Abstract We describe a scanning white-light interferometer for high-precision surface structure analysis. Interferograms each of the image points in field view instrument are generated simultaneously by object direction perpendicular to surface, while recording detector data digital memory. These interferograms then transformed into spatial frequency domain and height point is obtained examination complex phase as function frequency. The final step creation complete three-dimensional...

We describe a system for fast three-dimensional profilometry, of both optically smooth and rough surfaces, based on scanning white-light techniques. The utilizes an efficient algorithm to extract save only the region interference, substantially reducing acquisition analysis times. Rough discontinuous surfaces can be profiled without phase-ambiguity problems associated with conventional phase-shifting measures steps 100 μm, scans 10-μm range in 5 s, has surface repeatability 0.5 nm.

Interference microscopy plays a central role in noncontact strategies for process development and quality control, providing full 3D measurement of surface characteristics that influence the functional behavior manufactured parts. Here I briefly review history principles this important technique, then concentrate on details hardware, software, applications interference using phase-shifting coherence scanning principles. Recent advances considered here include performance improvements,...

I propose a systematic way to derive efficient, error-compensating algorithms for phase-shifting interferometry by integer approximation of well-known data-sampling windows. The theoretical basi the approach is observation that many common sources phase-estimation error can be related frequency-domain characteristics sampling window. Improving these therefore improve overall performance algorithm. Analysis seven-frame example algorithm demonstrates an exceptionally good resistance first- and...

A compact self-aligning laser radar has been constructed for coheren ranging and velocimetry using a diode modulated by feedback from light scattered diffusing target. The phenomenology of beat-signal generation in the device is discussed both experimental theoretical points view. ac-coupled modulation waveform asymmetric (similar to sawtooth) different two propagation directions leaving diode. Atheoreticalmodel, based on mode structure ofathree-mirrorFabry-Perot cavity, describes signal...

Combining phase and coherence information for improved precision in white-light interference microscopy requires a robust strategy dealing with the inconsistencies between these two types of information. We correct on every measurement by direct analysis difference map profiles. The algorithm adapts to surface texture noise level dynamically compensates optical aberrations, distortions, diffraction, dispersion that would otherwise lead incorrect fringe order. same also provides absolute...

Unexpected mechanical vibrations can significantly degrade the otherwise high accuracy of phase-shifting interferometry. Fourier analysis phase-shift algorithms is shown to provide analytical means predicting measurement errors as a function frequency, phase, and amplitude vibrations. The results this are concisely represented by phase-error transfer function, which may be multiplied noise spectrum predict response an interferometer various forms vibration. Analytical for phase error derived...

Introductory digital image processing optical techniques intensity based analysis methods temporal phase measurement spatial unwrapping in speckle photography and PIV applications.

We demonstrate a millimeter-wave range metamaterial fabricated from cuprate superconductor. Two complementary structures have been studied, which exhibit Fano resonances emerging the collective excitation of interacting magnetic and electric dipole modes.

A wavelength-tuned Fizeau interferometer is applied to the problem of flatness testing transparent plates. When plate positioned at a specific distance from reference surface and an integer-math 13-frame phase-shifting algorithm applied, system directly filters out unwanted interference arising backsurface reflections. The resulting front-surface profile exhibits less than 2 nm residual error attributable spurious reflections within plate.

We propose a computationally efficient theoretical model for low-coherence interferometric profilers that measure surface heights by scanning the optical path difference of interferometer. The incorporates both geometric and spectral effects means an incoherent superposition ray bundles through interferometer spanning range wavelengths, incident angles, pupil plane coordinates. This sum is efficiently performed in frequency domain, followed Fourier transform to generate desired simulated...

Abstract For optical measurements of areal surface topography, the instrument transfer function (ITF) quantifies height response as a lateral spatial frequency content surface. The ITF is used widely for full-field instruments such Fizeau interferometers, confocal microscopes, interference and fringe projection systems more complete way to characterize resolving power than single number Abbe limit. This paper comprehensive review ITF, including standardized definitions, prediction using...

Nanostructuring of magnetic materials, on a scale comparable to the dimensions domain boundaries, is known have significant effect properties material. Here we demonstrate simple and versatile technique for preparation two- or three-dimensional highly ordered macroporous cobalt, iron, nickel, nickel iron alloy films containing close packed arrays spherical holes uniform size (an inverse opal structure). The were prepared by electrochemical deposition from aqueous solution within interstitial...

Lyotropic liquid crystalline phases formed at high concentrations of nonionic surfactants provide a versatile templating medium that can be used to produce nanostructured materials with regular arrays pores nanometer dimension and extended periodicity. In this work, we have technique prepare cobalt films on gold substrates by electrochemical deposition from acetate dissolved in the aqueous domains hexagonal lyotropic phase Brij Low angle X-ray transmission electron microscope studies show...

High-performance data processing algorithms for phase-shifting interferometry accommodate adjustment errors in the phase shift increment as well harmonic distortions interference signal. However, a widely overlooked error source is combination of these two imperfections. Phase tuning increase sensitivity estimation to second-order and higher harmonics present Fizeau signals. I derive an analytical formula evaluating more realistically, part identify characteristics optimal PSI algorithm....

Vertical resolution is the most widely quoted and frequently misunderstood performance specification for equipment that measures surface topography. Here I propose to use internationally standardized terms definitions measurement noise topography repeatability as more meaningful quantifiers performance. A specific example an interference microscope operating with a 100 Hz, 1 k × pixel camera, sinusoidal phase modulation convert intensity data height map. The found experimentally be 0.072 nm...

Abstract Coherence scanning interferometry is one of the most accurate surface measuring technologies, and it increasingly applied to challenging structures, such as additive manufactured parts transparent films, directly in environments that resemble production areas more than metrology labs. Environmental disturbances may further compromise measurement accuracy. Data acquisition strategies reduce noise coherence include averaging a sequence repeated topography measurements or increasing...

We propose a practical theoretical model of an interference microscope that includes the imaging properties optical systems with partially coherent illumination. show effects on measured topography spatially extended, monochromatic light source at low numerical apertures can be approximated in simplified assumes and linear, locally shift-invariant transfer function accounts for aberrations attenuation diffracted plane wave amplitudes increasing spatial frequencies. Simulation instrument...

Two major fields of study in optics—holography and interferometry—have developed at times independently other together. The two methods share the principle holistically recording as an intensity pattern magnitude phase distribution a light wave, but they can differ significantly how these recordings are formed interpreted. Here we review seven specific developments, ranging from data acquisition to fundamental imaging theory three dimensions, that illustrate synergistic developments...

The unambiguous distance measurement range in two-color interferometry is generally understood to be limited the equivalent or synthetic wavelength, which inversely proportional wavelength separation of two colors. Here it shown that one may extend well beyond this limit by using optical phase information determine synthetic-wavelength fringe order.

The phase ambiguity in conventional interferometers can be removed by using two laser diodes of different optical frequencies to generate a synthetic wavelength. However, the stability requirements for two-color interferometric gauge that must provide unambiguous determination fringe order over large distance severe. We derive upper limits on wavelength uncertainty and express them as function path difference between object reference beams, measurement errors, A simple stabilization...