This dissertation presents techniques of three-dimensional microscopy. First, an economical method of microscopic image formation that employs a raster-scanning laser beam focused on a sample, while non-imaging detector receives the scattered light is presented. The images produced by this method are analogous to the scanning electron microscopy with visible effects of shadowing and reflection. Compared to a conventional wide-field imaging system, the system allows for a greater flexibility, as the variety of optical detectors, such as PMT and position-sensitive quadrant photodiode can be used to acquire images. The system demonstrates a simple, low-cost method of achieving the resolution on the order of a micron. A further gain in terms of resolution and the depth of focus by using Bessel rather than Gaussian beams is discussed. Then, a phase-imaging technique to quantitatively study the three-dimensional structure of reflective and transmissive microscopic samples is presented. The method, based on the simultaneous dual-wavelength digital holography, allows for higher axial range at which the unambiguous phase imaging can be performed. The technique is capable of nanometer axial resolution. The noise level, which increases as a result of using two wavelengths, is then reduced to the level of a single wavelength. The method compares favorably to software unwrapping, as the technique does not produce non-existent phase steps. Curvature mismatch between the reference and object beams is numerically compensated. The 3D images of porous coal samples and SKOV-3 ovarian cancer cells are presented.

In this dissertation, improved techniques in digital holography, that have produced high-resolution, high-fidelity images, are discussed. In particular, the angular spectrum method of calculating holographic optical field is noted to have several advantages over the more commonly used Fresnel transformation or Huygens convolution method. It is observed that spurious noise and interference components can be tightly controlled through the analysis and filtering of the angular spectrum. In the angular spectrum method, the reconstruction distance does not have a lower limit, and the off-axis angle between the object and reference waves can be lower than that of the Fresnel requirement, while still allowing the zero-order background to be cleanly separated. Holographic phase images are largely immune from the coherent noise commonly found in amplitude images. With the use of a miniature pulsed laser, the resulting images have 0.5um diffraction-limited lateral resolution and the phase profile is accurate to about several nanometers of optical path length. Samples such as ovarian cancer cells (SKOV-3) and mouse-embryo fibroblast cells have been imaged. These images display intra-cellular and intra-nuclear organelles with clarity and quantitative accuracy. This technique clearly exceeds currently available methods in phase-contrast opticalmicroscopy in both resolution and detail and provides a new modality for imaging morphology of cellular and intracellular structures that is not currently available. Furthermore, we also demonstrate that phase imaging digital holographic movies provide a novel method of non-invasive quantitative viewing of living cells and other objects. This technique is shown to have significant advantages over conventional microscopy.

A Holografia Computacional é uma técnica bem conhecida que permite a realização de uma grande variedade de Elementos Ópticos Difrativos. Elementos Ópticos Difrativos são dispositivos ópticos \"moldadores\" de onda projetados com base nas propriedades de difração de suas interfaces micro-estruturadas (ou de seus variáveis índices de refração). Considerando-se sua vasta escala de tecnologias de integração e repetição, usadas na fabricação de circuitos micro-eletrônicos, eles possuem um baixo custo de fabricação. Neste trabalho, o Algoritmo Iterativo da Transformada de Fourier foi aplicado para o cálculo de hologramas de Fourier binários destinados à modelagem da luz laser. A finalidade foi simular as propriedades dos elementos, considerando algumas distribuições luminosas desejadas, e gerar o \"layout\" das máscaras de fabricação destes hologramas. Urna das implementações realizadas, para que os resultados fossem melhorados durante as iterações, foi o cálculo de uma correção na janela de reconstrução que considera o erro de amplitude da reconstrução anterior. A possibilidade de visualizar as reconstruções binárias também é demonstrada, onde o olho humano é tratado como uma lente de Fourier. Um dispositivo óptico difrativo híbrido com perfil binário e contínuo, capaz de dividir um feixe de laser monocromático em um número arbitrário de linhas com um alto ângulo também é apresentado. Hologramas de Fourier de fase contínua e com 4 níveis de fase são implementados utilizando-se o Algoritmo Iterativo da Transformada de Fourier. Cálculos para a geração de hologramas de fase de Fresnel são realizados, combinando o Algoritmo Iterativo da Transformada de Fourier com a propagação da luz no espaço livre. / The Computer Holography is a well known technique that enables one to realize a wide range of Diffractive Optical Elements. Diffractive Optical Elements are optical waveshaping devices designed with base on the diffraction properties of their microstructured interfaces (or refractive-index gradients). They have potential low fabrication cost, considering their very large scale integration and replication technologies used in the fabrication of microelectronics circuits. In this work, the Iterative Fourier Transform Algorithm was applied for the calculation of binary computer generated Fourier holograrns for laser beam shaping. The purpose was to simulate the elements proprieties considering some desired light distributions and to generate the fabrication masks Iayout of these holograms. One of the implementations, performed to improve the results during the iterations, was the calculation of a amplitude correction in the reconstruction window that considers the amplitude error from the previous reconstruction. The possibility to visualize the binary holograms reconstructions is also demonstred, where the human eye is treated as a Fourier lens. A hybrid binary and continuous profile diffractive optical device capable of splitting a monochromatic laser beam into an arbitrary number of tines over wide angle is also presented. Continuous phase and four phase levels Fourier holograms are implemented using the lterative Fourier Transform Algorithm. Fresnel phase holograms calculations are performed by combining the Iterative Fourier Transform Algorithm with the free space light propagation.

A Holografia Computacional é uma técnica bem conhecida que permite a realização de uma grande variedade de Elementos Ópticos Difrativos. Elementos Ópticos Difrativos são dispositivos ópticos \"moldadores\" de onda projetados com base nas propriedades de difração de suas interfaces micro-estruturadas (ou de seus variáveis índices de refração). Considerando-se sua vasta escala de tecnologias de integração e repetição, usadas na fabricação de circuitos micro-eletrônicos, eles possuem um baixo custo de fabricação. Neste trabalho, o Algoritmo Iterativo da Transformada de Fourier foi aplicado para o cálculo de hologramas de Fourier binários destinados à modelagem da luz laser. A finalidade foi simular as propriedades dos elementos, considerando algumas distribuições luminosas desejadas, e gerar o \"layout\" das máscaras de fabricação destes hologramas. Urna das implementações realizadas, para que os resultados fossem melhorados durante as iterações, foi o cálculo de uma correção na janela de reconstrução que considera o erro de amplitude da reconstrução anterior. A possibilidade de visualizar as reconstruções binárias também é demonstrada, onde o olho humano é tratado como uma lente de Fourier. Um dispositivo óptico difrativo híbrido com perfil binário e contínuo, capaz de dividir um feixe de laser monocromático em um número arbitrário de linhas com um alto ângulo também é apresentado. Hologramas de Fourier de fase contínua e com 4 níveis de fase são implementados utilizando-se o Algoritmo Iterativo da Transformada de Fourier. Cálculos para a geração de hologramas de fase de Fresnel são realizados, combinando o Algoritmo Iterativo da Transformada de Fourier com a propagação da luz no espaço livre. / The Computer Holography is a well known technique that enables one to realize a wide range of Diffractive Optical Elements. Diffractive Optical Elements are optical waveshaping devices designed with base on the diffraction properties of their microstructured interfaces (or refractive-index gradients). They have potential low fabrication cost, considering their very large scale integration and replication technologies used in the fabrication of microelectronics circuits. In this work, the Iterative Fourier Transform Algorithm was applied for the calculation of binary computer generated Fourier holograrns for laser beam shaping. The purpose was to simulate the elements proprieties considering some desired light distributions and to generate the fabrication masks Iayout of these holograms. One of the implementations, performed to improve the results during the iterations, was the calculation of a amplitude correction in the reconstruction window that considers the amplitude error from the previous reconstruction. The possibility to visualize the binary holograms reconstructions is also demonstred, where the human eye is treated as a Fourier lens. A hybrid binary and continuous profile diffractive optical device capable of splitting a monochromatic laser beam into an arbitrary number of tines over wide angle is also presented. Continuous phase and four phase levels Fourier holograms are implemented using the lterative Fourier Transform Algorithm. Fresnel phase holograms calculations are performed by combining the Iterative Fourier Transform Algorithm with the free space light propagation.