A method for measuring the focal length of the lens by a Fizeau interferometer is proposed. Based on the Gaussian imaging equation and the longitudinal displacements of the object point and image point, a precise formula for focal length calculation is deduced. The longitudinal displacement of the object points is determined by the wavefront difference method with a subnanometer resolution. An experimental system for focal length measurements is set up to verify the principle. The sources of uncertainty in measurement are discussed. Both the positive and negative lens experimental results indicate that the measurement accuracy is less than 0.16% under normal experimental environment.

Focal length measurement based on the wavefront difference method by a Fizeau interferometer

A figure measuring interferometer (FMI) method is proposed for high-accuracy measurement of the focal length and distortion of optical systems simultaneously. FMI uses the Zernike coefficients of interference fringe to identify the image point position precisely, and then measures the distance between the image points under the different fields to determine the image height. The field of view can also be accurately obtained by a precise rotating platform. Linear fitting between the field of view and the image height is used to calculate the focal length and distortion. The experimental results indicate that FMI has a relative expanded standard uncertainty of less than 0.01% for focal length and 0.02% for distortion. In brief, the proposed method is feasible for measurement of the focal length and distortion with high accuracy, promising further industrial applications.

High-accuracy measurement of the focal length and distortion of optical systems based on interferometry.

Measurement of focal length based on laser-beam-spot tracking system using diffractive beam sampler

In this paper, we propose a scheme for measuring the focal length of a collimating optical instrument. First, a mathematical model for measuring the focal length of a collimator with double gratings is derived based on the moire fringe formula and the principles of geometric optics. Mathematical simulation shows that a slight difference in the focal length of two collimators has an important influence on the imaging law of moire fringes. Our solution has a good resolution ability for focal length differences within 5‰, especially in the small angle range below 4°. Thus, the focal length of collimators can be measured by the amplification of the slight difference. Further, owing to the relative reference measurement, the measurement resolution at the symmetrical position of focal length is poor. Then, in the designed experiment, a corresponding moire image at different angles is acquired using collimators with known focal length. The experimental results indicate that the root mean square error (RMSE) of the collimator corresponding to grating angles of 2°–4° is better than 4.7‰, indicating an ideal measurement accuracy of the proposed scheme. This work demonstrates that our proposed scheme can achieve an ideal accuracy in the measurement of a symmetrical optical path.

Research on Focal Length Measurement Scheme of Self-Collimating Optical Instrument Based on Double Grating

A cutting-edge precision technique for computation of focal length of a positive lens with double-hole mask is described. The technique is simple and versatile due to incorporation of the updated functions of image sensor device that supports reading the distance between beam spots instantaneously while the position of the specimen is being changed, as well as the reduction in several challenging measurement steps. Furthermore, this technique does not require prior knowledge of distances in the optical setup. High accuracy in focal-length measurement is obtained by precise beam spot distance analysis using image sensor integrated software. The acquired data exhibit considerably high precision and reproducibility.

Zhipu Chen

Papers

Focal length measurement by fiber point diffraction longitudinal interferometry