Slow+WFS

Basic Principles
The slow wavefront sensor, if used with starlight, could have the following functions:
 * 1) Slow tip/tilt correction (< 1 Hz) for alignment drifts.
 * 2) Fast tip/tilt correction for stars brighter than ~11th magnitude.
 * 3) Slow pupil position correction, to correct for e.g. rail alignment.
 * 4) Operation as a closed-loop AO system for visually-bright stars to improve IR visibilities (e.g. A stars at 9th magnitude).
 * 5) Fast tip/tilt correction using a beacon to correct for lab seeing and vibrations when a visible-reflecting dichroic is in place.

Calibration Method For Laboratory DM Using Starlight
A: Slow WFS Reconstructor Calibration B: Slow WFS only Lock C: Reconstructor Calibration for Fast WFS D: Dual Wavefront Sensor Matrix Calibration E: Beacon Calibration
 * 1) Auto-collimate internally with a flat mirror and a laser or WL source. Record the [Flat Slow WFS] positions.
 * 2) Move each actuator in turn and see how the wavefront sensor responds.
 * 3) Create an interaction matrix and invert using a standard technique, e.g. the Moore-Penrose pseudo-inverse.
 * 1) Tip/tilt from the Slow WFS feeds back to the tip/tilt mirror.
 * 2) Pupil alignment feeds back to BRT secondary, M12 or M10 (the furthest mirror from the telescope possible that sees both IR and Vis beams).
 * 3) High-order corrections feeds back to the lab DM (NB requires more than about 200Hz on the "Slow" WFS).
 * 1) Lock the system on a bright star using the "Slow WFS" as sensor.
 * 2) Record a time series of Fast WFS sensor positions and lab DM positions. This is a cloud of points in a N_WFS to N_DM space mapping, to which we want to fit a linear map.
 * 3) Project the time series onto each WFS axis in turn to find the column in the reconstructor corresponding to each sensor.
 * 4) Repeat for different azimuths.
 * 1) Take out static aberration on the lab DM (computed as part of B).
 * 2) Record a time series of Fast WFS and Slow WFS frames on a bright star.
 * 3) Similar to C3 above, create a matrix for slow WFS to fast WFS calibration.
 * 4) Repeat for different azimuths.
 * 1) Record the slow WFS centroid positions [Beacon Measured] corresponding to the beacon.
 * 2) Compute the target slow WFS centroid positions, which are 2*[Flat Slow WFS] - [Beacon Measured].

This produces the following operation modes... __Starlight Only__ __Beacon Only__
 * The reconstructor calibrated in (C) is used to map WFS positions to DM actuator positions. There is no servo feedback - the WFS positions are simply multiplied by a matrix and added to the DM.
 * The matrix in (D) is used to feed back offsets to the fast WFS.
 * Possibly, higher-order terms are averaged before being sent back.
 * Pupil location is fed back to the BRT secondary, M12 or M10 (see B above).
 * The reconstructor calibrated in (C) is used to map WFS positions to DM actuator positions. There is no servo feedback - the WFS positions are simply multiplied by a matrix and added to the DM.
 * A band-pass or long-pass filter is placed in front of the Slow WFS so that it only sees beacon light.
 * The matrix in (D) using offsets from (E2) is used to feed back offsets to the fast WFS.
 * Pupil location is fed back to the BRT secondary, M12 or M10 (see B above).

**Flux Requirement for AO Lock for Calibration**
In order to get good sky coverage of reference stars, we will assume that the AO calibration is done on a 4th magnitude A star. Assuming B-band and half of V-band (0.4 to 0.55 microns), 80,000 photons arrive at the top of the atmosphere in every 5 millsec for a 0.2 m aperture. Assuming that we need at least 100 photons for a lock, this puts a minimum system throughput requirement of 0.13%. With a CHARA throughput in the blue of about 2% and 65% WFS quantum efficiency, this means that an IR dichroic throughput of at least 10% is needed over the 0.4 to 0.55 micron band in order to lock the slow WFS on calibration stars.

Flux Requirement for Slow WFS Lock (starlight-only operation)
With the same arguments as above but a 5 second integration time, B magnitudes of 11.5 should enable slow WFS lock on sky. With a minimum 25% transmission requirement for the IR dichroic on average between 0.4 ant 0.55 microns, this becomes B=12.5. Red YSOs with B=14th magnitude will not have enough flux for slow WFS lock with starlight, and will require a beacon.

**Flux Requirement for Internal Seeing/Vibration Lock**
This is currently impossible to compute as we don't know the power spectrum or general amplitude of internal seeing ???

Calibration Method Using Beacon Only
//Is this possible? Or is starlight always needed? Could the calibration be done with one dichroic and the dichroic changed? How do the small wavefront errors in the dichroic (transmission and reflection) as well as alignment tolerances translate to modifications of the calibration algorithm?//

Optical Design
Laszlo's email from 7 Sep states that the existing system has //beams are arranged along a R=70 mm circle, 45 deg apart. The parabolic mirror is 8'' F/6. //The SPIE paper describing the system is ... (MJI had errors trying to upload it).

For an initial design, we will work with a pupil position 20m upstream from this mirror, meaning that the pupil-plane is 42mm behind the common focal-plane, where the pupils are 0.88mm in diameter and on a 3.3mm circle. Each sub-pupil in the F/6 paraboloid is F/47, meaning that the coma-free field of view is very large. By angling the mirrors immediately prior to the paraboloid, the pupil separation can be arbitrary, and could even be set so that the sub-pupils on the F/6 paraboloid overlapped on the system pupil-plane. However, the simplest option is definitely to maintain the 8-way arrangement.

__512x512 Camera Design__
asdf

__128x128 Camera Design__
MJI can not figure out how do get this to work with the 8-way arrangement as it stands. However, things could work with a 6-way arrangement where the 20cm sampled hexagons are arranged on a lenslet array like this: