Time efficient method for defocus error compensation in tomographic phase microscopy

Abstract

Abstract-We present a holographic method for defocus error compensation in tomographic phase microscopy, which enables high quality reconstruction in the presence of a meaningful run-out error of the measurement system. The proposed method involves indirect determination of the sample displacement from the in-focus plane. The sought quantity is deduced from the transverse movement of the rotating sample, which can be determined with high precision using correlationbased techniques. The proposed solution features improved accuracy and reduced computation time compared to the conventional autofocusing-based approach. The validity of the concept is experimentally demonstrated by tomographic reconstruction of an optical microtip.Tomographic phase microscopy (TPM) is a laser interferometric method enabling quantitative measurement of micro-scale semi-transparent samples. Its main advantage over conventional interferometric techniques is the possibility of charactering a three-dimensional (3D) internal structure of the specimen, instead of providing integrated information about phase delays [1]. In TPM, a laser interferometric (or digital holographic) microscope is used to obtain a set of quantitative phase images of the sample collected at various illumination directions in the range 0-180º. During the measurement, the scanning of a relative angle of illumination with respect to the sample is usually achieved by rotating the object under fixed on-axis illumination. In the next step, the captured angular measurements are processed with a filtered backprojection algorithm (FBPJ) [2]. The result of the processing is the reconstruction of a 3D distribution of the refractive index inside the specimen.The basic assumption underpinning the FBPJ algorithm is that probing radiation travels through the sample along straight lines. Consequently, the 2D phase maps are interpreted by FBPJ as line integrals of the refractive index evaluated along the illumination directions. As it was proven by many researches, the straight line propagation approximation is accurate for sharp imaging conditions [3,4]. However, in the presence of a defocus error, the reconstructed 3D structure suffers from blurring and other diffraction-related deformations. In fact, all conventional microscopy systems use high NA optics to achieve high transverse resolution, which inevitably shrinks the depth of focus (DOF) to a level of a few * E-mail: j.kostencka@mchtr.pw.edu.pl microns. Thus, defocusing phase images is a key factor affecting the final quality of tomographic reconstructions.The required sharp imaging condition not only puts restrictions on the spatial extent of an investigated sample but it also implies that the sample rotation has to be done precisely around the axis passing through the centre of the sample. Otherwise, the sample displacement in the direction of the optical axis causes defocusing of the phase maps and thus erroneous tomographic reconstruction. However, precise positioning of the sample in a rotary module of the TPM system is ti...