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Fine-tuning the rotational shearing interferometer to detect extrasolar planets
Direct detection of planets around stars can be enhanced using a rotational shearing interferometer that suppresses star infrared radiation.
14 December 2006, SPIE Newsroom. DOI: 10.1117/2.1200611.0476
One of the most intriguing scientific pursuits is searching for other planets with conditions suitable for life. The planets within our own solar system have all been explored to the point of concluding that none can support terrestrial life forms. The quest has accordingly been extended to planets around nearby stars, with some 200 detected so far. However, important challenges remain, one of the most pressing being direct imaging of extrasolar planets. To date, most have been spied using indirect methods that carefully register the movements and speeds of the stars that the planets orbit.1,2
The main problem in looking for these objects is that they are not bright. In visible light, the radiance of a host star is a billion times greater than that of a planet, and in infrared radiation a hundred thousand times greater.3 Small planet signals thus become lost. Proximity between star and planet represents additional complexity: seen from Earth, the planet with reference to the star subtends an angle of the order of an arcsecond. No detector can presently resolve a tiny planet signal near an enormous star signal when using a conventional telescope. However, suppressing the star's radiation makes it possible to extract the planet signal.4,5 An instrument that performs this function is the rotational shearing interferometer (RSI).6,7
The RSI concept is based on splitting the incident wavefront so that it can be compared with itself, as one of the resulting wavefronts is rotated.8 Figure 1 shows an RSI implemented as a modified Mach-Zehnder interferometer, with a dove prism on each arm. To rotate the wavefront, one of the prisms is rotated with respect to the other.7,8
Figure 1. Shown is a rotational shear interferometer with two beam splitters and a dove prism on each arm.
In previous work, we defined the conditions required for starlight cancellation with an RSI. First, the star had to be on the axis of the RSI, and second, the optical path difference (OPD) between the interferometer arms had be equal to λ/2.6 It should be noted, however, that these ideal conditions are almost impossible to achieve. Consequently, we decided to include the OPD and the angle between the optical axis and the direction of the star in the expression defining star incidence.9
We also analyzed the effect resulting from the star not being on the interferometer axis, and included an arbitrary OPD between the interferometer arms.9 Figure 2 shows a sketch of the interferometer and star-planet system. The interferometer is aligned with the telescope axis, but the star is outside the line of sight. Due to the great observation distance, our mathematical model considered the star and the planet as point sources, although more realistic assumptions would be required for stars much larger than the Sun.10
Figure 2. This diagram of the interferometer and star-planet system shows a star misaligned with respect to the interferometer axis.
For the stated conditions, we derived an expression for the irradiance of a star-planet system as a function of the star irradiance IS, the planet irradiance IP, the polar coordinates of the points at the detection plane ρ and θ, the wave number k, the OPD between the wave fronts of each arm of the interferometer δ, the rotation angle of the wave front Δθ, and four constants related to the location of the star-planet system (tilt angle of the star and orientation angles of the star and the planet: Θ, Ω, Г, and Λ):9
Using equation 1, we then simulated many incidence distributions for varying locations of the star-planet system using different OPD values. Our results allowed us to conclude that the planet signal decreases as the OPD and tilt angle increase.9
We have described some of our work on the conditions that should be met to detect extrasolar planets with an RSI. Currently, we are analyzing the prism tolerances for manufacturing errors.11 Future work will be focused on obtaining the planet signal as a function of the OPD and star tilt angle. We also plan to correct RSI optical component errors in the mathematical model.
Maximiliano Galán, Marija Strojnik, Gonzalo Paez, Enoch Gutiérrez, Paulino Vacas-Jacques
Optical Engineering, Centro de Investigaciones en Óptica
León, Guanajuato, Mexico
Maximiliano Galán is a graduate student at the Centro de Investigaciones en Óptica. He completed his MS in optics in 2005, working on planet detection and interferometric methods. Previously, he obtained a BS in physics from the University of Guadalajara, Mexico.