José A. Ferrari

Pulse-width modulation in defocused three-dimensional fringe projection

Shape measurements by fringe projection methods require high-quality sinusoidal fringes. We present a sinusoidal fringe generation technique that utilizes slightly defocused binary fringe projection. The proposed method is a spatial version of the well-known pulse-width modulation (PWM) technique of electrical engineering. PWM is easy to implement using off-the-shelf projectors, and it allows us to overcome the gamma problem (i.e., the nonlinear projector response) in the output light intensity. We will demonstrate that, with a small defocusing level--lower than with other techniques proposed in the literature--a high-quality sinusoidal pattern is obtained. Validation experiments using a commercial video projector are presented.

Diffracted field by an arbitrary aperture

Diffraction patterns of apertures on screens uniformly illuminated are standard calculations in undergraduate optics and acoustics courses. These calculations imply two-dimensional (2-D) integrations which are often performed in the far zone, at moderate angles of diffraction, i.e., using Fresnel and Fraunhofer approximations. In this note, the 2-D integration is reduced to a 1-D parametric integration over the perimeter of the aperture—resembling the Rubinowicz’s representation of the Kirchhoff diffraction integral—which allows numerical evaluation with few computational resources. The proposed formula allows mathematically exact calculation of the near-field, in the context of scalar wave theory. Explicit calculations for circular and elliptical apertures are shown.

Fast Hankel transform of nth order

An analytical form that provides a computationally efficient algorithm for numerical evaluation of the Hankel transform of nth order by fast-Fourier-transform techniques is presented and tested with some well-known functions.

Robust one-beam interferometer with phase-delay control.

A robust one-beam interferometer with external phase-delay control is described. The device resembles a Mach-Zehnder interferometer in which the two arms are together in one collimated beam. However, the proposed device is not an amplitude-division interferometer but a wave-front division one. The phase-delay control occurs at the interferometer output with the help of two polarizing beam splitters, a quarter-wave plate, a Faraday rotator, and a polarizer. An additional phase delay is introduced by application of an electrical current to the Faraday rotator or by rotation of the polarizer (the latter is of topological origin), which permits the use of techniques of phase-stepping interferometry.

Visualization of two-dimensional phase gradients by subtraction of a reference periodic pattern

We describe a simple method for visualization of phase objects. The phase object is placed between a printed two-dimensional periodic pattern and a CCD camera. The ray deflection that is due to the phase object distorts the image of the pattern. This image is subtracted from a reference image and then, by squaring and low-pass filtering, a measurement of the two-dimensional refractive-index changes is obtained. Because the optical system does not require special alignment or illumination, the method presented has potential application for detection of gas leaks in industrial environments.

Precision synchronous polarimeter with linear response for the measurement of small rotation angles.

A synchronous polarimeter was set up for the measurement of small rotation angles of the polarization plane of light. The polarimeter is based on a polarizer-Faraday modulator-analyzer structure with a synchronous detection scheme, which produces a linear system response. The theoretical background is studied, and the system performance is investigated experimentally. We achieved an accuracy of the order of 10(-4) deg, or 5 mg/dl of glucose in a 1-cm light path.

Cancellation of bending-induced birefringence in single-mode fibers: application to Faraday sensors

We demonstrate that one can cancel the bending-induced linear birefringence in single-mode fibers by inducing a controlled anisotropy in a direction orthogonal to the bending plane. In particular, the controlled anisotropy can be generated by application of a lateral compressive stress on the fiber. This effect can be applied for the construction of birefringence-free fiber coils in Faraday sensor heads (e.g., in current sensors) to improve their sensitivity.

One-beam interferometer by beam folding

A novel one-beam interferometer based on beam folding is described. The device resembles a Mach-Zehnder interferometer in which the two arms are located together in one collimated beam. Different halves of the same beam interfere with the help of a mirror--with its reflecting surface along the axis of the optical system--placed near the focal plane of the imaging lens. Phase-delay control is achieved by application of an electrical potential to a Pockels cell, which permits the use of techniques of phase-stepping interferometry.

A new scheme for phase-shifting ESPI using polarized light

A new scheme for achieving electronic speckle pattern interferometry (ESPI) is presented, in which two polarizing cube beam splitters placed together are used to achieve the superposition of orthogonal polarized light waves coming from the reference and the test object, respectively. Polarization phase stepping occurs by changing the so-called Pancharatnams phase by means of the rotation of a polarizer situated in front of a digital camera. Experiments were carried out to show the feasibility of the system. A compact system that uses a micropolarizer camera for achieving instantaneous ESPI is also proposed.

Reconstruction of perspective shifts and refocusing of a three-dimensional scene from a multi-focus image stack.

The convergence of optical imaging acquisition and image processing algorithms is a fast-evolving interdisciplinary research field focused on the reconstruction of images with novel features of interest. We propose a method for post-capture perspective shift reconstruction (in the x, y, and z directions) of a three-dimensional scene as well as refocusing with apertures of arbitrary shapes and sizes from an optimal multi-focus image stack. The approach is based on the reorganization of the acquired visual information considering a depth-variant point-spread function, which allows it to be applied to strongly defocused multi-focus image stacks. Our method is performed without estimating the depth map or segmenting the in-focus regions. A conventional camera combined with an electrically tunable lens is used for image acquisition and does not require scale transformation or registration between the acquired images. Experimental results for both real and synthetic data images are provided and compared to state-of-the-art schemes.