Color Digital Holography Based on Generalized Phase-Shifting Algorithm with Monitoring Phase-Shift

Color digital holography (DH) has been researched in various fields such as the holographic camera and holographic microscope because it acquires a realistic color object wave by measuring both amplitude and phase. Among the methods for color DH, the phase-shifting DH has an advantage of obtaining a signal wave of objects without the autocorrelation and conjugate noises. However, this method usually requires many interferograms to obtain signals for all wavelengths. In addition, the phase-shift algorithm is sensitive to the phase-shift error caused by the instability or hysteresis of the phase shifter. In this paper, we propose a new method of color phase-shifting digital holography with monitoring the phase-shift. The color interferograms are recorded by using a focal plane array (FPA) with a Bayer color filter. In order to obtain the color signal wave from the interferograms with unexpected phase-shift values, we devise a generalized phase-shifting DH algorithm. The proposed method enables the robust measurement in the interferograms. Experimentally, we demonstrate the proposed algorithm to reconstruct the object image with negligibly small conjugate noises.

Precise Measurement of the Surface Shape of Silicon Wafer by Using a New Phase-Shifting Algorithm and Wavelength-Tuning Interferometer

In wavelength-tuning interferometry, the surface profile of the optical component is a key evaluation index. However, the systematic errors caused by the coupling error between the higher harmonics and phase shift error are considerable. In this research, a new 10N − 9 phase-shifting algorithm comprising a new polynomial window function and a DFT is developed. A new polynomial window function is developed based on characteristic polynomial theory. The characteristic of the new 10N − 9 algorithm is represented in the frequency domain by Fourier description. The phase error of the new algorithm is also discussed and compared with other phase-shifting algorithms. The surface profile of a silicon wafer was measured by using the 10N − 9 algorithm and a wavelength-tuning interferometer. The repeatability measurement error across 20 experiments was 2.045 nm, which indicates that the new 10N − 9 algorithm outperforms the conventional phase-shifting algorithm.

Effect of Phase Error in Phase-Shifting Interferometer

Phase-shifting interferometry is widely used because it can measure phase with high accuracy. Changing optical path length with a PZT transducer and changing frequency of the optical source with a laser diode (LD) are two common methods to apply the desired phase shift between the arms in the interferometer. In any case, however, it is not easy to apply the desired shift accurately, and if not, measurement errors occur. In order to reduce the errors, the effect of the phase shift error has been analyzed numerically especially in the case with LD.