Holography: an interpretation from the phase-space point of view

On the independent significance of generalizations of the Wigner distribution function

The Wigner distribution function (WDF) is a significant time-frequency analysis tool in, e.g., the theory of optical coherence and signal processing. Recently, various generalizations of the WDF associated with linear canonical transforms have been proposed to improve and broaden its applications. It is useful to identify which of these novel distributions have independent significance for further investigation. We plot these distributions for a test signal using symbolic integration to find which distributions are linear coordinate transforms of the WDF or have unique features. Five distributions are determined to be linear coordinate transforms of the WDF. Two distributions show unique characteristics. We focus on the mathematical interpretation, properties, and possible applications of those two distributions. We demonstrate how one of them can be used in the analysis of partially coherent systems.

Fast modal decomposition for optical fibers using digital holography

Eigenmode decomposition of the light field at the output end of optical fibers can provide fundamental insights into the nature of electromagnetic-wave propagation through the fibers. Here we present a fast and complete modal decomposition technique for step-index optical fibers. The proposed technique employs digital holography to measure the light field at the output end of the multimode optical fiber, and utilizes the modal orthonormal property of the basis modes to calculate the modal coefficients of each mode. Optical experiments were carried out to demonstrate the proposed decomposition technique, showing that this approach is fast, accurate and cost-effective.

Information encryption in phase space

In this Letter, we propose an information encryption technique based on the theory of phase-space optics. We show that encoding the plaintext in phase space provides a higher level of security: first, the key-space is significantly enlarged. Second, it is immune to various known-plaintext (cyphertext) attacks to which the double-random phase encryption (DRPE) is vulnerable. Third, the bilinearity of phase-space distributions offers additional security. Theoretical analysis and numerical calculation results show that the proposed technique has significantly different responses to errors added to the cypheretext and the two phase keys in comparison to the classical DRPE.

Wigner analysis of three dimensional pupil with finite lateral aperture

A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions.

Chip-scale microscopy imaging

Chip-scale microscopy imaging platforms are pivotal for improving the efficiency of modern biomedical and bioscience experiments. Their integration with other lab-on-a-chip techniques would allow rapid, reliable and high-throughput sample analysis for applications in diverse disciplines. In typical chip-scale microscopy imaging platforms, the light path can be generalized to the following steps: photons leave the light source, interact with the sample and finally are detected by the sensor. Based on the light path of these platforms, the current review aims to provide some insights on design strategies for chip-scale microscopy. Specifically, we analyze current chip-scale microscopy approaches from three aspects: illumination design, sample manipulation and substrate/imager modification. We also discuss some opportunities for future developments of chip-scale microscopy, such as time multiplexed structured illumination and hydrodynamic focusing for high throughput sample manipulation.

Field-portable reflection and transmission microscopy based on lensless holography

We demonstrate a lensfree dual-mode holographic microscope that can image specimens in both transmission and reflection geometries using in-line transmission and off-axis reflection holography, respectively. This field-portable dual-mode holographic microscope has a weight of ~200 g with dimensions of 15 x 5.5 x 5cm, where a laser source is powered by two batteries. Based on digital in-line holography, our transmission microscope achieves a sub-pixel lateral resolution of ≤2 µm over a wide field-of-view (FOV) of ~24 mm(2) due to its unit fringe magnification geometry. Despite its simplicity and ease of operation, in-line transmission geometry is not suitable to image dense or connected objects such as tissue slides since the reference beam gets distorted causing severe aberrations in reconstruction of such objects. To mitigate this challenge, on the same cost-effective and field-portable assembly we built a lensless reflection mode microscope based on digital off-axis holography where a beam-splitter is used to interfere a tilted reference wave with the reflected light from the object surface, creating an off-axis hologram of the specimens on a CMOS sensor-chip. As a result of the reduced space-bandwidth product of the off-axis geometry compared to its in-line counterpart, the imaging FOV of our reflection mode is reduced to ~9 mm(2), while still achieving a similar sub-pixel resolution of ≤2 µm. We tested the performance of this compact dual-mode microscopy unit by imaging a US-air force resolution test target, various micro-particles as well as a histopathology slide corresponding to skin tissue. Due to its compact, cost-effective, and lightweight design, this dual-mode lensless holographic microscope might especially be useful for field-use or for conducting microscopic analysis in resource-poor settings.

Lensfree microscopy on a cellphone

We demonstrate lensfree digital microscopy on a cellphone. This compact and light-weight holographic microscope installed on a cellphone does not utilize any lenses, lasers or other bulky optical components and it may offer a cost-effective tool for telemedicine applications to address various global health challenges. Weighing approximately 38 grams (<1.4 ounces), this lensfree imaging platform can be mechanically attached to the camera unit of a cellphone where the samples are loaded from the side, and are vertically illuminated by a simple light-emitting diode (LED). This incoherent LED light is then scattered from each micro-object to coherently interfere with the background light, creating the lensfree hologram of each object on the detector array of the cellphone. These holographic signatures captured by the cellphone permit reconstruction of microscopic images of the objects through rapid digital processing. We report the performance of this lensfree cellphone microscope by imaging various sized micro-particles, as well as red blood cells, white blood cells, platelets and a waterborne parasite (Giardia lamblia).

Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications

Despite the rapid progress in optical imaging, most of the advanced microscopy modalities still require complex and costly set-ups that unfortunately limit their use beyond well equipped laboratories. In the meantime, microscopy in resource-limited settings has requirements significantly different from those encountered in advanced laboratories, and such imaging devices should be cost-effective, compact, light-weight and appropriately accurate and simple to be usable by minimally trained personnel. Furthermore, these portable microscopes should ideally be digitally integrated as part of a telemedicine network that connects various mobile health-care providers to a central laboratory or hospital. Toward this end, here we demonstrate a lensless on-chip microscope weighing approximately 46 grams with dimensions smaller than 4.2 cm x 4.2 cm x 5.8 cm that achieves sub-cellular resolution over a large field of view of approximately 24 mm(2). This compact and light-weight microscope is based on digital in-line holography and does not need any lenses, bulky optical/mechanical components or coherent sources such as lasers. Instead, it utilizes a simple light-emitting-diode (LED) and a compact opto-electronic sensor-array to record lensless holograms of the objects, which then permits rapid digital reconstruction of regular transmission or differential interference contrast (DIC) images of the objects. Because this lensless incoherent holographic microscope has orders-of-magnitude improved light collection efficiency and is very robust to mechanical misalignments it may offer a cost-effective tool especially for telemedicine applications involving various global health problems in resource limited settings.

High-throughput lens-free blood analysis on a chip

We present a detailed investigation of the performance of lens-free holographic microscopy toward high-throughput on-chip blood analysis. Using a spatially incoherent source that is emanating from a large aperture, automated counting of red blood cells with minimal sample preparation steps at densities reaching up to approximately 0.4 x 10(6) cells/muL is presented. Using the same lens-free holographic microscopy platform, we also characterize the volume of the red blood cells at the single-cell level through recovery of the optical phase information of each cell. We further demonstrate the measurement of the hemoglobin concentration of whole blood samples as well as automated counting of white blood cells, also yielding spatial resolution at the subcellular level sufficient to differentiate granulocytes, monocytes, and lymphocytes from each other. These results uncover the prospects of lens-free holographic on-chip imaging to provide a useful tool for global health problems, especially by facilitating whole blood analysis in resource-poor environments.

Multi-angle lensless digital holography for depth resolved imaging on a chip

A multi-angle lensfree holographic imaging platform that can accurately characterize both the axial and lateral positions of cells located within multi-layered micro-channels is introduced. In this platform, lensfree digital holograms of the micro-objects on the chip are recorded at different illumination angles using partially coherent illumination. These digital holograms start to shift laterally on the sensor plane as the illumination angle of the source is tilted. Since the exact amount of this lateral shift of each object hologram can be calculated with an accuracy that beats the diffraction limit of light, the height of each cell from the substrate can be determined over a large field of view without the use of any lenses. We demonstrate the proof of concept of this multi-angle lensless imaging platform by using light emitting diodes to characterize various sized microparticles located on a chip with sub-micron axial and lateral localization over approximately 60 mm(2) field of view. Furthermore, we successfully apply this lensless imaging approach to simultaneously characterize blood samples located at multi-layered micro-channels in terms of the counts, individual thicknesses and the volumes of the cells at each layer. Because this platform does not require any lenses, lasers or other bulky optical/mechanical components, it provides a compact and high-throughput alternative to conventional approaches for cytometry and diagnostics applications involving lab on a chip systems.

On-chip differential interference contrast microscopy using lensless digital holography

We introduce the use of a birefringent crystal with lensless digital holography to create an on-chip differential interference contrast (DIC) microscope. Using an incoherent source with a large aperture, in-line holograms of micro-objects are created, which interact with a uniaxial crystal and an absorbing polarizer, encoding differential interference contrast information of the objects on the chip. Despite the fact that a unit fringe magnification and an incoherent source with a large aperture have been used, holographic digital processing of such holograms rapidly recovers the differential phase contrast image of the specimen over a large field-of-view of approximately 24 mm(2).