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Moiré technique improves the measurement of atmospheric turbulence parameters

Light-beam deflections due to atmospheric turbulence are one order of magnitude more precise with the aid of moiré patterns.
20 February 2007, SPIE Newsroom. DOI: 10.1117/2.1200702.0569

Moiré is a useful means of measuring numerous physical quantities, such as refractive index gradients, optical device resolution, surface smoothness, stress, vibration parameters, and diffusion coefficients in liquids. Recently, we used a moiré technique to measure angle-of-arrival (AA) fluctuations in light propagating in the turbulent ground-level atmosphere on a telescope. This type of measurement is critical in evaluating astronomical imaging, aerial surveying, terrestrial geodesy, optical ranging, and wireless optical communication.

A moiré pattern is produced when two similar straight-line grids (or gratings) are overlaid and rotated relative to one other by a small angle (see Figure 1). In many applications, one of the superimposed gratings is the image of a physical grating. When image-forming light propagates in a perturbed medium, the image grating is distorted and the distortion is magnified by a moiré pattern. This moiré magnification can be expressed as1

where dm, d, and ? stand for the moiré fringe spacing, the pitch, and the angle of the gratings, respectively.

Figure 1. A moiré pattern, formed by superimposing two sets of parallel lines, one set rotated by angle ? with respect to the other.

Changes in ground surface temperature create turbulence in the atmosphere. Because AA fluctuations are a significant effect of atmospheric turbulence, they can be used to describe characteristic parameters of the phenomenon. AA measurements are a basic step in astronomical applications. Differential image motion monitoring systems2 and generalized seeing monitor systems3 are both based on these measurements, as well as the edge image waviness effect.4 The measurements can be carried out in different ways. In some conventional approaches, AA fluctuations are derived from the displacements of one or two image points on the image of a distant object in a telescope. Other techniques exploit the displacements of the image of an edge. Overall, however, the precision of these techniques is limited to the pixel size of the recording CCD.

We recently developed a technique, based on moiré fringe displacement, for measuring AA fluctuations that has two main advantages compared with other methods.5 First, the displacement of the image grating lines can be magnified by a factor of ~10, and the numerous lines of the image grating provide a large volume of data, which leads to very reliable results. Second, the acquisition of displacement data over a rather large area is very useful for evaluating the turbulence parameters that depend on displacement correlations.

Our technique is implemented as follows. A low-frequency grating is installed at a suitable distance from a telescope. An image of the grating forms at the focal plane of the telescope objective. Superimposing a physical grating of the same pitch as that of the image grating onto the latter generates the moiré pattern. Recording consecutive moiré patterns with a CCD camera connected to a computer and monitoring the traces of the moiré fringes in each pattern then yields AA fluctuations versus time across the grating image. A schematic diagram of the experimental setup is shown in Figure 2. Typical real-time moiré fringes obtained with this configuration are shown in Figure 3(a), with corresponding low-frequency illumination in Figure 3(b).

Figure 2. Schematic diagram of the experimental setup used for moiré atmospheric turbulence studies.

Figure 3. (a) Typical moiré pattern recorded using our experimental setup. (b) Corresponding low-frequency illumination.

Evaluating some atmospheric turbulence parameters requires correlating AA fluctuations at different scales. For this purpose, we can replace the probe grating in Figure 2 by the CCD and record consecutive frames of the carrier grating images. Rotating one of the frames by the desired angle and superimposing it on the other frames again generates moiré patterns. From the traces of the moiré fringes, we can derive the displacement correlations. Evaluations at different scales are performed simply by changing the angle between the superimposed images.6 Figure 4(a) shows a typical grating image recorded in a turbulent atmosphere. The typical moiré pattern formed by superimposing two images of the grating with a small angle difference is shown in Figure 4(b).

Figure 4. Typical image of a grating recorded in a turbulent atmosphere (a), and the moiré pattern produced by superimposing two images of the grating (b). To see animations, click on either panel (a) or (b).

We have used this technique to measure the modulation transfer functions of the ground-level atmosphere.7,8 At present, we are working on developing another moiré-based method to study turbulence parameters in the vertical direction. Our work shows that incorporating a moiré technique in the study of atmospheric turbulence parameters increases the precision of the measurements while reducing the distance required between target and observer. Our study also shows that the moiré technique can be used to investigate other turbulent media, such as gases and liquids.

Saifollah Rasouli
Physics Department, Institute for Advanced Studies in Basic Sciences (IASBS)
Zanjan, Iran

Saifollah Rasouli is a PhD student in the Physics Department of the IASBS and expects to graduate in 2007. His research interests are focused on the application of moiré techniques in vibrational and atmospheric turbulence studies. He obtained his BS in 1994 and his MS in 1997. From 1997 to 2003, he was a research assistant in an optics lab at the IASBS. He has worked on moiré technique, interferometry, optical metrology, fringe analysis, fiber index profile measurements, holography, and photosensitive materials. In addition, he has written five papers for SPIE conferences.

Mohammad Taghi Tavassoly
Physics Department, University of Tehran
Tehran, Iran

Mohammad Taghi Tavassoly is a professor of physics in the Physics department of the University of Tehran. His research interests include interferometry, Fresnel diffraction from phase objects, light scattering from rough surfaces, optical metrology, and moiré technique applications. He has been collaborating with the IASBS in Zanjan since 1995. In addition, he has written 15 papers for SPIE conferences.