Josef Stricker

Analysis of 3-D phase objects by moire deflectometry

Quantitative analysis of 3-D phase objects by moire deflectometry is suggested. The method is based on measuring the deflection of rays from a collimated light beam due to gradients in the refractive index. To analyze asymmetric density fields it is necessary to obtain data of deflections at sufficient angular viewing angles about the test section and to mathematically invert the data. The moire deflectometry inversion procedure is shown to be simpler than interferometry inversion since no numerical differentiation of the measured data has to be performed. The method is demonstrated by mapping a temperature field generated above the top of two heated cylinders.

Schlieren systems with coherent illumination for quantitative measurements

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.

Diffraction effects and special advantages in electronic heterodyne moire deflectometry

Effects of diffraction on the performance of electronic heterodyne readout of moire fringes are investigated. The sensitivity, accuracy, and resolution of the system are calculated, and it is shown that these features are significantly improved compared with the conventional intensity moire readout technique. The sensitivity of the system can be tripled without changing the distance between gratings. The system was evaluated experimentally by measuring the refractive-index derivatives of a weak phase object consisting of a large KD*P crystal. Effects of nonlinear fringe modulation were studied both theoretically and experimentally. It is shown that in this case the electronic phase is not linearly related to the fringe shift, and calibration of the system is necessary.

Deactivation of CO2(010) and CO2(001) by hydrogen and deuterium

The probabilities of deactivating the bending and asymmetric stretching modes of CO2 by hydrogen and deuterium are calculated semiclassically over the temperature range of 300–2000 °K. It is assumed that the molecular interaction potential consists of a superposition of atomic pair repulsion forces. For the CO2(010) –H2 case, an inverse temperature dependence of probability was found over the 300–500 °K range; no inverse temperature dependence was found for CO2(010) –D2. The calculations indicate that it is possible to attribute the vibrational relaxation to energy transfer between the vibrations of CO2 and the rotation as well as translation of H2/D2. The different temperature dependences are essentially due to the difference between H2 and D2 in rotational energy matching with CO2 vibrations. The calculated temperature dependence of the deactivation probabilities is in good agreement with experimental data. However, the measured absolute values are lower than the calculated ones.

Performance of moire deflectometry with deferred electronic heterodyne readout

Effects of diffraction and nonlinear photographic emulsion characteristics on the performance of deferred electronic heterodyne moire deflectometry are investigated. The deferred deflectometry is used for measurements of nonsteady phase objects for which it is difficult to complete the analysis of the field in real time. The sensitivity, the accuracy, and the resolution of the system are calculated, and it is shown that they are weakly affected by diffraction and by nonlinear recording. The features of the system are significantly improved compared with those of the conventional deferred intensity moire technique and are comparable with those of the on-line heterodyne moire. The system was evaluated experimentally by deferred measurements of the refractive-index gradients of a weak phase object consisting of a large KD*P crystal. This has been done by photographing the phase object through a Ronchi grating and analyzing the transparency with the electronic heterodyne readout system. The results are compared with the measurements performed on the same phase object with on-line heterodyne moire deflectometry and with heterodyne holographic interferometry methods. Good agreement was observed. Some practical considerations for system improvement are discussed.

A Comparison of Electronic Heterodyne Moire Deflectometry and Electronic Heterodyne Holographic Interferometry for Flow Measurements

Electronic heterodyne moire deflectometry and electronic heterodyne holographic interferometry are compared as methods for the accurate measurement of refractive index and density change distributions of phase objects. Experimental results are presented to show that the two methods have comparable accuracy for measuring the first derivative of the interferometric fringe shift. The phase object for the measurements is a large crystal of KD P, whose refractive index distribution can be changed accurately and repeatably for the comparison. Although the refractive index change causes only about one interferometric fringe shift over the entire crystal, the derivative shows considerable detail for the comparison. As electronic phase measurement methods, both methods are very accurate and are intrinsically compatible with computer controlled readout and data processing. Heterodyne moire is relatively inexpensive and has high variable sensitivity. Heterodyne holographic interferometry is better developed, and can be used with poor quality optical access to the experiment.

Heterodyne schlieren system

A new heterodyne technique for the quantitative analysis of schlieren images is described. The technique is based on phase measurements of signals generated by a photodetector observing the variations in light intensity caused by a traveling grating of slits located at the knife-edge plane of a conventional schlieren system. The phase of the signal is proportional to the displacement of the slit image on the knife-edge plane as a result of the light deflection passing through a phase object. The displacement is proportional to the ray deflection angle and hence to the local gradient of the index of refraction. The technique, which is quantitatively precise and sensitive, is demonstrated by measurement of deflections caused by a lens with a focal length of f = 20 m. A displacement of 0.22 mm and a deflection of an angle of 5.2 x 10(-4) rad were detected.

Bidirectional quantitative color schlieren

A quantitative bidirectional color schlieren system is presented, analyzed, and demonstrated. This method is capable of measuring simultaneously two components of deflection angles in two perpendicular spatial directions. The system acts as two independent schlieren setups with perpendicular knife-edge orientations. The method employs a two-color filter. A bidirectional heterodyne schlieren method is presented as well. The system is demonstrated by measuring various phase objects and compared with conventional schlieren. The sensitivity of the measurements can be significantly improved over the existing bidirectional schlieren methods. Moreover, the system is conceptually simple and inexpensive.

Sources of error in heterodyne moire deflectometry

Alignment problems, and the accompanying errors, in heterodyne moire deflectometry are considered. A change in the x-directed offset between two states of a phase object causes a constant phase error, and it is noted that the relative x coordinate of the two photographic plates (the two states of the phase object) must be positioned typically within 1 micron to avoid a detectable offset. Possible solutions for assuring the relative alignment of the two deflectograms are considered, including a sandwich technique and a two-color double-exposure implementation.

Vibrational deactivation of carbon monoxide by hydrogen from 250 to 2000 °K

Vibrational energy transfer probabilities for CO(v=1)+H2→CO(v=0)+H2, CO(v=1)+H2(v=0) →CO(v=0)+H2(v=1), and CO(v=2)+H2(v=0) →CO(v=0) +H2(v=1) are calculated semiclassically, over the temperature range of 250–2000 °K. It is assumed that the molecular interaction potential consists of a superposition of atomic pair potentials represented by Morse function. The potential range was taken as α=2.5 A−1. The calculations indicate that it is possible to attribute the vibrational relaxation to energy transfer between the vibrations of CO and the vibration rotation as well as translation of H2. Calculated values of V–T and V–V probabilities are in good agreement with experimental data. It is also shown that the V–V probability for CO(v=2)+H2(v=0) →CO(v=0)+H2(v=1) is very large compared with the V–V probability for CO(v=1)+H2(v=0) →CO(v=0)+H2(v=1).