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A diffractive optical element is described that can be used to implement a very simple self-aligning electronic speckle-pattern interferometer and holographic interferometer that requires only a laser source and a camera in the optical setup.
A scanning probe consisting of a source and receive fiber pair is used to measure the phase difference between wave fronts scattered from the front and rear surfaces of an aspheric optic. This system can be thought of as a classical interferometer with an aperture synthesized from the data collected along the path of the probe. If the form of either surface is known, the other can be deduced. In contrast with classical interferometers, the method does not need test or null plates and has the potential to be integrated into the manufacturing process.
Using a Michelson white-light interferometer, we measure the group-delay dispersion and third-order dispersion coefficients, d2(phi)/d(omega)2 and d3(phi)/d(omega)3, of chromium-doped forsterite (Cr:Mg2SiO4) over wavelengths of 1050-1600 nm for light polarized along both the c and b crystal axes. In this interval, the second-order dispersion for the c axis ranges from 35 fs2/mm to -14 fs2/mm, and the third-order dispersion ranges from 36 fs3/mm to 142 fs3/mm. For the b axis the second-order dispersion ranges from 35 fs2/mm to -15 fs2/mm and the third-order from 73 fs3/mm to 185 fs3/mm. Our data are relevant for the development of optimized dispersion compensation tools for Cr:Mg2SiO4 femtosecond lasers. These measurements help to clarify previously published results and show some significant discrepancies that existed, especially in the third-order dispersion. Our results should furthermore be useful to build up an analytic expression for the index of refraction of chromium forsterite.
Inspection of the refractive-index distribution in fused silica is very sensitive to thermally induced measurement errors. A model is derived for the estimation and interpretation of thermal errors applicable to interferometric homogeneity investigations. The outlines of the model are supported by experimental investigations and numerical calculations. The results state a mandatory temperature stability of deltaT = 0.02 K for a required reproducibility of sigma(delta(n)) < or = 1 x 10(-7) and a lower sensitivity of higher-order Zernike terms. Requirements of the interferometer environment include spatial and temporal stability. Only a small part of the frequency spectrum of temporal instabilities contributes significantly to the measurement error and is therefore critical for the system. Experimental values are given for different environmental conditions.
Testing for flatness of an optical parallel plate in a Fizeau interferometer suffers from problems caused by multiple-beam interference noise. Each internal-reflection component can be separated from the signal by its modulation frequency in a wavelength-scanned interferometer; however, the frequency depends on the thickness and the refractive-index dispersion of the test plate and on the nonlinearity of the scanning source. With a new 19-sample wavelength-scanning algorithm we demonstrate the elimination of the reflection noise, the effect of the dispersion up to the second order of the reflectance of the test plate, and as the nonlinearity of the source. The algorithm permits large tolerance in the air-gap distance, thus making it somewhat independent of the thickness of the test plate. The minimum residual reflection noise with this algorithm for testing a glass plate is approximately lambda/600. Experimental results show that the front surface of the test plate was measured within 1 nm rms of its true shape over a 230-mm-diameter aperture.
There is increasing demand for in situ shape measurements performed on ultraprecision processing machines. One major source of error during interferometric measurements performed on machines is fringe displacement due to external disturbances. We have developed an interferometer equipped with an electro-optic phase modulator that measures the phase of interference fringes before they are displaced by air turbulence. The frequency characteristics of air turbulence induced by a heat source are derived from successive measurements of a test surface. Experimental results show that the phase of the interference fringes can be accurately measured in the presence of air turbulence when the intensity of the fringes is sampled at a speed of several hundred hertz.
Deformation study of curved engineering and technical surfaces, such as pipes and pressure vessels, has gained much importance in the recent past. Speckle interferometric techniques and their electronic and digital analogs, which are whole field techniques, have been effectively applied for practical nondestructive testing applications over the years. However, little work has been done that discusses the speckle fringe formation with a fruitful theoretical formulation to study deformation analysis of curved surfaces. We propose an extended theory for speckle fringe formation on curved surfaces, which can be applied to the study of curved engineering and technical specimens under various loading conditions such as in-plane, out-of-plane, and out-of-plane shear configurations. Simulated contours are generated by use of finite element models with similar loading conditions, and the data are analyzed and compared with the obtained experimental results.
It has long been known that image plane holography with low-coherence illumination achieves optical sectioning of a volume object. A method is analyzed that is similar to image plane holography, but the interferometric arrangement utilizes the interference between two object-bearing beams instead of the basic object and reference beams.
Multiple-wave achromatic interferometric techniques are used to measure, with high accuracy and high transverse resolution, wave fronts of polychromatic light sources. The wave fronts to be measured are replicated by a diffraction grating into several copies interfering together, leading to an interference pattern. A CCD detector located in the vicinity of the grating records this interference pattern. Some of these wave-front sensors are able to resolve wave-front spatial frequencies 3 to 4 times higher than a conventional Shack-Hartmann technique using an equivalent CCD detector. Its dynamic is also much higher, 2 to 3 orders of magnitude.
A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-microm synthetic wavelength.
Photonic crystal fibers (PCFs) are microstructured waveguides that are used in metrology, nonlinear optics, and coherent tomography. PCF studies are focused mainly on the improvement of dispersion properties and wide spectral single-mode operating domains. Consequently, in the astronomical context this kind of fiber is a good candidate for use in the design of a fiber-linked version of a stellar interferometer for aperture synthesis. We discuss the potential of these fibers to take advantage of wide spectral single-mode operation. We propose an experimental setup that acts as a two-beam interferometer that uses PCFs to measure fringe contrast at four wavelengths (670, 980, 1328, and 1543 nm), which correspond to the R, I, J, and H astronomical bands, respectively, with the same couple of PCFs. For this purpose we use, for the first time to our knowledge, a piezoelectric PCF optical path modulator.
Weighted averaging of a sequence of phase-shifted interference patterns yields a fringe-free intensity image that can be useful for machine vision, lateral metrology, defect detection, and other supplementary tasks in a surface-profiling interferometer. Coefficients for effective fringe-removal algorithms follow from a Fourier analysis of phase-shifting errors. Theoretical and experimental examples illustrate the substantially improved performance of a well-designed weighted average over a simple linear sum of data frames.
Utilizing a new average atom code, we calculate the index of refraction in C, Al, Ti, and Pd plasmas and show many conditions over which the bound-electron contribution dominates the free electrons as we explore photon energies from the optical to 100 eV (12 nm) soft x rays. For decades measurement of the electron density in plasmas by interferometers has relied on the approximation that the index of refraction in a plasma is due solely to the free electrons and therefore is less than 1. Recent measurements of Al plasmas using x-ray laser interferometers observed fringes bending in the opposite direction than expected due to the bound-electron contribution causing the index of refraction to be larger than 1. During the next decade x-ray free-electron lasers and other sources will be available to probe a wider variety of plasmas at higher densities and shorter wavelengths, so understanding the index of refraction in plasmas is essential.
Cavity-mode wavelengths in air are determined by measuring a laser's frequency while it is locked to the mode in vacuum during a calibration step and subsequently correcting the mode wavelength for atmospheric pressure compression, temperature difference, and material aging. Using a Zerodur ring cavity, we demonstrate a repeatability of +/- 2 x 10(-8) (3sigma), with the wavelength accuracy limited to +/- 4 x 10(-8) by knowledge of the absolute helium gas temperature during the pressure calibration. Mirror cleaning perturbed the mode frequency by less than deltav/v approximately 3 x 10(-9), limited by temperature correction residuals.
Real-time digital holography is used to study the diffusion process in transparent liquid solutions. Holograms of an object diffusively reflecting through an experimental cell containing diffusing solutions are recorded at different time instances. The recording medium is a CCD chip. The holographic interference of the object at two time instances is carried out numerically in a PC and is used to determine the diffusion coefficient. Holographic interferometric fringes can be displayed on a PC monitor in near real time. The software developed for this method determines the diffusion coefficients automatically. The calculated diffusion coefficients obtained with this method matched well with literature values.
We propose and demonstrate a new technique for measuring the temporal variations of the surface slope of an object. This real-time shearometric arrangement takes advantage of the dynamic properties of holograms in photorefractive crystals. The accuracy of the measurements should make this technique suitable for real-time structural intensity determinations.
Time-averaged in-line digital holography is applied for vibration analysis. In particular, by use of a double-exposure approach, simultaneous determination of vibration mode shape and mean static state deformation during a vibration cycle are obtained. The subtraction of two numerically reconstructed digital holograms recorded at the same resonant frequency but with a small difference in amplitude shows the mixing of Bessel-type time-averaged fringes owing to vibration and of the double-exposure fringes owing to differences in the mean deformation of the object. It is shown that separation of these fringe patterns can be readily accomplished numerically. An experimental demonstration of this effect by use of in-line digital holography for relatively small membranes is demonstrated.
A digital speckle pattern interferometer based on a complementary metal-oxide semiconductor (CMOS) camera is described. The temporal evolution of dynamic deformation is measured using interframe phase stepping. The flexibility of the CMOS detector is used to identify regions of interest with full-field time-averaged measurements and then to interrogate those regions with time-resolved measurements sampled at up to 70 kHz. A numerical and analytical investigation shows that the maximum surface velocity that can be reliably measured with interframe phase stepping corresponds to +/-0.3 times the surface velocity at which the interferogram is sampled at the Nyquist limit.