Axial displacement measurement with high resolution of particle movement based on compound digital holographic microscopy

Abstract In-line digital holographic particle imaging is gifted with high axial resolution but axial displacement of nearly-in-focus or in-focus particle is unable to be measured because of twin-image problem. Both in-focus and out-of-focus particles can be measured by off-axis digital holographic particle imaging but with poor axial resolution. These two make particle tracking in three-dimensional more complicated. This paper proposes a compound method of in-line and off-axis digital holographic microscopy to measure the axial displacement of both the in-focus and out-of-focus particle with improved resolution up to nanometer scale collectively. In the proposed compound digital holographic microscopy (CDHM), the critical reconstruction distance (CRD) is calculated. The twin image effect can be resolved by ensuring the reconstruction distance is larger than the CRD, then in-line digital holographic particle imaging can be effectively applied. If the reconstruction distance is smaller than the CRD, the ring pixels of optical path length (RPOPL) method is applied to improve resolution. The axial displacement of silica particles 5  μ m and 10  μ m in diameter fixed on the piezoelectric stage were successfully measured using CDHM method at resolution up to 4 nm (in-focus particle) and 2 nm (out-of-focus particle).