3D high speed characterization of phase objects using the transport of intensity equation

Abstract

ABSTRACT In this work we will extend the traditional TIE setup of phase retrieval of a phase object through axial translation of the CCD by employing a tunable lens (TL-TIE). This setup is also extended to a 360 o tomographic 3D reconstruction through multiple illuminations from different angles by rotating the phase object. Finally, synchronization between the CCD, and the tunable lens is employed using a reconfigurable hardware to automate the 3D 360 o tomographic reconstruction process. Keywords: Non-interferometric, Transport of intensity equation, Tomography, Multiplicative technique. 1. INTRODUCTION Phase objects are widely used in micro-optic, life sciences and bio-photonics. Phase contains the most important information about an optical field that related to the shape, surface and refractive index of an object. Especially in biological study of cells, which are nearly undetectable in bright field microscopy but exhibit strong phase contrast, acquiring phase information is crucial. Many methods of phase contrast are applied by using laser and special equipment for obtaining phase information such as Frits Zernike’s Phase Contrast Microscopy first described in 1934 [1], and differential micro interferometer with po larized waves in 1955 [2], but these method lack in providing quantitative phase information leading to be difficult in interpretation. Considerable efforts have there for been undertaken in few decades to devise proper reconstruction algorithms. Traditionally, 3D phase information is obtained using interferometric or holographic techniques [3,4]. While these techniques are very sensitive to vibrations, and vibration ca ncelation platforms are needed to obtain decent results, non-interferometric intensity based techniques of phase retrieval such as the transport of intensity equation (TIE) do not suffer from such a drawback [5-9]. TIE offers an experimentally approach for retrieving phase quantitatively from several defocused images which containing intensity alone. These intensity images are the diffraction patterns at different observation planes through axially translating th e CCD. The TIE specifies the relationship between phase and intensity thorough a derivative operation. The TIE gains many unique advantages over interferometry techniques [8,9] such as: it works with partially coherent illumination, simple computation, non-interferometry, and does not requires a complicated system. However, this technique still has some challenges; it typically requires at least two images in series at two neighboring longitudinal planes, and it suffers from experimental accuracy and noise cancellation issues [10]. Basically, in order to capture those images , the camera should be mech anically translated along the optical axis, within a sub-pixel accuracy (~1 µm). Recently, instead of the slow mechanical translation, a Tunable Lens was proposed to modify the TIE setup (TL-TIE) for dynamic phase objects [11]. In this paper, we employ a new TIE setup to reconstruct the phase (depth information) of an object thorough introducing a tunable-lens into a 4f system. In this setup, the change in the focal length of the tunable lens replaces the effect of