AdOpt@TNG Tip-Tilt Performance Tool Page

The correction performances of an Adaptive Optics (AO) system depend upon a large number of parameters. The goodness of the correction is strictly related to the atmospheric behaviour, to the costructive characteristics of the AO module, to theparameters ruling the control loop of the system and to the brightnessof the guide star. In the case of pure tip-tilt compensation the main sources of error in thecorrection are:

  • The finite Signal to Noise ratio (SNR) in the reference wavefront tilt measured by the sensor.

  • The angular separation between the tilt guide star and the astronomical observed object. When the two object are separated by a finite angle the respective wavefronts are not equal because they pass through different portions of the amosphere, and the sensor experiences a tilt that is different from that of the target. This effect is called Tilt Anisoplanatism.

  • The finite time lag between the sensor measurement and the application of the correction. The AO system needs a certain amount of time to execute the whole control loop and since the atmosphere is varying constantly, the correction is applied to a tilt that is different from that sensed.

  • The presence of high order aberrations in the tilt reference wavefront. The guide star centroid position is not only affected by the tip-tilt but also by some aberrations having an azimuthal dependence in their shape such as the coma. This effect leads to a non perfect evaluation of the real tilt with a consequent estimation error. This effect is called Centroid Anisoplanatism.

These errors could be considered, at the first order, uncorrelated. Because of the non trivial complexity of the expressions describing the performances of a tip-tilt system we have thought to provide a tool to help the interested people to understand what the AdOpt@TNG tip-tilt module could perform in terms of Strehl Ratio (SR) and of Full Width at Half Maximum (FWHM).

Download the tool for IDL4
Download the tool for IDL5
Download the tool for IDL 5.2
Download the tool for IDL 5.4 and IDL 5.5

The tool has been written in IDL (for versions 4.x and 5.x) programming language, and to run it, it is necessary to have IDL software installed on the client machine.The steps to run the tool are the following:

  • Download the file ttperf.dat
  • Enter IDL
  • Restore the file: IDL > restore,"ttperf.dat"
  • Run the tool: IDL > ttperf

The formulas used to compute SR and FWHM have been taken from Olivier & Gavel (1994) and Parenti & Sasiela (1994).
The fixed parameter used in the tool are:

Diameter of the telescope 3.58 m
Efficiency of the whole system 0.52
APDs quantum efficiency 0.65
Dark counts per APD 10 e-/s
APD peak sensitivity wavelength 0.7 µm
APD wavelength bandpass 0.22 µm
Integration time 0.9 loop time
Wavefront sensor Field of View 2 arcsec
Atmospheric transmission 0.7
Wind velocity dispersion 10 m/s
Static aberration blur 0.1 arcsec

In the whole calculation the zenithal angle of the observed object has not been taken into account. The observations are supposed to be made close to the zenith or up to 30 degrees far: in this range the degradating effects of the increased airmass can be considered negligible. In Fig.1 it is shown the user interface of the AdOpt@TNG tip-tilt performances tool.

The tool user interface
Fig.1 The user interface of the AdOpt@TNG tip-tilt performances tool

The input field are four: the Seeing in arcsecs at 0.6µm, the Control LoopTime in seconds, the angular distance of the guide star from the astronomicalobject in arcsecs (Guide Star Off-Axis) and the Tilt Isoplanatic Angle at 0.6µm in arcsecs. The two last field allow for 300 arcsec as a maximum value.
The Observation Band field allows to choose between four IR bands (I, J, H and K) the wavelength at which the astronomical object is observed.It is possible to select simultaneously more than one band.
The Output field allows to select the output between SR and FWHM; only one output can be selected at a time.
The button Compute executes the calculation, plots the results in the graphic window below and refreshes the information window at its right. The information window displays some useful values related to the atmosphere and to the residual error of the corrected wavefront.
In particular are shown the Fried Parameter r0, the ratio between the telescope diameter and r0, the AO atmospheric correlation time t0, the tilt isoplanatic angle, the variance of the corrected wavefront tilt and the wavefront variance of the high order modes (uncorrected), both in squared radians. In the FWHM plot the seeing lines should appear in yellow.
IDL sometimes causes problems in color tables handling especially if applications using wide color tables are simultaneously running as, for example,Netscape. If the seeing lines appear white or of another color, exit from the tool and from IDL, close the resposnsible application and re-run the tool: then it should work.
The button Generate Postscript, if pressed, creates the postscript file version of the plot displayed in the graphic window. The name of the postscript file can be changed typing in the field Filename.
The title of the plot contains the values related to the seeing, the control loop time, the off-axis angle and the tilt isoplanatic angle.
The Quit button ends the tool and the IDL prompt is returned.

Particular considerations have to be done as far as the Tilt Isoplanatic Angle is concerned. The initial value of 35 arcsec is referred to the Roque de Los Muchachos atmospheric turbulence profile. Changing this value means to simulate another turbulence vertical distribution: for example, decreasingthe value is equal to put a high altitude layer containing a significant amount of turbulence and this is the typical situation responsible of smallisoplanatic angles.
Changes in the turbulence profile do not mean changesin the seeing value if the total amount of turbulence is preserved.At the opposite if the seeing value changes also the tilt isoplanatic angle changes. In the tool if the seeing is changed the value of the tilt isoplanatic angle does not vary because we left maximum freedom to the userto choose its value. If one needs to know the correct value for the tilt isoplanatic angle, for different seeing values at the Roque de Los Muchachossite, he can refer to the Fig.2 where the angle values are plotted for a seeing ranging from 0.3 to 0.8 arcsec (at 0.6m).

Tilt isoplanatic angle
Fig.2 The tilt isoplanatic angle vs. the seeing at 0.6m

Useful References

  • S.C Olivier and D.T. Gavel, "Tip-Tilt compensation for astronomical imaging", JOSA A, Vol. 11, pp. 368-378, 1994
  • R.R Parenti and R.J. Sasiela, "Laser-guide star system for astronomical application", JOSA A, Vol. 11, pp. 288-309, 1994

For any comments please contact Adriano Ghedina.

For any comments please contact Massimo Cecconi.