Fresnel lenses and other faceted or micro-optic devices are increasingly used in multiple applications like solar light
concentrators and illumination devices. As applications are more exigent this characterization is of increasing
importance. We present a technique to characterize the surface topography of optical surfaces. It is especially well
adapted to Fresnel lenses where abrupt surface slopes are usually difficult to handle in conventional techniques. The
method is based on a new photometric strategy able to codify the height information in terms of optical absorption in a
liquid. A detailed topographic map is simple to acquire by capturing images of the surface. Some experimental results
are presented. A single pixel height resolution of ~0.1 μm is achieved for a height range of ~50 μm. A surface slope
analysis is also made achieving a resolution of ~±0.15°.
Phase-shifting algorithms are methods used for recovering the modulating phase of an interferogram sequence
obtained by Phase Stepping Interferometry (PSI) techniques. Typically, the number of interferograms in a PSI
sequence is from 3 to around 9 interferograms, although we can find algorithms that works with more than
9 interferograms. In this paper, we are going to show the analysis and design of phase-shifting algorithms
from the point of view of the linear systems paradigm from digital signal processing. We will show how this
paradigm describes in a general fashion the phase-shifting algorithm systems, and how we can easily design
tunable phase-shifting algorithms using this simple scheme.
For a successful phase demodulation it is important to have a good quality fringe pattern image. For this
reason preprocessing fringe patterns is, many times, an unavoidable task. Often, noise removal is the main
problem to be solved, however, the use of ordinary linear filters is not always a proper procedure specially in
the presence of high density fringes because the signal and noise are mixed in the Fourier space. Also, as fringe
pattern images are two-dimensional functions, frequencies are two-component vectors which requires consider
the filtering direction. We present a new denoising technique for preprocessing fringe pattern images which
requires to previously estimate the fringe orientation. For cases of high noise levels we modify the proposed
technique by means of a regularized local cost function in order to get a better noise response. We present a
noise response analysis of the proposed technique, some experimental results and its application to wrapped
phase maps denoising.
Reliable inspection of large surfaces with low depth recovery error is needed in a wide variety of industrial applications,
for example in external defect inspection in aeronautical surfaces. Active triangulation measurement systems with a rigid
geometrical configuration are inappropriate for scanning large objects with low measuring tolerances due to the fixed
ratio between the depth recovery error and the lateral extension. Therefore, with a rigid triangulation setup, if we are
interested in defect inspection over extended surfaces then we have to assume errors proportional to the field of view that
can preclude a precise local defect measurement. This problem can be solved by the use of multiresolution techniques.
In this work we demonstrate the application of an active triangulation multiresolution method for defect
inspection of large aeronautical panels. The technique is based on a standard camera-projector system used together with
a second auxiliary camera that can move freely. The result is a global measurement with a superposed local measurement
without any optimization, explicit registration or recalibration process. The presented results show that the depth
recovery error of the local measurement permits the local defects measurement together with a wide-area inspection.
There are two main steps in the analysis of photoelastic fringe patterns: the isoclinics and isochromatics computation. For the isochromatic computation there exist several possibilities but one of the best, from the point of view of reliability and automatization, is the phase shift technique. However all phase shift isochromatic algorithms need a good estimation of the isoclinic direction angle that is a challenging task in presence of low birrefringence, isotropic points and monochromatic illumination. In this work we discuss the application of a novel isoclinic direction calculation method based in a phase shifting technique and a fast direction estimation regularized filter. Experimental results show that the proposed method together with a standard phase shifting isochromatic estimation is a good option for the automatic analysis of photoelastic fringe patterns under different illumination conditions, load levels and sample complexity, making possible further processing steps as full-field stress separation.
The industry dealing with microchip inspection requires fast, flexible, repeatable, and stable 3-D measuring systems. The typical devices used for this purpose are coordinate measurement machines (CMMs). These systems have limitations such as high cost, low measurement speed, and small quantity of measured 3-D points. Now optical techniques are beginning to replace the typical touch probes because of their noncontact nature, their full-field measurement capability, their high measurement density, as well as their low cost and high measurement speed. However, typical properties of microchip devices, which include a strongly spatially varying reflectance, make impossible the direct use of the classical optical 3-D measurement techniques. We present a 3-D measurement technique capable of optically measuring these devices using a camera-projector system. The proposed method improves the dynamic range of the imaging system through the use of a set of gray-code (GC) and phase-shift (PS) measures with different CCD integration times. A set of extended-range GC and PS images are obtained and used to acquire a dense 3-D measure of the object. We measure the 3-D shape of an integrated circuit and obtained satisfactory results.
3-D triangulation measurement systems with a fixed geometrical configuration have practical limitations that make them inappropriate for a wide variety of applications. The reason is that the ratio between the depth recovery error and the lateral extension is a constant that depends on the geometrical setup. Therefore, with a fixed triangulation setup, there is a tradeoff between field of view and depth resolution. As a consequence, measuring large areas with low depth recovery error necessitates the use of multiresolution techniques. In this work, we propose a multiresolution technique based on a camera-projector system previously calibrated and a second auxiliary camera that can move freely. The method consists of making first a measurement with a large field of view (coarse measurement). Afterwards, the geometrical configuration of the 3-D rig is changed to acquire a small field of view (fine measurement) that is referred to the original reference system and calibration parameters by means of the auxiliary camera. Using this method, a multiresolution reconstruction is possible without any optimization, registration, or recalibration process. Experimental results, which show a decrease of approximately one order of magnitude in the depth recovery error between fine and coarse measures, demonstrate the feasibility of the proposed method.
Phase detection is an important issue when dealing with optical metrology techniques for which the magnitude to be
measured is encoded through the phase of a given fringe pattern. Asynchronous phase detection techniques are
employed when the rate of phase change (frequency) it is not known. These techniques always present a variable
frequency response, in other words, their ability to recover properly the phase depends strongly on the local frequency.
In many experiments, it is possible to have a rough knowledge about the range of frequencies involved. Therefore, it
constitutes a great advantage to have a procedure to design an asynchronous demodulation method which is suited to a
particular frequency response for a given experiment. In this way, we get a better behaviour against noise which leads to
more accurate and reliable phase extraction.
In this work we present a technique to design asynchronous demodulation algorithms with a desired frequency response
using a Fourier-based technique. The method allows the design of algorithms with a limited algebraic error in the
recovered phase which have better properties than standard asynchronous phase detection techniques as it is shown in
numeric and real experiments.
XtremeFringe is a new library for fringe pattern processing which incorporates modern methods for automatic
analysis including fringe pattern demodulation, fringe pattern filtering and phase unwrapping methods. XtremeFringe
is written in C# and is usable as an assembly from any .NET language (C#, C++ .NET, J#) and additionally as a
Matlab toolbox, which ensures an easy adaptation in custom applications, providing the user with a versatile and
powerful tool for fringe pattern analysis in a flexible way. The functions of XtremeFringe are suitable to be employed
in metrological applications such interferometry, photoelasticity, Moire techniques, holography, etc. supplying the user
with up-to-date fringe analysis tools.
In this work, we demonstrate the capabilities of the XtremeFringe library, processing different examples showing the
ability of the library to analyze complex fringe patterns in a fast, reliable and automatic way.
A novel calibration method for whole field three-dimensional shape measurement by means of fringe projection is presented. Standard calibration techniques, polynomial-and model-based, have practical limitations such as the difficulty of measuring large fields of view, the need to use precise z stages, and bad calibration results due to inaccurate calibration points. The proposed calibration procedure is a mixture of the two main standard techniques, sharing their benefits and avoiding their main problems. In the proposed method, an absolute phase is projected over marked planes placed at unknown positions. The corresponding absolute phase and marks positions are recovered for each plane location. Using Zhang's calibration method, internal camera parameters (also called intrinsic parameters) and the spatial position for each plane are computed. Later on, a polynomial fit of depth with respect to the phase is performed. To obtain the absolute position of an object point, the depth coordinate is obtained by means of the polynomial calibration and its absolute phase. Then the lateral coordinates are computed from the depth, the internal parameters, and the pixel coordinates of the imaged point. Experimental results comparing the proposed method with the standard polynomial-based calibration are shown, demonstrating the feasibility of the proposed technique.
We present a high-speed 3-D spatiotemporal shape measurement technique by means of structured light. Current methods use a constant number of images that do not take into account the available temporal continuity of the measured object. That is, they focus on acquiring and processing as quickly as possible a fixed number of images to solve for the correspondence problem and later obtain the 3-D shape by triangulation. The number of images used imposes the use of some spatial support. The major contribution of our research is a new spatiotemporal scheme that, depending on the object's movement, adaptively uses the maximum number of projected images consistent with the local temporal continuity, therefore solving the correspondence problem with the minimum possible spatial support for each position. This is achieved by the use of a hybrid color pattern composed of an analog sinusoidal periodic code in the red channel and a digital binary spatial code in the blue channel that is cyclically displaced. No subpixel calculation is used and it is possible to implement error correction strategies that make the method fast and reliable, enabling dynamic online 3-D measurement of objects in movement.
Sequential methods like the regularized phase tracker (RPT) are commonly used for fringe pattern
demodulation with closed fringes. The only drawback of the RPT method is the necessity to implement
a two-dimensional (2D) fringe following scanning in order to obtain the expected modulated
phase. In this article we present a new method to demodulate single fringe patterns with closed
fringes which use a simple 2D row by row scanning strategy. This is an important contribution
because the 2D row by row scanning is extremely fast and easy to implement unlike the fringe following
scanning. We have called this method the <i>phase curvature tracker </i>(PCT) because it uses the
frequency curvature as regularizer to obtain the expected phase as a C<sup>2</sup> function with continuous
A new method for 3-D shape registration of prismatic objects is presented. The term prismatic object denotes any object with sharp boundaries on its surface. These kinds of objects cannot be correctly registered with typical existing methods, which require smooth overlapping of the whole surface. The method presented here is based on the use of reference marks, placed on a planar glass plate that is attached to the prismatic object. Two 3-D range measurements of the object are then acquired, before and after rotating the object by approximately 180 deg. Using the reference marks on the glass and two different calibrations of the 3-D range scanning system, these two range measurements can be correctly merged to provide a full 3-D range scan of the prismatic object.
In this work, we present a method for the asynchronous direct demodulation of spatiotemporal fringe patterns by the estimation of the quadrature sign (sign of the fringe pattern quadrature signal) from one of the irradiance gradient components. The technique is based in the normalization of one plane of a spatio-temporal fringe pattern, an arcos demodulation and a final sign correction by means of the estimated quadrature sign. We present two experimental applications of the direct demodulation method presented. The first application is the measurement of surface topography by RGB Shadow-Moire. The second application is isochromatics retardation measurement by load stepping photoelasticity. In both cases good results are obtained confirming the suitability of the presented technique.
A method to enlarge the dynamic range of a CCD-based laser beam profiler is presented. The method is based on extended-image-range techniques. The algorithm that generates the extended-irradiance-range image is described in detail.
In fringe pattern processing, quadrature operators are useful to obtain the corresponding modulating phase. In the case that a carrier exists (spatial or temporal), there are good methods for phase demodulation as Fourier analysis and asynchronous methods, for example. However, if there is no carrier or is too low, robust demodulation from a single image is a difficult task.
In this work we present some recent advances in the processing of single fringe patterns with closed fringes based in a isotropic <i>n</i>-dimensional quadrature transform. In particular we address several problems related with the application of this quadrature operator. One of these problems is the Fringe direction, its role in the demodulation process is discussed and a practical method for its computation is presented. Fringe pattern normalization is also an important subject in the demodulation process from a singe image, taking this into account we present a technique for isotropic fringe pattern normalization based in the <i>n</i>-dimensional quadrature transform. All these techniques together configure a robust method for automatic demodulation of single fringe patterns. The performance and limitations of the method are discussed and illustrated by experimental results.
A well-founded and computationally fast method is presented for filtering and interpolating noisy and discontinuous wrapped phase fields that preserves both the 2(pi) discontinuities that come from the wrapping effect and the true discontinuities that may be present. It also permits the incorporation of an associated quality map, if it is available, in a natural way. Examples of its application to the computation recovery of discontinuities phase fields from speckle interferometry fracture measuring are presented.
We provide a simple solution for the particular problem of the in-service inspection of aeronautic surfaces in order to detect bumps that otherwise it is made visually and usually less reliably. Bumps and other surface defects can be a symptom of a more serious internal damage. We have extended the use of the well know shadow Moire technique to be implemented in convex curved surfaces. The use of flexible Ronchi grating allows its adaptation to a convex general surface. The effect is the contrast enhancement of only the small defects sweeping-off other misleading height profile fringes. The result obtained are quite satisfactory compared to the use of flat reference gratings. The experimental set- up consists of a plastic foil with a printed Ronchi grating stretched between three points which adapts to nay cylindrical or conical convex surface independently of the relative grating-surface orientation. Static quantification of defects profiles is also possible by means of with an attached CCD camera. Visual detectability of local surface structures lye in the range of approximately 30 micrometers in depth.
In this work we present the application of a regularization algorithm to the processing of photoelastic fringe patterns. The method used is a modified phase tracking algorithm applied to phase-shifted images. In particular, we present an algorithm for isoclinics-isochromatics separation that uses only five images. The performance of the method is discussed and experimental results are presented.
In this work we present two methods for the analysis of moire deflectograms. The first method is a Fourier-transform technique. The second method uses a regularization based method. Both methods are applied to realistic deflectograms and their performances are discussed.
The Moiré Deflectometry has been used with success for determination of refractive index, temperature gradients analysis, topography and parallelism control of surfaces and others, Nowadays it’s been applied this method to oftalmic lenses testing. However the Moiré Deflectometry applied to oftalmic industry need an automatization of the tests, which present some advantages in the quality control process made in industries working with its. In this work we present results of the spherical aberration and astigmatism coefficients, curvature radii and power measures, of different oftalmic lenses. This results are compared with other ones obtained by means of other techniques, in general, more expensive and tedious that Moiré Deflectometry.