Interferometers fringe

In a rotating interferometer, fringe shifts have been observed between light beams that propagate parallel and antiparallel with the direction of rotation [4]. This Sagnac effect requires an unconventional explanation. 

Fig. 2.9 Measured interferogram for a single telescope (green) and a two aperture interferometer (blue) for a point source. The interferometer fringe pattern is equivalent to the single telescope one multiplied by a cosine given by the baseline separation...

The absorption spectra of I2 (Gerstenkorn and Luc 1978,79) and of 130ie2 (Cariou and Luc 1980) have been measured in the visible region with a precision of 10 to lO"" cm l by Fourier transform spectroscopy and serve collectively to give excellent secondary wavenumber standards between 14000 and 24000 cm l. Interferometer fringes provide convenient interpolation between these calibration lines. 

FIGU RE 15.12 Interferometer fringes obtained by scanning the applied magnetic field, using a pair of -pulses, separated in time by 800 xs. Symbols experimental data line a fit of the central two fringes to the form A sin (A r) + C. 

Nonetheless, the syimnetric interferometer remains very useful, because there, the wavelengdis of fringes with even cliromatic order, N, strongly depend on the refractive index, n, of the central layer, whereas fringes with odd cliromatic order are almost insensitive to This lucky combhiation allows one to measure the thickness as well as the refractive index of a layer between the mica surfaces independently and siniultaneously [49]. 

Partial reflections at the iimer optical interfaces of the interferometer lead to so-called secondary and tertiary fringe patterns as can be seen from figure B 1.20.4. These additional FECO patterns become clearly visible if the reflectivity of the silver mirrors is reduced. Methods for analysis of such secondary and tertiary FECO patterns were developed to extract infonnation about the topography of non-unifonn substrates [54]. 

In the symmetric, three-layer interferometer, only even-order fringes are sensitive to refractive index and it is possible to obtain spectral infonnation of the confined film by comparison of the difierent intensities of odd-and even-order fringes. The absorption spectmm of tliin dye layers between mica was investigated by Muller and Machtle [M, M] using this method. 

The advent of lasers allowed optical interferometry to become a useful and accurate technique to determine surface motion in shocked materials. The two most commonly used interferometric systems are the VISAR (Barker and Hollenbach, 1972) and the Fabry-Perot velocity interferometer (Johnson and Burgess, 1968 Durand et al., 1977). Both systems produce interference fringe shifts which are proportional to the Doppler shift of the laser light reflected from the moving specimen surface. Both can accommodate a speci-... 

Figure 3.11. VISAR fringe record and the velocity profile at the calcite/lithium fluoride interface at about 18 GPa. The excellent time resolution of the interferometer allows an unambiguous determination of the rarefaction shock (d) in calcite (Grady, 1986).

Experimentally, this technique is very similar to the TDI technique described above. A laser beam is incident normally on a diffraction grating or a preferentially scratched mirror deposited on the surface to obtain the normally reflected beam and the diffracted beams as described above. Instead of recombining the two beams that are located symmetrically from the normally reflected beam, each individual beam at an angle d is monitored by a VISAR. Fringes Fg produced in the interferometers are proportional to a linear combination of both the longitudinal U(t) and shear components F(t) of the free surface velocity (Chhabildas et al., 1979), and are given by... 

Figure 1. Monochromatic two source interference (a) Young s points, (b) Michelson interferometer, (c) 3D representation of far-held interference fringes over all viewing angles showing both Michelson fringes at the poles and Young s fringes at the equator .

Young s Interference Experiment (1.5) A Young s interferometer basically consists of a stop with two holes ( array elements ), illuminated by a distant point source, and a screen which picks up the light at a sufficiently large distance behind the holes. The light patch produced by the stop is extended and shows a set of dark fringes which are oriented perpendicularly to the direction which connects the centers of the two openings. 

In order to observe fringes, the screen should be placed in the regime of Fraunhofer diffraction where F/B B/X. In practice, such an interferometer can be realized by placing the stop immediately in front of a collecting optics, e. g., a lens or a telescope, and by observing the fringes in its focal plane (F = fes). 

Basic Interferometer Properties (1.6-9) Although the relationship between element aperture diameter, baseline, and wavelength is quite simple, it is instructive to visualise the influence of each of these characteristics. To this end, we consider a Young s interferometer with element diameters D = Im, a baseline B = 10m at a wavelength A = 1/nm in the animations. The intensity profile across the fringe pattern on the detector (screen) is shown with linear and logarithmic intensity scales in the lower two panels. The blue line represents the intensity pattern produced without interference by a single element. 

We still need to consider the coherence properties of astronomical sources. The vast majority of sources in the optical spectral regime are thermal radiators. Here, the emission processes are uncorrelated at the atomic level, and the source can be assumed incoherent, i. e., J12 = A /tt T(ri) (r2 — ri), where ()(r) denotes the Dirac distribution. In short, the general source can be decomposed into a set of incoherent point sources, each of which produces a fringe pattern in the Young s interferometer, weighted by its intensity, and shifted to a position according to its position in the sky. Since the sources are incoherent. 

We are now ready to derive an expression for the intensity pattern observed with the Young s interferometer. The correlation term is replaced by the complex coherence factor transported to the interferometer from the source, and which contains the baseline B = xi — X2. Exactly this term quantifies the contrast of the interference fringes. Upon closer inspection it becomes apparent that the complex coherence factor contains the two-dimensional Fourier transform of the apparent source distribution I(1 ) taken at a spatial frequency s = B/A (with units line pairs per radian ). The notion that the fringe contrast in an interferometer is determined by the Fourier transform of the source intensity distribution is the essence of the theorem of van Cittert - Zemike. 

The external geometric differential delay (see below) of an off axis source is exactly balanced within a Fizeau interferometer, resulting in fringes with the same phase on top of each source in the field. The position of a source may differ from the position of zero OPD in a Michelson interferometer depending on how dissimilar entrance and exit pupils are. The fringe contrast of off-axis sources also depend on the temporal degree of coherence of the detected light. 

Obviously, the analysis of the correlation between the two fields emerging from the telescope and related devices makes necessary to avoid dissymmetry between the interferometric arms. Otherwise, it may result in confusion between a low correlation due to a low spatial coherence of the source and a degradation of the fringe contrast due to defects of the interferometer. The following paragraphs summarize the parameters to be controlled in order to get calibrated data. 

The fringes contrasts are subject to degradation resulting from dissymmetry in the interferometer. The optical fields to be mixed are characterized by a broadband spectrum so that differential dispersion may induce a variation of the differential phase over the spectrum. Detectors are sensitive to the superposition of the different spectral contributions. If differential dispersion shifts the fringes patterns for the different frequency, the global interferogramme is blurred and the contrast decreases. Fig. 5 shows corresponding experimental results. 

Figure 5. Evolution of the fringes contrast C as a function of the differential dispersion (a.u.) The maximum of this function corresponds to the cancellation of differential dispersion between the fibre arms of the interferometer.

Figure 7. Influence of the polarization preservation in a fibre interferometer. Right Standard fibre use leads to a complex pulse response associated with fringe degradations with polarization crosstalk. Left Using polarization preserving fibre, the two polarization modes give rise to contrasted fringes and can be separated using a polarizer.

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