Survey of diffractive-refractive scintillation theory

Journolo/ Amosphmr und Turrvrmkd Physic s, Vol. 51, No. 9110, pp 739-742. 1989 Prmted III Great Britain.

0021-9169~89 $3 CO+ .oO Pergamon Press plc

Survey of diffractive-refractive scintillation theory H. 0. VATS Physical Research Laboratory, Ahmedabad 380 009, India (Received in jinul,fr,rm 30 April 1989) article describes the basic features of diffractive-refractive scintillation theory. The theory deals with both diffractive scattering caused by irregularities whose scale is less than the Fresnel scale and refractive scattering caused by irregularities whose scale is greater than the Fresnel scale. This theory can be applied to almost all scintillation phenomena in nature. Some of these applications are briefly discussed. Abstract-This

1. INTRODUCTION

scattering

For five decades Professor Henry G. Booker remained interested in the phenomenon of scattering of electromagnetic waves in a medium containing refractive index fluctuations. During this period, he looked at this interesting phenomenon from several different angles. The intermittent existence of a strong scattering phenomenon in the F-region of the ionosphere came to light with the development of worldwide radio communications in the HF band in the 1930s. The phenomenon was frequently seen with the aid of fixed frequency HF radars known as ionosondes. It showed up as a marked spreading of the echoes from the F-region of the ionosphere, generally known as spread-F. The first paper on spread-F appeared in late 1930s (BOOKER and WELLS, 1938). Fading of high frequency waves reflected from the ionosphere has been observed since the introduction of long distance HF radio communication about 60 years ago. With the object of producing a theory for the fading of waves reflected from the ionosphere, BOOKER et al. (1950) introduced the concept of a random diffracting screen. This approach was dealt with in greater detail by RATCLIFFE (1956). This led to the development of scintillation theory in several situations : e.g. satellite scintillation, radio and optical star scintillation, interplanetary scintillation and recently interstellar scintillation and perhaps intergalactic scintillation. For a particular scintillation phenomenon a very important scale, known as Fresnel scale F, can be defined as F = (iZ/27c)“*,

(1)

where i and Z are the wavelength and the distance between the irregular medium and observer. Scattering by irregularities whose scale is of the order of F or less, known as diffractive scattering, involves

through

small angles of about J./(2nF).

(2)

Refractive scattering is scattering by irregularities whose scale is appreciably greater than F (BOOKER and MAJIDIAHI, 1981; VATS et al., 1981). This case involves smaller deviations through angles of the order of A/ (27&J),

(3)

where L,, is the outer scale of the spectrum of fluctuations. Here we shall describe the approach which takes care of both diffractive and refractive scattering in the medium. The medium containing refractive index fluctuations may be either (i) a thin phase changing screen, a situation where the electromagnetic waves interact with irregularities in the medium in a very small portion along the line of sight, or (ii) a fluctuating medium that extends from the transmitter to the receiver all along the line of sight. BOOKERet al. (1985) compare calculations for a continuously extended fluctuating medium with those for a centrally located phasescreen having a spectrum of irregularities of the same type, that is, with the same mean square fluctuation of phase, the same outer scale L, and the same spectra1 index p. It was found that, both for the scintillation index and for the normalized intensity correlation function in the reception plane, the results are approximately the same both for a fluctuating medium that extended continuously from the transmitter to the receiver and for a centrally located phasescreen having the same mean square fluctuation of phase. Keeping this in mind, we will confine ourselves here to the thin phase changing screen, which can really be a screen or an equivalent of the extended medium in the manner described above. Some applications of the diffractive-refractive scattering approach will also be described. 739

740

H. 0. 2. BASIC APPROACH

As outlined by BOOKERand MAJIDIAHI (1981), for a given wavelength, it is often convenient to specify the distance between the screen and the reception plane by specifying the value of F. Using the selected autocorrelation function p(x) (it may be noted that p(x) will have different forms for the types of irregularity spectrum present in the medium under consideration), we can formulate two functions, both depending on x and on the angular spatial frequency k. These functions are f(x,k)

= 2p(x)-p(x-kf*)-p(x+kF*)

(4)

and

gkk) = expI- (A~)‘~f(O,k)-f(x,k)~l -w

I-@??f(Rk)l.

(5)

From these functions it is possible to derive the experimental parameters of the scintillation phenomenon in the reception plane. These parameters are the spatial correlation function C(x) (VATS and SHAH, 1989) the fractional fluctuation of intensity I(k) and the scintillation index S,, namely

I(k) = 4

g(x, k) cos (kx) dx

(7)

VATS

ditions under investigation (VATS, 1981), the outer scale irregularities play a prominent role in creating the intensity scintillation in the reception plane. The observed fine structure of the order of 10 m on the ground is mainly due to structures in the ionosphere with scales around 50 km (BOOKER and MAJIDIAHI, 1981). Yet another application of this approach to the ionospheric scintillation observations of KUMAGAI and OGAWA (1986) in mid-latitude brings out important information about the irregularities. These observations, shown by the continuous line in Fig. 1, indicate that the minor radius of the pattern in the reception plane reduces from 280 m to 130 m as the scintillation index increases. These results are in general agreement with UMEKI et al. (1977), VATS (1981), and FRANK and LIU (1983). These authors have put this argument in a different way, stating that the autocorrelation time or coherence time decreases as the scintillation increases. The transverse correlation distance, which is directly proportional to the minor radius, is equal to the coherence time multiplied by the drift velocity of the pattern on the ground. All these are valid facts about the observed pattern, but should not be confused with the irregularities responsible for the pattern. For a typical ionosphere the irregularity spectrum is a power law with exponent p - 3. BOOKER and MAJIDIAHI (1981) showed that, for this spectrum of irregularities, (A4)” - IO3 radians* produces a scintillation index approximately equal to 1, and (A4)’ - 10-I radians’ produces a weak scintillation index approximately equal to 0.1. Using these parameters, we have calculated the irregu-

and

s,

=&

z

I(k) dk. w

With this mathematical formulation, it is possible to carry out several investigations relating to scintillation phenomena, e.g. the effect of the irregularity spectrum and strength on the spatial correlation and scintillation index. It is also possible to deduce the relationship between the observed pattern scale and the irregularity scale. Some of these aspects will be used in the next sections.

3. LARGESCALE IRREGULARITIES DURING SCINTILLATION

INTENSE

EVENTS

300

2 z!

MINOR RADIUS

z F 3 8= E 200wz + z : 2

-

/H

loor’/ 0.2

0.4

0.6

SCINTILLATION

VATS et al. (1981) used this approach for a quantitative explanation of the intense equatorial scintillation at 40, 140 and 360 MHz. From these investigations it was found that, for the ionospheric con-

0.0

I.0

INDEX

Fig. I. Observed minor radius of the pattern in the reception plane (+@-), left scale in meters, and calculated minor radius of the irregularity in the medium ( -). right scale in kilometers, versus the scintillation index.

Survey of diffractiveerefractive

larity scale in the medium and the results are shown by the dotted curve in Fig. 1. The ordinate on the left is for the pattern in the reception plane (continuous curve) in meters, and that on the right is for the irregularity in the medium (dotted curve) in kilometers. From this it is clear that for a weak scintillation, diffractive scattering by irregularities & Fresnel scale dominate, whereas for a strong scintillation, refractive scattering by irregularities > Fresnel scale dominate. In almost all cases of ionospheric scintillation we know that the scintillation is weak at the beginning of the event; scintillation activity then gradually increases and becomes strong. After some time (say, from a few minutes to one hour), the activity starts decreasing and finally vanishes. From this it is clear that there is weak scintillation at the beginning and at the end of an event. This scintillation will be essentially due to diffractive scattering. On the other hand, in the middle of a scintillation event, when scintillation is strong, there will be refractive scattering due to the irregularities greater than the Fresnel scale.

4. HF FADING AND SPREAD-F BOOKER and TAO (1987) and BOOKER et al. (1987) applied the approach to HF fading in two cases, namely, (i) the fading of HF waves returned from the F-region for vertical incidence, the receiver being near the transmitter, and (ii) fading in long distance HF ionospheric communications for oblique incidence. For vertical incidence, the calculated quasi-periods of twinkling range from about one hour down to about a couple of minutes. while the calculated quasi-periods of fading range from about a couple of minutes down to about a tenth of a second. To apply this approach to ionospheric long distance communications in the HF band during a particular interval of time for particular locations of transmitter and receiver, it is necessary to make reasonable assumptions concerning the profiles of ionization density and the outer scale for each hop of the path. Then calculations can be made for the scintillation parameters, c.g. the quasi-periods of fading and twinkling. Some typical results for penetration frequencies of 4 and 12 MHz (representing night-time and day-time conditions respectively) are presented by BOOKERet al. (1987). Yet another application of this theory is to explain frequency-spread-F in the ionograms (BOOKER et al., 1986). These authors were able to identify the main features to be taken into account, and brought out the role played by HF scintillation for vertical incidence upon the F-region. For well-developed frequencyspread, the high-frequency cdgc of the blur does not

741

scintillation theory

give a good estimate of the maxima in the fluctuating ionization density existing at the peak of the region. The high-frequency edge of the blur is the frequency above which multiple refractive scattering alone can no longer return any significant energy to the ionosonde.

5. LASER SCINTILLATION

IN THE ATMOSPHERE

This approach was also applied to laser scintillation by BOOKER and VATS (1985). These investigations were carried out for laser propagation between two points close to ground level at an equal height of 2 m above the surface of the earth. The distance between the transmitter and receiver was taken to be from 1 to 8 km. The relation between the rms fluctuation of refractive index at optical frequencies and the rms fluctuation of temperature in ‘C was taken to be @#

I’* = 1.4 x 10mh(AT)’ I’*.

(9)

The temperature was assumed to possess a rms fluctuation from 0.03 to 3°C. The refractive index fluctuations in the atmosphere are assumed to have a Kolmogoroff spectrum (USCINSKI, 1977) for which

where K is the usual Bessel function. The calculation showed that, except for short range and small temperature fluctuations, refractive scattering by largescale irregularities dominates diffractive scattering by small-scale irregularities. For sufficiently small temperature fluctuations, the intensity spectra show a maximum at approximately the Fresnel scale. In these circumstances the important phenomenon is diffractive scattering by irregularities whose scale is of the order of the Fresnel scale and less. The key scintillation parameters for a helium-neon (He-NC) laser at 0.63 m wavelength were calculated, and are shown in Table 1.

6. CONCLUSIONS

Professor Henry G. Booker made several pioneering contributions to radio physics. One of these is diffractive-refractive scintillation theory. Although some applications of this theory are briefly outlined here, many more applications are possible. The unique feature of this theory lies in its simplicity and applicability to almost all scintillation phenomena in nature.

742 Table 1. Scintillation

H. 0. parameters

VATS

for transmission at a wavelength of 6.33 x lo-’ m between terminals an atmosphere with a rms temperature fluctuation of 1°C Range,

Outer scale, m Fresnel scale, m rms fluctuation of phase, rad Intensity correlation scale, m Twinkling scale, m rms fluctuation in arrival angle, rad Fractional correlation bandwidth Actual correlation bandwidth, Hz Fading rate for 1 m s- I cross wind, Hz Twinkling rate for 1 m s ’ cross wind, Hz

2.0 7.1 x 1om3 8.8 x 10’ 3.5 x 1o-4 0.14 2.9x 1O-4 2.4x lo-’ 1.2 x lOI 9.1 x lo2 2.2

km

2

3

2.0 1.0x lo-* 1.2 x lo2 2.3 x lo-” 0.44 4.4 x 1om4 5.3 x 1om4 2.5 x 10” 1.4x IO3 0.73

1.8 1.4x 1om2 1.7x IO3 1.5 x 1om4 1.4 6.8 x 10m4 1.1 x 1omm4 5.2 x 10’” 2.1 x 10) 0.23

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4 1.4 2.0 x lo-* 2.1 x lo3 8.7 x 1O-5 4.6 1.2 x 10-j 1.9 x 1om5 8.9 x lo9 3.7 x lo2 0.069