ESPRESSO front end exposure meter: a chromatic approach to radial velocity correction

ESPRESSO Front End Exposure Meter - A chromaticapproach to radial velocity correction

Marco Landonia,b, Marco Rivab, Francesco Pepec, Paolo Conconib, Filippo M. Zerbib,Alexandre Cabrald, Stefano Cristianie and Denis Megevandc

a Universitadegli Studi dell’Insubria. Via Valleggio 11, I-22100 Como, Italy.;b INAF - Osservatorio Astronomico di Brera, Via Bianchi 46, I23807 Merate (LC), Italy.;

c Observatory of Geneve, 51, ch. des Maillettes, CH-1290 Sauverny.;d University of Lisbon - Faculty of Science, Cidade Universitaria - Edificio C5, Campo Grande

1749-016 Lisboa.;e INAF - Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, I-34143 Trieste

ABSTRACT

This paper presents the Espresso Exposure Meter (EM) implementation. ESPRESSO,1–3 the Echelle SPec-trograph for Rocky Exoplanets and Stable Spectroscopic Observations, will be installed on ESOs Very LargeTelescope (VLT). The light coming from the Telescope through a Coud Focus4 of all the Four Telescope Units(UTs) will be collected by the Front End Unit that provides Field and Pupil stabilisation and injects the beamsinto the Spectrograph fibers.5 An advanced Exposure Meter system will be used to correct Radial Velocity (RV)obtained from the scientific spectrum for the Earth relative motion. In this work we will present the perfor-mance of an innovative concept for the Exposure Meter system based on a Charge Coupled Device (CCD) witha chromatic approach for the calculation of the Mean Time of Exposure (MTE). The MTE is a crucial quantityused for the correction of RV for the Earth relative motion during the exposure. In particular, splitting thelight in different chromatic channels on the CCD, we will probe for potential chromatic effects on the calculationof the MTE in each channel and how they could be used in order to perform the correction of RV. The paperis accompanied by a fully described numerical analysis that keeps into view a key performance evaluation fordifferent stellar spectral types (B to M spectral main sequence classes).

Keywords: Exposure meter, Radial velocity correction, CCD numerical simulations, ESPRESSO, Exoplantes,Ground base observation of exoplanets

1. INTRODUCTION

In order to compute the precise radial velocity (RV) of a star, a correction for the Earth relative motion mustbe performed. In particular, the Earth projected velocity on the line of sight may vary up to 1m/s per 1 minuteof exposure. For this reason, the measured RV on the scientific spectrum needs to be corrected by the earthrelative motion at the Mean Time of Exposure (MTE). The MTE is defined as

MTE =

∫ TSTE

tf(t)dt∫ TSTE

f(t)dt(1)

where t is the time, f(t) is the measured flux at time t and TS, TE are the start time and the end time of thescientific exposure. MTE might be very different form just the mean value of TS and TE, especially when theatmospheric conditions change significantly during the exposure. In HARPS (see technical report 3M6-TRE-HAR-33103-0007) the correction is assessed using a simple exposure meter based on a photomultiplier counterand no chromatic effects are investigated. In the case of ESPRESSO, the Exposure Meter is construct by twomain components: a simple grating (150 lines/mm) and a technical camera equipped with a CCD. In particular,

Further author information: E-mail: [email protected]

Techniques and Instrumentation for Detection of Exoplanets VI, edited by Stuart Shaklan, Proc. of SPIE Vol. 8864, 88640F · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2023227

Proc. of SPIE Vol. 8864 88640F-1

the grating disperses the small portion of the scientific light that feeds the exposure meter and the MTEs arecalculated on, as instance, three different channels following the formulas

MTE1 =

∫ TSTE

tf1(t)dt∫ TSTE

f1(t)dt(2)

MTE2 =

∫ TSTE

tf2(t)dt∫ TSTE

f2(t)dt(3)

MTE3 =

∫ TSTE

tf3(t)dt∫ TSTE

f3(t)dt(4)

where f1(t), f2(t) and f3(t) is the integrated measured flux on the relative channel on the spectrum. This methodallows obtaining a very precise measurement of the MTE according not only to the spectral type of star thatit is observed but also against chromatic atmosphere perturbation. In particular, as reported in the followingsections, the MTE could vary significantly between the three channels.

The most challenging situation is materialized when the scientific object is observed under sky conditionin which a thin cloud passes in front of the target. In this case, the MTE could be significantly different inthe blue and red region of the spectrum. In fact, assuming that the covering factor is reasonable, the fluxreceived in the blue part of the spectrum is roughly constant while in the middle/near infrared region theluminosity is significantly dimmed. This dimming is caused by a reduced atmosphere transmission efficiency,due to absorption of redder photons by molecules of the water vapor in the thin clouds. For this reason, the useof a simple spectrum at the level of the exposure meter allows to capture variation of the MTE according to thewavelength, significantly reducing the error on the RV, in comparison to the calculation of the MTE only onintegrated (white) light as shown in the Results chapter of this paper.

2. OPTICS AND OPTOMECHANICAL CONFIGURATIONS

This section is preliminary for the understating of the following sections since it illustrates the configuration (interms of optics and optomechanics) of the device.

2.1 Design philosophy, spectral bandwidth and overall optical Efficiency

The design of the ESPRESSO exposure meter has been assessed in order to comply with the requirement ofradial velocity precision measurement. In particular, starting from three top level requirement of accuracy (10cm/s single UT low resolution, 1 m/s single UT low resolution, 5 m/s for multi-UT and 10 m/s single UT lowresolution) the exposure meter design allow to maintain the error induced on the measurement of MTE belowthe photonic accuracy reached at the level of the scientific Echelle spectrum. As an example, suppose to observean mv=8 class-G star with the scientific goal to measure the shift of its absorption lines on the photospherewith an accuracy of 10 cm/s. The MTE calculated by the Exposure Meter must be below the error induced onthe scientific spectrum of the star by the photonic accuracy and, for this reason, the measure on the scientificspectrum will only be shot-noise limited.

The Exposure Meter (shown in Figure 1) works on the same spectral band of the scientific Echelle grating.6

In particular, the spectral bandwidth is 380nm to ∼ 800nm. However, from 380nm to 400 nm the exposuremeter is completely blind due to a pass band filter that is required by the dispersive grating in order to avoidthe overlap of the orders with m > 1. The total efficiency of the exposure meter is presented Figure 2. Thecalculation also considers the quantum efficiency of the Sony ICX285, which is the baseline detector.


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Figure 2. ESPRESSO Exposure meter efficiency.


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Figure 4. ESPRESSO Exposure meter optical setup.

2.2 Optical design setup

The Exposure meter is a simple spectrograph-like device. In particular, it receives extra light from the fiber thatwill feed the ESPRESSO and materialise a simple spectrum onto the detector. The Extraction of the light isdescribed in Conconi et al 2013 (APSU design, SPIE 2013 in press) and is made out by a crowned mirror thatpick off the extra light due to the F/3.5 aperture of the fiber link (the spectrograph aperture is F/2.5). Thenthe light is focused onto a bundle of fibers that reproduces the same fiber I/F of the Anamorphic Pupil SlicerUnits entrance on both sides. Fiber link interface is illustrated in Figure 3 and 5 With this trick we have at theexposure meter entrance the same optical I/F of the APSU (with less light). Figure 4 shows the general opticallayout of the instrument. The collimation is made by a Standard Edmund triplet (30229 A.1) made out by N-F2and N-BK7, and the refocusing is obtained through the same objective. A Richardson disperser grating will bemounted into the collimated beam, while a filter wheel will be equipped with neutral filter in order to cope withdifferent star brightnesses. A custom coating will be done on the opposite side of the filters in order to cut theblue wavelength up to 400nm. This trick is necessary in order to avoid order overlapping. The useful Exposure


Figure 5. ESPRESSO Exposure meter fiber link.

meter bandwidth will be then ∼ 400-800nm.

2.3 Optomechanical setup

The exposure meter is made out by:

• Fiber link

• Collimator

• Filter Wheel

• Dispersing grating

• Refocuser

• Detector

• Optical Bench

The fiber link head, as shown in Figure 3, is identical to the APSU one and will be fixed to its aluminumsupport through 4 x M2.5 screws. The support as a whole will be screwed onto the bench via 3 x M10 screws.The collimator and the grating, illustrated in Figure 6 and 7, will be mounted on the bench through 3 x M4screws.

Since the exposure meter must have to cope with the different star brightness it has been decided to put afilter wheel equipped with Optical Neutral filters characterized by different optical depth. It has been chosena Pi-MICS AFW65. The filters are glued onto the holders and the wheel is fixed to a dedicated support thatallow the insertion of the system in the reduced space. Figure 8 shows the adopted setup. Finally, the opticalbench is made through the adoption of a properly milled aluminum plate. The milling process will also realizethe mechanical references for the alignment in order to guarantee a nominal precision roughly of 30µm. Alsothe threaded holes for the opto-mechanical mounting will be done during the same milling process. Figure 9 isa pictorial view of the optical bench itself.


Figure 6. ESPRESSO Exposure meter collimator optomechanical setup.

Figure 7. ESPRESSO Exposure meter grating optomechanical setup.


Figure 8. ESPRESSO Exposure meter filter wheel optomechanical setup.

Figure 9. ESPRESSO Exposure meter optical bench view


3. SIMULATION FRAMEWORK

3.1 Preliminary definitions, assumptions and theoretical quantities

3.1.1 Flux received and star model

Stars are modeled as a blackbody radiatior. In particular, the differential flux recevied between λ and λ + dλis computed as

dφ

dλ= B(λ, T ) × ExpMefficiency(λ) × λ

hc× φ? × 10

−mv2.5 (5)

Stellar class Average surface temperature Apparent magnitude

B - main sequence (blue) ∼ 25.000 K from 0th to 20th

G - main sequence (yellow) ∼ 5.300 K from 0th to 20th

M - main sequence (red to brown) ∼ 2.500 K from 0th to 20th

Table 1. Star spectral types and properties considered for the performed simulations.

where B(λ, T ) is the plankian function, φ? is the reference flux such that the differential flux at 5550 Ais 1000 photons s−1 cm−2 A−1 for a 0th magnitude star in the V Band (Johnson UVB filter) and mv is theapparent magnitude of the star considered. ExpMefficiency is a function that takes into account the efficiencyreported in Figure 2. Since the design approach of the exposure was such that three chromatic channels willbe used for the calculation of the MTE, simulations have been performed considering different stellar spectralclasses, whose properties are reported in Table 1.

3.1.2 Sky model

The sky emission is modeled as a simple powerlaw assuming that the sky surface brightness is ∼ 21 mv arcsec−1

in the visible V band. In the case of low resolution mode and multi-UT mode, the subtended area is 0.785arcsec2. For this reason and for the quite short exposure time of the Exposure Meter TCCD its contribution isnegligible (at least up to 19th-20th magnitude).

3.1.3 λ∆λ dispersion function

Since the exposure meter is, at the end, a small spectrum of the scientific light that exits the instrument, forthe simulation is mandatory to know the position of the image in function of the wavelength. In Figure 10 thefunction that models the position of the image against the wavelength of the choosed grating is plotted. It willbe adopted for the numerical simulations. The relative dispersion between wavelengths are reported in Figure11. Note that, despite a non linear dispersion, the peak to valley between the two edge is less than 4µm, which isof the order of a fraction of the detector pixel. For this reason, the dispersion can be safely considered constant.

3.1.4 PSF model of the Exposure Meter optics

Through the adoption of ray tracing (Zemax analysis) the point spread function of the instrument has beenevaluted. The PSF is quite stable though different wavelength but slightly differences are apparent (in theorder of few pixels). The PSF is reasonably assumed to ba gaussian. In particular, Figure 12 illustrates thePSF dimension (in um) while Figure 13 shows what appears on the detector when an impulsive signal (Diracdelta-function) is applied in front of the overall exposure meter optics.

3.1.5 Fiber image

The image of the fiber for the considered case (Multi UT mode, High resolution 1UT or low resolution 1UT) ismodeled through the drawing of the relative polygon on the detector matrix. In particular, at the level of thefocal plane of the exposure meter where the detector lies there are reported in Table 2:


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Figure 12. ESPRESSO Exposure meter PSF function against λ.


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Figure 13. ESPRESSO Exposure meter PSF function against λ in a pictorial representation.

Mode Description Image

Single 1UT High Resolution mode Octagonal fiber with dimension of 70 µm

Single 1UT Low Resolution mode Octagonal fiber with dimension of 140 µm

Multi-UT mode Rectangular fiber with dimension of ∼ 280 µm

Table 2. Image fibers on the focal plane and configuration.

3.1.6 Image on the focal plane

At the level of the detector the images of the fibers reported in Table 2 must be corrected for the PSF functiondescribed in the previous sections. The equation takes into account the canonical definition of convolution in adiscrete domain:

Imagedetector(i, j) = Imagefiber ⊗ PSF (λ) =

j=+ inf∑j=− inf

i=+ inf∑i=− inf

Image(i, j) × PSF (m− j,m− j) (6)

3.1.7 Slit loss and dependence on seeing

The seeing at wavelength λ follows the formula

S(λ) = S5500A

(λ

5500A)−

16 (7)

Figure 14. Seeing vs slit efficiency curve adopted for simulations


where S5500 is the seeing measured at 5500A. This relation obviously affects the amount of light that enter thespectrograph since the subtended slit is a pinhole of ∼ 1′′ for the Low Resolution mode. For the simulation amean seeing of 1′′ is assumed (up to mv ∼ 15, for mv greater than 15 0.70′′ seeing is assumed) and the efficiencydue to slit-loss is considered. As instance, at 5500 the efficiency for a seeing of 1 is about 50%. In other words,only 50% of the scientific light is able to reach the spectrograph while the remnant photons are back reflected forthe guiding system.5,7 The seeing-efficiency curve is reported in Figure 14. The behavior has been assessed intwice way, numerical and analytical, in order to ensure a good estimation of the slit loss related to seeing effect.

3.1.8 CCD configuration

The frequency for the readout of the technical CCD of the Exposure Meter has been evaluated taking intoaccount noises from the detector, accuracy on the measurement on the flux and computational overhead. InTable 3 are reported the readout frequencies adopted for the simulation that are a baseline for the on-sky regime.

Scientific goal Telescope config and mv limit Read frequency CCD gain and bin

10 cm s−1 1UT - mv 10 T/1000 or less High (3 or 4 e- ADU−1) , 2x2 bin1 m s−1 1UT - mv 15 T/100 or less Low (1 or 2 e- ADU−1), 2x2 bin10 m s−1 1UT - mv 20 T/10 Low, 2x2 bin5 m s−1 multiUT - mv 20 T/10 ∗ (nUT ) Low, 2x2 bin

Table 3. CCD configuration for the Exposure meter

4. DETECTOR SIMULATION FOR PERFORMANCES EVALUATION

This section presents the algorithm adopted to generate a generic Exposure Meter CCD detector. The result isused in order to evaluate the performance of the overall system. For numerical reason, the spectrum is simulateddividing in bin of ∼ 20A. Starting from the definition of the received differential flux, wavelength dispersion andPSF a CCD is generated as follow:

• Compute the number of photon received from the scientific object in a bin of 20 A by the integration ofEquation (5). In particular, the total number of photon received in a 20 A wide bin is

phstartbin =

∫ binend

binstart

B(λ, T ) × ExpMefficiency(λ) × λ

hc× φ? × 10−

mv2.5 dλ (8)

• Compute the number of photon received in a bin of a 20 A from the sky by the integration of the formula

phstartbin =

∫ binend

binstart

2 × 10−17 × ExpMefficiency(λ) × λ

hc× φ? × 10−

mv2.5 dλ (9)

The differential flux of 10−17 erg cm−2 s−1 A−1 correspond to the mean sky background level at ESOParanal .

• Draw the image of a fiber (according to which mode is under simulation, see Table 2) in the detector atthe position binstart+binend

2 adopting the relation ( λ∆λ ) reported in Figure 10 and imposing that the total

number of counts is such that it is equal to the number of scientific photon plus the photons received fromthe sky (energy conservation). Uniform illumination of the fiber image is assumed.

• Apply Equation (6) in order to convolve the drawn image with the instrumental PSF response at wavelengthbinstart+binend

2

• Add the result to the overall image (which contains the draws of each fiber in their proper positions).


• Repeat from step 1 unitl binend = 8000 A.

• Apply the binning adopting a resize of the image.

• Multiply the overall results for the integration time considered.

At this point, the image generated is saved and stored for further computation (in particular for the theoreticalMTE, that must be compared with the measured one after detector noises) and the noises from the detector areadded in the following way:

• Generate the Dark Current signal for each pixel adding a number in which the parameter of the e-sec−1 px−1 is the value of the dark current (from datasheet if available). If the binning is selected, in eachpixel the dark current signal will be also proportional to number of binned pixels .

• Generate the Photon Noise replacing the flux calculated (λ t) value of each pixel of the ExposureMeter CCD with one drawn from a Poisson distribution (N) in which the parameter of the PDF is thecurrent value of the pixel.

Pr(N = k) =e−λt(λt)k

k!(10)

• For each pixel check the saturation level. If the pixel exceeds the maximum number of electrons allowedin the potential well its value will be fixed at the saturation threshold (reported in the CCD datasheet).

• Generate the readout noise adding a mask to the CCD generated as a Normal random number withµ = 0 and rms equal to the RON value reported in the datasheet.

• Apply the ADC conversion of the CCD and check if the ADU is saturated. For this reason, the value ofeach pixel in converted from e- to ADU through the ccd-gain factor (e- ADU−1). In case of saturation, thevalue of the pixel is forced to 2ADUbits , where ADUbits are the number of bits available to the electronicsof CCD for the readout.

Figure 15 show the result of the simulation for an M spectral type class with apparent magnitude mv = 15.The first panel shows the obtained detector at the end of the generation (with noises), the second panel showsthe extracted spectrum (in ADU) and the third panel the average S/N ratio of the spectrum.

5. RESULTS AND DISCUSSION

The performance of the exposure meter, in terms of accuracy and precision of the MTE calculation, has beenevaluated starting from the most common scientific cases requirement. In particular, the simulation frameworkhas been stressed in two different situations: a zero order evaluation in which it is assumed to observe thescientific target with no perturbation at the level of the atmosphere or on the instrument itself and a secondorder evaluation in which a chromatic perturbation is considered. As noted in the previous sections, when achromatic perturbation occurs, the received flux is dimmed especially in the red part of the received light. Thissituation is typical when observing the target through a thin cloud.

As an overall consideration, the flow diagram of Figure 16 reports in detail how a generic simulation ofa scientific exposure has been implemented. Briefly, knowing the required exposure time for reaching desiredradial velocity accuracy, the TCCDs of the Exposure meter are read out (in this case, simulated) and stored forthe final computation of the MTE. The integration times (readout frequencies) of the TCCD are investigatedin Table 3. Finally, the simulation software performs the calculation of the MTEs in each channel on ideal ccd(noise free) in order to evaluate its actual value, and on real ccd with relative noises (as explained in the previoussections). The differences between the actual value and the simulated one (after noises) is then converted in RVaccuracy error induced by the exposure meter assuming that, in the worst case, an error of 0.6s corresponds to1 cm/s in the RV measurement. This is, of course, the worst case since the value depends on the declination ofthe target. For the simulation, dependences on < α, δ > are not investigated.


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Figure 16. Flow chart for the strategy adopted for the scientific simulation. Each simulation is repeated 100 times inorder to investigate general statistical properties.


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Figure 17. ESPRESSO Exposure Meter channels.

Figure 18. Pictorial representation of the chromatic perturbation applied to the system.

Simulations are repeated 100 times in order to investigate the r.m.s. error and the general behaviour of thesystem. The channels, which simulations refer to, are indicated by the pictorial representation of Figure 17. Westress again the fact that the dispersion axis is inverted at the level of the focal plane in which the detector lies(from red to blue).

5.1 First scientific case - 10 cm s−1 RV accuracy

In order to evaluate the performance of the designed Exposure Meter for the 10 cm/s scientific goal, the simula-tions start with the assumption of the integration time needed for reach this accuracy at the level of the scientificspectrum (from now, referred as photonic accuracy). In particular, the limit magnitude for the 10 cm/s is mv =10 since the required integration time for the photonic accuracy of 10 cm/s is about 2 hours. For mv < 10 theerror induced on the calculation of the MTE by the Exposure Meter is negligible (<< 1 cm/s) and the accuracyon the scientific spectrum is always show-noise limited. Moreover, for magnitude mv < 2 the exposure meter isnot required since the integration time should be very short (less than 10 seconds). However, since in the opticaldesign a filter wheel has been implemented the Exposure Meter could be used with a read out frequency limitedby the maximum sampling frequency of the camera (12 fps, as instance).For mv = 10, the limit case, two simulation has been assessed. In the first one, no perturbation are applied onthe system or on the atmosphere. Results are presented in Figure 20 and 21 and Table 4 and 5 . In particular,for the 100 simulations the error induced by the Exposure Meter on the channels are presented in the boxes ofFigure 20 for the spectral type B,G and M investigated while r.m.s. error are tabulated in Table 4 and 5 . Thesecond case considers a chromatic perturbation modelled by the function of Figure 18 where its behaviour canbe seen. The effect of the perturbation on the spectra at the level of the exposure meter, plotted against time,could be spotted in Figure 19. The second order simulations carried out also adopt symmetric perturbation intime, in order to better emulate the actual sky condition on different exposures.

Channel / Spectral type B G Mr.m.s error on Channel 1 1.2 cm/s 0.5 cm/s 0.1 cm/sr.m.s error on Channel 2 0.3 cm/s 0.2 cm/s 0.2 cm/sr.m.s error on Channel 3 0.4 cm/s 0.5 cm/s 1.3 cm/s

Table 4. Root mean square error for 10cm s−1 scientific goal, mv = 10 and no perturbation on the system


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Figure 20. ESPRESSO Exposure Meter performance for 10cm/s goal with mv = 10 with perturbations on the system oratmosphere.


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Table 5. Root mean square error for 10cm s−1 scientific goal, mv = 10 with perturbation applied on the system

Figure 21. ESPRESSO Exposure Meter performances against a chromatic perturbation on the red part (cloud passingthrough).

5.1.1 Why a multicolour exposure meter ? Comparison between spectrum and white light

It is now important to note that the use of the small spectrum at the level of the exposure meter significantlyreduce the error on the MTE when such a perturbation occurs at the level of the atmosphere. In particular,if the MTE is calculated only on the integrated white light for this simulation it gives a value of 2.9377e+03s. The MTE, since a perturbation occurred, is obviously different from the simple half value of the integrationtime (which is 3000s in this case).However, when inspecting the MTE on channel 1(red) and channel 3 (blue) the results are significantly differentsince in the red band less light reached the instrument due to the perturbation (note that the situation couldbe exactly symmetric if the perturbation occurs in the blue part instead of happening in the red one. In detail,MTE(Ch1) = 2.6550e+03 and MTE(Ch3) ∼ 3000s. Now, comparing the MTE on channel1 with the MTE onwhite light gives a difference of ∼ 282 s that corresponds to an error of 4.7 m/s. For this reason, the correctionof the relative shift of a stellar absorption line in the red region of the spectrum using only the MTE calculatedon the integrated light would cause an error of several meters per second. These kind of consideration also applyfor the next simulations of 1m/s and 10 m/s of scientific goals. In the case of multi-UT mode no perturbationare applied since the light comes from different arms of the instrument and the sky conditions could also beslightly different.

5.2 Second scientific case - 1 m s−1 RV accuracy

As in the previous case, two kind of simulations have been carried out. For 1 m s−1 the limit magnitude ismv = 15 since the exposure time needed to reach the desired accuracy is about 1.5 hours. For magnitudemv < 15 the error induced by the exposure meter is negligible in comparison to the requirement of the 1 m s−1

accuracy and, in any case, the error induced by this subsystem is lower than the photonic precision reached atthe level of the scientific spectrum. Results are reported in Figures 22, 23 and Tables 6, 7.


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Figure 23. - ESPRESSO Exposure Meter performance for 1m/s scientific goal with perturbations applied to the system


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Channel / Spectral type B G Mr.m.s error on Channel 1 0.30 m/s 0.1 m/s 0.05 m/sr.m.s error on Channel 2 0.1 m/s 0.05 m/s 0.1 m/sr.m.s error on Channel 3 0.12 m/s 0.15 m/s 0.2 m/s

Table 6. Root mean square error for 1 m s−1 scientific goal, mv = 15 without perturbation applied on the system

Channel / Spectral type B G Mr.m.s. error on Channel 1 0.37 m/s 0.20 m/s 0.1 m/sr.m.s. error on Channel 2 0.10 m/s 0.10 m/s 0.2 m/sr.m.s. error on Channel 3 0.10 m/s 0.15 m/s 0.25 m/s

Table 7. Root mean square error for 1 m s−1 scientific goal, mv = 15 with perturbation applied on the system

The adoption of a spectrum, as illustrated in the previous scientific case, reduced significantly the error whenthe chromatic perturbation occurred. In particular, if the system only adopt the MTE on the integrated whitelight, the error on the red part of the spectrum for inaccurate Earth-motion correction would be of about severalmeters per second.

5.3 Third scientific case - 10 m s−1 RV accuracy

For the 10 m s−1 accuracy scientific case the limit magnitude is about 19-20 (worst case considered for thesimulation). For brighter object (e.g. mv = 16, 18) the error induced by the exposure meter in its channels isnegligible (less than 1 m s−1) compared to the photonic accuracy reached at the level of the scientific spectrum.For this reason, the measurements are shot noise limited and not affected by the error that occurs on the MTEcomputed by adopting the designed Exposure Meter. Since, in this case, the requirements are quite loose andreasonable perturbations affects the MTE for an amount that is less than 10 m s−1 only a zero order simulationhas been carried out. Results are reported in Figure 24 and Table 8.

5.4 Multimode setup - An introduction to 5 m s−1 RV accuracy case

In the case of multi-UT observation mode, the spectrograph and the exposure meter collect the light fromthe scientific target from more than 1 telescope. For this reason, the flux received is n-times that receivedfrom only one UT. As a representative case, a simulation for an mv = 20 object has been carried out. Inparticular, in order to reach a photonic accuracy of 5 m s−1 an exposure of 3h is required with only one UT.This integration time is quite high in comparison to a typical exposure time in an Observation Block (less than 2hours). However, adopting 2-UT configuration the time needed is reduced by a factor of 2 since 2 UTs feeds thespectrograph simultaneously. In Figure 25 and Table 9 are reported the errors induced by the exposure meterwith a configuration of 2-UT, adopting parameters reported in Table 3.

Figure 24. - ESPRESSO Exposure Meter performance for 10 m/s scientific goal without perturbation


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Channel / Spectral type B G Mr.m.s error on Channel 1 2.5 m/s 2.2 m/s 0.7 m/sr.m.s error on Channel 2 1.0 m/s 0.95 m/s 1 m/sr.m.s error on Channel 3 1.5 m/s 2.0 m/s 3 m/s

Table 8. Root mean square error for 10 m s−1 scientific goal, mv ∼ 20 without perturbation applied on the system

Figure 25. - ESPRESSO Exposure Meter performance in the multi-UT configuration (no perturbations are applied).

Channel / Spectral type B G Mr.m.s error on Channel 1 3.2 m/s 3.0 m/s 1.1 m/sr.m.s error on Channel 2 1.6 m/s 2.4 m/s 2.0 m/sr.m.s error on Channel 3 1.6 m/s 2.8 m/s 3.0 m/s

Table 9. ESPRESSO Exposure Meter r.m.s. error on the three channel in multi-UT configuration


REFERENCES

[1] Megevand, D., Zerbi, F. M., Cabral, A., Di Marcantonio, P., Amate, M., Pepe, F., Cristiani, S., Rebolo, R.,Santos, N. C., Dekker, H., Abreu, M., Affolter, M., Avila, G., Baldini, V., Bristow, P., Broeg, C., Carvas,P., Cirami, R., Coelho, J., Comari, M., Conconi, P., Coretti, I., Cupani, G., D’Odorico, V., De Caprio,V., Delabre, B., Figueira, P., Fleury, M., Fragoso, A., Genolet, L., Gomes, R., Gonzalez Hernandez, J.,Hughes, I., Iwert, O., Kerber, F., Landoni, M., Lima, J., Lizon, J.-L., Lovis, C., Maire, C., Mannetta,M., Martins, C., Moitinho, A., Molaro, P., Monteiro, M., Rasilla, J. L., Riva, M., Santana Tschudi, S.,Santin, P., Sosnowska, D., Sousa, S., Spano, P., Tenegi, F., Toso, G., Vanzella, E., Viel, M., and ZapateroOsorio, M. R., “ESPRESSO: the ultimate rocky exoplanets hunter for the VLT,” in [Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series ], Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series 8446 (Sept. 2012).

[2] Pepe, F. A. and al., “Espresso: the echelle spectrograph for rocky exoplanets and stable spectroscopicobservations,” Ground-based and Airborne Instrumentation for Astronomy III 7735, 77350F–1/77350F–9,SPIE (2010).

[3] Zerbi, F. M. and all, “Espresso design: the realization of an innovative multi-telescope ultra-stable highresolution spectrograph for the vlt,” Ground-based and Airborne Instrumentation for Astronomy IV 8446,8446–1/8446–13, SPIE (2012).

[4] Cabral, A. and all, “Espresso: design and analysis of a coude-train for a stable and efficient simultaneousoptical feeding from the four vlt unit telescopes,” Ground-based and Airborne Telescopes IV 8444, 8444–1/8444–13, SPIE (2012).

[5] Riva, M., Landoni, M., Zerbi, F. M., Megevand, D., Cabral, A., Cristiani, S., and Delabre, B., “ESPRESSOfront end opto-mechanical configuration,” in [Society of Photo-Optical Instrumentation Engineers (SPIE)Conference Series ], Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 8446(Sept. 2012).

[6] Spano, P., Megevand, D., Herreros, J. M., Zerbi, F. M., Cabral, A., di Marcantonio, P., Lovis, C., Cristiani,S., Rebolo, R., Santos, N., and Pepe, F., “Optical design of the ESPRESSO spectrograph at VLT,” in[Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series ], Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series 7735 (July 2010).

[7] Landoni, M., Riva, M., Zerbi, F. M., Megevand, D., Cabral, A., and Cristiani, S., “ESPRESSO front-end guiding algorithm,” in [Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series ],Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 8451 (Sept. 2012).


Documents

ESPRESSO front end exposure meter: a chromatic approach to radial velocity correction