Nonlinear ray tracing in focused fields, part 3. Monochromatic wavefront aberration: tutorial.

Using the flux tracing algorithm developed in the previous two parts, we examine the nonlinear rays that pass through the focus of a lens containing monochromatic aberrations. Lens aberration is modeled differently in the numerical propagation algorithms relating to the thin lens and the ideal lens cases. For the former, an additive phase term is applied to the transmission function of the thin lens, which describes a distortion in the thickness function of the lens, and for the latter an additive phase term is added to the pupil function of the lens (the Fourier transform of the image plane).

Nonlinear ray tracing in focused fields, part 2. Tracing the flux: tutorial.

In this three-part paper series, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name "nonlinear ray tracing." In the first part we focused on the high-speed calculation of focused three-dimensional complex wavefields in the paraxial approximation for and laser modes. The algorithms developed in the first paper are first used to generate the three-dimensional grid of samples of the complex wavefield in the focal region.

Nonlinear ray tracing in focused fields, part 1. Calculation of 3D focused wavefields: tutorial.

In this three-part paper series, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name "nonlinear ray tracing." In this first part, we provide a tutorial on the high-speed calculation of three-dimensional complex wavefields, which is a necessary precursor to flux tracing. The basis of this calculation is the angular spectrum method, a well-known numerical algorithm that can be used to efficiently and accurately calculate diffracted fields for numerical apertures <0.

Wavenumber Calibration Protocol for Raman Spectrometers Using Physical Modelling and a Fast Search Algorithm.

A wavenumber calibration protocol is proposed that replaces polynomial fitting to relate the detector axis and the wavenumber shift. The physical model of the Raman spectrometer is used to derive a mathematical expression relating the detector plane to the wavenumber shift, in terms of the system parameters including the spectrograph focal length, the grating angle, and the laser wavelength; the model is general to both reflection and transmission gratings. A fast search algorithm detects the set of parameters that best explains the position of spectral lines recorded on the detector for a known reference standard.

Improved Wavelength Calibration by Modeling the Spectrometer.

Wavelength calibration is a necessary first step for a range of applications in spectroscopy. The relationship between wavelength and pixel position on the array detector is approximately governed by a low-order polynomial and traditional wavelength calibration involves first-, second-, and third-order polynomial fitting to the pixel positions of spectral lines from a well known reference lamp such as neon. However, these methods lose accuracy for bands outside of the outermost spectral line in the reference spectrum.

Automated Raman Micro-Spectroscopy of Epithelial Cell Nuclei for High-Throughput Classification.

Raman micro-spectroscopy is a powerful technique for the identification and classification of cancer cells and tissues. In recent years, the application of Raman spectroscopy to detect bladder, cervical, and oral cytological samples has been reported to have an accuracy greater than that of standard pathology. However, despite being entirely non-invasive and relatively inexpensive, the slow recording time, and lack of reproducibility have prevented the clinical adoption of the technology.

Label-free color staining of quantitative phase images of biological cells by simulated Rheinberg illumination.

Modern microscopes are designed with functionalities that are tailored to enhance image contrast. Dark-field imaging, phase contrast, differential interference contrast, and other optical techniques enable biological cells and other phase-only objects to be visualized. Quantitative phase imaging refers to an emerging set of techniques that allow for the complex transmission function of the sample to be measured.

An Algorithm for the Removal of Cosmic Ray Artifacts in Spectral Data Sets.

Cosmic ray artifacts may be present in all photo-electric readout systems. In spectroscopy, they present as random unidirectional sharp spikes that distort spectra and may have an affect on post-processing, possibly affecting the results of multivariate statistical classification. A number of methods have previously been proposed to remove cosmic ray artifacts from spectra but the goal of removing the artifacts while making no other change to the underlying spectrum is challenging.

Multicomponent analysis using a confocal Raman microscope.

Measuring the concentration of multiple chemical components in a low-volume aqueous mixture by Raman spectroscopy has received significant interest in the literature. All of the contributions to date focus on the design of optical systems that facilitate the recording of spectra with high signal-to-noise ratio by collecting as many Raman scattered photons as possible. In this study, the confocal Raman microscope setup is investigated for multicomponent analysis.

Multiwavefront digital holographic television.

This paper presents the full technology chain supporting wide angle digital holographic television from holographic capture of real world objects/scenes to holographic display with an extended viewing angle. The data are captured with multiple CCD cameras located around an object. The display system is based on multiple tilted spatial light modulators (SLMs) arranged in a circular configuration.

Digital computation of the complex linear canonical transform.

An efficient algorithm for the accurate computation of the linear canonical transform with complex transform parameters and with complex output variable is presented. Sampling issues are discussed and the requirements for different cases given. Simulations are provided to validate the results.

Twin removal in digital holography using diffuse illumination.

A method to numerically remove the twin image for inline digital holography, using multiple digital holograms, is discussed. Each individual hologram is recorded by using a statistically independent speckle field to illuminate the object. If the holograms are recorded in this manner and then numerically reconstructed, the twin image appears as a different speckle pattern in each of the reconstructions.

Additional sampling criterion for the linear canonical transform.

The linear canonical transform describes the effect of first-order quadratic phase optical systems on a wave field. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, sampling an analog function according to existing rules will not generally permit the reconstruction of the analog linear canonical transform of that function from its samples.

Introducing secure modes of operation for optical encryption.

We analyze optical encryption systems using the techniques of conventional cryptography. All conventional block encryption algorithms are vulnerable to attack, and often they employ secure modes of operation as one way to increase security. We introduce the concept of conventional secure modes to optical encryption and analyze the results in the context of known conventional and optical attacks.

Numerical sampling rules for paraxial regime pulse diffraction calculations.

Sampling rules for numerically calculating ultrashort pulse fields are discussed. Such pulses are not monochromatic but rather have a finite spectral distribution about some central (temporal) frequency. Accordingly, the diffraction pattern for many spectral components must be considered.

Extended focused imaging for digital holograms of macroscopic three-dimensional objects.

When a digital hologram is reconstructed, only points located at the reconstruction distance are in focus. We have developed a novel technique for creating an in-focus image of the macroscopic objects encoded in a digital hologram. This extended focused image is created by combining numerical reconstructions with depth information extracted by using our depth-from-focus algorithm.

Reduction of speckle in digital holography by discrete Fourier filtering.

We present a digital signal processing technique that reduces the speckle content in reconstructed digital holograms. The method is based on sequential sampling of the discrete Fourier transform of the reconstructed image field. Speckle reduction is achieved at the expense of a reduced intensity and resolution, but this trade-off is shown to be greatly superior to that imposed by the traditional mean and median filtering techniques.

Generalized Yamaguchi correlation factor for coherent quadratic phase speckle metrology systems with an aperture.

In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.

Paraxial speckle-based metrology systems with an aperture.

Digital speckle photography can be used in the analysis of surface motion in combination with an optical linear canonical transform (LCT). Previously [D. P.

Reconstruction of partially occluded objects encoded in three-dimensional scenes by using digital holograms.

We propose a task-specific digital holographic capture system for three-dimensional scenes, which can reduce the amount of data sent from the camera system to the receiver and can effectively reconstruct partially occluded objects. The system requires knowledge of the object of interest, but it does not require a priori knowledge of either the occlusion or the distance the object is from the camera. Subwindows of the camera-plane Fresnel field are digitally propagated to reveal different perspectives of the scene, and these are combined to overcome the unknown foreground occlusions.

Speckle photography: mixed domain fractional Fourier motion detection.

A reflection-based optical implementation of two simultaneous scale-invariant fractional Fourier transforms (FRTs) is used to develop a novel compact speckle photographic system. The system allows the independent determination of both surface tilting and in-plane translational motion from two sequential mixed domain images captured using a single camera.

Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform.

The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation.

Fast numerical algorithm for the linear canonical transform.

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST.

Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms.

By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach.