Analysis of axial scanning range and magnification variation in wide-field microscope for measurement using an electrically tunable lens

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.