One of the useful phase imaging technique especially for biological applications is “Transport-of-intensity equation” or TIE in brief. This method is a computational method in its nature which was suggested in 1983 by Michael Reed Teague. It generally describes a coupling between phase and intensity of a wavefront. In most practical applications by illuminating the target by a constant intensity light source we get phase distribution on a wavefront (looks like a plane) can be obtained by a defocused image.
A great advantage of TIE is that the resulting phase does is not required to get decomposed and it does not need a specialized equipment for imaging. Moreover, despite the fact that it naturally derived for coherent light source, it still doing a good job on partially coherent source. That make it more more flexible for biological application since with partially coherent illuminations acquire better optimum spatial resolution and lower SNR (signal-to-noise ratio). In order to get phase information with only intensity measurements at several distances along its propagation direction, the phase can be quantitatively retrieved by solving the equation deterministically.
A traditional hologram is recorded on a photo-graphic plate. The holographic image is created by illuminating the developed holo-gram with the laser that was used to create the hologram.
The advent of high-resolution image sensors has made it possible to instead record a hologram digitally, allowing the holographic image to be created by a computer, rather than re-illuminating the developed hologram. The computer actually creates two images: an amplitude (intensity) and a phase image. As unstained cells are transparent, most of the information resides in the phase image.
Holographic microscopy creates (quantitative) phase images by letting a sample beam and a reference beam interfere to create an interference pattern or hologram Application of digital holography in microscopy is especially important, because of the extremely narrow depth of focus of high magnification systems.
Since the conventional process of holographic recording on photographic plates is rather complicated and time-consuming, recently the emphasis has been shifting towards digital holography. In digital holography, hologram is sampled by a high-resolution CCD array and the detected light intensity profile is transferred to a computer as an array of numbers. The propagation of optical field, which is completely and accurately described by the diffraction theory, is done via numerical reconstruction of the image as another numerical array of complex numbers representing the amplitude and phase of the optical field.
Furthermore, in addition to the ability of rapid image acquisition and the accessibility of quantitative amplitude and phase information, various image processing technique can be applied to the complex field, which is not possible in real space holography. Previously, numerical reconstruction was performed using Fresnel transform, Huygens convolution, and angular spectrum methods. Digital holography has been utilized for microscopic image formation. The examples include imaging of microstructures and biological systems. Below is an experimental DHM setup.
Here we talk about the hybrid setup capable of performing simultaneous DHM and TIE phase reconstructions to compare both methods and validate TIE as an accurate phase retrieval method. Simultaneous measurements using two quantitative phase imaging techniques, digital holographic microscopy (DHM) and transport of intensity equation (TIE) methods, are used in this Lab to compare volumetric changes in live cells.
Designed by
Shahab Bahreini
Edited by Alireza Sheikhsofla