Estimation of accuracy of optical measuring systems with respect to object distance

It is well-known that the change in the distance from the optical system to the object affects the image quality. Optical measurement systems, which are aberration-free for a specified position of the measured object, are then limited by induced aberrations for other object positions due to the dependence of aberrations on the varying object position. The consequence of this effect is a change in measurement accuracy. Our work provides a theoretical analysis of the influence of aberrations, which are induced by the change in the object position, on the accuracy of optical measuring systems. Equations were derived for determination of the relative measurement error for monochromatic and polychromatic light using the dependence of the third-order aberrations on the object position. Both geometrical and diffraction theory is used for the analysis. The described effect is not removable in principle and it is necessary to take account to it in high accuracy measurements. Errors can be reduced by a proper design of optical measuring systems. The proposed analysis can be used for measurement corrections.