [PERSON] and [PERSON] developed a five-sample algorithm [25; 32] that can compensate for the phase shift miscalibration. However, this algorithm cannot compensate for coupling errors.