Inserting an electrically tunable lens (ETL), such as liquid lens or tunable acoustic gradient lens, into a microscope can enable fast axial scanning, autofocusing, and extended depth of field.However, placing the ETL at different positions has different influences on image quality. Specially, in a wide-field microscope for measurement, the magnification has to be constant when introducing an ETL, otherwise it will affect measurement accuracy. To determine the best position of ETL, axial scanning range and magnification variation are quantitatively analyzed and discussed in finite and infinite microscopes through theoretical analysis, optical simulation, and experiment for four configurations: when ETL is placed at the back focal plane of objective, at the conjugate plane of objective's back focal plane between two relay lenses, or behind two relay lenses, and at imaging detector plane. The obtained results are as follows. When ETL is placed at the back focal plane, the system has a large scanning range, but the magnification varies because the back focal plane is inside the objective. When ETL is placed between two relay lenses, the magnification stays constant, but the scanning range is small. When ETL is placed behind two relay lenses, the magnification keeps invariant and the scanning range is large, but ETL and two relay lenses are inside the microscope and the system has to be customized.Finally, when ETL is placed at imaging detector plane, the magnification stays constant, but the scanning range is 0, which means the system has no axial scanning capability. Research highlights• An electrically tunable lens (ETL) is introduced into a wide-field microscope for measurement.• Axial scanning range and magnification variation are analyzed and discussed.• Theoretical analysis, ZEMAX optical simulation and experiments are performed. K E Y W O R D S axial scanning range, liquid lens, magnification variation, wide-field microscope for measurement

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The dynamic behaviors and vortex interaction modes of two tandem inverted flags at different gap distances and flow velocities are investigated experimentally in this paper. The results show that the straight, flapping, and deflected modes can still be observed with a successive increase in the flow velocity. The fixed-phase, different-frequency, changing-phase, alternating-phase, and aperiodic flapping modes are further found in the flapping mode. Considering the fixed phase difference and predominance of the fixed-phase mode, we mainly focus on this mode. The amplitude of the front flag is almost similar to that of an isolated flag due to the unaffected leading-edge vortex when they are both in the flapping mode, while it is smaller for the rear flag, indicating the great significance of the rear flag amplitude for studying the dynamic behaviors of two tandem inverted flags. First, the relation between the amplitude of the rear flag and the phase difference contains two linear segments with almost the same slope and a constant segment, fully demonstrating their strong correlation rather than the irrelevance. Second, the rear flag and the trailing-edge vortex (TEV) of the front flag are found to interact via the strong and weak interaction modes. Only in the strong interaction mode can the rear flag extract energy from the TEV of the front flag at lower critical flow velocity, resulting in a larger amplitude than that of the front flag. In general, a small gap distance is more conducive to energy harvesting at low flow velocity, while a large gap distance is more beneficial at high flow velocity.