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Spatial coherence profilometry is a method for measurement of the geometrical form of objects. In addition to the two lateral coordinates x and y, it measures the longitudinal coordinate z. In this way the complete 3D description of the object's surface is acquired. The main piece of the presented method is a Michelson interferometer illuminated by a monochromatic spatially extended light source. The surface of the object whose geometrical form should be measured is used as one mirror of the Michelson interferometer. By moving of the measured object along the optical axis, the intereference is observable only if the object's surface occurs in the vicinity of the so-called reference plane. The reference plane is given by the position of the object mirror when the Michelson interferometer is balanced. The described effect follows from the form of the spatial coherence function originated by the spatially extended light source. If the intensity at the output of the interferometer is recorded as a function of the position of the measured object, a typical correlogram arises. This correlogram is similar to that known with white-light interferometry. From the maximum of the correlogram, the z coordinate of the object's surface can be determined. Usually a CCD camera is used as the detector at the output of the Michelson interferometer. Then z coordinates of many surface points are parallel measured in the course of one measurement procedure and the 3D description of the object's surface is acquired. The scanning in the lateral direction is not necessary. Thus the described method provides a spatial coherence analogy to white-light interferometry which is based on temporal coherence. Unlike white-light interferometry, the described method does not require a broadband light source, the interferometer is illuminated by a monochromatic light source, usually a laser.

We review the principle and the applications of unconventional holography, called coherence holography 1,2 , which we recently proposed as a general technique for the synthesis and the control of 3-D spatial coherence function. An object recorded in a hologram is reconstructed as the three-dimensional distribution of a complex spatial coherence function, rather than as the complex amplitude distribution of the optical field itself that usually represents the reconstructed image in conventional holography. We introduce a newly proposed simple optical geometry for the direct visualization of the reconstructed coherence image, along with the experimental results validating the proposed principle. We also show that coherence holography has potential applications in optical coherence tomography and profilometry 3 as well as in basic science of coherence vortices 4 .

Based on the fringe formation in the k-vector space, we proposed an angular spectrum scanning technique for absolute interferometry. Instead of sweeping the optical frequency over a wide range of spectrum, we tune the angular spectrum by changing the incident angle of a monochromatic plane wave with a spatial light modulator (SLM). In the experiment, we built an equivalent spatially incoherent "ring source" to realize the angular spectrum scanning, and applied an algorithm to compensate the offset fluctuation of the fringe intensity.

A technique of imaging with a spatial coherence function, referred to as coherence holography, is proposed. A hologram of a three-dimensional object is recorded with coherent light in the same manner as in conventional holography, but the hologram is illuminated with spatially incoherent light to reconstruct the object as the three-dimensional distribution of a spatial coherence function, rather than as the amplitude or the intensity distribution of the optical field. A simple optical geometry for direct visualization of the reconstructed coherence image is proposed, and the results of preliminary experiments of a computer-generated coherence hologram (CGCH) are presented, which demonstrate the potential of CGCH as a means for optical coherence tomography and profilometry.

An interferometer based on the spatial coherence detection has been developed for absolute height measurement. The location of a coherence peak resulting from the illumination of an extended quasi-monochromatic spatially incoherent light source with zone-plate-like spatial structure gives the longitudinal depth information. Besides simplifying the control of the light source structure, LCD-SLM eliminates the mechanical movement. Experiments of step height detection and profilometry of an object with a rough surface are presented that demonstrate the validity of the principle.

We address the basic issue of the observation condition in a synthetic coherence function applied to optical tomography and profilometry, which has not been made clear in previous papers. We present a more general theory for interference fringe formation for spatial coherence control with a synthetic source. The generalized theory predicts the existence of the observation condition that can make the measurement insensitive to the tilt of the object, which will open the new possibility of measuring objects with rough surfaces. We present experimental results that quantitatively verify the validity of the principle and the prediction.

A new scheme for synthesizing three-dimensional longitudinal spatial coherence function is proposed. By manipulating the irradiance of an extended quasi-monochromatic spatially incoherent source with a spatial light modulator, we generated a special optical field that exhibits high coherence selectively for the specified location along the optical axis of propagation and for the specified inclination between the two mirrors in the interferometer. The feasibility of the proposed principle is demonstrated by measuring a step height made by standard gauge blocks. The proposed scheme permits one to perform phase shift without recourse to mechanical movement. The quantitative experimental proof of the principle is presented.