Heterodyne far-field optical microscopy, from the beginning of its development, has been an efficient tool for surface characterization with a high resolution. The use of a nondestructive optical imaging to collect metrological information is of ever-increasing importance. The importance follows from its simplicity of use and potentially high accuracy.
Optical heterodyne microscopes made possible the observing and measuring of submicron structures. This is due to a possibility of precise measurement of phase and amplitude of the reflected signal at an intermediate frequency. In a conventional heterodyne microscope, the path of the reference and signal beams are separated, and the instrument is sensitive to vibrations and other environmental influences. Differential microscopes are relatively free of this shortcoming because the reference and signal components of the probe beam propagate along the same path (common path scheme). But this system requires a complex algorithm for processing the signal reflected from an object because the signal is not linear with respect to the surface profile. The microscope scan represents a nonlinear function of the convolution of the point-spread function and the optical profile. The interpretation of a complex response demands special superresolving processing in the analysis of microscopic objects with submicron size based on image formation theory.
A resolution of the problem of image formation in modern microscopy as usual can be divided into two parts: first, the interaction of the illuminating beam with the object surface; second, the signal formation in the microscope optical system. The resolving process at the first stage depends on the object profile. In our notation, a profile can be partitioned approximately into three categories according to its depth: rather shallow, shallow, and deep. This classification depends also on the lateral scale of an object. The first category corresponds to depth h âª Î»â4. In this case, an object is visualized as a layer of negligible thickness resulting in a phase shift proportional to the height variation of the surface. If the object profile is shallow (h â¤ Î»â4), the interaction between the optical field and the object surface can be described by the local reflection coefficient approach. This model is based on local properties of the surface and neglects multiple-scattering effects. But it takes into account the finite thickness of an object, and both phase and amplitude components are needed for response interpretation in the scalar approach. If the profile is deep (h > Î»â4), a rigorous electromagnetic theory is applied.