An optical arrangement for the non-contact measurement or testing of properties of a solid's surface, such as curvature, shape, contour, roughness or alignment. An optical arrangement includes structure for establishing a gap between the solid's surface and a reference edge, structure for imaging the gap on a detector, and an analyzing system connected to the detector. The analyzing system is designed to determine gap widths lying adjacent to each other on the basis of the output signals of the detector, and to determine curvature, shape, contour or roughness of the solid's surface on the basis of the gap widths lying adjacent to each other. From the comparison of the images obtained from any two positions within a drilled hole, deductions can be made, among other things, about any tilt between the measuring object and the measuring system.