Daniel Malacara-Doblado - Academia.edu (original) (raw)

Papers by Daniel Malacara-Doblado

Fundamentals and Basic Optical Instruments, 2017

Fundamentals and Basic Optical Instruments, 2017

Optics Communications, 2021

The graphical representation of the surface level or topography of optical surfaces and wavefront... more The graphical representation of the surface level or topography of optical surfaces and wavefronts is a relatively simple problem if the optical surface is a simple and smooth one. However, the problem is not so simple if the surface has many bumps and valleys. Typically, mainly for common optical systems, elevation maps provide sufficient information. However, in the case of ophthalmic surfaces elevation is not the most important parameter to be determined. Each point of the surface has three ophthalmic important parameters to be represented, i.e., local values of the curvature, the astigmatism and the axis orientation. This is not a simple matter, and several solutions had been used in the past. A new simple map that can be used to represent the three parameters in ophthalmic surfaces, progressive lenses and free form surfaces is proposed in this article.

Optics Communications, 2018

In this article we will develop a method to integrate Shack-Hartmann and Hartmann pattern with he... more In this article we will develop a method to integrate Shack-Hartmann and Hartmann pattern with hexagonal cells, using a polynomial representation (modal integration) over each hexagonal cell. Since each hexagonal has six sampling points, one at each vertex, instead of the typical four sampling points in square cells, it is possible to have a different representation of the wavefront in each cell, each with different aberration terms. The local curvatures and low order aberrations in each cell are calculated more accurately than for square cells. All the analytical functions over each hexagonal cell have a different unknown piston term, that is calculated with a method to be described here. As a result, wavefront retrieval and representation of freeform optical surfaces for some optical systems can be made, due to the calculation of aberrations in each hexagonal cell.

Progress in Optics, 2017

Abstract This chapter describes the general subject of optical testing of optical elements and sy... more Abstract This chapter describes the general subject of optical testing of optical elements and systems. First, the mathematical representations of wavefronts and optical surfaces are treated, including the well-known Zernike polynomials. Next, we describe general geometrical and interferometric methods to evaluate optical surfaces, classifying them according to the parameter they measure: wavefront deformations, transverse aberrations, or local curvatures. Next, the main methods of fringe analysis and phase shifting interferometry are extensively described. We conclude by discussing the testing of aspheric surfaces in some detail. A complete list of references is provided, so that the interested reader can delve more deeply into a particular subject.

Applied Optics, 2017

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests, we measure th... more 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.

Applied Optics, 2016

In the Hartmann test, a wave aberration function W is estimated from the information of the spot ... more In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.

Optical Engineering, 2016

Abstract. When testing lenses with Hartmann methods, a wave aberration function W is typically es... more Abstract. When testing lenses with Hartmann methods, a wave aberration function W is typically estimated. This W represents the deviations of the wavefront surface w with respect to an ideal wavefront E. In this test, the distance r from the observation screen to the second lens surface is considered, and, as in the case of W, by considering paraxial approximations, two estimations of w can be directly constructed from Hartmann test data without calculating W. We have compared these two estimations by taking into account small r values; a possible and suitable condition to measure some relatively high-power lenses. The importance of estimating w can be useful for improving some optical measurements as power map reconstructions.

Applied Optics, 2015

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigma... more 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.

Current Developments in Optical Design and Optical Engineering IV, 1994

ABSTRACT

Fabrication and Testing of Aspheres, 1999

In this paper we present a review of the state of the art of aspheric wavefront evaluation method... more In this paper we present a review of the state of the art of aspheric wavefront evaluation methods. Null and non-null configurations are defined and described. Phase shifting interferometry and phase demodulating methods with a spatial carrier are treated with special emphasis on the testing of aspheric wavefronts.

International Conference on Applications of Optics and Photonics, 2011

Many optical systems need to be evaluated but they cannot be disassembled to test the imaging len... more Many optical systems need to be evaluated but they cannot be disassembled to test the imaging lens separately. Then, they have to be tested in a retroreflecting configuration, frequently called double-pass. A typical example of this procedure is in the optical eye. In this manuscript we will describe the different possibilities that might exist when these tests are performed. The

Interferometry VII: Applications, 1995

ABSTRACT

Interferometry VII: Applications, 1995

ABSTRACT

International Conference on Optical Fabrication and Testing, 1995

ABSTRACT

Second Iberoamerican Meeting on Optics, 1996

ABSTRACT

Applied Optics, 2014

Principal meridians of the corneal vertex of the human ocular system are not always orthogonal. T... more Principal meridians of the corneal vertex of the human ocular system are not always orthogonal. To study these irregular surfaces at the vertex, which have principal meridians with an angle different from 90°, we attempt to define so-called parastigmatic surfaces; these surfaces allow us to correct several classes of irregular astigmatism, with nonorthogonal principal meridians, using a simple refractive surface. We will create a canonical surface to describe the surfaces of the human cornea with a short and simple formula, using two additional parameters to the current prescription: the angle between principal meridians and parharmonic variation of curvatures between them.

Optical Engineering, 1997

ABSTRACT

Optical Engineering, 1997

ABSTRACT

Fundamentals and Basic Optical Instruments, 2017

Fundamentals and Basic Optical Instruments, 2017

Optics Communications, 2021

The graphical representation of the surface level or topography of optical surfaces and wavefront... more The graphical representation of the surface level or topography of optical surfaces and wavefronts is a relatively simple problem if the optical surface is a simple and smooth one. However, the problem is not so simple if the surface has many bumps and valleys. Typically, mainly for common optical systems, elevation maps provide sufficient information. However, in the case of ophthalmic surfaces elevation is not the most important parameter to be determined. Each point of the surface has three ophthalmic important parameters to be represented, i.e., local values of the curvature, the astigmatism and the axis orientation. This is not a simple matter, and several solutions had been used in the past. A new simple map that can be used to represent the three parameters in ophthalmic surfaces, progressive lenses and free form surfaces is proposed in this article.

Optics Communications, 2018

In this article we will develop a method to integrate Shack-Hartmann and Hartmann pattern with he... more In this article we will develop a method to integrate Shack-Hartmann and Hartmann pattern with hexagonal cells, using a polynomial representation (modal integration) over each hexagonal cell. Since each hexagonal has six sampling points, one at each vertex, instead of the typical four sampling points in square cells, it is possible to have a different representation of the wavefront in each cell, each with different aberration terms. The local curvatures and low order aberrations in each cell are calculated more accurately than for square cells. All the analytical functions over each hexagonal cell have a different unknown piston term, that is calculated with a method to be described here. As a result, wavefront retrieval and representation of freeform optical surfaces for some optical systems can be made, due to the calculation of aberrations in each hexagonal cell.

Progress in Optics, 2017

Abstract This chapter describes the general subject of optical testing of optical elements and sy... more Abstract This chapter describes the general subject of optical testing of optical elements and systems. First, the mathematical representations of wavefronts and optical surfaces are treated, including the well-known Zernike polynomials. Next, we describe general geometrical and interferometric methods to evaluate optical surfaces, classifying them according to the parameter they measure: wavefront deformations, transverse aberrations, or local curvatures. Next, the main methods of fringe analysis and phase shifting interferometry are extensively described. We conclude by discussing the testing of aspheric surfaces in some detail. A complete list of references is provided, so that the interested reader can delve more deeply into a particular subject.

Applied Optics, 2017

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests, we measure th... more 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.

Applied Optics, 2016

In the Hartmann test, a wave aberration function W is estimated from the information of the spot ... more In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.

Optical Engineering, 2016

Abstract. When testing lenses with Hartmann methods, a wave aberration function W is typically es... more Abstract. When testing lenses with Hartmann methods, a wave aberration function W is typically estimated. This W represents the deviations of the wavefront surface w with respect to an ideal wavefront E. In this test, the distance r from the observation screen to the second lens surface is considered, and, as in the case of W, by considering paraxial approximations, two estimations of w can be directly constructed from Hartmann test data without calculating W. We have compared these two estimations by taking into account small r values; a possible and suitable condition to measure some relatively high-power lenses. The importance of estimating w can be useful for improving some optical measurements as power map reconstructions.

Applied Optics, 2015

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigma... more 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.

Current Developments in Optical Design and Optical Engineering IV, 1994

ABSTRACT

Fabrication and Testing of Aspheres, 1999

In this paper we present a review of the state of the art of aspheric wavefront evaluation method... more In this paper we present a review of the state of the art of aspheric wavefront evaluation methods. Null and non-null configurations are defined and described. Phase shifting interferometry and phase demodulating methods with a spatial carrier are treated with special emphasis on the testing of aspheric wavefronts.

International Conference on Applications of Optics and Photonics, 2011

Many optical systems need to be evaluated but they cannot be disassembled to test the imaging len... more Many optical systems need to be evaluated but they cannot be disassembled to test the imaging lens separately. Then, they have to be tested in a retroreflecting configuration, frequently called double-pass. A typical example of this procedure is in the optical eye. In this manuscript we will describe the different possibilities that might exist when these tests are performed. The

Interferometry VII: Applications, 1995

ABSTRACT

Interferometry VII: Applications, 1995

ABSTRACT

International Conference on Optical Fabrication and Testing, 1995

ABSTRACT

Second Iberoamerican Meeting on Optics, 1996

ABSTRACT

Applied Optics, 2014

Principal meridians of the corneal vertex of the human ocular system are not always orthogonal. T... more Principal meridians of the corneal vertex of the human ocular system are not always orthogonal. To study these irregular surfaces at the vertex, which have principal meridians with an angle different from 90°, we attempt to define so-called parastigmatic surfaces; these surfaces allow us to correct several classes of irregular astigmatism, with nonorthogonal principal meridians, using a simple refractive surface. We will create a canonical surface to describe the surfaces of the human cornea with a short and simple formula, using two additional parameters to the current prescription: the angle between principal meridians and parharmonic variation of curvatures between them.

Optical Engineering, 1997

ABSTRACT

Optical Engineering, 1997

ABSTRACT