The Atmospheric Dispersion Corrector Software for the VST

The Atmospheric Dispersion Corrector Software for the VST

M. Brescia, P. Schipani, G. Spirito, F. Cortecchia, G. Marra, F. Perrotta INAF – Capodimonte Astronomical Observatory

Via Moiariello 16, I-80131 Napoli, Italy http://www.na.astro.it

ABSTRACT

The effects of atmospheric differential refraction on astrophysical measurements are well known. In particular, as a ray of light passes through the atmosphere, its direction is altered by the effects of atmospheric refraction. The amount of this effect depends basically on the variation of the refractive index along the path of the ray. The real accuracy needed in the atmosphere model and in the calculation of the correction to be applied is of course, considerably worse, especially at large zenith angles. On the VLT Survey Telescope (VST) the use of an Atmospheric Dispersion Corrector (ADC) is foreseen at a wide zenith distance range. This paper describes the software design and implementation aspects regarding the analytical correction law discovered to correct the refraction effect during observations with VST.

Keywords: adapter/rotator, Atmospheric Dispersion Corrector, control software, telescope 1. INTRODUCTION

The VST (VLT Survey Telescope) is a 2.61 m alt-az f/5.5 modified Ritchey-Chretien telescope. It is provided by one focus station in Cassegrain optical configuration, where there will be installed the 16Kx16K OmegaCAM imaging camera, committed to an international consortium in collaboration with ESO (European Southern Observatory). High image quality performance is guaranteed by an active control of the optics, acting on both primary and secondary mirror. Due to its mounting configuration and active optical control requirements, a careful attention has been paid to the Adapter/Rotator (AD/ROT) combined system. It includes facilities for the fine telescope positioning (autoguiding system), for the optical quality optimization (sensing and ADC). In the next sections a description of the ADC software control design is reported.

2. ADC OPTICAL ARCHITECTURE

The VST adapter is provided with two different correctors with refracting and dispersing elements. One corrector (here in after the "Two-Lens" corrector) is composed by two lenses and operates from U to I bands (0.320 ÷1.014 μm) at 0°

zenith angle; the other (here in after the "ADC" - Atmospheric Dispersion Corrector) is composed by two rotating double prisms and one different lens to observe from B to I bands (0.365 ÷ 1.014 μm) at different angles until 52° from zenith (Fig. 2-1).

Fig. 2-1 The two optical configurations of the VST: 2-lens corrector (left) and ADC ray tracing layout (right)

The overall assembly has been designed as an integrated system, using FEA (Finite Element Analysis) to evaluate the effects of gravitational deformations on the image quality degradation. The main project guide-line has been to consider telescope and camera as a unique system. The optical design of the VST correctors has been optimized together with that of the mirrors and of the detector dewar window of OmegaCAM camera. The telescope covers a very large field of view (1.47° diagonal), with a high resolution (0.21"/pixel) and a high image quality (80% of EE enclosed in two pixels).

The optics design has been optimized also in order to have two compacts interchangeable correcting systems.

3. ADC THEORETICAL ASPECTS

The light coming from celestial objects is continuously refracted by the effect of the refraction index variation of atmosphere which is present between object and observer. This variation is mainly caused by changes of air temperature, pressure and water vapour concentration with altitude. Furthermore, the refraction quantity is strongly depending on observation wavelength and the resulting effect is not only a deflection of light beam from its original direction, but also a spectral enlargement of the beam, known as dispersion. For an object with zenith angle z and at a specific wavelength range, the angular atmospheric dispersion δ is proportional to tan(z), [4]. For a telescope with focal length F, this dispersion produces a linear dispersion Fδ at focus, that can be minimized by an optical system composed by thin prisms positioned at a distance D from telescope focus. The use of an Atmospheric Dispersion Corrector (ADC) determines an angular deviation Fδ/D in the opposite direction of the atmosphere. Obviously the image plane shift, caused by the introduction of prisms in the optical path, must be minimized. For this purpose, the prisms should be machined in such a way that the combination of their refraction index produces a minimizing effect of the image plane shift, at the whole wavelength range chosen. Of course the angular deviation depends also from the zenith angle, and, in case of its variation during exposures, the ADC must be designed in such a way that the distance between prisms can be changed (linear ADC), causing a change in the distance between prisms and focus, or by means of a counter-rotation between the two prisms (angular ADC), maintaining them always aligned with their dispersion directions parallel and opposite to the atmospheric dispersion. In this last case a particular attention must be paid to the prism rotation direction, because, in case of wrong rotation versus, the dispersion introduced by prisms follows the sine component of rotation angle, instead of its cosine one, giving an additional effect to the atmospheric dispersion already present. With these considerations, by denoting with α1 and α2 the respective prism angles, and with n1 and n2 the respective prism glass refraction indexes at a fixed mean wavelength λ, it is obtained:

( ( ) ) ( ^{( )} )

( ) ( )

1 1 2 2

1 1 2 2

1 1 0

glass glass

telescope

glass glass

n n

F n n

D

α λ α λ

δ α λ α λ

⎧ − + − = ⎫

⎪ ⎪

⎨ ⎬

= Δ − Δ

⎪ ⎪

⎩ ⎭

(1.1)

where

Δ n

^{glass i_}

is the refraction index variation of i^th glass type, expressed in radiants (rad).

In the following all formulas implemented in the software code is described, together with the whole control strategy adopted to correct light beam from atmospheric dispersion without introducing an image plane shift.

4. THE VST ADC DESIGN

In the VST the angular ADC consists of two couples of prisms (in the following specified simply as two prisms), with a separation between them fixed at 10 millimeters (mm). For each couple, the two prisms are based upon, respectively, Schott PSK3 and LLF1 glass types, and designed in such a way that their introduction in the light path does not cause any shift of the spot on image focal plane (zero-shift), or at least a negligible shift in the case of wavelength bands more sensible to the atmosphere refraction effect, [1], [3]. The correction mechanism is based on the counter-rotation of the two prisms by an angle around the optical axis. This rotation angle depends on run-time values of barometric pressure, air temperature, telescope zenith angle and wavelength. The last one is determined by the particular filter type currently used during an exposure. The angle rotation is done for zenith angle values included in a range where a correction with ADC is feasible. This range comes from optical requirements and is fixed as [0, 52] of zenith angle degree.

The filters foreseen for VST observations are listed below, reporting the related wavelength application range and its central value. The values are expressed in nanometers (nm).

• Filter B band 390.0 : 440 : 490.0

• Filter V band 500.0 : 550 : 600.0

• Filter g’ band 408.6 : 477 : 546.3

• Filter r’ band 554.6 : 623 : 691.7

• Filter i’ band 695.0 : 763 : 831.0

• Filter z’ band 850.0 : 910 : 970.0

The VST ADC control SW (SoftWare) package is basically composed by a module, responsible of all calculations referred to atmospheric dispersion and prism angle rotation, sending activation command to all specific HW (HardWare) devices, forming the VST ADC opto-mechanical system, running on a real-time VME-based environment.

There are also provided some engineering GUI (Graphical User Interface) panels able to configure and manage all basic ADC control specifications. The control commands useful to coordinate ADC operations, can be sent by means of the following ways:

• Operational state changes can be achieved through specific GUI widgets.

• Basic setup of corrector type, in/out commands for 2-lens or ADC on the light path, can be done through standard ADC setup keywords.

• Complete control and configuration of all ADC functionalities can be performed by using specific engineering GUI panels (see description below).

Main VST specific functionalities implemented in the ADC module are referred to:

• command to choose the optical configuration to be positioned in the light path (2-lens or ADC)

• Calculation of rotation angle for ADC prisms, given: air pressure, temperature, wavelength and zenith angle

• Command to move (rotate) prisms

• Commands to enable/disable the ADC tracking, with periodical correction (rotation) of prism angle based on coming information from current telescope AZ/ALT positions during exposures

• command to send back actual prism angle and wavelength information to main axes tracking process 4.1. ATMOSPHERIC DISPERSION CALCULATION

Concerning the atmospheric angular dispersion δ, the atmospheric model implemented has been derived from the same one already designed in the VLT case [4]. The reason why the same model has been used is because VST will be located at the same VLT site, having so the same atmospheric features. Let consider the air refraction R(λ, P, T) constant at a fixed couple of parameters P (barometric pressure) and T (air temperature) and at a given wavelength λ, expressed in micron (μm):

760 mmHg 15 °C P T

=

=

( )

⁶

2 2

29498.1 255.4

,760,15 64.328 10

1 1

146 41

R λ

λ λ

= + + ⋅

−

⎛ ⎞ ⎛ ⎞

− ⎜ ⎝ ⎟ ⎠ − ⎜ ⎝ ⎟ ⎠

(1.2)

By scaling the 1.2 to the case of generic P and T values, it can be obtained:

( ) ( ) ( )

( )

1 1.049 0.0157 10 6

, , ,760,15

720.883 1 0.003661

P T P

R P T R

λ λ

T

⎡ + − − ⎤

⎣ ⎦

= +

(1.3)

From equation 1.3 it can be calculated the refraction difference in a given wavelength band

[ λ

min,

λ

max

]

, for the following values of P and T:

(

min

) (

max

)

760 mmHg 0 °C

,760,0 ,760,0 P

T

R R λ R λ

=

=

Δ = −

(1.4)

From these expressions it can be derived the atmospheric angular dispersion δ as follows [6]:

tan( ) 760 2.9

P R z

δ

= TΔ

+

(1.5)

By knowing laws referred to the prism refraction indexes, the formulas 1.1 can be used to derive the ADC rotation law.

4.1.1. PRISM REFRACTION INDEX CALCULATION

The refraction indexes referred to the two prisms, as implemented in the module vstadcw, are calculated using following formulas as furnished by ray tracing Zemax program.

• Schott PSK3 glass

( )

2 2 2 4 6 8

1 0 1 2 3 4 5

0

2 1

2 2

4 3

5 4

6 5

2.37934497 1.06537572 10 1.15134644 10 3.21629422 10

2.18263808 10 1.27672801 10

vetro

n a a a a a a

a a a a a a

λ λ λ

⁻

λ

⁻

λ

⁻

λ

⁻

−

−

−

−

−

= + + + + +

=

= − ⋅

= ⋅

= ⋅

= − ⋅

= ⋅

(1.6)

• Schott LLF1 glass

( ) ( ) ( )

( ) ( )

2 2 4 6

2

2

3 6 3 3

3

1 0.028 1.53552879 4.79358528 10

7.20688357 10 8.63049326 10 6.81673678 10

2.81597725 10

vetro

n A BL CL D E F

L A B C D E F

λ λ λ λ λ λ

λ λ

−

−

−

−

−

= + + + + +

= −

=

= ⋅

= − ⋅

= − ⋅

= ⋅

= − ⋅

(1.7)

4.1.2. PRISM ANGLE ROTATION CALCULATION

As said above, the ADC angle rotation

θ

is calculated given specific parameters: air pressure and temperature, furnished by ESO Paranal Astronomical Site Monitor (ASM) and periodically refreshed at run-time in the TCS DB branch, wavelength band, depending on the current filter type, and telescope zenith angle position, coming through TCS DB and updated at run-time by tracking control process. Some other parameters are constants and pre-configured in the TCS DB branch and are referred to specific VST features. They are the prism orientation angle

α

_prism (equal for both prisms), the telescope focal length

F

_ADC, specific for the VST optical configuration including ADC on light path (the focal length can assume two different values depending on the current optical configuration present in the light path, 2- lens corrector or ADC), and the normalized prism base H = h/d, (calculated for

θ = 0 deg

and normalized with respect to prism diameter d). Their values, as stored in the DB (DataBase) branch of VST SW module, are the following:

( )

1.03121266 0.017998 14396

0.0180

o prism

ADC

prism

rad

F mm

H h tg d

α

α

= =

=

= = =

(1.8)

In the case of the VST angular ADC, the prism counter-rotation effect produces an angular rotation that can be derived, through simple geometrical considerations (Fig. 4-1), by correlating

α

_prism with

θ

:

( )

'

_prism

arctg H cos

α = ⋅ ϑ

^(1.9)

Fig. 4-1 the geometrical link between prism angle α and prism rotation angle θ From equations 1.1 and 1.9 it can be obtained:

( ) ( )

( )

( ) ( ) ( )

( ) ( ) ( )

1 2

1 1 max 1 min

2 2 max 2 min

'

VST

prism glass glass

glass glass glass

glass glass glass

F n n

D

n n n

n n n

δ α λ λ

λ λ λ

λ λ λ

= Δ − Δ

Δ = −

Δ = −

(1.10)

Combining equations 1.9 and 1.10 it derives the following expression:

( cos ) (

1

( )

2

( ) )

VST

glass glass

F arctg H n n

D

δ = ϑ ⋅ Δ λ − Δ λ

^(1.11)

In the VST case, the distance D between prisms and focus is constant, while the real parameter to be calculated at run- time is the rotation angle of prisms

θ

. From equation 1.11 the final formula for the ADC rotation angle, as implemented in the SW module, can be derived as follows:

( ) ( )

(

1 2

)

arccos 1 (

^VST

)

glass glass

tg F

H D n n

ϑ δ

λ λ

⎛ ⎞

= ⎜ ⎜ ⎝ ⋅ Δ − Δ ⎟ ⎟ ⎠

(1.12)

5. THE ADC CONTROL SOFTWARE

The ADC control software system is based on a distributed architecture following the common strategy applied overall the entire VST control system. The following scheme shows the data/commands flow foreseen to control the ADC.

Fig. 5-1 the VST ADC control software data/commands flow diagram

5.1. SOFTWARE CONTROL PROCESS

The handling of all functionalities and control coordination actions on VST ADC opto-mechanical system can be performed, at workstation (WS) level, through specific engineering graphical user interface (GUI) panels or sub panels, designed for either normal operational and maintenance/test uses. From the normal operation mode point of view, the handling of the process can be done in the following ways:

• From the mode switching command interface, in order to switch states for both WS and Local Control Unit (LCU) ADC modules

• From main VST TCS GUI vstguiTCS (see Fig. 5-2)

Fig. 5-2 the main VST TCS GUI panel and its widget class specific to control ADC

If a complete control on all ADC functionalities is required, the way is to use engineering GUI panels, as described in the following. After the ONLINE command issued to switch in ONLINE state both ADC modules, the first operation to be done (MANDATORY), whatever is the action required on the ADC, is to be sure that the ADC corrector is actually in the light path. This can be done by verifying the “ADC STATE” field, in order to be sure that the “ON FOCAL PLANE” sentence is displayed. Otherwise, the command ADCIN must be issued in order to put ADC in the light path.

Whenever it is required to leave out ADC from light path, replacing it with 2-lens corrector, the command ADCOUT must be issued. After these preliminary, but MANDATORY, actions, the ADC functionalities can be managed by opening another panel (Fig. 5-3).

Fig. 5-3 the panel “vstadcControl”

With this panel it is possible to give all specific commands and to configure all their needed input parameters, moving the prisms at the end, either in single step or tracking mode. Finally, it is possible, for maintenance/test purposes, to select and move single prism and/or ADC/2-lens corrector motors by launching the LCU engineering panel, Fig. 5-4

Fig. 5-4 the LCU engineering panel “vstadclgui”

All commands that can be issued to WS ADC process vstadcwControl are accepted exclusively if the following preliminary events have occurred:

• The process is in state ONLINE

• The ADC corrector is already in the light path position There are two kind of commands foreseen for the ADC:

1. indirect positioning: given the celestial object coordinates or the current telescope zenith angle, the next angular position for the prisms is calculated. Also available tracking functionality is an indirect positioning command.

2. direct positioning: by specifying an absolute rotation angle to be reached by prisms The direct positioning can be issued by means of the following specifications:

• maximum angular position feasible (deg)

• minimum angular position feasible (deg)

• absolute rotation angle (deg)

• relative rotation angle (deg)

The indirect positioning mode can be basically summarized by the following:

• a feasible wavelength range is specified

• current ambient data (temperature and pressure) are refreshed from ASM. If not available, the default DB values are used

• the constants referred to telescope features are loaded from DB (focal length, prism base etc.)

• In case of command ADCACT the celestial object coordinates are obtained as the current telescope position at a given time step. After that the command ADCCOOR is issued

• In case of command ADCCOOR the object coordinates are converted into altazimutal ones and finally the zenith angle is obtained. After that the command ADCZDIS is issued

• In case of command ADCZDIS, next ADC prism correction angle is calculated by the internal function CalcRotation(). The output will be the value, in degrees, of the rotation angle to be reached by prisms.

Final step is to send an appropriate motion command to prism motors (MOVEADC), by using as LCU interface the local ADC process vstadclServer. As the motion command is completed, the TCS WS tracking process trkwsControl is informed of the new ADC angular position, together with current wavelength used, through internal commands, respectively, SETADC and SETLAM.

A wrong condition notification (with an immediate stop of any current ADC action), is issued whenever one of the following events occur:

• Any change of TCS state (mode switching)

• Any error reply or motion timeout coming from ADC LCU

• A new command is issued to ADC while the past one has not replied OK.

To stop, at any time, ADC motors, the command STOPADC can be issued, while to enable or disable tracking capability, the commands, respectively, ENATRK and DISTRK could be issued.

6. THE ADC TEST SIMULATION MODEL

As described above the VST atmospheric dispersion corrections are obtained by means of a rotation of the prisms taking into account both atmospheric and zenith angle parameters. The variation law of such angles was reported in equation 1.12. In order to test and to optimize the correctness of this law, a matlab-based ADC model was designed, obtaining the

angular rotation of prisms vs. the zenithal angle of the telescope. This theoretical rotation law has been compared with the ray tracing ADC model, designed by VST optical engineering staff to build the real ADC system, using Zemax software. This comparison is shown in Fig. 6-1.

Fig. 6-1 ADC prism vs. telescope zenith angles in the comparison between Zemax and Matlab simulations The comparison between Matlab and Zemax model is done at the zenith angle range between 0 and 52 degrees. The VST ADC optical system was infact designed to apply an effective dispersion in this range, while the 2-lens corrector will be applied out of this angular range. The comparison shows that the angular rotation law can be considered very precise from 0 to 40 degrees. A little difference appears from 42 to 52 degrees. The reason is that the two simulations have been implemented considering two atmospheric models that, when the air mass starts to be predominant, reveal some difference. The Matlab atmospheric model has been basically derived by the VLT one, while the Zemax model is inherited in the ray tracing software and some of its theoretical details are not known. We decided to adopt the VLT atmospheric model to be implemented in the ADC software basically because the VST will be located at the same site.

It must be also considered that the ADC, as well as for other optical systems on the telescope, requires a fundamental test “on sky”, where it could be possible to derive a lookup table containing more precise prism angular positions that can be linearly interpolated to obtain offsets to be applied at ADC theoretical calculations in order to optimize the dispersion correction to be applied at any zenith angle during exposures.

The zenith angle is not the only parameter to be considered in the ADC calculations. Another element that of course can affect the prism angular correction is the observing wavelength. As underlined in section 4, the observing wavelength range depends on which filter is currently on the light path. The Fig. 6-2 shows an example of the VST focal plane spot behavior by applying ADC corrections at different wavelength ranges. The left picture is for telescope at zenith, while the right one is the same of Fig. 6-1 but obtained at different filter wavelength ranges.

Fig. 6-2 the ADC ray tracing results at zenith (left) and the ADC correction law at different wavelength ranges

7. CONCLUSIONS

The ADC opto-mechanical system is going to be installed at the telescope integration workshop, where a series of engineering tests are foreseen before to install the VST at Paranal VLT site. The ADC model and numerical simulations, performed crossing Matlab modeling and Zemax ray tracing procedures, show that the atmospheric dispersion corrector would be able to correct the light path position from atmospheric refraction in a wide zenith angle range, from 0° to 52°.

Furthermore, the optimization of correction effect has been done by strongly correlating the telescope altitude zenith angle position with the particular wavelength range coming from the current optical filter present on the light path.

Doing so, a more precise correction from refraction is applied during exposures. This careful approach has been required by the intrinsic features of the VST (short focal length together with a wide field of view). A more accurate prism rotation calculation will be fixed during test sessions “on sky”, foreseen during the telescope commissioning period.

8. REFERENCES

1. “Astrophysical Quantities”, C.W. Allen, Third Edition, The Athlone Press, London & Atlantic Highlands, 1997 2. “Atmospheric Dispersion Corrector Design Description”, N. Fiebig, VLT Software, VLT-SPE-ESO-17230-1046,

issue 1.0, ESO Garching (Munich), 1996.

3. “The Importance of Atmospheric differential refraction in spectrometry”, A.V. Filippenko, PASP, 94, 715, 1982.

4. “Computation of angular atmospheric refraction at large zenith angles”, HM Nautical Almanac Office, Royal Greenwich Observatory, N° 63, issue 3.1, 1995.

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