## Abstract

Measurements of the space–time correlation function of images at the focus of a large telescope have been made. They indicate that the image boiling has a directional component that is parallel to the motion of the turbulence in the pupil plane.

© 1981 Optical Society of America

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### Equations (4)

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(1)
$$C({\mathbf{x}}_{1},{\mathbf{x}}_{2},\tau )\equiv \frac{\u3008\mathrm{\Delta}I({\mathbf{x}}_{1},t)\mathrm{\Delta}I({\mathbf{x}}_{2},t+\tau )\u3009}{\u3008I({\mathbf{x}}_{1},t)\u3009\hspace{0.17em}\u3008I({\mathbf{x}}_{2},t)\u3009},$$
(2)
$$\mathrm{\Delta}I(\mathbf{x},t)=I(\mathbf{x},t)-\u3008I(\mathbf{x},t)\u3009,$$
(3)
$$C(\mathrm{\Delta}\mathbf{x},\tau )=\frac{\u3008\mathrm{\Delta}I(\mathbf{x},t)\mathrm{\Delta}I(\mathbf{x}+\mathrm{\Delta}\mathbf{x},t+\tau )\u3009}{{\u3008I(\mathbf{x},t)\u3009}^{2}}.$$
(4)
$$C(\mathrm{\Delta}x,\mathrm{\Delta}y,\tau )\propto {\left|{\int}_{-\infty}^{\infty}\int A(\xi ,\eta )A*(\xi +u\tau ,\eta )\times \text{exp}\left[\frac{-2\pi i}{\mathrm{\lambda}f}(\xi \mathrm{\Delta}x+\eta \mathrm{\Delta}y)\right]\text{d}\xi \text{d}\eta \right|}^{2},$$