Interferometric profilometry of absolute optical thickness of transparent plate using wavelength tuning fringe analysis

The separation of the refractive index and absolute geometric thickness from the absolute optical thickness of a transparent parallel plate has been a long-standing issue. For the measurement of the separation, the absolute optical thickness should be measured with a nanoscale uncertainty. A combination of phase-shifting techniques and wavelength tuning was recently proposed to measure the absolute optical thickness of a transparent plate. However, as the phase-shifting technique is extremely sensitive, it is necessary to use the excess fraction method to eliminate the phase-shift error. In this study, the absolute optical thickness of an optical flat, with a thickness of 6 mm and diameter of 100 mm, was measured using wavelength-tuning fringe analysis without using the sensitive phase-shifting technique. Initially, the coarse value of the absolute optical thickness was determined by a wavelength-tuning Fourier analysis. The discontinuous errors that occurred during the wavelength tuning were compensated for and eliminated using an unwrapping correlation analysis, yielding a smooth thickness distribution. The experimental data indicate that the standard deviation of the thickness measurement was 7.071 nm, attributed to temperature variations in the laboratory. Finally, the absolute optical thickness was determined at a probability of 95 % by employing the Student's t-test using 20 experimental data points.