Observations of Jupiter oscillations have been performed with several techniques. Deming et al. observed in the thermal infrared (1989), Schmider et al. used Doppler spectrometry with a sodium cell (1991) and Mosser et al. tried the Fourier transform spectrometry (1993 & 2000). These observations were limited by the fast rotation of the planet leading to results incompatible with theory. To overcome the limitations, Schmider et al. (2007) and Gaulme et al. (2008) proposed to achieve multi-sites observations with an instrument based on a Mach-Zehnder interferometer, called SYMPA (Seismic Imaging Interferometer for Monitoring Planetary Atmospheres). Three campaigns of observations have been carried out with two instruments, one by site, between 2003 and 2005. The recent data analysis (Gaulme et al. 2011) put in evidence the detection of Jovian pulsations conform to the theoretical models. Nevertheless, the identification of the modes on a spherical harmonic basis was unfortunately impossible, because of the low duty cycle and of the atmospheric turbulence. This is the reason why we propose to achieve the observations from space, with a space-borne instrument.
In this paper, we present the prototype of the Doppler Spectro-Imager Echoes . The instrument principle is directly inherited from SYMPA. The study, funded by the Centre National d’Etudes Spatiales (CNES), is focused on the Mach-Zehnder interferometer. The first paragraph details the optical design of the Mach-Zehnder and the theoretical performances. The second paragraph explains the measurements to be achieved thanks to a dedicated test bench. Finally, the last paragraph presents the first experimental results obtained on the prototype.
The instrumental concept is studied to form four images in phase quadrature. The Mach-Zehnder (MZ) interferometer is placed in a parallel beam. The four outputs of the MZ are folded on a single detector by the four corner mirrors (M1, M2, M3, M4) and form four images thanks to four identical objectives. From these four images, we can use the “ABCD” method (Wyant 1975) which permits to get rid of the continuum component of the incident light. These images are obtained thanks to a specific optical design, based on a modified MZ interferometer (Fig. 1).
The “empty MZ” is composed of two blocks (K1 and K2) made in K5G20. These blocks are composed of two optical elements glued together and separated by a semi reflective treatment. Because the size of these blocks is different, an “empty” Optical Path Difference (OPD) is introduced.
The sensitivity of the MZ to velocity field is the result of an optimization increasing the sensitivity of the phase and decreasing the contrast with the OPD change. By exploration of the solar spectrum, we looked for features giving contrast maxima. The best sensitivity is obtained for an OPD of 5048 μm at 519.5 nm. This OPD is created by introducing glass plates in the arms of the interferometer. A tilted plate in BK7G18 is placed in each arm in order to eliminate stray light and to make the fringes regular and rectilinear (B1-B2 and B3). One of the plates is sliced into two parts, the prismatic one (B2) being mounted on a piezoelectric plate in order to achieve the OPD modulation. The modulation will be helpful to blur the fringes during the pixel sensitivity calibration processes, but its main function is to create phase shifts of kπ/2 (k = 0, 1, 2, 3) to calibrate the response of each channel. Finally, a quarter wave plate, based on two quartz plates with perpendicular optical axes (Q1 and Q2), achieves the phase quadrature. Then, polarizer cubes are placed at each output and produce a kπ/2 phase shift. So we obtain four images in phase quadrature:
Where I0 is the continuum component of the incident light, γ is the fringe contrast and ϕ is the fringe phase that we want to measure. From the phase measurement, we can obtain the radial velocity vr which contains the information:
where λ0 is the central wavelength, Δ the OPD and c the speed of light.
The choice of the optical glasses respects two criteria. First, materials must be resistant to radiations. Then, thermal dilatation coefficients must compensate refractive index variations. That is why we have selected: K5G20 and BK7G18 from Schott, and crystalline quartz wave plates.
Optimization of the thermal stability
In order to ensure the best thermal stability, the MZ must operate at a precise temperature, called stability temperature. Simulations of the phase versus temperature result in a minimization of the thermal effect for a value of the temperature of 18.9°C. If the experimental temperature does not respect this condition, the optical parameters of the MZ have to be redefined. Indeed, there is a relation between glass plate thicknesses and stability temperature.
The protocol consists in measuring the phase of the fringes at different temperatures (5 measurement points are sufficient). The Figure 2 represents the theoretical phase in function of the temperature, and the fit of this curve.
From the equation of the fit curve, we can deduce the stability temperature which is located at the minimum of the curve. The image processing allows the stability temperature determination with a precision of 0.01°C. A modification of the plate thickness will lead in a change in this stability temperature. An interesting point is that the BK7G18 plates have an effect on the stability temperature and on the OPD whereas the quartz plates only impact the OPD. The protocol will consist in adjusting the stability temperature Ts to the required value by modifying the thicknesses of the BK7G18 plates eB. Then, the OPD will be retrieved by the adapted modification on the quartz plate thickness eQ.
As the thicknesses will be modified, the first version of the prototype will not be glued. The optical elements will be maintained mechanically or by molecular adherence.
The aim of Echoes is to analyze the solar spectral lines reflected at the surface of Jupiter. That is why it must operate in the visible domain. On top of that, the quantum efficiency of the detectors is better in the visible. Considering this requirement, the maximum of sensitivity is reached with the optimized parameters given in Table 1:
|Central Wavelength (λ0)||519.5 nm|
|Filter band pass (FWHM)||1 nm|
|Field of View (FoV)||± 2.9°|
Considering these performances, the theoretical fringe contrast is 5%. The FoV is determined to observe the whole planet at a minimal distance of 0.02 AU. It corresponds to an input pupil size of 2 cm.
EXPERIMENTAL STUDY OF THE PROTOTYPE
In this paragraph, we present the tests and controls to be achieved on the prototype with respect to the specifications listed in Table 2.
Specifications to be respected
|Differential transmission||< 5%|
|Wavefront quality||26 nm rms (λ/20 @ 519.5 nm)|
|Phase quadrature||90°± 10°|
|OPD||5048 μm ± 10 μm|
|Loss of contrast||< 5% of the theoretical contrast|
|Stability temperature||18.9°C ±0.1°C|
|Variation of the thermal sensitivity of the OPD||< 20 m s-1 K-1 in the FoV|
|Parallelism of output beams||< 20’’|
In order to verify the specifications, a dedicated test bench is implemented (Fig. 3).
The light source is provided by an integrating sphere. The MZ will be integrated in a thermal vacuum tank. A combination of polarizer cubes and mirrors, called “Periscope - Polarizer”, separates the image in two: one by polarization direction. The desired wavelength is observed in the seventh order. Finally, two images are observed side by side on the detector.
The tests and controls to be achieved on the prototype are divided into three main parts:
- Calibration and alignment of the test bench (calibration of the diffraction grating dispersion, polarization of the optical elements).
- Control of the Mach-Zehnder (transmission, polarization and wavefront quality in each arm, parallelism of the output beams, phase shift between the two arms).
- Adjustment of the Mach-Zehnder (adjustment of the OPD, maximization of the contrast, determination of the stability temperature).
A software developed at OCA permits the control of the test bench and the acquisition of the images. We can adjust the parameters of the detector (image size, gain, etc.), the temperature of the cooler and the position of the piezoelectric plate. Matlab programs are included in the software for the image processing: determination of the OPD, of the fringe contrast and of the stability temperature. With this interface, we can adjust the Mach-Zehnder while viewing the result in real time. The image processing allows reaching the required precisions to respect the specifications.
CONTROL OF THE SEMI REFLECTIVE COATINGS
In this paragraph, we present the first results obtained on the K1 and K2 blocks (Fig 1). The aim is to control the semi reflective coatings before the integration of the Mach-Zehnder to verify if the specifications on the transmission and on the phase quadrature are respected.
The semi-reflective coatings are specified to transmit and reflect 50% of the incident light regardless of the polarization. The absorption must be less than 3%.
Control of the transmissions
A first test bench for the control of the transmission of the blocks has been implemented (Fig. 4). This bench consists in measuring the photometry at the two outputs of each prism.
We occult one path and we acquire series of images. We repeat the process for the other arm. Measurements have been achieved separately on each prism block. The values of transmissions and reflections are measured in each polarization, P and S, and are given in Table 3.
Measured transmissions and reflections of the coatings
From these values, we can determine the transmission and the contrast at each output of the Mach-Zehnder, for each polarization (Table 4).
Transmission and contrast at each output
We can see that the differential transmission is less than 2% which respects the specification of 5%. The absorption of the coatings is around 12% which does not respect the specification of 3%. Section (4.3.) gives the consequence of these measured values on the expected performance.
Control of the polarization
The dedicated test bench (see section 3.) is now used to control the polarization of the coatings. A light source is injected through an adjustable slit and directed to the MZ. A combination of mirrors is studied to image easily each output separately. At the output of the MZ, we have the “periscope – polarizer” module, the diffraction grating and finally, the interferential filter which is placed upstream of the detector (Fig. 5).
The Fig. 6 represents parts of the images obtained at each output of the MZ, resized for the image processing.
The “empty MZ” produces interference fringes because the size of the two blocks K1 and K2 is different. Fringes are obtained in the spectral and spatial dimensions (the OPD varies with the wavelength and with the FoV).
Protocol of the phase shift calculation:
- Determination of a Y0 reference position in Y, calculated by cross-correlation
- Determination of the filter profile in X at this position Y0 for spectral calibration
- Determination of the position X0 of the filter maximum of transmission by a fit
- Calculation of the phase at this position (X0,Y0) for each output and each polarization. The phase is given by the argument of the Fourier transform.
- Calculation of the phase shift for each polarization
The theoretical phase shift between the two outputs of the MZ is 180°. The error to the phase quadrature is ΔΦ1 in the polarization 1 and ΔΦ2 in the polarization 2. The results (averages over several images) are the following:
These results give an idea of the precision of the measurement, of the order of a few degrees, sufficient for our task. The specification of the error to the phase quadrature is reached. We notice that the difference between the two polarizations is low, so it will not increase the noise level in the phase measurement. These preliminary results will be supplemented by other measurements.
The standard deviation on the velocity variations due to the photon noise is given by:
where σ0 is the central wavenumber and N the total number of photons. By considering the measured transmissions (4.1.) and the errors to the phase quadrature (4.2.), the degradation of the performances in terms of velocity measurement is 23% (Eq. 8).
The study being limited to a R&D, we decided to accept the coatings with present values, although slightly out the specification range, in order to achieve the complete test set. Indeed, the most crucial part of the test is the thermal sensitivity and the final adjustment of the MZ, and the determination of the calibration procedure.
CONCLUSION AND PERSPECTIVE
As the first results have been achieved and accepted, the prototype is currently under integration. The test bench has been implemented, and the calibration of the diffraction grating will occur in September 2012. As this calibration requires working with the solar light, optical fibers will achieve the light path from outdoor to the test bench.
The control of the Mach-Zehnder will be finished this autumn: differential transmission, wavefront quality, parallelism of the output beams and phase shift between the two outputs. We expect the adjustment for the end of 2012: adjustment of the OPD, maximization of the contrast and determination of the stability temperature. When the thicknesses will be modified (cf. section 2.2.), we will achieve the measurement of the thermal stability which requires the detection of an OPD variation of 170 pm. The Mach-Zehnder will be integrated in a thermal vacuum tank regulated at ± 0.4° by a cooler.
We plan an adaptation of the prototype to be placed on the MEO telescope (Calern, France) to achieve observations of Jupiter at the end of 2013. It is important to validate the performances of the instrument in real observation conditions.
The authors are very grateful to the Centre National d’Etudes Spatiales (CNES) and Thales Alenia Space (TAS) for the thesis funding, and CNES for the support for the Mach-Zehnder R&D.