Objective With the development of technology and the requirement of industrial manufacturing, the automatic measurement of key dimensions of products in the production process has gradually replaced the traditional manual measurement. As a non-contact measuring instrument, line laser triangulation instrument has the advantages of simple structure, small size and wide application. However, the uncertainty of measurement for this instrument is physically limited by the speckle, which are formed when the measured surface is illuminated by the laser. Fortunately, this uncertainty can be improved by reducing the laser wavelength or increasing the numerical aperture of the optical system. Lasers with a short wavelength of 405 nm are already widely used in triangulation instruments, and increasing the numerical aperture of the optical system is another one method to further reduce the measurement uncertainty. However, the further increase of numerical aperture brings great difficulties to the design of optical systems while keeping the field of view unchanged.

Methods To improve the measurement uncertainty of the line laser triangulation measurement instrument, this paper designs a bi-telecentric system with large numerical aperture with the two-dimensional Q-type polynomial freeform surface. Firstly, the working principle of the triangulation measurement instrument is introduced. Based on the principle and the specifications of the line laser triangulation measurement instrument, the parameters of the imaging optical system are analyzed. Then, the optical system based on double-Gauss optical layout is designed and the optical stop is placed on the focal plane of front group and back group. The position and number of freeform surfaces in the imaging optical system are determined by using the aberration sensitivity analysis and the freeform surface aberration characteristics. Finally, the optical system is optimized with optical design software to achieve the best performance.

Results and Discussions Two-dimensional Q-type polynomial freeform surfaces are set to each surface, and the RMS radius of the system point diagram was used as the error function to determine the contribution degree of each surface to aberration optimization. The final choice is to set the surfaces S2, S6, S9, and S14 as two-dimensional Q-type polynomial free surfaces. After optimization, the optical system is consisted of seven lenses, four of which are based on two-dimensional Q-type polynomial freeform. The designed system has a numerical aperture of 0.2, and an field of view of 10 mm×14 mm. The design results of this system are evaluated using RMS radius of the spot diagram, modulation transfer function (MTF) distortion and telecentricity. The MTF of the system is better than 0.6, the maximum distortion is 0.21%, and the telecentricity is less than 0.3° for the objective and image sides.

Conclusions Line laser triangulation measurement instrument is a high-precision, small-size and widely used measuring instrument. It can meet the demand for high-speed measurement of product dimensions in industrial production. A large numerical aperture telecentric Scheimpflug imaging optical system for line laser triangulation is designed using a two-dimensional Q-type polynomial free-form surface. Compared with the spherical system, the imaging quality of the system is improved without increasing the number of lenses and the system size. The designed optical system has the advantages of large numerical aperture, double telecentricity and high imaging quality, which can effectively improve the measurement uncertainty of the instrument. It has important application in triangulation instruments with high measurement accuracy.