Absolute surface profilometry of an object with large gaps by means of monochromatic laser interferometry

Abstract

We propose a technique for monochromatic laser interferometry capable of absolute surface profilometry of an object with large height gaps exceeding a half wavelength. The technique does not use a broadband source, such as a low-coherence or multi-wavelength source, or a wavelength-tunable device, which causes a dispersion problem. Instead, we make use of the phase change of monochromatic light through the angular shift of illumination introduced by tilting the optical axis of the interferometer. For oblique illumination at angle θ, the phase difference between the test and reference surfaces separated by distance d is given by ΔΦ = 2kd cosθ , where k = 2π /λ is a wavenumber. In effect, the change of illumination angle θ functions as the change of wavelength λ . Therefore, while using a monochromatic laser light source, we can realize the same effect as a multi-wavelength source. From the relation between the illumination angle and the phase change, the absolute distance d between the test and reference surfaces can be determined without ambiguity of an integer multiple of a half wavelength associated with monochromatic interferometry. The large gap height can be determined also without ambiguity from the change of the absolute distance d across the boundary of the gap. Because the resolution of the absolute distance measurement by means of illumination angle change is not high enough by itself, we enhance the resolution by the following procedure. We first estimate the gap height to an integer multiple of a half wavelength by tilting the optical axis. Then the fractional portion of the phase is measured by setting the optical axis perpendicular to the test surface as in conventional interferometry. By combining the integer and the fractional portion, we can determine the absolute gap height with high accuracy and a large dynamic range exceeding a half wavelength. We present an experimental demonstration with a traditional Twyman-Green interferometer, in which a He-Ne laser was used as a monochromatic light source, and a test surface with a ~0.1 mm height gap was formed by two block gauges attached to a flat surface. The repeatability for five measurements was found to be as high as 0.1nm (in 1 sigma).