0000000000517015
AUTHOR
L. Muñoz-escrivá
Subjective Refraction Techniques in the Frame of the Three-Dimensional Dioptric Space
A novel heuristic approach to the well-known representation of the dioptric power in a three-dimensional space is presented. It is shown how this theoretical framework is ideal for discussing the principles of several subjective refraction methods. In particular, this formalism is used to justify the stenopaic slit refraction, the Barnes subjective refraction technique, and the Jackson cross-cylinder procedure. In view of this analysis, some modifications to the traditional procedures are proposed.
Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system
The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approxi…
Manufacture of pupil filters for 3D beam shaping
In a previous work we presented a new method for binarizing pupil filters designed to control the three-dimensional (3D) irradiance distribution in the focal volume of apodized systems. The method is based in the fact that the 3D amplitude point spread function of an axially-symmetrical system can be recovered entirely from a one-dimensional (1D) set of regularly spaced amplitude samples. Hence we proposed the use of 1D iterative Fourier transform algorithm to binarize a, properly mapped, version of the amplitude transmittance of the filter. The binary masks obtained consist of a set of opaque and transparent concentric annular zones. In this paper we have built two of these masks with oppo…
An experiment to study the structure of the focal volume in apertured focusing systems
We present a simple experiment, specifically designed for students of undergraduate optics courses, where the influence of an aperture stop position on the three-dimensional structure of the focal volume of focusing systems is studied. The experiment, which involves only simple optical elements, permits an undergraduate student to generate different focal structures by simply axially displacing the aperture stop.
Three-dimensional behavior of apodized nontelecentric focusing systems.
The scalar field in the focal volume of nontelecentric apodized focusing systems cannot be accurately described by the Debye integral representation. By use of the Fresnel–Kirchhoff diffraction formula it is found that, if the aperture stop is axially displaced, the focal-volume structure is tuned. We analyze the influence of the apodizing function and find that, whereas axially superresolving pupil filters are highly sensitive to the focal-volume reshaping effect, axially apodizing filters are more inclined to the focal-shift effect.
Three-ring filters increase the effective NA up to 1.46 in optical sectioning fluorescence microscopy
Single-photon fluorescence confocal microscopy techniques can be combined with the use of specific binary filters in order to increase their optical sectioning capability. We present a novel class of axially super-resolving binary pupil filters specially designed to reach this aim. These filters let us to obtain a relevant compression of the z-response together with the reduction of the photo-bleaching effect typically inherent to apodization techniques. The fact of joining both the three-ring filters we propose in the illumination path, and the confocal detection gives rise to an important effective increase of lenses of effective numerical aperture.
One-dimensional iterative algorithm for three-dimensional point-spread function engineering.
We present a new method with which to binarize pupil filters designed to control the three-dimensional irradiance distribution in the focal volume of an optical system. The method is based on a one-dimensional iterative algorithm, which results in efficient use of computation time and in simple, easy to fabricate binary filters. An acceptable degree of resemblance between the point-spread function of the annular binary filter and that of its gray-tone counterpart is obtained.
Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: comment.
Landgrave and Berriel-Valdos presented axial and radial sampling expansions for three-dimensional light amplitude distribution around the Gaussian focal point. [J. Opt. Soc. Am. A 14, 2962 (1997)]. The expansions were obtained under the assumption that the pupil function was rotationally symmetric. We present a new derivation of the axial expansion that does not make use of arbitrary formal assumptions used by Landgrave and Berriel-Valdos and eliminates some faults of the derivation given by Arsenault and Boivin, who published this expansion in 1967 [J. Appl. Phys. 38, 3988 (1967)]. We also discuss generalizations of the axial expansion to the case of pupils that exhibit no symmetry with re…
Focal-shift formula in apodized nontelecentric focusing systems
A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.
Statistical analysis when dealing with astigmatism: assessment of different spherocylindrical notations.
Ophthalmic epidemiological studies frequently deal with ocular refractive errors, which are commonly expressed in the form sphere/cylinder x axis. However, this representation has been shown not to be the most suitable one for performing statistical analysis. Although alternative analytical and graphic methods to represent this kind of data have been developed, these formalisms have often gone unnoticed by researchers, despite their usefulness and versatility. Besides, there has been no discussion of how each of them fits in with a particular type of study. In this paper, several mathematical representations of dioptric power are revisited in a comprehensive way. The aim is to encourage res…