Confocal imaging of thin films C.J.R. Sheppard and T.J. Connolly Physical Optics Department, School of Physics University of Sydney, NSW 2006 Australia ABSTRACT The confocal imaging of thin film structures is investigated. A theoretical treatment of imaging of stratified media with continuously varying refractive index is presented, and the inverse problem of reconstructing the refractive index profile from a confocal image discussed. 2 INTRODUCTION The confocal microscope exhibits an optical sectioning property which allows formation of 3-D images of thick structures. Image formation in confocal reflection is fundamentally different from that in a conventional reflection microscope in that even an object exhibiting no transverse detail can be imaged. For example the axial position of a surface whose normal is parallel to the optic axis can be located using confocal microscopy. This is the basis of confocal surface profilometry 1,2• As an extension of the imaging of single plane, confocal microscopy can be used to investigate the structure of thin films as may be produced as optical filters, integrated circuits, integrated optics waveguides and optoelectronic devices. It should be noted that confocal microscopy can locate the position of an axial discontinuity in refractive index: i.e. it gives differential phase imaging, with the differentiation in the axial direction. This is understandable by consideration of the 3-D coherent transfer function which is single-sided resulting in Schlieren imaging. The axial image of a reflecting surface can be calculated by integrating over the angular spectrum of the incident illumination 45 It is found that the axial response depends slightly on the material properties which affect the angular variation in reflection coefficient 6 For a single thin film on a substrate, the axial image can also be calculated by integration over the angular spectrum, taking into account the angular variation in reflection coefficient of the structure 7,8• flj method incorporates the effects of depth distortion and spherical aberration introduced by the dielectric slab, and also multiple reflections. It is interesting to note that if the reflection coefficient is calculated as a series of reflections of different orders, then each term results in the image of an interface. If the film is thick then the higher orders are well-separated axially and can be neglected. Comparison of experimental and theoretical investigations of thin-film thickness measurements have been reported elsewhere 8 If the refractive index of the film is only slightly different from the surroundings a simplified model based on superposition of the images of the two interfaces can be used 8• This is particularly useful for investigating the axial resolution of confocal microscopy. The two-plane resolution for the film thickness (defined in a similar way to Rayleigh criterion for transverse imaging of points) is found 8 to be close to a wavelength for a numerical aperture of 0.95. 3. CONFOCAL IMAGING OF A GENERAL STRATIFIED MEDIUM Consider a confocal microscope in which a stratified medium is placed in the focal region. The illumination can be considered to be comprised of an angular spectrum of plane waves, each of which is reflected by the medium with an amplitude reflection coefficient r(O). If the objective lens is illuminated with a plane 104 ISPIE Vol. 2184 Three-Dimensional Microscopy (1994) 0-8194-1479-4/94/$6.00