Ronchi test with a square grid

High-resolution phase-shifting Ronchi test

A method adding phase-shifting capacity in two mutually perpendicular axes to the Ronchi test is presented in this work. The phase of the object with the position of the reflected ray on the grating was identified and used to solve the equation of reflection in two orthogonal directions. In this manner, the test-surface figure was obtained. The procedure was demonstrated with an inverse qualitative test and a direct, quantitative test. Both tests give results comparable to Fizeau interferometry, with the precision of the order of 25 nm peak to valley. This technique is a good alternative to interferometry because, in addition to its inherent high-resolution, it is possible to obtain the radius of curvature and conic constant, which interferometers, requiring auxiliary optics, cannot provide. This method also has a high dynamic range and is not as susceptible to vibrations or turbulence. The setup can be built with low-cost, readily available components, is easily aligned, uses a white light source, and can be made very lightweight and compact, which makes it ideal for mounting onto existing polishing machines in any optical fabrication workshop, to perform in situ surface metrology.

Exact equations to measure highly aberrated wavefronts with the Hartmann test

An exact vector expression for the deformations of a wavefront from any chosen reference surface, as a function of the directions of the real and reference rays, is deduced. It can be used with slope measuring test methods, such as Hartmann or Ronchi tests, but the need for a spherical reference is removed. We present simulated and experimental results to show the feasibility of this proposal.

Lensometer with autocollimation and a square Ronchi grid

A lensometer based on an autocollimation system and a square Ronchi grid was designed, constructed, and tested. Refractive powers of monofocal, astigmatic, bifocal, and progressive lenses were measured. The focal plane was identified when no spots, or a minimum number of fringes, are observed on the bironchigram (pattern with a square Ronchi grid). For cylindrical lenses, the spots were transformed in fringes along the $ x $x and ${y}$y directions from which the cylindrical and spherical powers were obtained. For the progressive lenses, a zero spots circle moved on the bironchigram plane along the umbilic zone while the square Ronchi grid was moved along the optical axis. This lensometer is compact, cheap, and precise. Our measurements and errors were very similar to those obtained with a commercial lensometer.

Fresnel diffraction analysis of Ronchi and reverse Hartmann tests

This paper presents a Fresnel diffraction analysis of classical Ronchi and reverse Hartmann tests. Simplified analytical expressions of the intensity patterns observed by the camera are established, allowing quantitative measurements of the wavefront slopes of the tested optical system. The wavefronts are then reconstructed from their slopes using a double Fourier transform algorithm. The optimization of the operational parameters of the system is discussed in view of different quality criteria, including relative pupil shear and contrast factors in both monochromatic and polychromatic light. Practical examples of applications are studied with the help of numerical simulations, demonstrating that measurement accuracies better than λ/100 RMS are achievable on properly dimensioned systems. Finally, the technique is also applicable to wavefront sensing in adaptive optics systems.

Small petal tools performance for parabolizing optical surfaces

Small rigid petal tools, driven by a traditional polishing machine, were used to parabolize 20 mirrors 14 cm in diameter and 192 cm of curvature radius. Small rigid circular tools (SCTs), driven manually, were used to parabolize another 20 identical surfaces. A Ronchi test with a square grid was used to evaluate the performance of both techniques. If small rigid petal tools are used, the surface quality, the reproducibility in the production process, and the time spent required to generate the surfaces are markedly better than using SCTs.

Nonparaxial geometrical Ronchi test for spherical mirrors: an inverse ray-tracing approach

A geometrical model based on an inverse ray-tracing approach to describe the Ronchi test for a concave spherical mirror is presented. In contrast to the conventional ray-tracing method, which refers to information unavailable in ronchigrams, the proposed model provides an explicit relation between the available information in the ronchigram and the parameters of the setup (radius of the sphere, position of the source, position and orientation of the observation, and grating planes). This allows for extracting the parameters of interest by a simple fitting procedure, as demonstrated by an application. The derived model exhibits new unexplored potential applications of the Ronchi test, establishing it as a very useful, simple, and universal tool for optical evaluation.

Improved method for rapid shape recovery of large specular surfaces based on phase measuring deflectometry

Incorporating the modal and zonal estimation approaches into a unifying scheme, we introduce an improved three-dimensional shape reconstruction version of specular surfaces based on phase measuring deflectometry in this paper. The modal estimation is first implemented to derive the coarse height information of the measured surface as initial iteration values. Then the real shape can be recovered utilizing a modified zonal wavefront reconstruction algorithm to simultaneously achieve consistently high accuracy and dramatically rapid convergence. Moreover, the iterative process based on an advanced successive over-relaxation technique shows a consistent rejection of measurement errors, guaranteeing the stability and robustness in practical applications. The reconstruction results of numerical examples of the sphere, hyperbolic, and arbitrary surfaces, as well as an experimentally measured sphere mirror demonstrate the validity and efficiency of the proposed improved method. In the simulations, the proposed method increases the rate of convergence by fourfold compared with the existing zonal approach and realizes three orders of magnitude improvement in reconstruction accuracy compared with the modal technique when handling the sample points of 401×401  pixels of a sphere surface. Furthermore, the computation time decreases approximately 74.92% in contrast to the zonal estimation, and the surface error is about 6.68 μm with reconstruction points of 391×529  pixels of an experimentally measured sphere mirror. In general, this new method can be conducted with fast convergence speed and high accuracy, providing an efficient, stable, and real-time approach for shape reconstruction in practical situations.

Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.

Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions

PURPOSE

To measure the wavefront aberration at different locations in progressive-power lenses (PPL's) isolated and in situ (PPL's plus eye).

METHODS

A Hartmann-Shack wavefront sensor was used to measure progressive-power lenses and human eyes either independently or in combination. In each selected zone, the lens was placed and tilted accordingly to simulate natural viewing conditions. We measured 21 relevant locations across an isolated PPL (plano lens of power addition of 2 D). In six of the locations, the wavefront aberration of the eye plus PPL were obtained in two ways: (1) by direct measurement of the system and (2) by adding the individual wavefront aberrations of the eye and the lens for each appropriate zone. In every case, we obtained the wavefront aberration as Zernike polynomials expansions, the root mean square error, the point-spread function, and the Strehl ratio.

RESULTS

Along the corridor of the PPL, third-order coma and trefoil, and astigmatism were the dominant aberrations. In areas of the PPL outside the corridor, astigmatism increased, whereas other aberrations remained similar to the lens center. Small differences were found between the direct and calculated methods used to obtain the wavefront aberration of the eye with the lens, and the possible sources of errors were discussed. In some lenses zones, the aberrations of the lens may be compensated by the particular aberrations of the eye, yielding improved optical performance over that present in the lens alone.

CONCLUSIONS

We designed and built a wavefront sensor to perform spatially resolved aberration measurements in ophthalmic lenses, in particular in PPL's, either isolated or in combination with the eye. The aberrations appearing in the PPL were compared with those in normal aged eyes.

Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates

We present a simple algorithm that makes possible the simulation of ronchigrams for any optical system in which it is possible to make an exact ray tracing. We report the simulations for the following grids: the Ronchi classical, square, circular, radial, circular-radial, biparabolic, elliptic-hyperbolic, bipolar, and bielliptic ones.

Only one fitting for bironchigrams

We present an algorithm that uses a square grid in a Ronchi test. We assume that the point coordinates of this pattern (termed a bironchigram) are affected by Gaussian errors. To calculate the optical path difference, we apply only one nonlinear least-squares fit to the dot coordinates. The relevant equations are deduced, and experimental results are shown.

Characterization of excimer lasers for application to lenslet array homogenizers

We investigate the best method of characterizing high-divergence lasers, such as excimer lasers, to suppress fine-scale intensity nonuniformity that is due to coherence effects of lenslet homogenizers. We show by a detailed analysis of the lenslet homogenizer that, for highest accuracy, a direct measurement of the value of the autocorrelation function should be made at the separation p of the lenslet elements, identified as the critical spatial period. We show that the commonly used characterization of lasers by the 1/e(2) width of the angular divergence is not the most accurate test and may overstate or understate the effectiveness of a given laser.

Profilometry of toroidal surfaces with an improved ronchi test

An implementation of the well-known Ronchi test technique, which allows for the profilometric measurement of nonrotationally symmetrical surfaces, is presented and applied to the measurement of toroidal surfaces. Both the experimental setup and the data-processing procedures are described, and parameters such as the radius of curvature of the sample surface, the orientation of its principal meridians, and the position of its vertex are measured by means of the values of the local normal to the surface obtained at a set of sampling points. Integration of these local normal values allows for the reconstruction of the three-dimensional profile of the toroidal surface considered with micrometric accuracy, and submicrometric surface details may be calculated by use of surface-fitting procedures. The density of sampling points on the surface may be tailored to fit test requirements, within certain limits that depend on selection of experimental setup.

Optical alignment of segmented mirrors to the fluorescence detectors of the Pierre Auger observatory

Segmented mirrors will be used in the telescopes of the Pierre Auger Fluorescence detector. To align the segments, we have developed four methods in which (a) the image of the stop border, (b) the image of a screen with concentric circles, and (c) the Ronchi pattern are used. In addition to these, we have developed a new method, (d), in which instead of the Ronchi ruling, we have used a circular grid. In this case we obtain a moiré pattern for each segment by means of which the experimental setup is simplified, and the sensitivity of the alignment is improved.

n-Hindle-sphere arrangement with an exact ray trace for testing hyperboloid convex mirrors

We present calculations with an exact ray trace to determine the dimensions that define one or two Hindle spheres, since the paraxial theory is incongruent for convex hyperboloid mirrors with small f numbers. The equations are generalized to calculate the dimensions of n Hindle spheres, since in this way it is possible to reduce the dimensions of the spheres more. Actual calculations are done for the secondary mirrors of the Benemerita Universidad Autonoma de Puebla and Large Milimetric Telescopes; experimental results are shown for the latter.