This PDF file contains the front matter associated with SPIE Proceedings Volume 9960, including the Title Page, Copyright information, Table of Contents, and Conference Committee listing.

A real time phase shift interference microscopy system is presented using a polarization based Linnik interferometer operating with three synchronized, phase masked, parallel detectors. Using this method, several important applications which require high speed and accuracy are demonstrated in 50 volumes per seconds and 2nm height repeatability, dynamic focusing control, fast sub-nm vibrometry, tilt measurement, submicron roughness measurement, 3D profiling of fine structures and micro-bumps height uniformity in an integrated semiconductor chip. Using multiple wavelengths approach we demonstrated phase unwrapped images with topography exceeding few microns.

In this paper, we use swept source optical coherence tomography combined with air-puff module (air-puff SS-OCT) to investigate the properties of the cornea. During OCT measurement the cornea was stimulated by short, air pulse, and corneal response was recorded. In this preliminary study, the air-puff SS-OCT instrument was applied to measure behavior of the porcine corneas under varied, well-controlled intraocular pressure conditions. Additionally, the biomechanical response of the corneal tissue before, during and after crosslinking procedure (CXL) was assessed. Air-puff swept source OCT is a promising tool to extract information about corneal behavior as well as to monitor and assess the effect of CXL.

White light interferometry (WLI) is not typically used to image bacterial biofilms that are immersed in water because there is insufficient refractive index contrast to induce reflection from the biofilm’s interface. The soft structure and water-like bulk properties of hydrated biofilms make them difficult to characterize in situ by any means, especially in a non-destructive manner. Here we describe a new method for measuring and monitoring the thickness and topology of live biofilms using a WLI microscope. A microfluidic system was used to create a reflective interface on the surface of biofilms. Live biofilm samples were monitored non-destructively over time. The method enables surface metrology measurements (roughness, surface area) and a novel approach to measuring thickness of the thin hydrated biofilms. Increase in surface roughness preceded observable increase in biofilm thickness, indicating that this measure may be used to predict future development of biofilms. We have also developed a flow cell that enables WLI biofilm imaging in a dynamic environment. We have used this flow cell to observe changes in biofilm structure in response to changes in environmental conditions - flow velocity, availability of nutrients, and presence of biocides.

Surface metrology must increasingly contend with sub-micron films, whose prevalence now extends to products well beyond semiconductor devices. For optical technologies such as coherence-scanning interferometry (CSI), transparent sub-micron films pose a dual challenge: film effects can distort the measured top surface topography map, and metrology requirements may now include 3D maps of film thickness. Yet CSI’s sensitivity also presents an opportunity: modeling film effects can decode surface and thickness from the distorted signal. Early model-based approaches entailed practical trade-offs between throughput and field of view, and restricted the choice of objective magnification. However, more recent advances allow full-field surface films analysis using any objective, with sample-agnostic calibration and throughput comparable to film-free measurements. Beyond transparent films, model-based CSI provides correct topography for any combination of dissimilar materials with known visible-spectrum refractive indices. Results demonstrate single-nm self-consistency between topography and thickness maps.

Patterned sapphire substrates (PSS) wafers are used in LED manufacturing to enhance the luminous conversion of LED chips. The most critical characteristics in PSS wafers are height, width, pitch and shape of the pattern. The common way to measure these characteristics is by using surface electron microscope (SEM). White light interferometry is capable to measure dimension with nanometer accuracy and it is suitable for measuring the characteristics of PSS wafers. One of the difficulties in measuring PSS wafers is the aspect ratio and density of the features. The high aspect ratio combined with dense pattern spacing diffracts incoming lights and reduces the accuracy of the white light interferometry measurement. In this paper, a method to improve the capability of white light interferometry for measuring PSS wafers by choosing the appropriate wavelength and microscope objective with high numerical aperture. The technique is proven to be effective for reducing the batwing effect in edges of the feature and improves measurement accuracy for PSS wafers with circular features of 1.95 um in height and diameters, and 700 nm spacing between the features. Repeatability of the measurement is up to 5 nm for height measurement and 20 nm for pitch measurement.

We review some full-field interferometric techniques which have been successfully applied in different applications related to the aerospace industry. The first part of the paper concerns the long-wave infrared (LWIR) digital holographic interferometry which allows the measurement large displacements that occur when space structures undergo large temperature excursions. A second part of the paper concerns different developments in interferometric nondestructive testing (NDT) techniques intended to improve their usability in aerospace industrial environments. Among others, we discuss LWIR speckle interferometry for simultaneous deformation and temperature variation measurements and new post-processing techniques applied to shearography for an easier detection of flaws in composite structures.

Holographic metrology, unlike most other applications of holography, has always thrived and continues to thrive by continuously incorporating new supporting technologies that make it more powerful and useful. Successes, failures, lives, and deaths are examined and recognized as evolutionary steps that position the field where opportunities are as great and as many as ever. This is a story of that evolution. Comparisons and analogies with other applications of holography such as data storage, archiving, the arts, entertainment, advertising, and security and their evolution are interesting. Critical events, successes, mistakes, and coincidences represent milestones of abandonment or failure to deliver in many holography communities that followed a different evolutionary path. Events and new technical developments continue to emerge in supporting fields that can revive and expand all holography applications. New opportunities are described with encouragement to act on them and take some risks. Don’t wait until all of the required technology and hardware are available, because good scientists always act before then. The paper is about “making holography great again” and your opportunity to be a part of the upcoming revolution. Although the discussion focuses on holographic metrology, the same principles should apply to other holography communities.

Following a major upgrade, the two advanced detectors of the Laser Interferometer Gravitational-wave Ob- servatory (LIGO) held their first observation run between September 2015 and January 2016. The product of observable volume and measurement time exceeded that of all previous runs within the first 16 days of coincident observation. On September 14th, 2015 the Advanced LIGO detectors observed the transient gravitational-wave signal GW150914, determined to be the coalescence of two black holes, launching the era of gravitational-wave astronomy. We present the main features of the detectors that enabled this observation. At its core Advanced LIGO is a multi-kilometer long Michelson interferometer employing optical resonators to enhance its sensitivity. Four very pure and homogeneous fused silica optics with excellent figure quality serve as the test masses. The displacement produced by the event GW150914 was one 200th of a proton radius. It was observed with a combined signal-to-noise ratio of 24 in coincidence by the two detectors. At full sensitivity, the Advanced LIGO detectors are designed to deliver another factor of three improvement in the signal-to-noise ratio for binary black hole systems similar in masses to GW150914.

Classical Time Averaging and Stroboscopic Interferometry are widely used for MEMS/MOEMS dynamic behavior investigations. Unfortunately both methods require an extensive measurement and data processing strategies in order to evaluate the information on maximum amplitude at a given load of vibrating object. In this paper the modified strategies of data processing in both techniques are introduced. These modifications allow for fast and reliable calculation of searched value, without additional complication of measurement systems. Through the paper the both approaches are discussed and experimentally verified.

The quality-guide phase unwrapping is an important technique that is based on quality maps which guide the unwrapping process. The efficiency of this technique depends in the adjoin-list data structure implementation. There exists several proposals that improve the adjoin-list; Ming Zhao et. al. proposed an Indexed Interwoven Linked List (I2L2) that is based on dividing the quality values into intervals of equal size and inserting in a linked list those pixels with quality values within a certain interval. Ming Zhao and Qian Kemao proposed an improved I2L2 replacing each linked list in each interval by a heap data structure, which allows efficient procedures for insertion and deletion. In this paper, we propose an improved I2L2 which uses Red-Black trees (RBT) data structures for each interval. Our proposal has as main goal to avoid the unbalanced properties of the head and thus, reducing the time complexity of insertion. In order to maintain the same efficiency of the heap when deleting an element, we provide an efficient way to remove the pixel with the highest quality value in the RBT using a pointer to the rightmost element in the tree. We also provide a new partition strategy of the phase values that is based on a density criterion. Experimental results applied to phase shifting profilometry are shown for large images.

A method to reduce the phase measurement errors generated from internal-reflection light noise in a Fizeau interferometer is proposed. In addition to an ordinary phase-shift by a mechanical translation of the reference surface, the test surface is also mechanically translated between each phase measurement to further modulate the signal phase. For spherical tests, a mechanical phase-shift generally generates a spatial non-uniformity in the phase increment across the observing aperture. It is shown that a minimum of three positional measurements is necessary to cancel out the systematic error caused by this non-uniformity. Linear combinations of the three measured phases can also cancel the additional primary spherical aberrations that occur when the test surface is out of the null position of the confocal configuration.

In this contribution we propose two Hilbert-Huang Transform based algorithms for fast and accurate single-shot and two-shot quantitative phase imaging applicable in both on-axis and off-axis configurations. In the first scheme a single fringe pattern containing information about biological phase-sample under study is adaptively pre-filtered using empirical mode decomposition based approach. Further it is phase demodulated by the Hilbert Spiral Transform aided by the Principal Component Analysis for the local fringe orientation estimation. Orientation calculation enables closed fringes efficient analysis and can be avoided using arbitrary phase-shifted two-shot Gram-Schmidt Orthonormalization scheme aided by Hilbert-Huang Transform pre-filtering. This two-shot approach is a trade-off between single-frame and temporal phase shifting demodulation. Robustness of the proposed techniques is corroborated using experimental digital holographic microscopy studies of polystyrene micro-beads and red blood cells. Both algorithms compare favorably with the temporal phase shifting scheme which is used as a reference method.

Traditionally, (dark field) imaging based, particle detection systems rely on identifying a particle based on its irradiance. It can be shown that for a very smooth wafer with 0.1 nm surface roughness (rms) this approach results in a particle detection limit larger than 20 nm. By carefully studying the physical mechanism behind this practical limit, we have developed an alternative interferometric measurement technique that is able to improve upon this limit. This technique is based on the interferometric amplification of the particle signal, while choosing the phase of the reference beam carefully as not to amplify the coherent background speckle. Although this allows to detect particles that are 30% smaller, compared to irradiance based detection this technique poses much more stringent requirements on the wavefront errors of the imaging optics.

Wire grid polarizers (WGP), are sub-wavelength gratings with applications in display projection system due to their compact size, wide field of view and long-term stability. Measurement and testing of these structures are important to optimize their use. This is done by first measuring the Mueller Matrix of the WGP using a Mueller Matrix Polarimeter. Next the Finite Difference Time Domain (FDTD) method is used to simulate a similar Mueller matrix thus providing the period and step height of the WGP. This approach may lead to more generic determination of sub-wavelength structures including diffractive optical structures.

The sensitivity achieved by large ring-laser gyroscopes will make it possible to detect faint relativistic effects related to the rotation of the Earth’s mass. This task requires a strict control of the ring cavity geometry (shape and orientation), which can be performed by a novel network of portable heterodyne interferometers, capable of measuring the absolute distance betweeen two retro-reflectors with a nominal accuracy better than 1nm. First steps have been taken towards the realization of this device and a starting prototype of distance gauge is under development and test.

Accurate measurement of angles is extremely important in various metrological applications. Interferometry has always been an excellent technique for accurate measurements. Several methods have been proposed for accurate tilt measurement using interferometric techniques. Almost all of them use the Michelson configuration which is extremely sensitive to environmental vibrations and turbulences. We know that a cyclic interferometer is extremely stable. Even though it is not sensitive to displacement changes, it is twice sensitive to tilt compared to that of a Michelson interferometer. We have enhanced the sensitivity to measure tilt using multiple reflections in a cyclic interferometer. Since the input beam is collimated, we have studied the effect of aberration of the input beam on the accuracy of tilt measurement. Experimental results on this study are presented in this paper.

The optical shape measurement methods relying on digital cameras require that the imaging geometry is known to high accuracy. One needs a camera model and a corresponding calibration procedure that establishes its parameters based on some dedicated dataset. We elaborate the recently suggested concept of the smooth generic camera calibration, emphasizing its utility for the metrological applications. First, we briefly outline the model and its advantages with respect to the state-of-the-art, then elaborate the ideas of consistently propagating the data uncertainties in the calibration process and utilizing the inherent smoothness in the imaging geometry, and finally present the experimental results of calibrating several non-trivial camera setups.

In some manufacturing applications the alignment of fine structures formed on the surface of a part such as micro-scribed patterns on solar panels can be critical to the panel performance. Variations in pattern uniformity may degrade the efficiency of the solar panel if the pattern deviates significantly from designed parameters. This paper will explore the use of moire patterns to interpret the angular alignment of such structures on 3 dimensional non-planar shapes. The moire interferometry pattern creates a beat between the scribed pattern and a reference pattern that is a function of both the shape of the part as well as the shape of the scribed pattern. Both the part shape variations and the patterns of interest are typically much smaller than can be seen visually. Similar challenges exist when inspecting specular models or testing low quality optics. The moire effect allows small displacements to be measured from patterns that are well below the resolution of the camera systems that are used to view the patterns. Issues such as the separation of the shape of the part from the alignment of the fine structure as well as resolution and robustness of the technique will be explored in this paper.

We propose to combine the Fourier transform profilometry (FTP) and phase-shifting profilometry (PSP) to reduce motion induced artifacts. The proposed method can be divided into three steps: Step 1 is to obtain a temporarily unwrapped absolute phase map of the entire scene using the FTP method, albeit the absolute phase map has motion introduced artifacts; Step 2 is to generate continuous relative phase maps without motion artifacts for each isolated object by spatially unwrapping each isolated phase map retrieved from the FTP method; and Step 3 is to determine the absolute phase map for each isolate region by referring to the temporally unwrapped phase using PSP method. Experimental results demonstrated success of the proposed method for measuring rapidly moving multiple isolated objects.

Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.

Light-emitting diodes (LED) increasingly replace conventional filaments in various illumination applications due to higher performance and efficiency. However, their common luminous intensity profiles do not match all requirements and need to be adapted using secondary beam shaping optics. Aside from reflectors, such optics are commonly realized by freeform optical components. More sophisticated tasks such as safety and security applications are covered by strict regulations and demand a well defined spatial distribution of the emitted light. Up to now, correct functionality is only verified at system level by determining the resulting radiation pattern with a photogoniometer after packaging the optic with the light source and the fixture. However, the correct functionality of the individual optical component is usually not verified and in a fail case, the actual error source cannot be identified. A new measurement method based on experimental ray tracing (ERT) is introduced that enables performance testing of beam shaping secondary optics at component level. Rays emerging from a virtual point source are traced through the device under test. The angle of the refracted ray is recorded as a function of the incident angle. In an additional step, the resulting radiation distribution is determined based on the energy conservation law. Measurement result of a freeform lens for marine application are presented as an example and compared to results from a photogoniometer.

In the design of a lens the most important parameter is the paraxial focal length. Though, most focal length measurement methods are not measuring the paraxial focal length, but a focal length influenced by aberrations. We have developed a method to determine the paraxial focal length of strong focusing lenses using experimental ray tracing in a 2D cross section measurement. The method developed by us gives a much higher accuracy in measuring the paraxial focal length than the compared methods according to the German Institute for Standardization and Neal et al.. It shows an accuracy of up to 0.15% in measurement.

In our previous publications, we had successfully made a deflectometry measurement by using a portable laser projector. In this research, we propose the beam weighting centroid method rather than previous the phase shifting method for quantification of the angular direction of the testing beam in the tested optics entrance pupil. By projecting the angular sequential lines on tested optics entrance pupil, the wavefront aberration is reconstructed from two orthogonal directions measurements, in a similar way to the line scanning deflectometry. The limited gray scale problem of laser projector during the phase shifting measurement is therefore eliminated. The reconstructed wavefront is proven to yield a more accurate result than the phase shifting methods at the cost of more image frames and acquisition time.

In the context of measurement technology, optical methods have a number of unique features. On the other hand the user is faced with serious challenges. One of the biggest challenges that currently attracts high attention in both the technical as well as life sciences, relates to exceeding the physical limits of resolution. Nowadays people prefer to talk about super-resolution. However, this concept creates an often excessive expectation, since this way only the diffraction limit can be achieved in many practical cases. Not to forget are those negative consequences that arise from the high information density in optical signals. The nature of light and its fascinating interaction with matter that makes our visual sense on the one hand the most valuable information carrier, often prevents on the other hand, the metrologically correct interpretation of the results. Nevertheless, it can be proven by numerous examples that no alternative to the optical principles exists. Because critical structures are getting smaller and functional surfaces are becoming increasingly complex, the wavelength of light provides the most flexible and traceable standard to cope with the challenges. But the potential of optical methods, often seduced to an overload of the wish list or to unrealistic promises. Therefore, this paper is dedicated to the tension between desire and reality in optical measuring techniques.

Measuring and understanding the transient behavior of a surface with high spatial and temporal resolution are required in many areas of science. This paper describes the development and application of a high-speed, high-dynamic range, digital holographic interferometer for high-speed surface contouring with fractional wavelength precision and high-spatial resolution. The specific application under investigation here is to characterize deformable mirrors (DM) employed in aero-optics. The developed instrument was shown capable of contouring a deformable mirror with extremely high-resolution at frequencies exceeding 40 kHz. We demonstrated two different procedures for characterizing the mechanical response of a surface to a wide variety of input forces, one that employs a high-speed digital camera and a second that employs a low-speed, low-cost digital camera. The latter is achieved by cycling the DM actuators with a step input, producing a transient that typically lasts up to a millisecond before reaching equilibrium. Recordings are made at increasing times after the DM initiation from zero to equilibrium to analyze the transient. Because the wave functions are stored and reconstructable, they can be compared with each other to produce contours including absolute, difference, and velocity. High-speed digital cameras recorded the wave functions during a single transient at rates exceeding 40 kHz. We concluded that either method is fully capable of characterizing a typical DM to the extent required by aero-optical engineers.

This paper discusses on holographic imaging based on six lateral phase derivatives. Six lateral derivatives are generated by a high-resolution reflection mode holographic grating that is designed in a “kite” configuration. The integration of the derivative yields the phase and the optical thickness. Demonstration of the proposed approach is carried out for the case of the analysis of the supersonic flow of a small vertical jet, 5.56mm in diameter.

In this paper, the new vector analysis for the three dimensional deformation measurement method with same sensitivity in three directions is proposed in order to analyze the deformation in an arbitrary direction on a measured object. The new analysis method is investigated by the results of experiments. The analysis is also employed in the three dimensional deformation measurement concerning a buckling phenomenon. In this measurement process, the usefulness of new vector analysis based on three dimensional speckle interferometry with the same sensitivity concerning each direction is discussed. As the results, the in-plane and out-of-plane deformations in the buckling phenomenon can be detected.

On the basis of the cyclic lateral shearing interferometer, a single beam off-axis digital holography system has been developed for diagnostics of small scale transient flow field. The wavefront of the incident beam is split into sample wavefront and reference wavefront that nearly travel along the same path with opposite directions by a ring cavity. The system produces off-axis digital hologram with high spatial carrier frequency which is useful in separating the reconstruction term from the zero order term. The system is also easy to align and resilient to environmental disturbance. In the laser driven CH film experiments conducted on the Shenguang-II facility, dual-wavelength measurements based on this system were performed to determine in which form, plasma or neutral particles, the jet is generated.

High pressure shock profiles are monitored using a long Fiber Bragg Grating (FBG). Such thin probe, with a diameter of typically 150 μm, can be inserted directly into targets for shock plate experiments. The shocked FBG’s portion is stressed under compression, which increases its optical group index and shortens its grating period. Placed along the 2D symmetrical axis of the cylindrical target, the second effect is stronger and the reflected spectrum shifts towards the shorter wavelengths. The dynamic evolution of FBG spectra is recorded with a customized Arrayed Waveguide Grating (AWG) spectrometer covering the C+L band. The AWG provides 40 channels of 200-GHz spacing with a special flattop design. The output channels are fiber-connected to photoreceivers (bandwidth: DC - 400 MHz or 10 kHz – 2 GHz). The experimental setup was a symmetric impact, completed in a 110-mm diameter single-stage gas gun with Aluminum (6061T6) impactors and targets. The FBG’s central wavelength was 1605 nm to cover the pressure range of 0 – 8 GPa. The FBG was 50-mm long as well as the target’s thickness. The 20-mm thick impactor maintains a shock within the target over a distance of 30 mm. For the impact at 522 m/s, the sustained pressure of 3.6 GPa, which resulted in a Bragg shift of (26.2 ± 1.5) nm, is measured and retrieved with respectively thin-film gauges and the hydrodynamic code Ouranos. The shock sensitivity of the FBG is about 7 nm/GPa, but it decreases with the pressure level. The overall spectra evolution is in good agreement with the numerical simulations.

CCD cameras and CMOS devices are the major electronic components of industrial metrology, which are vulnerable to high level electromagnetic exposure. Typical sources of exposure of electronics to ionizing radiation are the Van Allen radiation belts for satellites, nuclear reactors in power plants for sensors and control circuits, particle accelerators for control electronics particularly particle detector devices, residual radiation from isotopes in chip packaging materials, cosmic radiation for spacecraft and highaltitude aircraft, and nuclear explosions for potentially all military and civilian electronics. A total dose 5 ×10³ rad was delivered to silicon-based devices in seconds to minutes caused long-term degradation. We demonstrated adaptive grating, 3D image sensor for NDE metrology which is non vulnerable for high level X-Ray1 and 3 × 10⁶ rad gamma radiation exposure. Sensor is based on adaptive holographic grating generated by 632.8 nm He-Ne laser - in doped electro optic Bismuth Titanate (BTO) monocrystal. Mathematical algorithm of bipolar model conductivity in BTO crystal has been applied for experimental analyses. Applications of proposed sensor for airspace, military, nuclear and civil engineering industries have been discussed.

The ultrahigh static displacement-acceleration sensitivity of a mechanical sensing chip is essential primarily for an ultrasensitive accelerometer. In this paper, an optimal design to implement to a single-axis MOEMS accelerometer consisting of a grating interferometry cavity and a micromachined sensing chip is presented. The micromachined sensing chip is composed of a proof mass along with its mechanical cantilever suspension and substrate. The dimensional parameters of the sensing chip, including the length, width, thickness and position of the cantilevers are evaluated and optimized both analytically and by finite-element-method (FEM) simulation to yield an unprecedented acceleration-displacement sensitivity. Compared with one of the most sensitive single-axis MOEMS accelerometers reported in the literature, the optimal mechanical design can yield a profound sensitivity improvement with an equal footprint area, specifically, 200% improvement in displacement-acceleration sensitivity with moderate resonant frequency and dynamic range. The modified design was microfabricated, packaged with the grating interferometry cavity and tested. The experimental results demonstrate that the MOEMS accelerometer with modified design can achieve the acceleration-displacement sensitivity of about 150μm/g and acceleration sensitivity of greater than 1500V/g, which validates the effectiveness of the optimal design.

There is a temperature drift of an accelerometer attributed to the temperature variation, which would adversely influence the output performance. In this paper, a quantitative analysis of the temperature effect and the temperature compensation of a MOEMS accelerometer, which is composed of a grating interferometric cavity and a micromachined sensing chip, are proposed. A finite-element-method (FEM) approach is applied in this work to simulate the deformation of the sensing chip of the MOEMS accelerometer at different temperature from -20°C to 70°C. The deformation results in the variation of the distance between the grating and the sensing chip of the MOEMS accelerometer, modulating the output intensities finally. A static temperature model is set up to describe the temperature characteristics of the accelerometer through the simulation results and the temperature compensation is put forward based on the temperature model, which can improve the output performance of the accelerometer. This model is permitted to estimate the temperature effect of this type accelerometer, which contains a micromachined sensing chip. Comparison of the output intensities with and without temperature compensation indicates that the temperature compensation can improve the stability of the output intensities of the MOEMS accelerometer based on a grating interferometric cavity.

In single exposure off-axis interferometry, multiple information can be recorded by spatial frequency multiplexing. We investigate optimum conditions for designing 2D sampling schemes to record larger field of view in off-axis interferometry multiplexing. The spatial resolution of the recorded image is related to the numerical aperture of the system and sensor pixel size. The spatial resolution should preserve by avoiding crosstalk in the frequency domain. Furthermore, the field of view depends on the sensor size and magnification of the imaging system. In order to preserve resolution and have a larger field of view, the frequency domain should be designed correctly. The experimental results demonstrate that selecting the wrong geometrical scheme in frequency domain decrease the recorded image area.

Spectrally-resolved interferometry (SRI) is a very useful technique to measure distances and surface profiles based on the analysis of the spectral interferogram. The most attractive feature of SRI is to obtain the spectral phase to extract the measuring distance at once without any scanning mechanism opposed to the low coherence scanning interferometry although phase shifting techniques can be involved in SRI to improve the measurement accuracy in some cases. However, the measurement range of SRI is relatively small because of the fundamental measuring range limitations such as the maximum measurable range and the minimum measurable range. Moreover, the important issue in SRI is the direction ambiguity because it always provides the positive values, regardless of the direction. In case of measuring optical path difference (OPD) when the reference path is longer than the measurement path, the measurement result of SRI is the same as the distance in the opposite case. Then, SRI only uses one direction to measure distances or surface profiles for the linearity of the measurement results due to these fundamental characteristics although its whole measuring range is two times longer. In this investigation, we propose a very simple and effective technique to eliminate the direction ambiguity and the dead zone, which limit the measurable range in SRI. By using a dispersive material, the nonlinear spectral phase caused by the dispersion can provide useful information and determine the direction of measuring distances. In addition, the dead zone can be successfully removed by two complementary measurement results in dichroic SRI.

A new two-step phase shifting interferometry technique for evaluation of a fatigue process zone (FPZ) in notched metal and alloy specimens is proposed. In comparison with well-known destructive and nondestructive methods evaluating FPZ, this technique possesses higher accuracy and performance and allows defining the FPZ size for notched specimens made of metals and alloys with low, moderate or high plasticity. The technique is fulfilled by retrieval of a total surface relief of a studied notched specimen, extraction of surface roughness and waviness phase maps from the retrieved surface relief, calculation of a surface roughness parameter R_a spatial distribution and definition of the FPZ size by using an extracted surface roughness phase map. Obtained experimental results have confirmed assumption that the surface roughness of notched specimens after cyclic loading reaches its maximum values at the FPZ boundary. This boundary is produced as the narrow strip containing pixels possessing the maximum values on the spatial distribution of the roughness parameter Ra near a notch root. The basic distances d* defining the FPZ sizes were measured for notched specimens made of a low-carbon steel and aluminum alloys 2024–Т6 and 7075–T3. Results of the distances d* measurement are very close to respective results obtained with the help of other methods for the FPZ evaluation.

We propose the design of a new technique for measuring the spectral resolution of a Czerny-Turner Spectrometer based on spectral interferometry of ultrashort laser pulses. It is well known that ultrashort pulse measurement like SPIDER and TADPOLE techniques requires a precise and well characterized spectrum, especially in fringe resolution. We developed a new technique, to our knowledge, in which by measuring the nominal fringe spacing of a spectral interferogram one can characterize the spectral resolution in a Czerny-Turner spectrometer using Ryleigh’s criteria. This technique was tested in a commercial Czerny-Turner spectrometer. The results demonstrate a consistent spectral resolution between what was reported by the manufacturer. The actual calibration technique was applied in a homemade broadband astigmatism-free Czerny-Turner spectrometer. Theory and experimental results are presented.

A computer software is proposed in order to determine the centroids of the spots in a Hartmann pattern or Hartmanngrams. The software was developed using algorithms for segmentation of images, which are techniques used in digital image processing. Centroid determination for a Shack-Hartmann pattern is the key point to obtain reliable results. We focus in obtaining good centroid determination for Hartmanngrams under conditions of high noise. The proposed algorithms are the essential part of this work, as they are morphological algorithms, which mainly are modifications of the weighted averaging algorithm. They have several advantages, such as, the adjustment to the shape of every spot of the Hartmanngram and that it is an interactive and automatic software. Although the software is more complete and reliable than other techniques and algorithms, since it can analyze complicated pictures of Hartmanngrams and measure the centroids of the spots.

A comparison between two experimental techniques to characterize retardance as a function of applied voltage of liquid crystal variable retarders (LCVR) is presented. In the first method the variable retarder was rotated between two polarizers with their transmission axes parallel, and the retardance was calculated from the Fourier series coefficients for each applied voltage. The second method involved using two polarizers with their transmission axes perpendicular to each other, the variable retarder was placed between the polarizers with its optical axis at 45° from the horizontal, and a final stage known as "phase unwrapping" is used on experimental data to obtain the voltage-retardance function. With these two experimental methods, the voltage-retardance relationship was obtained. To verify the accuracy of this characterization a second experiment involving the production of specific polarization states was performed as the basis of a Mueller polarimeter. A method based on measuring the optical signal resulting from the application of a predetermined set of fixed values of retardance in each retarder was used. 16 elements of the Mueller matrix of a polarizer with its transmission axis at 0° and 90° were measured, and the results are compared to the expected theoretical values.

Speckle shear interferometry, or shearography, has been more and more frequently used in the industry for in-field nondestructive inspections of flaws in composite materials used in the aerospace and oil and gas industry. Nowadays new applications has emerged demanding the ability to operate in harsher environments. Bringing interferometric systems to harsh environments is not an easy task since they are very sensitive to many harsh environmental factors. Due to the quasi-equal-path property, shearography is an intrinsically robust interferometric technique that has been successfully used in the field, but there are still limits to overcome. Mechanical vibrations are probably the most challenging factor to cope in the field measurements. This work presents a potentially robust shear interferometer configuration. It uses a Wollaston prism as the shearing element rather than a traditional Michelson interferometer and polarizers to achieve the phase shift. The use of the Wollaston prism makes the optical setup more compact and robust, given that a rotating polarizer is the only movable part of the interferometer.

In this research, we introduce a new system based on the ghost imaging, for measuring the surface profile of an object using optical frequency comb laser and a single-pixel camera. The optical frequency comb laser was used to record the relative phase of the object precisely whilst the ghost imaging technique was applied to reconstruct the object's profile. The effect of using a mask on the parameters such as number of object point, number of measurements and sparse number related to the complexity of the object for reconstruction was studied by a simulation. The performance of the system strongly depends on the design of the mask. The random mask and the Hadamard mask were used to estimate the performances in the optical frequency comb profilometry.

Standard phase-shifting interferometry (PSI) generally requires collecting at least three phase-shifted interferograms to extract the physical quantity being measured. Here, we propose a simple two-frame PSI for the testing of a range of optical surfaces, including flats, spheres, and aspheres. The two-frame PSI extracts modulated phase from two randomly phase-shifted interferograms using a Gram-Schmidt algorithm, and can work in either null testing or non-null testing modes. Experimental results of a paraboloidal mirror suggest that the two-frame PSI can achieve comparable measurement precision with conventional multi-frame PSI, but has the advantages of faster data acquisition speed and less stringent hardware requirements. It effectively expands the flexibility of conventional PSI and holds great potential in many applications.

We propose a simple yet effective phase demodulation algorithm for two-shot fringe patterns with random phase shifts. The phase to be recovered is decomposed into a linear combination of finite terms of orthogonal polynomials; the expansion coefficients and the phase shift are exhaustively searched through global optimization. The technique is insensitive to noise or defects, and is capable of retrieving phase from low fringe-number interferograms. The retrieved phase is continuous and no further phase unwrapping process is required. The method is expected to be promising to process interferograms with regular fringes.

By combining self-mixing interferometer (SMI) and grating interferometer (GI), a self-mixing grating interferometer (SMGI) is proposed in this paper. Self-mixing interference occurs when light emitted from a laser diode is diffracted by the doublediffraction system and re-enters the laser active cavity, thus generating a modulation of both the amplitude and the frequency of the lasing field. Theoretical analysis and experimental observations show that the SMGI has the same phase sensitivity as that of the conventional GI and the direction of the phase movement can be obtained from inclination of the interference signal. Compared with the traditional SMI, the phase change of interference signal in SMGI is independent of laser wavelength, providing better immunity against environmental disturbances such as temperature, pressure, and humidity variation. Compared with the traditional GI, the SMGI provides a potential displacement sensor with directional discrimination and quite compact configuration.