CRONOGRAMA DE ACTIVIDADES A DESARROLLAR EN EL

The Earth’s atmosphere extends to several hundred kilometres above the Earth’s surface and is made up of four main temperature zones: troposphere, stratosphere, mesosphere and the thermosphere. The transition regions between these four temperature zones are known as the tropopause, stratopause and mesopause respectively.

The troposphere is the first layer beginning at ground level and extends to 7 km at the poles and 17 km at the equator, with variations due to local weather conditions (Sturman and Tapper, 1996). The troposphere experiences a large amount of vertical mixing due to solar heating of the Earth’s surface. It has a maximum air temperature near the surface of the Earth, which is on average 15◦_{C, decreasing to approximately}

-60◦_{C at its upper region (Andrews, 2004). Because the troposphere contains more}

than 80% of the atmospheric mass (Sturman and Tapper, 1996), the majority of optical turbulence found in the atmosphere occurs in this layer, with small amounts of optical turbulence extending to higher altitudes. The temperature variations that give rise to optical turbulence are considered to be significant only in the troposphere (Hardy, 1998). Typically optical turbulence is greatest near ground level and decreases exponentially with increasing altitude with the exception of peaks that occur due to wind shear (Hardy, 1998).

The tropopause marks the transition zone from the troposphere to the stratosphere. The thickness of the tropopause varies with latitude and season because of differing surface heats. It lies at an average altitude of approximately 11 km in mid-latitudes regions such as New Zealand (Sturman and Tapper, 1996). Seasonal variations can significantly change the height of the the tropopause. In New Zealand, the tropopause may lie 2 – 4 km higher during summer than during winter (Sturman and Tapper, 1996). At the tropopause there is often a peak in optical turbulence due to wind shear (Hardy, 1998). Above the tropopause there is a rapid decrease in turbulence. The effects of optical turbulence become insignificant at altitudes above 25 km (Hardy, 1998).

Figure 1.4 indicates the approximate temperature profile present in the atmosphere with increasing altitude, extending up to 25 km.

1.2.1 Describing Atmospheric Turbulence

When consideringoptical turbulence, one traditionally discusses the refractive index fluctu- ations experienced (Andrews, 2004). Many volumes have been written about the effects of atmospheric turbulence on the incident wavefront, such asRoddier(1981) andRoggemann et al. (1997).

1.2. A Turbulent Atmosphere 5

Figure 1.4: Vertical structure of the atmosphere.

ground temperature gradients (Jumper et al., 2007). As the potential temperature gradi- ents tend towards zero in a mixing region of the atmosphere then the optical turbulence also tends toward zero.

The refractive index structure function, DN(ρ), provides a useful function for char-

acterising optical turbulence and arises from the analysis of the optical transfer function (Roggemann et al., 1997). It is the square of the difference of two random processes and is defined as (Roggemann et al., 1997)

DN(ρ) = h|N(ρ0)−N(ρ0−ρ)|2i, (1-1)

where N(ρ0_{) is the refractive index of the atmosphere at a spatial position ρ}0_{. hi denotes}

the ensemble average.

Assuming Kolmogorov turbulence, the structure function takes on a 2/3 law depen- dence on ρ (Roddier, 1981),

DN(ρ) = CN2ρ2/3, (1-2)

whereC2

N is therefractive index structure constant, a measure of the turbulence strength.

In practice C2

N is not constant as it varies with geographical location, altitude and time.

Roddier(1981) suggests that turbulence is concentrated into thin layers with typical thicknesses of 100 – 200 m whereC2

N increases by more than one order of magnitude above

its background level. Below 4 km above sea level, the local terrain plays an important role, forcing air movement in particular directions (Sturman and Tapper, 1996). The behaviour of turbulence above 4 km is almost independent of location. Typically the turbulence is strongest near ground level, reaches a minimum around 6 – 9 km, then slightly increases

to a secondary maximum near the tropopause and decreases again in the stratosphere. As C2

N is highly dependent on altitude, it is better described as a function of altitude h.

C2

N(h) provides a measure of a turbulent layer’s contribution to the induced aberrations.

A useful parameter for characterising the resolution of an imaging system isFried’s parameter or theturbulence coherence length, r0 (Fried, 1966). r0 describes the telescope

diameter for which nearly diffraction-limited resolution can be obtained if there is no attempt to compensate for atmospheric turbulence. It is defined as (Tyson, 1991)

r0 = · 0.423k2sec(ζ) Z C_N2(h)dh ¸_−3/5 , (1-3)

wherek = 2π/λis the wavenumber for a given wavelengthλ andζ is the zenith angle. r0

is widely used to describe a variety of atmospheric phenomenon.

Another useful parameter for characterising the effects of atmospheric turbulence is the isoplanatic angle, θ0. This defines the maximum angular separation between two

object for which turbulence induced distortions are essentially identical (Kl¨uckers et al., 1998). θ0 is defined as (Parenti and Sasiela, 1994)

θ0 = · 2.91k2_sec8/3_(ζ) Z C2 N(h)h5/3dh ¸_−3/5 . (1-4)

Unlike r0,θ0 is dependent onh5/3 indicating that weak high altitude layers have a signif-

icant impact on θ0.

Atmospheric turbulence is in a constant state of motion. TheGreenwood frequency, fG, describes the rate at which the turbulence structure above a site changes with time.

It is defined as (Tyson and Frazier, 2004) fG = 0.255 · k2_secζ Z C2 N(h)V(h)5/3dh ¸_3/5 , (1-5)

where V(h) is the average wind velocity as a function of altitude h. fG determines how

quickly an AO system is required to respond to adequately compensate for the aberrations induced by atmospheric turbulence.

A closely related parameter to fG is the turbulence coherence time, τ0, which is

defined as (Kl¨uckers et al., 1998) τ0 = · 2.91k2_secζ Z C2 N(h)V(h)5/3dh ¸_−3/5 . (1-6)

1.3. Measuring Atmospheric Turbulence 7