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We analyze and synthesize one type of planachromatic microscope objective lens (planachromats). Formulas are described for the calculation of basic parameters of such optical systems for various configurations of the optical system. The application of the described technique is shown on an example of the optical design of planachromat. [c] 2010 Optical Society of America OCIS codes: 080.0080, 110.0180, 120.3620, 220.2740, 220.3630.

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. [c] 2010 Optical Society of America OCIS codes: 120.3940, 120.6650, 120.2830, 260.2030, 080.0080.

Our work deals with the influence of light wavelength on values of wave aberration coefficients and image quality for an axial object point, and a technique for calculation of the dependence of aberration coefficients on the wavelength is proposed. Moreover, the formula for calculation of the monochromatic and polychromatic Strehl definition using chromatic aberration coefficients is derived and the tolerance limits are given. The proposed method of determination of chromatic aberration coefficients is shown for the case of the imaging of an axial object point by a rotationally symmetric optical system. Relations that enable calculation of chromatic aberration coefficients are derived. Finally, the proposed method is applied on an example of an achromatic doublet, and the results of calculations are compared with the values obtained using commercial optical design software (ZEMAX, OSLO). OCIS codes: 080.1005, 080.1010, 220.1010, 220.0220, 110.3000.

Our work deals with a theoretical analysis of an influence of a deviation from the sine condition of an optical system on the kinematics of aperture rays, which are transformed by this optical system. An exact formula for calculation of the value of the departure from the sine condition that has to be satisfied by an optical system to achieve a constant speed of transformed rays is derived. Approximate relations valid in the scope of the Seidel third-order aberrations theory are also derived and examples of optical systems that satisfy these conditions are presented. Obtained results are important for a design of scanning optical systems used, e.g., for distance measurements and laser systems for surface refinement of materials. OCIS codes: 080.0080, 080.2740, 080.3620, 120.4820.

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. OCIS codes: 220.0220, 220.3620, 220.1000, 080.0080, 080.3620, 080.1010.

Our work describes a technique for testing the centricity of optical systems by using the point spread function. It is shown that a specific position of an axial object point can be found for every optical element, where the spherical aberration is either zero or minimal. If we image such a point with an optical element, then its point spread function will be almost identical to the point spread function of the difffraction-limited optical system. This consequence can be used for testing the centricity of precisely fabricated optical elements, because we can simply detect asymmetry of the point spread function, which is caused by the decentricity of the tested optical element. One can also use this method for testing optical elements in connection with a cementing process. Moreover, a simple formula is also derived for calculation of the coefficient of third-order coma, which is caused by the decentricity of the optical surface due to a tilt of the surface with respect to the optical axis, and a simple method for detecting the asymmetry of the point spread function is proposed. OCIS codes: 220.4840, 220.1010, 120.0120, 120.4630, 120.4820, 120.4800.