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.

Zonal integration of circular Hartmann and Placido patterns with non-rotationally symmetric aberrations.

Placido disk methods for corneal topography use a target with concentric rings in order to obtain measurements of the corneal surface, codifying the topography from the deformations of the rings' image. Knowing exactly how the corneal surface departs from a rotational symmetric shape is difficult by using Placido rings. This is due to the fact that any ray deviations in the angular direction (sagittal transverse aberrations) are not easily detected and measured. This is the so-called skew ray error. For that reason, this technique has been considered as limited, especially when one tries to measure corneal aberrations with large rotational symmetry errors. However, we considered that the Placido disk topography has the potential to obtain a full description of the corneal surface as long as the skew ray error is fixed. Here, we present a solution based in the assumption that a corneal topography calculated with the presence of the skew ray error has hidden information that can be extracted by applying some basis of the classical Hartmann test. To achieve that solution, we improve some aspects of the Hartmann test to be later applied in the processing of Placido disk images. Our solution gives us the ability to solve the skew ray error in a simple and direct method, with an effectiveness that is probed by the computing of some simulated representative surfaces without rotational symmetry and the performance of our algorithm.

Zonal processing of Hartmann or Shack-Hartmann patterns.

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests, we measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this paper, we describe a proposed new zonal procedure. This method finds a different analytical expression for each square cell formed by four sampling points in the pupil of the system. In this manner, a full single analytical expression for the wavefront is not obtained. The advantage is that small localized errors that cannot be adjusted by a single polynomial function can be represented with this method. A second advantage is that the analytical function for each cell is obtained in an exact manner, without the errors in a trapezoidal integration.

Transversal aberrations at arbitrary Hartmann-plane distances: application in the least-squares fitting of Hartmann data.

In a previous work, we introduced the concept of transversal aberrations {U,V} calculated at arbitrary Hartmann-plane distances z=r [Appl. Opt.55, 2160 (2016)APOPAI1559-128X10.1364/AO.55.002160]. These transversal aberrations can be used to estimate the wave aberration function W, as well as the classical transversal aberrations {X,Y} calculated at a theoretical plane z=f, where f is the radius of a reference semisphere. However, when the ray identification is difficult to achieve at z=f, the use of {U,V} can be of great help. In the context of a least-squares fitting of the Hartmann data, the use of {U,V} is proposed by analyzing some simple examples for the case of a W with aberration terms up to the third order. These examples also consider the hypothesis f≫W, as presented in the majority of the optical applications.

Least-squares fitting of Hartmann or Shack-Hartmann data with a circular array of sampling points.

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigmatism by means of measurements of the transverse aberrations using a Hartmann or Shack-Hartmann test is described. The sampling points are distributed in a ring centered on the pupil of the optical system. The properties and characteristics of rings with three, four, five, six, or more sampling points are analyzed with more detail and better mathematical analysis than in previous publications.

Modal processing of Hartmann and Shack-Hartmann patterns by means of a least squares fitting of the transverse aberrations.

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests measure wavefront slopes, which are equivalent to ray transverse aberrations. Numerous integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. Frequently, a least squares fit of the transverse aberrations in the x direction and a least squares fit of the transverse aberrations in the y direction is performed to obtain the wavefront. In this work, we briefly describe a modal method to integrate Hartmann and Shack-Hartmann patterns by means of a single least squares fit of the transverse aberrations simultaneously instead of the traditional x-y separate method. The proposed method uses monomial calculation instead of using Zernike polynomials, to simplify numerical calculations. Later, a method is proposed to convert from monomials to Zernike polynomials. An important obtained result is that if polar coordinates are used, angular transverse aberrations are not actually needed to obtain all wavefront coefficients.

Modal integration of Hartmann and Shack-Hartmann patterns.

Instead of measuring the wavefront deformations directly, Hartmann and Shack-Hartmann tests measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this work we describe a modal method to integrate Hartmann and Shack-Hartmann patterns using orthogonal wavefront slope aberration polynomials, instead of the commonly used Zernike polynomials for the wavefront deformations.

Hartmann tests to measure the spherical and cylindrical curvatures and the axis orientation of astigmatic lenses or optical surfaces.

The measurement of astigmatic lenses, optical surfaces or wavefronts are a highly studied problem and many different instruments have been commercially fabricated to perform this task. Many of them use a Hartmann arrangement to obtain the result. In this paper, we analyze with detail the algorithms that can be used to make the necessary calculations and propose several alternatives with different advantages and disadvantages. Different mathematical algorithms that are involved in the calculation process have been given whereas any description of the instrument itself is not proposed, but only the different mathematical algorithms that are involved in the calculation process.

Primary wavefront aberrations calculation from a defocused image or a Hartmanngram.

A wavefront aberration can be retrieved from a defocused image or a Hartmanngram by several different methods using diffraction theory and Fourier transforms. In this manuscript, we describe an alternate method for wavefront aberration determination from a defocused image or a Hartmanngram using a geometric l approximation. The main assumption is that the image is defocused, with the observation plane outside the caustic limits. The result will be applied to the retrieval of a wavefront with primary aberrations from a Hartmanngram or defocused image without the need for any transversal aberration integration.