Artery Pulse Waveform Acquired with a Fabry-Perot Interferometer.

For most patients admitted to a hospital, it is a requirement to continuously monitor their vital signs. Among these are the waveforms from ECG and the pulmonary arterial pulse. At present, there are several electronic devices that can measure the arterial pulse waveform. However, they can be affected by electromagnetic wave radiation, and the fabrication of electronic sensors is complicated and contributes to the e-waste, among other problems. In this paper, we propose an optical method to measure arterial pulse based on a Fabry-Perot interferometer composed of two mirrors. A pulse sensor formed by an acrylic cell with a thin membrane is used to gather the vasodilatation of the wrist, forming an air pulse that is enacted by means of a tube to a metallic cell containing a mirror that is glued to a thin silicone membrane. When the air pulse arrives, a displacement of the mirror takes place and produces a shift of the interference pattern fringes given by the Fabry-Perot. A detector samples the fringe intensity. With this method, an arterial pulse waveform is obtained. We characterize this optical device as a test of concept, and its application to measuring artery pulse is presented. The optical device is compared to other electronic devices.

Wavelength-stepping algorithm for testing the thickness and front and back surfaces of optical plates with high signal-to-noise ratio.

We propose a least-squares phase-stepping algorithm (LS-PSA) consisting of only 14 steps for high-quality optical plate testing. Optical plate testing produces an infinite number of simultaneous fringe patterns due to multiple reflections. However, because of the small reflection of common optical materials, only a few simultaneous fringes have amplitudes above the measuring noise. From these fringes, only the variations of the plate's surfaces and thicknesses are of interest. To measure these plates, one must use wavelength stepping, which corresponds to phase stepping in standard digital interferometry. The designed PSA must phase demodulate a single fringe sequence and filter out the remaining temporal fringes. In the available literature, researchers have adapted PSAs to the dimensions of particular plates. As a consequence, there are as many PSAs published as different testing plate conditions. Moreover, these PSAs are designed with too many phase steps to provide detuning robustness well above the required level. Instead, we mathematically prove that a single 14-step LS-PSA can adapt to several testing setups. As is well known, this 14-step LS-PSA has a maximum signal-to-noise ratio and the highest harmonic rejection among any other 14-step PSA. Due to optical dispersion and experimental length measuring errors, the fringes may have a slight phase detuning. Using propagation error theory, we demonstrate that measuring distances with around 1% uncertainty produces a small and acceptable detuning error for the proposed 14-step LS-PSA.

Simultaneous phase and amplitude modulation for dual-sensitivity profilometry of discontinuous objects.

Fringe projection profilometry (FPP) is a well-known technique for digitizing solids. In FPP, straight fringes are projected over a digitizing solid, and a digital camera grabs the projected fringes. The sensitivity of FPP depends on the spatial frequency of the projected fringes. The projected fringes as seen by the camera are phase modulated by the surface of the digitizing object; the demodulated phase is usually wrapped. If the digitizing object has discontinuities larger than the fringe period, the phase jumps are lost. To preserve large phase discontinuities, one must use very low spatial frequency (low-sensitivity) fringes. The drawback of low-sensitivity FPP is that the demodulated phase has low signal-to-noise ratio (SNR). Much higher SNR is obtained by projecting shorter wavelength, at the cost of obtaining wrapped phase. A way out of this problem is to use dual-wavelength FPP (DW-FPP). In DW-FPP, two sets of projected fringes are used, one with long wavelength and another with shorter wavelength. Due to harmonics and gamma distortion, in DW-FPP, one usually needs four phase-shifted fringes for each sensitivity. Here we are proposing to combine the two sensitivities simultaneously, one coded in phase (PM) and the other coded in amplitude (AM), in order to obtain phase and amplitude modulated (DW-PAM) fringes. The low-sensitivity phase is coded as AM of the DW-PAM fringes. The main advantage of DW-PAM fringes is that one reduces the number of phase-shifted fringes by half: instead of using eight phase-shifted fringes (four for low and four for high sensitivities), one would need only four DW-PAM fringes. Of course, if one wants to increase the harmonic rejection of the recovered phase, one may use a higher order phase-shifting algorithm (PSA).

Surface Profile Studies of Photoinduced Gratings Made with DCG Films with Optional Papain Development.

The use of surface relief structures is increasing in the field of optics. A study of photoinduced relief using dichromated gelatin films with different thickness is described in this paper. Two light sources were used: a laser (λ = 468 nm) and an ultraviolet mercury-metal halide lamp. Gratings with low spatial frequencies were contact-copied on the DCG (dichromated gelatin) films. Two development processes were used, one included washing the plates with just water and the other with a mixture of water and papain. This enzyme is used to improve the gratings' relief which was studied with a profilometer. For the development process with just water, it was found that when gratings were recorded using visible or UV light, the height profile inversely correlated to spatial frequencies. For short exposure times, the reliefs showed a sinusoidal profile. When visible light was used, the DCG areas where the Ronchi grating had transparent slits showed a flat relief and the areas where the Ronchi grating had opaque slits showed a round peak, with the peak being taller than the flat surface. In contrast, when UV light was used, the flat surfaces were taller than the peaks. The relief height increased up to seven times when papain was used.

Birefringent optofluidic gratings.

A set of parallel microfluidic channels behaving as a diffraction grating operating in the Raman-Nath regime has been fabricated and studied. The diffraction efficiency of such structure can be tuned by selecting a liquid with a particular refractive index and/or optical anisotropy. Alternatively the optical properties of the liquid can be characterised by measuring the diffraction efficiency and the state of polarization of the diffracted beam. In this work, the microfluidic channels under study have been filled with penicillin molecules dissolved in water. Due to the chirality of the penicillin, the liquid has been found to have circular birefringence of 2.14 × 10-7. The addition of the anisotropic liquid modifies the polarization properties of the microfluidic diffraction grating. The diffraction efficiency of the grating has been characterised for different probe beam wavelengths and states of polarization. Currently the diffraction efficiency of the device is low - 1.7%, but different approaches for its improvement have been discussed.

Liquid refractive index measured through a refractometer based on diffraction gratings.

We developed two versions of refractometers to measure the refractive index of liquids. One refractometer comprises a glass cell with a surface relief grating on the inner face of one of its walls, while the other one is a microfluidic channel in the form of serpentine that behaves as a grating. Measurements of the liquid refractive index were performed by sensing the first order intensity. Several liquids have been used including an organic one. Calibration plots are shown.

Fourier spectra for nonuniform phase-shifting algorithms based on principal component analysis.

We develop an error-free nonuniform phase-stepping algorithm (nPSA) based on principal component analysis (PCA). PCA-based algorithms typically give phase-demodulation errors when applied to nonuniform phase-shifted interferograms. We present a straightforward way to correct those PCA phase-demodulation errors. We give mathematical formulas to fully analyze PCA-based nPSA (PCA-nPSA). These formulas give a) the PCA-nPSA frequency transfer function (FTF), b) its corrected Lissajous figure, c) the corrected PCA-nPSA formula, d) its harmonic robustness (RH), and e) its signal-to-noise-ratio (SNR). We show that the PCA-nPSA can be seen as a linear quadrature filter and, as consequence, one can find its FTF. Using the FTF, we show why plain PCA often fails to demodulate nonuniform phase-shifted fringes. Previous works on PCA-nPSA (without FTF), give specific numerical/experimental fringe data to "visually demonstrate" that their new nPSA works better than its competitors. This often leads to biased/favorable fringe pattern selections which "visually demonstrate" the superior performance of their new nPSA. This biasing is herein totally avoided because we provide figures-of-merit formulas based on linear systems and stochastic process theories. However, and for illustrative purposes only, we provide specific fringe data phase-demodulation, including comprehensive analysis and comparisons.

Design of nonlinearly spaced phase-shifting algorithms using their frequency transfer function.

Here we show how to design phase-shifting algorithms (PSAs) for nonuniform/nonlinear (NL) phase-shifted fringe patterns using their frequency transfer function (FTF). Assuming that the NL phase steps are known, we introduce the desired zeroes in the FTF to obtain the specific NL-PSA formula. The advantage of designing NL-PSAs based on their FTF is that one can reject many distorting harmonics of the fringes. We can also estimate the signal-to-noise ratio for interferograms corrupted by additive white Gaussian noise. Finally, for non-distorted noiseless fringes, the proposed NL-PSA retrieves the modulating phase error free, just as standard/linear PSAs do.

Profilometry with digital fringe-projection at the spatial and temporal Nyquist frequencies.

A phase-demodulation method for digital fringe-projection profilometry using the spatial and temporal Nyquist frequencies is presented. It allows to digitize tridimensional surfaces using the highest spatial frequency (π radians per pixel) and consequently with the highest sensitivity for a given digital fringe projector. Working with the highest temporal frequency (π radians per temporal sample), the proposed method rejects the DC component and all even-order distorting harmonics using 2-step phase shifting; this robustness against harmonics is similar to that of the popular 4-step least-squares phase-shifting algorithm. The proposed phase-demodulation method is suitable for the digitization of piecewise continuous surfaces because it does not require spatial low-pass filtering. Gamma calibration is also unnecessary because the projected fringes are binary, and the harmonics produced by the binary profile can be attenuated with a slight defocusing on the digital projector. Viability of the proposed method is supported by experimental results showing complete agreement with the predicted behavior.

A Wavefront Division Polarimeter for the Measurements of Solute Concentrations in Solutions.

Polarimeters are useful instruments that measure concentrations of optically active substances in a given solution. The conventional polarimetric principle consists of measuring the rotation angle of linearly polarized light. Here, we present a novel polarimeter based on the study of interference patterns. A Mach-Zehnder interferometer with linearly polarized light at the input is used. One beam passes through the liquid sample and the other is a reference beam. As the linearly polarized sample beam propagates through the optically active solution the vibration plane of the electric field will rotate. As a result, the visibility of the interference pattern at the interferometer output will decrease. Fringe contrast will be maximum when both beams present a polarization perpendicular to the plane of incidence. However, minimum visibility is obtained when, after propagation through the sample the polarization of the sample beam is oriented parallel to the plane of incidence. By using different solute concentrations, a calibration plot is obtained showing the behavior of visibility.

Fourier analysis of RGB fringe-projection profilometry and robust phase-demodulation methods against crosstalk distortion.

In this paper, we apply the frequency transfer function formalism to analyze the red, green and blue (RGB) phase-shifting fringe-projection profilometry technique. The phase-shifted patterns in RGB fringe projection are typically corrupted by crosstalk because the sensitivity curves of most projection-recording systems overlap. This crosstalk distortion needs to be compensated in order to obtain high quality measurements. We study phase-demodulation methods for null/mild, moderate, and severe levels of RGB crosstalk. For null/mild crosstalk distortion, we can estimate the searched phase-map using Bruning's 3-step phase-shifting algorithm (PSA). For moderate crosstalk, the recorded data is usually preprocessed before feeding it into the PSA; alternatively, in this paper we propose a computationally more efficient approach, which combines linear crosstalk compensation with the phase-demodulation algorithm. For severe RGB crosstalk, we expect non-sinusoidal fringes' profiles (distorting harmonics) and a significant uncertainty on the linear crosstalk calibration (which produces pseudo-detuning error). Analyzing these distorting phenomena, we conclude that squeezing interferometry is the most robust demodulation method for RGB fringe-projection techniques. Finally, we support our conclusions with numerical simulations and experimental results.

Synthesis of multi-wavelength temporal phase-shifting algorithms optimized for high signal-to-noise ratio and high detuning robustness using the frequency transfer function.

Synthesis of single-wavelength temporal phase-shifting algorithms (PSA) for interferometry is well-known and firmly based on the frequency transfer function (FTF) paradigm. Here we extend the single-wavelength FTF-theory to dual and multi-wavelength PSA-synthesis when several simultaneous laser-colors are present. The FTF-based synthesis for dual-wavelength (DW) PSA is optimized for high signal-to-noise ratio and minimum number of temporal phase-shifted interferograms. The DW-PSA synthesis herein presented may be used for interferometric contouring of discontinuous industrial objects. Also DW-PSA may be useful for DW shop-testing of deep free-form aspheres. As shown here, using the FTF-based synthesis one may easily find explicit DW-PSA formulae optimized for high signal-to-noise and high detuning robustness. To this date, no general synthesis and analysis for temporal DW-PSAs has been given; only ad hoc DW-PSAs formulas have been reported. Consequently, no explicit formulae for their spectra, their signal-to-noise, their detuning and harmonic robustness has been given. Here for the first time a fully general procedure for designing DW-PSAs (or triple-wavelengths PSAs) with desire spectrum, signal-to-noise ratio and detuning robustness is given. We finally generalize DW-PSA to higher number of wavelength temporal PSAs.

360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.

360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.

Temporal phase-unwrapping of static surfaces with 2-sensitivity fringe-patterns.

Here we describe a 2-step temporal phase unwrapping formula that uses 2-sensitivity demodulated phases for measuring static surfaces. The first phase demodulation has at most 1-wavelength sensitivity and the second one is G-times (G>>1.0) more sensitive. Measuring static surfaces with 2-sensitivity fringe patterns is well known and recent published methods combine 2-sensitivities measurements mostly by triangulation. Two important applications for our 2-step unwrapping algorithm is profilometry and synthetic aperture radar (SAR) interferometry. In these two applications the object or surface being analyzed is static and highly discontinuous; so temporal unwrapping is the best strategy to follow. Phase-demodulation in profilometry and SAR interferometry is very similar because both share similar mathematical models.

High-resolution low-noise 360-degree digital solid reconstruction using phase-stepping profilometry.

In this paper we describe a high-resolution, low-noise phase-shifting algorithm applied to 360 degree digitizing of solids with diffuse light scattering surface. A 360 degree profilometer needs to rotate the object a full revolution to digitize a three-dimensional (3D) solid. Although 360 degree profilometry is not new, we are proposing however a new experimental set-up which permits full phase-bandwidth phase-measuring algorithms. The first advantage of our solid profilometer is: it uses base-band, phase-stepping algorithms providing full data phase-bandwidth. This contrasts with band-pass, spatial-carrier Fourier profilometry which typically uses 1/3 of the fringe data-bandwidth. In addition phase-measuring is generally more accurate than single line-projection, non-coherent, intensity-based line detection algorithms. Second advantage: new fringe-projection set-up which avoids self-occluding fringe-shadows for convex solids. Previous 360 degree fringe-projection profilometers generate self-occluding shadows because of the elevation illumination angles. Third advantage: trivial line-by-line fringe-data assembling based on a single cylindrical coordinate system shared by all 360-degree perspectives. This contrasts with multi-view overlapping fringe-projection systems which use iterative closest point (ICP) algorithms to fusion the 3D-data cloud within a single coordinate system (e.g. Geomagic). Finally we used a 400 steps/rotation turntable, and a 640x480 pixels CCD camera. Higher 3D digitized surface resolutions and less-noisy phase measurements are trivial by increasing the angular-spatial resolution and phase-steps number without any substantial change on our 360 degree profilometer.