INTERFEROMETRY METHOD FOR ELLIPSOMETRY, REFLECTOMETRY, AND SCATTEROMETRY MEASUREMENTS, INCLUDING CHARACTERIZATION OF THIN FILM STRUCTURES
CROSS-REFERENCE TO RELATED
 This application claims priority to each of: U.S. Provisional Patent Application Serial No. 60/409,147 filed Sep. 9, 2002 and entitled "Back-Focal Plane Ellipsometry, Reflectometry and Scatterometry By Fourier Analysis Of Vertically-Scanned Interference Data;" U.S. Provisional Patent Application Serial No. 60/452,615 filed Mar. 6, 2003 and entitled "Profiling Complex Surface Structures Using Height Scanning Interferometry;" and U.S. Provisional Patent Application Serial No. 60/478,300 filed Jun. 13, 2003 and entitled "Scanning Interferometry." Each of said provisional patent application is incorporated herein by reference.
 The invention relates to surface topography measurements of objects having thin films or discrete structures of dissimilar materials. Such measurements are relevant to the characterization of flat panel display components, semiconductor wafer metrology, and in-situ thin film and dissimilar materials analysis.
 Ellipsometry can be used to analyze the optical properties of a complex surface. Ellipsometry relies on the difference in complex reflectivity of a surface when illuminated at an oblique angle, e.g. 60°, sometimes with a variable angle or with multiple wavelengths. Many types of ellipsometer are known in the art.
 To achieve greater resolution than is readily achievable in a conventional ellipsometer, microellipsometers measure phase and/or intensity distributions in the back focal plane of the objective, also known as the pupil plane, where the various illumination angles are mapped into field positions. Such devices are modernizations of traditional polarization microscopes or "conoscopes," linked historically to crystallography and mineralogy, which employs crossed polarizers and a Bertrand lens to analyze the pupil plane birefringent materials.
 Embodiments of the invention are based, at least in part, on the realization that the various angles of incidence in an interferometer (e.g., having a high NA objective) can be distinguished by the corresponding spatial frequencies in an interference pattern generated by scanning the test sample or reference mirror relative to the interferometer (e.g., towards or away from the objective used to focus light onto the test sample or reference mirror). Therefore, a mathematical spatial frequency decomposition of such an interference pattern provides access to the relative amplitude and phase of the light reflected (or scattered) from a sample surface as a function of angle. This knowledge, together with a calibration of the illumination distribution in the pupil of the objective and the polarization state of the illumination across the pupil plane, provides the multiple-angle reflection (or scattering) amplitude and phase information for every pixel in the field of view, without having to directly image the
pupil plane onto a detector array. These multiple-angle data can be used to provide sample surface characteristics such as thin film thickness and/or the complex index of refraction on a pixel-by-pixel basis with high lateral resolution, simultaneously with surface height profile information.
 Embodiments of the invention typically include an interferometer, for example an interference microscope having an interference objective of the Mirau, Linnik, Michelson type or the like. The objective illuminates and collects light from a sample surface over a range of incident angles <|). For example, <|)=0 to 50° for an interference objective having a numerical aperture (NA) of about 0.75. The polarization of the illumination may be radial, linear, circular, field-dependent, or adjustable. Typically, the apparatus further includes a mechanical scanner for displacing the sample surface along an axis parallel to the optical axis of the objective (or equivalent motion objective with respect to the sample) while an electronic camera collects interference intensity data for an array of pixels corresponding to field positions on the sample. Alternatively, a reference leg of the interferometer may be scanned. The result is intensity vs. sample position data for each pixel for a sequence of objective distances from the sample, stored in computer memory.
 In some embodiments, the computer transforms the interference data for each pixel into the frequency domain e.g. by Fourier analysis, to recover the magnitude and phase of the constituent spatial frequencies present in the interference data. The computer analyzes these data, compares the magnitude and phase to a model representing the surface structure of the sample, including incident-angle, polarization and/or wavelength-dependent optical properties of the sample. This analysis determines parameters such as surface height and thin film thickness.
 Some embodiments select wavelengths or send multiple wavelengths into the interferometer to perform a detailed analysis of the optical properties of materials as function of wavelength, in addition to analyzing their angledependence. Some embodiments analyze the scattered light from the sample to determine surface structure information by the diffractive and scattering properties of the surface as a function of incident angle and wavelength.
 Embodiments of the invention include many advantages. For example, embodiments may provide a means for analyzing a surface structure for its optical properties and surface topography simultaneously, e.g., on a pixel-by-pixel basis, by frequency-domain decomposition of interference patterns generated by vertical scanning of the sample with respect to the interference objective. Such an approach provides access to the angle-dependent and wavelength-dependent optical properties of the surface, using both amplitude and phase information from the reflected light without the need to directly access the pupil plane of the instrument.
 We now generally summarize different aspects and features of one or more embodiments of the invention.
 In general, in one aspect, the invention features a method including: imaging test light emerging from a test object over a range of angles to interfere with reference light on a detector, wherein the test and reference light are derived from a common source; for each of the angles, simulta