Imaging lenses, as a type of important optical element, are widely used in microscopes, cameras, and lasers. The demand for imaging lenses has considerably increased because of the rapid development of the optical industry, and there is an important need for a method that can efficiently measure the wave aberration of imaging lenses. The existing methods mainly include interferometry and geometric methods.Interferometry can achieve high accuracy. However, this has limitations in practice because of its low dynamic range, high costs, and inability to be used for online optics testing. Furthermore, this method cannot measure the off-axis aberration of imaging lenses. The accuracy of the Shack-Hartmann test method is limited by the size and quality of the microlens array and the low sampling rate of the data used to reconstruct the wavefront. The Ronchi test method is usually used to measure low-order aberrations and cannot completely evaluate wavefronts. The accuracy of Moiré deflectometry greatly depends on the grating quality. To overcome the existing difficulties, we propose a new method for measuring the off-axis aberration of imaging lenses. This method has the advantages of high dynamic range, simple equipment, low cost, and is not sensitive to the testing environment. Furthermore, complex camera calibration processes are avoided.

During the reversed Hartmann test, rays are emitted from the pinhole of the camera. These rays leave the exit pupil of the lens and intersect the liquid crystal display (LCD) screen. The wave aberration of the lens can be calculated using the aberration theory as long as the coordinates of the idea intersection points, real intersection points, and exit pupil plane are obtained. Therefore, a measurement system is built, and the coordinates of the real intersection points are obtained using a phase shift algorithm. Meanwhile, the model of the experiment system is built in software with calibrated parameters. The coordinates of the idea intersection points and the exit pupil plane can be obtained by ray-tracing. The derivative of wave aberration can be calculated using these three sets of coordinates. Finally, the wave aberration of the lens can be obtained by integration.

The simulation results show that our method can realize good accuracy. When the field angle is 5°, the errors of the result for a plano-convex lens are only 2.43% in RMS and 3.51% in PV (Fig. 4). The primary astigmatism measured using the proposed method is proportional to the square of the field of view and the square of the entrance pupil’s diameter, and the primary coma is proportional to the field of view and the cube of the entrance pupil’s diameter (Fig. 6), which is consistent with the theory of primary aberration. These proportional relationships are used to confirm the feasibility of the proposed method. Furthermore, this method is also used in the experiment to measure the aberrations of a plano-convex lens at different field angles. The errors are not high (4.13% in RMS and 4.08% in PV), even at a field angle of 5.17°. Therefore, this method is feasible in the experiment.

This study proposes a novel off-axis aberration measurement method based on phase measuring deflectometry. The reversed ray-tracing method is presented based on the theory of aberration and the reversed Hartmann test viewpoint at first, and then the method for obtaining wave aberration is introduced. The difference between the actual wave aberration and that measured wave aberration using our method is then analyzed at different field angles in the simulation for a plano-convex lens, confirming that the reversed wave aberration can replace the forward wavefront aberration. Finally, in the experiment, a plano-convex lens with a diameter of 60mm is tested at different field angles, and the measurement system is built. The result is compared with that of the simulation to confirm the accuracy of the experiment and analyze the sources of errors. The method proposed in this study is simple. The off-axis aberration of an imaging lens can be measured effectively with an LCD screen and a charge coupled device (CCD) camera, and it provides a feasible method to realize the online off-axis aberration measurement.