ASIAN JOURNAL OF PHYSICS

of intensity (TI) equation.  Thus, in this non-interferometric technique, it is possible to obtain the phase distribution of the object if the intensity is recorded at different planes during the propagation of the diffracting optical field.  In this work, we discuss the latest advances in fast tomographic 3D phase retrieval technique using the TI equation which uses either a tunable lens or a spatial light modulator (SLM) to replace the slow mechanical translation of the CCD. These novel TIE configurations are suitable for dynamical events such as imaging biological processes.

                Another important aspect is the partial coherence in the transport of intensity phase imaging.  For both coherent and partially coherent light, the TIE is equivalent to a continuity equation relating intensity changes upon propagation to a flux vector describing the flow of intensity, which for stationary fields is equivalent to energy conservation. The TIE enables the recovery of flux from intensity measurements. For coherent fields, this flux is proportional to the gradient of the field’s phase and therefore, the retrieved flux can be used to retrieve phase.  For partially coherent light, the field has no analogue to phase. Instead, one can retrieve the thickness of samples that are illuminated by partially coherent light provided the coherence effects are taken into account. In this issue, we review two methods to do so for general states of coherence where additional measurements are required to characterize both the illumination and the sample and for Kohler illumination where partial coherence manifests as a blurring of the recovered phase. This blurring effect can be compensated for by deconvolution methods.This blurring effect can be compensated for by deconvolution methods.

                A fundamental advantage of holography is that it enables 3D imaging and display. A holographic display based on complex wavefront modulation was proposed. Complex wavefront modulation is realized by double phases and Fourier filter. The optimized filter is proposed to suppress the noise and improve the accuracy of the complex modulation. The modulated beam by single phase-only spatial light modulator passes through a 4f optical system to synthesize the expected complex modulated wavefront on the output plane, with an appropriate spatial filter in the Fourier plane. The proposed spatial filter structure is efficient for the realization of complex wavefront modulation with a phase-only modulator. The performance of holographic display is also improved by complex wavefront modulation, compared with the holographic display based on phase-only wavefront modulation. The proposed encoding and display technique is theoretically demonstrated, as well as validated in numerical simulations. The proposed encoding method, avoiding the iteration calculation, can be more suitable for dynamic holography display.

                One of the standard techniques used for 3D metrology in industry is based on fringe projection profilometry. A comparative analysis and implementation of a low cost, portable, and full field of view fringe projection profilometry imaging system was discussed in details using off-the-shelf components. The constructed system is equipped with different recording and reconstruction capabilities depending on the user’s constraints of accuracy, speed, and portability. A detailed comparative analysis and complete discussion of all the different steps of the recording and reconstruction process of the FFOV-FPP imaging system is conducted. Specifically, fringe analysis, phase error compensation methods, and spatial and temporal phase unwrapping is discussed in details.  A 3D image fusion using an iterative closest point (ICP) algorithm for a FFOV reconstruction was also developed Experimental results at each step of the process will be shown and the accuracy of the system is discussed.

                Recording materials based on photorefractive effect applied to the area of 3D imaging was also discussed. Photorefractive (PR) materials have been used in numerous applications over the last five decades especially in the field of holography. The underlying theory has been developed with various approximations of the Kukhtarev equations which model the PR material. Propagation of optical waves through a PR material demands the solutions of the coupled set of material equation and the wave equation. In this paper, two aspects of PR materials that can result in potential applications were summarized. The first pertains to propagation of beams through a PR material and simultaneous generation of higher orders, with potential applications in the area of dynamic phase shifting digital holography. The second is the resulting mechanical deformation of the material due to a combination of the PR and piezoelectric effect, which can have potential applications in the area of hybrid PR structures.

It is hoped that this feature issue on 3D imaging excites readers to pursue further developments in the area and opens the door to exciting applications.

George Nehmetallah

EECS Department, The Catholic University of America, Washington DC 20064, USA

Jonathan Petruccelli

Department of Physics, Univ. at Albany- State Univ. of New York, 1400 Washington Avenue, Albany, NY 12222, USA