Resolution Limit of Mach-Zehnder Two-Wavelength Phase-Shifting Speckle Interferometer

Two-wavelength speckle interferometry (SI) is widely used for shape measurements of rough surfaces. A surface under test arranged in an interferometer is illuminated with laser light having two different wavelengths. In the most simplified case the two interferograms are intensity-subtracted where the fringe distance in the detected pattern provides the information about the difference in height of the corresponding positions of the test surface. The distance between two fringes can be associated with the synthetic wavelength Lambda, equivalent to the envelope of a beat frequency. In interferometry the use of the synthetic wavelength Lambda is valid as long as the wavelengths of the two interfering waves are approximately equal. Since the height resolution is directly linked to the synthetic wavelength, a decrease of Lambda will lead to an increased resolution of height. This statement, however, is only valid if the employed wavelengths are similar. We present how the choice of wavelengths of a Mach-Zehnder setup affects the resolution of the interferometer. On the one hand the term of synthetic wavelength is reviewed analytically concerning wavelengths with increasing Delta lambda. On the other hand we verified these results with a numeric simulation. In addition to the analytic model, the numeric simulation includes a more advanced surface model including roughness. As a result we provide a recommendation under what circumstances the decrease of Lambda leads to an increased height resolution.