Optical systems with variable optical characteristics (zoom lenses) find broader applications in practice nowadays and methods for their design are constantly developed and improved. We describe a relatively simple method of the design of zoom lenses using the third-order aberration theory. It presents one of the possible approaches of obtaining the Seidel aberration coefficients of individual members of a zoom lens. The advantage of this method is that Seidel aberration coefficients of individual elements of a given optical system can be obtained simply by solving of a set of linear equations. By using these coefficients, one can determine residual aberrations of the optical system without detailed knowledge about the structure of its individual elements. Furthermore, we can determine construction parameters of the optical system, i.e., radii of curvature and thicknesses of individual elements of a given optical system. The proposed method makes it possible to determine which elements of the optical system can be designed as simple lenses and which elements must have a more complicated design, e.g., doublets or triplets.

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Noncontact optical metrology based on the chromatic confocal principle is becoming increasingly important for fast and accurate measurements of surface topography, distance, and layer thickness in engineering and industry. These sensors are based on the wavelength dependence of longitudinal chromatic aberration of optical systems, and the distance or thickness of the measured sample is coded into spectral information. We provide a theoretical analysis of a problem of the thickness measurement of transparent samples (glass plane-parallel plates or lenses) with respect to material dispersion. Our work deals with a description and analysis of induced measurement errors in the cases of measurement of the thickness of a plane-parallel plate and the central thickness of a lens. Relations are derived for a quantitative evaluation of these errors and a method is presented for minimizing the influence of these errors on the accuracy of measurement.

New parameters for calculation of third-order aberration coefficients (Seidel aberration coefficients) are introduced. The formulas for Seidel aberration coefficients are linear in these new variables. With these new variables it is possible to calculate the shape and the refractive index of the glass of the individual lenses of the optical system, which was not possible before.

In this work a detailed analysis of the problem of imaging of objects lying in the plane tilted with respect to the optical axis of the rotationally symmetrical optical system is performed by means of geometrical optics theory. It is shown that the fulfillment of the so called Scheimpflug condition (Scheimpflug rule) does not guarantee the sharp image of the object as it is usually declared because of the fact that due to the dependence of aberrations of real optical systems on the object distance the image becomes blurred. The f-number of a given optical system also varies with the object distance. It is shown the influence of above mentioned effects on the accuracy of the laser triangulation sensors measurements. A detailed analysis of laser triangulation sensors, based on geometrical optics theory, is performed and relations for the calculation of measurement errors and construction parameters of laser triangulation sensors are derived.