Armando Gómez-Vieyra

Geometric theory of wavefront aberrations in an off-axis spherical mirror

We present, analyze, and evaluate expressions for the wavefront aberrations in an off-axis spherical mirror. These formulas are derived from the optical path difference between an ellipsoid and a sphere, assuming a relatively small pupil and a small angle of incidence, as will be described in detail. Some well-known and also some useful new aberration expressions are obtained. They can be used to design and analyze cavities, spectrographs, and retinal adaptive optics imaging systems.

Methodology for third-order astigmatism compensation in off-axis spherical reflective systems

The main constraint of classical off-axis reflecting systems is the primary astigmatism that has long been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by using the proper configuration. These configurations could be derived from the marginal ray fans equation, and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three off-axis mirrors have been derived and analyzed, which have not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors. The developed methodology is verified by ray-tracing analysis of some examples.

Hartmann and Hartmann-Shack spot identification and centroid evaluation by a new efficient segmentation and thresholding algorithm

In this paper, we describe a new method to identify the spots and to obtain the coordinates for the centroids from a Hartmann and Hartmann-Shack screen test when some noise and reflection errors are present using an independent dynamic thresholding method. The proposed algorithm is a robust one, working with almost no interactive operation. It proved to be good for noise removal in the presence of relatively high noise with low and uneven contrast and spot reflections. The process involves the binarization of the image through a thresholding operation. Subsequently, a data segmentation algorithm is used for spot identification. The spot identification and indexing is performed independently. Finally, the coordinates of each centroid are obtained using an appropriate masking for each spot. To test the procedure we used first synthetic images obtained from some specified functions and later we used a Hartmanngram image from a human cornea.

Calculation of wavefront aberrations in off-axis spherical mirror with object or image at the infinite

With the current retinal imaging systems, laser cavities and astronomical spectroscopes, there is the need to employ off-axis reflective systems. These systems, often used in configurations where the object or image are at the infinite with respect to the spherical mirrors, are the most used in this type of instrumentation. Expressions for the wavefront aberrations in an off-axis spherical mirror with image or object at the infinite are presented, analyzed and evaluated. Formulas are derived from the optical path difference between a paroboloid, as reference surface, and a sphere. Exact and approximate expressions, assuming a relative small pupil and a small angle of incidence are presented. They can be used to design and analyze some off-axis reflective systems.

A Low-Complexity Delta-Sigma Modulator (

In recent years, inverter-based sigma-delta (ΔΣ) modulators have received great attention as a suitable approach for the design of low-voltage, low-power, switched-capacitor ΔΣ. This method uses digital inverters as the active elements to construct the integrators in the ΔΣ loop. In some applications, a reduced silicon area implementation is an important constraint; this demands the use of only one inverter in the integrator. This paper proposes to use the common-source amplifier as the building block to achieve the operation of integration instead of the digital inverter. This leads to the operation of the amplifier in strong inversion combined with low-voltage supply and compact chip area. The idea was confirmed with a prototype fabricated in a 0.5-μm CMOS technology available through Metal Oxide Semiconductor Implementation Service (MOSIS). Using 250 kHz of sampling frequency, measurement results show a signal-to-noise and distortion ratio of 70 dB over a bandwidth of 125 Hz. The circuit consumes 38 μW when powered from a single 1.5-V supply voltage and uses 200 × 260 μm of active area. Circuit simulations in SPICE show the potential of this method to work with 450 mV of power supply in a 50-nm CMOS technology.

\Delta \Sigma

Recent advances in the acquisition of in-vivo high resolution retinal images through the use of Adaptive Optics (AO) have allowed the identification of cellular structures such as cones and rods, in and out of the fovea, in such a way that their histological characteristics can be studied in-vivo and later compared to data obtained post-mortem. In this work, an algorithm is proposed for the detection of photoreceptors; it consists of two stages: Early Cell Detection (ECD), to detect all candidate cells, and Refinement of Cell Detection (RCD), to reduce over-detection of photoreceptors. The algorithm has been tested using synthetic and real images, the latter acquired with an Adaptive Optics Scanning Light Ophthalmoscope (AOSLO). The proposed algorithm was compared against the one developed by Li and Roorda, and both algorithms were tested on synthetic and real images, yielding similar algorithm performance on both kinds of images when they had only cones; however, the algorithm developed by Li and Roorda, when applied to real images having cones and rods, identifies photoreceptors in vascular tissue, in addition to showing low rod detection.

) for Low-Voltage, Low-Power Operation

In the current retinal imaging systems, laser cavities or astronomical spectroscopes, there is the need to employ off-axis reflective systems. These systems often use different configuration where the object or image could be at finite distances or at infinity with respect to the spherical mirrors. In this work, expressions for the wavefront aberrations in an off-axis spherical mirror with image point or object point from different cases are presented, analyzed and evaluated. Assuming a relatively small pupil and a small angle of incidence, these formulas are derived from the optical path difference between a reference surface (paraboloid, ellipsoid or hyperboloid), and a sphere. They can be used to design and analyze some off-axis reflective systems.

Identification of retinal cells in in-vivo high resolution images

The main constraint of classical off-axis reflecting systems is the primary astigmatism that by long time has been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by one proper configuration. These configurations could be derived from the marginal ray fan equation and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three offaxis mirrors have been derived and analyzed, which has not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors.

The wavefront aberrations in off-axis spherical mirror with object point or image point

The astigmatism in reflective imaging systems can be eliminated by a proper configuration. However, the spherical and coma are the main residual aberrations in third order theory, but the behavior of all aberrations is not yet fully The main aberration of classical off-axis reflecting systems is primary astigmatism. The astigmatism in off-axis spherical understood. Expressions for the wavefront aberrations in an off-axis spherical mirror are presented. These formulas are derived from the optical path difference between an ellipsoid and a sphere, assuming a relatively small pupil and a small angle of incidence as it will be described with detail. Using the principle of the optical path difference, we developed the mathematical expressions that describe the third order wavefront aberrations in a two spherical mirror system when the object is finite.

Methodology for the third order astigmatism compensation in off-axis spherical reflective systems

The wavefront aberration is the difference between the real wavefront forming an image of an object point and a close reference sphere, described as an aberration function. This wavefront aberration function has been expressed by different authors as different polynomial families or polynomial series. This polynomial has their own characteristics and applications. The physical interpretation is customarily done in terms of Seidel, Zernike, Stephenson and many other aberrations. We will compare these different representations and will propose a new one.