Laboratory test of the Mach-Zehnder co-phasing technique

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ELTs: Motivation and Description

In the next decades, astronomy will profit from a diverse set of observing capabilities, covering a broad range of wavelengths, on the ground and in the space. Two main reasons make the development of large ground based telescopes critical to expand astrophysical knowledge. First, the possibility of observing in a range covering from the optical to the infrared. Second, ground based facilities can deploy much more complex instrumentation than spaced-based missions.
Three broad topics are proposed by the Astrophysical Community: Cosmology, Galaxies, and Planetary Systems and Stars. Scientific cases will benefit from the wide capabilities of large telescopes, including sensitivity, wavelength coverage, field of view (FOV), spectral resolution, photometric and astrometric accuracy, high image quality and stability. We briefly describe some scientific cases including the required capabilities and instrumentation to carry out those programs.
A number of Extremely Large Telescopes (ELT) projects are currently in phase of design study. They differ mainly in the primary mirror selection, although segmentation is the common solution adopted in every case. We describe the different approaches proposed by the most important ELT projects.
The image quality is affected by segmentation. This chapter includes a brief description of the effects induced by wavefront errors on the image quality, with special attention to the effect of segmentation misalignment.

The role of ELTs in Astronomy

The enormous capabilities of the next generation of telescopes will expand the frontiers of astrophysical knowledge and will be the key to answer many unresolved questions. As a consequence, a large number of scientific cases have been proposed for ELTs, covering different astrophysical contexts ranging from our own Solar System to the very early epochs of the Universe. The European Astrophysical community, under the auspices of the OPTICON (Optical Infrared Coordination Network), has classified these different scientific cases into three main categories: Cosmology, Stars and Galaxies, and Planetary Systems and Stars. We briefly present some of these science highlights that motivate and encourage the development of ELTs.
In the coming decades, one of the most important challenges of observational cosmology will be to measure the evolution of the spatial distribution and properties of the baryonic content of the Universe in its different phases: galaxies and intergalactic gas. Establishing the statistical evolution of galaxies from their epoch of formation (more than 13 Giga-light-years away) to the present day, requires taking hundreds of high-resolution spectra (R>5000) of very faint objects (typically >25 AB mag) over a wide area (FOV ~ 5′).
At the same time, mapping the 3-dimensional distribution of the cosmic gas in the Universe requires the acquisition of high quality spectra of faint objects in the distant universe, numerous enough to finely sample the large observed areas (FOV ~ 5′). These observations are necessary to discriminate among the competing theories at stake today. Their requirements call for ELTs, which have high enough sensitivity and FOVs. The Figure 1.1.1 shows an example of simulated distribution of cosmic gas at z=2.
Stars are one of the main components of galaxies, therefore it is of critical importance to understand how they form and evolve. With ELTs, stars of mass comparable to the Sun may be resolved in the outskirts of galaxies as far as the Virgo cluster (the closest cluster to the Milky Way). Reaching the Virgo cluster is important since it hosts a significant population of elliptical galaxies at the same distance and spanning a large range of magnitudes. With a very high spatial resolution (~10mas), required to diminish the effect of crowding, and a collecting power capable to reach typical magnitudes of ~35 in the optical band, we will be able to define the turn-off point of the color-magnitude diagrams of the studied stellar populations.
The discovery of extra-solar planets has placed our solar system in a new context and has revived the theoretical investigations of the formation and evolution of planetary system. These theories can be tested directly by measuring the gas phase dynamics and the chemical structure of protoplanetary disks. For this program high spatial (<80mas) and spectral (R~105) resolutions at thermal infrared wavelengths are required.
According to the scientific programs, the required capabilities can be gathered in four different operation modes:
i) Wide Field Mode: In this mode the angular resolution is limited by atmospheric conditions. It provides high sensitivity over a large FOV (~5’-10’).
ii) Classical Adaptive Optics Mode: This mode will provide diffraction-limited FOV around 10” in the infrared.
iii) Multi Conjugate Adaptive Optics (MCAO) Mode: MCAO (Beckers 1988) permits the extension of the diffraction-limited FOV beyond the limits of the isoplanatic patch. Moderate image quality can be reached over FOV of 30” in the visible and 2’ in the infrared.
iv) Extreme Adaptive Optic Mode: This mode provides diffraction limited images with very high quality but in small FOV (~1”-10”). The high spatial resolution and IR sensitivity of an ELT enables one of the most attractive and high priority targets of ELTs: to find the Earth like extra-solar planets around nearby bright stars.

ELT Projects

The technology developed for 10-m class telescopes serves as starting point for the design study of ELTs. In the current generation of large telescopes, two concepts primary mirrors have been pursued: monolithic mirrors and segmented mirrors.
Two technologies have been developed for current monolithic mirrors. The first one is the construction of a single large mirror made from borosilicate glass, but having large hollowed out regions to keep the weight down. This borosilicate honeycomb design has been pioneered by Angel & Hill (1982) and it has been successfully cast in the two 8.4-m primary mirrors of the Large Binocular Telescope (Hill & Salinari 2003). The second design is the thin mirror approach, primarily built by two companies, Corning (USA) and Schott (Germany). They used materials with good thermal properties, ULE (Corning) and Zerodur (Schott). Thin mirrors are being used for the four 8-m Very Large Telescope (VLT White Book, 1998). Although somewhat larger monolithic mirrors could be made, manufacturing complexity and relative cost increase with size. Therefore, the most realistic approach that can be extended to the ELTs involves the use of segmentation.
The feasibility of making segmented mirrors was first demonstrated by the Multiple Mirror Telescope (MMT) (Beckers et al, 1981) and TEMOS (Lemaître&Wang, 1993). The MMT was composed of six identical 1.8-meter telescopes in a single altitude-azimut mount. By contrast the TEMOS concept uses a primary mirror composed of large circular segments and a monolithic active secondary (Baranne&Lemaitre, 1987).
Three large segmented-mirror telescopes already exist: Keck I, Keck II (Nelson et al 1985)— which are two 10-m class telescopes composed by 36 hexagonal segments of 0.9m side— and the Hobby-Eberly Telescope (HET, Krabbendam et al 1998)- which is a 9-m telescope composed of 91 segments, each of 0.6 m side. Several others are being developed or have been proposed, including: Gran Telescopio de Canarias (GTC, Castro et al 2000) which has a similar configuration to Keck and the Southern African Large Telescope (SALT, Meiring et al 2003), whose design is based on HET. The Mexican Infrared-Optical Telescope (TIM, Cruz-Gonzalez, 2003), is a 8-m segmented telescope with 19 hexagonal segments with a maximum diameter of 1.8m. A very interesting project is the Large Aperture Multi-Object Spectroscopic Telescope (LAMOST, Wang et al 1996), which is a Schmidt telescope with a 5 degree FOV and active optics. The 6-m spherical primary mirror consists of 37 hexagonal spherical mirrors, each of them having a diagonal of 1.1m and a thickness of 75mm. The reflecting corrector of 4.5-m is located at the center of curvature of the primary mirror, it consists of 24 hexagonal plane submirrors, each of them having a diagonal of 1.1m and a thickness of 25mm. The available large focal plane of 1.75 meters in diameter may accommodate up to 4000 fibers, by which the collected light of distant and faint celestial objects down to 20.5 magnitude is fed into the spectrographs, which promises a very high spectrum acquiring rate of several ten-thousands of spectra per night.
ELT projects are currently in the concept study stage. The main discussions concerning the optical design turn on the choice of the primary mirror, which concerns the shape of the pupil, the size and shape of the segments and the density of the pupil, taken as the percentage of pupil filled with reflective surface.
The great advantage of spherical mirrors is their segment fabrication as all segments are identical. This option has been adopted for the 100-m project Overwhelmingly Large Telescope (OWL) due to the large number of segments to be fabricated, ~3000, with the consequent disadvantage of considerably increasing the complexity of the optical design in order to correct spherical aberrations.
Although the development of segmented mirrors dates from the last decade, there is still no agreement on the choice of the segment parameters. The Thirty Meter Telescope (TMT) proposed by an American-Canadian consortium opts for hexagonal segments of 0.5 to 1m side following the example of Keck. The uses of small segments reduce cost factors related to the fabrication equipment, transportation and coating chambers. It simplifies the support mechanism and it allows higher optical quality of the individual segment. On the other hand, the choice of large segments reduces the number of actuators and edge sensors required to control the shape of the mirror. At the same time it simplifies the telescope structure and reduces the edge sensor noise propagation. This alternative has been adopted for the 25-m Giant Magellan Telescope (GMT) and the 20-m Large Petal Telescope (LPT). The GMT used 6 circular segments while LPT employs 8 irregular hexagonal segments to fill a circular shape with a minimum of edges. The shape and size of the segments plays an important role on the diffraction effects observed in the focal plane. This aspect is of relevant importance since the diffraction effects can lead to confusion in the study of faint pointlike sources.
We remark the fast focal ratio of the primary to allow a compact telescope structure. This will make mirror manufacture harder.
The primary mirror choice will play a fundamental role in the performance of diffraction images of point sources. Several simulation studies have been carried out in order to analyse the effect of segment size and shape on the image quality (Kuhn et al 2001, Marchis & Cuevas 1999). Zamkotsian et al (2003-2004) performed the comparison of the point-spread-function (PSF) for three different mirror approaches, as seen in Figure 1.2.1. They found particularly interesting the case of polygonal petals, because the number of diffraction spikes in the PSF is minimised leading to large areas of low levels of scattered light close to the core. This is important for high dynamic range imaging.
For certain scientific cases diffraction effects due to segment misalignment are not negligible. Diffraction effects from highly segmented mirrors have been studied in detail elsewhere (Zeider & Montgomery 1998, Troy & Chanan 2003, Yaitskova et al 2003, Bello et al, 2000), and we will briefly present them here.

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Image quality of a highly segmented mirror

In the last twenty years hard efforts have been concentrated in order to improve the image quality of telescopes. Those efforts are focused in the correction of wavefront errors introduced by the atmosphere, by the use of Adaptive Optic (AO) Systems, as well as the reduction of wavefront errors related to the telescope optic quality, by the use of Active Optic Systems. Image quality will also be affected by segmentation. Gaps, individual segment aberrations, edge miss-figure errors and piston and tip-tilt misalignments result in new diffraction effects which are qualitative and quantitatively different according to the size and segment number.
In this section we briefly describe the effect of segmentation on the image quality paying special attention to the effect of segmentation misalignments. We also describe the most important properties of atmosphere turbulence and its influence on the image quality.

Effect of segmentation on the image quality

Generally segments have six degrees of freedom: translation along two axes in the plane of the segment, rotation about a vertical axis, rotation about two horizontal axes (tip and tilt), and translation along the vertical axis (piston). Misalignments of the three first degrees of freedom are not critical for the image quality (Mast 1982). However, movement of pistons or tip-tilts produce wavefront discontinuities which damage the image quality.
In order to quantify the quality of the image, several criteria are used. Yaitskova et al (2003), employ peak intensity and mean halo intensity of the PSF. Diericks (1992) proposed the Central Intensity Ratio (CIR), defined as the ratio between the central intensity given by the telescope divided by the central intensity given by an equivalent perfect telescope without aberrations but under the same seeing conditions. We limit this discussion to the Strehl ratio, a criteria frequently employed in astronomy. It is equal to the ratio between the central intensity of the aberrated PSF and the central intensity of the diffraction-limited PSF.
Figure 1.3.1 Pupil of a 50m class segmented telescope with 714 segments without any error (left) and its corresponding PSF(right).
The presence of piston will not influence the segment PSF. However, it will modify the grid term introducing a noisy speckle background. In Figure 1.3.2, we represent a segmented pupil with piston RMS error equal to 120nm and its corresponding PSF over a field of 0.5”. The size of the speckle field is equal to the size of the segment PSF, and does not depend on the value of the piston error.

Table of contents :

Chapter 1 ELTs: Motivation and Description
1.1. The role of ELTs in Astronomy
1.2. ELT Projects
1.3. Image quality of a highly segmented mirror
1.3.1. Effect of segmentation on the image quality
1.3.2. Influence of atmospheric turbulence on the image quality
Chapter 2 Review of co-phasing Techniques
2.1. Diffraction co-phasing techniques
2.2. Co-phasing techniques based on Curvature sensors
2.3. Other alternatives for co-phasing
2.4. Pyramid sensor for measuring dephased errors
2.5. Interferometric techniques for co-phasing segmented mirrors
Chapter 3 Mach-Zehnder co-phasing technique
3.1. General Description
3.2. Analytical study of a Mach-Zehnder Interferometer
3.2.1. Analytical expression of 1-D interferograms: the piston error case
3.2.2. Behaviour of the MZ signal when introducing an OPD
3.2.3. Behaviour of the MZ signal with pinhole size
3.3. Coronograph: a simplified approach to the Mach-Zehnder interferometer
3.4. Numerical Simulations
3.4.1. Simulation of 1-D MZ signal
3.4.2. Aliasing effect
3.4.3. Influence of Turbulence on the MZ signal
3.4.4. Influence of Gaps on the MZ signal
3.4.5. Influence of the edge defects on the MZ signal
3.4.6. Pixelisation and Sampling
3.4.7. Multi-wavelength measurement
3.4.8. Tip-Tilt considerations
3.5. Performance of a Mach-Zehnder co-phasing sensor
3.5.1. MZ co-phasing sensor performance as a function of atmospheric turbulence
3.5.2. MZ co-phasing sensor performance as a function of gaps
3.5.3. MZ co-phasing sensor performance as a function of edge defects
3.5.4. MZ co-phasing sensor performance as a function of photon noise
3.6. Summary
Chapter 4 Laboratory test of the Mach-Zehnder co-phasing technique
4.1. Optical design for testing the MZ co-phasing technique
4.1.1. Segment Simulator
4.1.2. Turbulence Simulator
4.1.3. Mach-Zehnder interferometer layout
4.2. Analysis of the experimental results
4.2.1. Performance without atmosphere
4.2.2. Performance with atmosphere
4.3. Summary
Chapter 5 Comparison of co-phasing techniques
5.1. Signal Characterisation
5.1.1. Sensibility to atmosphere, gaps and edge defects
5.2. Piston Retrieval
5.2.1. Precision, Capture Range and limiting magnitude
5.2.2. APE the Active Phase Experiment
5.3. Practical and Manufacturing considerations
5.4. Summary
Chapter 6 Conclusions and Perspectives

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