Low order aberrations and high performance coronagraphy

High performance coronagraphs, such as the PIAA coronagraph, are very sensitive to small errors in tip-tilt and other low order wavefront aberrations (such as focus and astigmatism). There is a fundamental relationship between the Inner Working Angle of a coronagraph (how close to the star it can image a planet or disk), the contrast ratio at which it is operating, and its sensitivity to low order aberrations: detection of high contrast sources very close to the optical axis requires exquisite control of low order aberrations. This is fundamentally due to the fact that the wavefront from a source close to the optical axis is very similar to a low order aberration on the star wavefront.
Efficient operation of high performance coronagraphs therefore requires control of low order aberrations well beyond what is typically required for imaging systems. On the 0.7m diameter EXCEDE, achieving the full coronagraph performance (1e-6 contrast at 1 λ/D) requires control of tip-tilt to about λ/100, equivalent to a ~2 milliarcsecond angle on the sky in B band. Other low order modes (Focus, astigmatism) have similar requirements. Tip and tilt are the most challenging low order aberrations, as they can easily be produced by pointing error, thermal effects and vibrations in the optical train.
The key to controlling these aberrations is to continuously measure them and use this information to :

Drive actuators (fine steering mirror, spacecraft pointing, deformable mirror) to actively remove the aberrations from the beam in a closed loop control
Record the measured residual aberrations to identify, in the final coronagraphic image, if features are due to low order aberrations or due to real astrophysical sources

Most wavefront control systems are not designed to accurately measure low order aberrations: they are usually designed to measure and correct a large number of wavefront modes to optimize image quality, and this measurement is usually done before the coronagraph, so alignment between the coronagraph focal plane mask and the zero-point of the wavefront control system is challenging, and likely to change with time. EXCEDE relies on measurement of wavefront errors directly in the science focal plane (were the speckles encode wavefront errors). While this approach is robust for measurement of mid-spatial frequencies, it is not suitable for low order aberrations. For example, a pointing error will not be detected until it starts to be large enough to leak into the science image and compromize the science return of the mission- low order aberrations will be detected only when large, and with poor sensitivity. The best option for measuring low order wavefront errors is therefore to use the light blocked by the focal plane mask, as it will allow high sensitivity of the aberration before they start producing a significant light leak into the science image. The next section describes how this can be done efficiently and to high accuracy.

The Coronagraphic Low Order Wavefront Sensor (CLOWFS) concept

Most coronagraph concepts use a focal plane mask to block starlight. The bright starlight falling on the mask is not used for science, and is therefore available for low order eavefront sensing. Low order aberrations are actually best sensed using this light, as they will deform the central PSF core (for example, tip-tilt will move the PSF core). The CLOWFS therefore uses this light, which is reflected to a fast camera, to measure these aberrations. In the CLOWFS concept, two hardware improvements to this simple scheme improve sensitivity and robustness:

The focal plane mask is not made fully reflective, instead, it is opaque in its very center, and the annulus around it is reflective. This offers two significant advantages:
- The central part of the PSF contains most of the photons but little signal: low order aberrations modify the wings of the PSF more than its center. For example, tip-tilt produces a small shift of the PSF, which does not change surface brightness at the PSF peak location (where the spatial derivative of the PSF surface brightness is zero). By blocking the central part of the PSF, only the part of the PSF with the best signal to noise ratio is preserved, and a small aberration produces an easily measured macroscopic change in the light reflected by the reflective annulus
- With a non-reflective central disk in the focal plane mask, the LOWFS signal for a tip-tilt aberration is a change in the morphology of the LOWFS image, not a translation of the re-imaged spot. This removes issues associated with referencing the LOWFS image to the focal plane mask position, and makes the LOWFS immune to vibration and flexures in the LOWFS path.
The LOWFS camera is defocused slightly. This allows unambiguous measurement of Focus. If the LOWFS detector were conjugated to the focal plane mask, only the amplitude (not the sign) of focus could be measured. With this defocus, the sign and amplitude of Focus are measured.

Fig 1: Coronagraphic Low Order Wavefront Sensor (CLOWFS) concept, shown here on a PIAA type coronagraph. Bright starlight falling on the focal plane mask is used to measure low order aberrations with a dedicated fast camera. [png]

Fig 2: Focal plane mask for the CLOWFS. This focal plane mask was manufactured for the first laboratory demonstration of the concept. The central opaque disk is 100 micron radius, and the reflective annulus around it is 100 micron wide. [png]

LOWFS algorithm, performance and design optimization

The LOWFS is a linear sensor. To calibrate the LOWFS, actuators are moved (for example tip and tilt) while the LOWFS records the corresponding modes in the image. These modes are used as calibration to analyze all LOWFS images. A simple linear decomposition of LOWFS images into the sum of a reference image and the LOWFS modes yield the values of the corresponding low order aberrations. This algorithm is fast (linear) and does not rely on modeling of the LOWFS response (which is measured, not modeled).
The LOWFS allows measurement of tip-tilt close to the theoretical fundamental limit of 1/(sqrt(N) π) λ/D (single axis, 1-σ), with N the total number of photon in the beam ahead of the focal plane mask. A detailed analysis of the LOWFS is provided in Guyon et al. 2010, along with a quantitative description of how the LOWFS design parameters affect its performance. An example result of this analysis is shown in Fig. 3, where the sensitivity for different low order aberrations is shown as a function of relative size of the inner opaque disk to the reflective annulus, and of the defocus distance in the LOWFS camera.

Past and Existing LOWFS+PIAA systems

The LOWFS was first implemented on a PIAA coronagraph testbed at the Subaru Telescope. This fist prototype achieved 1e-3 λ/D closed loop tip-tilt control in air with a PIAA coronagraph and a 1Hz sampling frequency (results shown in Fig 3). A second faster LOWFS is now also in operation on the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system, and is running at 100Hz sampling frequency in near-IR for ground-based coronagraphy. LOWFS systems are also in preparation for the PIAA coronagraph at the High Contrast Imaging Testbed at NASA JPL and the NASA Ames PIAA testbed.

Fig 3: Laboratory performance for the CLOWFS. Upper left: Measured CLOWFS reference frame and influence functions for the 5 axis controlled in the experiment. Pre-PIAA and post-PIAA modes look extremely similar, as expected. Top right: Open loop simultaneous measurement of pre and post-PIAA modes. The measured amplitudes match very well the sine-wave signals sent to the actuators, and the CLOWFS is able to accurately measure all 4 modes shown here with little cross-talk. Since this measurement was performed in open loop, the measurement also include unknown drifts due to the limited stability of the testbed. Bottom left: Closed loop measurement of the residual error for the 5 modes controlled. The achieved pointing stability is about 1e-3 λ/D for both the pre-PIAA and post-PIAA tip/tilt. Bottom right: Position of the actuators during the same closed loop test. [png]