* Steward Observatory Fellow in Astronomical Instrumentation and Technology.
E-mail<EMAIL_ADDRESS>
# Design and development of a high-speed Visible Pyramid Wavefront Sensor for
the MMT AO system

Narsireddy Anugu  Steward Observatory, University of Arizona, 933 N. Cherry
Ave., Tucson AZ 85721, USA  Olivier Durney  Steward Observatory, University of
Arizona, 933 N. Cherry Ave., Tucson AZ 85721, USA  Katie M. Morzinski  Steward
Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ 85721, USA
Phil Hinz  University of California, Santa Cruz 1156 High St, Santa Cruz, CA
95064  Suresh Sivanandam  Department of Astronomy and Astrophysics, University
of Toronto, 50 St. George Street, Toronto, ON, Canada, M5S 3H4  Jared Males
Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ
85721, USA  Andrew Gardner  Steward Observatory, University of Arizona, 933 N.
Cherry Ave., Tucson AZ 85721, USA  Chuck Fellows  Lunar and Planetary
Laboratory, University of Arizona, 1629 E University Blvd, Tucson, AZ 85721
Manny Montoya  Steward Observatory, University of Arizona, 933 N. Cherry Ave.,
Tucson AZ 85721, USA  Grant West  Steward Observatory, University of Arizona,
933 N. Cherry Ave., Tucson AZ 85721, USA  Amali Vaz  Steward Observatory,
University of Arizona, 933 N. Cherry Ave., Tucson AZ 85721, USA  Emily Mailhot
Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ
85721, USA  Jared Carlson  Steward Observatory, University of Arizona, 933 N.
Cherry Ave., Tucson AZ 85721, USA  Shaojie Chen  Department of Astronomy and
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON,
Canada, M5S 3H4  Masen Lamb  Department of Astronomy and Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON, Canada, M5S 3H4
Adam Butko  Department of Astronomy and Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON, Canada, M5S 3H4  Elwood Downey  Steward
Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ 85721, USA
Jacob Tylor  Department of Astronomy and Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON, Canada, M5S 3H4  Buell Jannuzi  Steward
Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ 85721, USA

###### Abstract

MAPS, MMT Adaptive optics exoPlanet characterization System, is the upgrade of
legacy 6.5m MMT adaptive optics system. It is an NSF MSIP-funded project that
includes (i) refurbishing of the MMT Adaptive Secondary Mirror (ASM), (ii) new
high sensitive and high spatial order visible and near-infrared pyramid
wavefront sensors, and (iii) the upgrade of Arizona Infrared Imager and
Echelle Spectrograph (ARIES) and MMT high Precision Imaging Polarimeter
(MMTPol) science cameras. This paper will present the design and development
of the visible pyramid wavefront sensor. This system consists of an
acquisition camera, a fast-steering tip-tilt modulation mirror, a double
pyramid, a pupil imaging triplet lens, and a low noise and high-speed frame
rate based CCID75 camera. We will report on hardware and software and present
the laboratory characterization results of the individual subsystems, and
outline the on-sky commissioning plan.

###### keywords:

Adaptive optics, Adaptive secondary mirror, pyramid wavefront sensor, MMT,
MAPS

##  1 INTRODUCTION

MAPS[1], MMT Adaptive Optics exoPlanet characterization System is the upgrade
of MMT 6.5m[2] 20-year old adaptive optics system[3, 4]. MAPS is an NSF MSIP-
funded project (PI: Phil Hinz; now – Katie M. Morzinski) that includes (i)
development of new actuators and control electronics for the adaptive-
secondary-mirror (ASM)[5], (ii) new high-sensitive and high-spatial-order
visible and near-infrared pyramid wavefront sensors (VPyWFS and IRPyWFS), and
(iii) the upgrade of science cameras: Arizona infrared imager and echelle
spectrograph (ARIES)[6], and MMT High Precision Imaging Polarimeter
(MMTPol)[7]. The key advantage of having of ASM type deformable mirror is that
it reduces the number of optical elements in the telescope’s AO system,
thereby decreases the thermal noise of the system ($<10$% emissivity[8]) and
increases throughput. The MAPS key astrophysical science programs[1] are to
study exoplanet atmospheres[9] and debris disks in the near-infrared and
thermal wavelengths ranging 1–5 $\mu$m by exploiting the MMT 6.5m collecting
area and its high-angular resolutions, and ARIES high-spectral resolutions and
MMTPol precision polarization measurements. MAPS is a collaborative project
with research groups from the University of Arizona, Arizona State University,
Minnesota Institute for Astrophysics, and the University of Toronto.

Figure 1:  MAPS on the MMT 6.5m - showing ASM, wavefront sensors unit (W-unit)
and science cameras: ARIES and MMTPol. The pyramid wavefront sensor images are
read to aocameras computer using a camera link. The computed slopes are sent
to AO Reconstructor Computer (aorc). The aorc computes the ASM position
control commands from the slopes matrix and sends them to the ASM central hub
for making corrections. Next ARIES and MMTPol records AO corrected science
observations.

Figure 2:  (Top) optical and (bottom) mechanical design of MAPS waterfront
sensor unit.

An overall design of the MAPS-ASM (see Hinz et al. 2018[5]) and infrared
pyramid wavefront sensor (see Liu et al. 2018[10] and Butko et al. 2018[11])
are reported in the previous SPIE proceedings. New actuators and control
electronics for the ASM have been built and characterized thoroughly at the
labs of Steward Observatory, University of Arizona. The ASM performance
results (Vaz et al. 2020[12]) and a general overview of MAPS (Morzinski et al.
2020[1]) can be found in this proceedings.

Figure 1 shows the layout of the MAPS on MMT 6.5m when installed. The VPyWFS
and IRPyWFS are in the post-final-design-review stage, with their review
completed in July 2020 (committee: Dr. Brian McLeod, Dr. Sandrine Thomas, and
Dr. Jared Males). This paper will present the design and development of
VPyWFS. Section 2.1 presents the opto-mechanical design of VPyWFS, which
consists of an atmospheric dispersion corrector (ADC), a K-mirror, a fast-
steering tip-tilt modulation mirror, an acquisition camera, a double pyramid
sensor, a pupil imaging triplet lens, and a low readout noise and high-speed
frame rate camera. We already acquired critical subsystems of VPyWFS,
including a wavefront sensor camera, fast steering tip-tilt modulator, and
acquisition camera. Their performance is characterized and is summarized in
Section 3. In the end, we outline the current status of the project and on-sky
commissioning plans.

##  2 Design of Visible wavefront sensor

###  2.1 Opto mechanical design

VPyWFS is designed to $30\times 30$ sub-aperture wavefront sensing with 1ms
temporal response, and we plan to correct 220 modes of the adaptive secondary
mirror. We have completed all the optical (lead: Olivier Durney) and
mechanical (lead: Manny Montoya) design. Procurement of all parts requested.
The design and component specifications have been carefully developed to
ensure that we meet the very demanding performance requirements for studying
exoplanets systems[1]. Figure 2 shows the high-level architecture of VPyWFS.
The VPyWFS system is divided into four channels:

  * •

Base channel consists of a WFS dichroic, periscope fold mirror, input triplet
lens, atmospheric dispersion corrector, beamsplitter, fast steering tip-tilt
modulator, and image derotator (K-mirror).

  * •

Acquisition channel consists of a Neutral Density (ND) filter wheel, imaging
doublet lenses, a Basler acquisition camera.

  * •

VPyWFS Channel consists of a double pyramid, pupil imaging camera triplet lens
and CCID75 camera.

  * •

IRPyWFS Channel consists of a similar double pyramid, pupil imaging camera
triplet lens, and SAPHIRA camera in a cryostat.

####  2.1.1 The base channel

The MMT 6.5 m primary mirror and 0.642 m ASM create an f/15 converging beam,
and this beam is the input for the WFS unit. The WFS dichroic splits the light
between the WFS and ARIES or MMTPol science camera. An advanced custom-
designed periscope fold mirror is designed to enable (i) 1 arc-minute WFS
patrol field to select AO natural guide star and (ii) WFS nodding to take sky-
backgrounds on the science cameras. The one arc-minute patrolling field
capability increases the availability of AO natural guide stars.

Input triplet is a custom designed 35 mm lens that re‐images the input
telescope f/15 beam onto the tip of the double pyramid of either VPyWFS or
IRPyWFS with f/50 focus. Glass substrates used in this triplet are S‐FPL53,
S‐NSL5, and S‐TIL1. The input triplet is on procurement from Rainbow optics.

Atmospheric Dispersion Corrector (ADC) is used to correct PSF elongation
caused due to the atmospheric dispersion for the operational waveband of the
wavefront sensors $0.6-1.8~{}\mu$m. For example, the atmospheric dispersion in
the visible band ($0.6-1.0~{}\mu$m) causes an elongation of PSF around 740 mas
for the Zenith angle of $60^{\circ}$. In contrast, the diffraction-limited PSF
size in visible is 19-31 mas. The mitigation of this dispersion is essential
for wavefront sensing. A custom ADC is designed using two prisms with a size
of 25.4mm separated by 9mm, and with prism angle of $74.741^{\circ}$. Glass
substrates used for the prisms are S‐PHM53 and S‐TIM8. This is being procured
from BMV Optical Technologies.

Beamsplitter filter wheel splits the light and shares between the acquisition
and wavefront sensor channels.

A fast steering tip-tilt modulation mirror is used to increase dynamic range
of our pyramid wavefront sensor because the sensor quickly becomes non-linear
and can saturate with small wavefront aberrations. A circular modulation is
selected to use with modulation amplitude of $\pm 10\lambda/D$, i.e., $\pm
714~{}\mu$rad at $\lambda=700$nm to account for worse atmospheric turbulence.
The pyramid modulation is conducted with high dynamic and stiffness Piezo tip-
tilt platform assembly, PI S‐331.2SH. This tip-tilt stage has strain gauges to
measure the position of the mirror moving. A 15mm silver coated mirror from
Edmund Optics, 34-388, is used. A circular modulation is generated by applying
a sine waveform on the two tip-tilt axes with a 90-degree shift between them.
This tip-tilt stage is controlled by an E-727 digital three-channel Piezo
controller.

K‐Mirror is an image derotator to keep the pupil aligned between ASM and
VPyWFS or IRPyWFS to account for the Earth’s rotation. We made a custom design
that consists of a prism and a mirror. A prism is used instead of individual
mirrors K‐M1 and K‐M3. The prism facets are protected silver coated and have
sizes of $31\times 22$ mm. A 20 mm mirror (K‐M2) is mounted on a 3‐degrees of
freedom stage to co‐align input and output beams to the optical axis. The
K-mirror is being procured from BMV Optical Technologies.

Figure 3:  The visible pyramid wavefront sensor: (left) double pyramid,
(middle) camera triplet lens and (right) Yorick-Yao[13] simulated pyramid
wavefront sensor pupil images on the detector.

####  2.1.2 The VPyWFS channel

A pyramid wavefront sensor is a pupil plane wavefront sensor that splits the
focal plane into four quadrants on a detector[14]. The wavefront slopes from
the detector images are calculated using the quad-cell centroid of pixel
intensities. The number of sub-apertures in a classical Shack-Hartmann lenslet
array is equal to the number of pixels across one of the pupils in the pyramid
wavefront sensor. The pyramid wavefront sensor is very sensitive[15] compared
to the Shack-Hartmann sensor by using less number of pixels and also having
the freedom of changing the dynamic range by adjusting the radius of
modulation up to $\pm 10\lambda/D$ for bright stars and/or binning the
detector camera pixels for faint stars.

The VPyWFS system operates in $0.6-1\mu$m wavelengths. Its design (see Figure
3) consists of an achromatic double pyramid, a pupil imaging triplet lens, and
the CCID75 detector camera. Table 1 summarize the design specifications.

Double pyramid splits the focal plane into four quadrants. It consists of two
four-sided prisms aligned back to back. The Zemax design is taken from the
LBTI’s design – a highly successful pyramid wavefront sensor[16] – and
optimized for MAPS specifications. For easy manufacturing, the form factor was
changed from round to square. Each pyramid is a 4‐faceted isosceles pyramid
with an extruded square base. Critical pyramid parameters like apex angles and
center thicknesses are optimized for the $1/10$ pixel shift/blur requirements
over a range of modulations from none to $10\lambda/D$. The front prism
$16\times 16$ mm is made from N-SK11, and the back prism $20\times 20$ mm is
made from N-PSK53, and they are bonded back‐to‐back using Norland61. The
double pyramid is being on procurement from WZWOPTICAG.

Camera triplet lens: The pyramid wavefront sensor’s success depends on the
size and separation of the pupils on the detector. We selected $30\times 30$
pixels pupil size for the high-spatial orders of wavefront measurement. The
pupil separation between any two pupil quadrants is $39$ pixels. The 39-pixel
pupil separation is problematic for binning (factor 2 and 4), and so we plan
to defocus and increase this to 40 pixels. A custom achromatic triplet was
designed to re-image the four quadrants of the pupil plane on our CCID75
camera[17] with the appropriate pupil size and separation geometry. Glass
substrates used are N‐BAK1, N‐KZFS5, and S‐LAM60. We require $80\times 80$
pixels Regions Of Interest (ROI) on the detector. We are procuring it from
Rainbow Research optics.

Table 1: The visible pyramid wavefront sensor design specifications. Parameter | value
---|---
Pupil diameter (sub-ap) | 30 px
Final pupil separation | 39 px (we aim 40 px)
Wavelength range |  $0.6-1.0\mu$m
Field of view | $2\times 2^{\prime\prime}$
Modulation amplitude | $\leq\pm 10\lambda/D$
Pupil Jitter [pixel] |  $\leq 1/10$ px
Pupil distortion |  $\leq 1/10$ px
Detector size | CCID75, $160\times 160$ ${\rm px}^{2}$
Detector pixel pitch |  $21\mu$m
Detector ROI |  $80\times 80$ ${\rm px}^{2}$
Input F/# | f/15
Frame rate | 1kHz
Figure 4:  (Left) The architecture of CCID75 reproduced from Schuette et al.
(2014)[17]. It has 160 (Horizontal) $\times 160$ (Vertical) imaging area –
subdivided into twenty 16 (H) $\times 80$ (V) pixel channels. Each channel has
a separate readout chain (serial readout register and output amplifier).
(Right) Quantum efficiency is around 80% for $0.6-0.9\mu$m wavelengths.

CCID75[17] is a $160\times 160$-pixel CCD that has been demonstrated to
operate at frame rates above 1 kHz with readout noise $\sigma_{\rm R}<3$e-/px.
This camera does not use electron avalanche photodiode (eAPD) technology as in
electron-multiplying CCD (EMCCD) but still provides arguably a low readout
noise and fast frame rates using deeply depleted split frame transfer and 20
readout outputs. A drawback of EMCCD is that the avalanche gain does not come
for free but with excess noise, typically 1.47, as the avalanche-
multiplication is statistical in nature, leading to increased noise in the
output signal. Furthermore, over usage of the avalanche gain attracts trap
assisted tunneling noise[18]. EMCCD is the best suited for applications where
the signal levels are readout noise limited, and the conventional CCD output
performs when available signal levels are photon-noise limited.

Figure 4 shows the CCID75 architecture, (i) a deeply depleted split frame
transfer CCD with two frame store areas, and (ii) 20 readout outputs. Each
output is associated with an array of 16 (Horizontal) $\times 80$ (Vertical)
imaging pixels. The CCID75 camera is provided courtesy of Air Force Research
Laboratory and MIT Lincoln Laboratory. SciMeasure built the CCID75 control
electronics. For this camera, the SciMeasure built 32 programs, called ReCall
Settings (RCL) in the non-volatile memory of the controller. By selecting an
appropriate RCL, we can get appropriate ROI, on-chip binning, and frame rate.
The characterization details of CCID75 are found in Section 3.

####  2.1.3 IRPyWFS channel

The availability of two wavefront sensors covering the visible and near-
infrared wavelengths is rare, but it allows a 100% efficiency by boosting the
sky coverage of AO guide stars. IRPyWFS would allow the use of the science
object as the guide star. IRPyWFS will operate in 0.85-1.8$\mu$m, allowing red
type stars, including M-type, to be used for AO guidance. IRPyWFS uses a
breakthrough sub-electron and fast frame rate detector based on electron
avalanche photodiode (eAPD) detector, SAPHIRA[18]. The details of the design,
cryostat, and detector are described in previous SPIE proceedings[10, 11]. A
flip mirror is used to select VPyWFS or IRPyWFS based on the science
requirement and color and brightness of the guide star in the field of view
(see Figure 2).

####  2.1.4 Acquisition camera channel

The acquisition camera operates in $0.65-1.05\mu$m wavelengths, and it enables
us to find the target and AO guide stars in the field of view. A custom double
achromatic doublet lens separated by 7 mm with a diameter 25.4 mm is used to
image the incoming beam on a Baseler camera, CABR720 (see Figure 5). This lens
will be attached to the camera in C‐mount. The Baseler CABR720 camera is a
$1280\times 1024$ NIR CMOS GigE camera with $5.3\mu$m pixel pitch, 60Hz frame
rate, and 36e-/px total noise. The acquisition camera has a neutral density
(ND) filter wheel with slots of 1%, 10%, 25%, 50% ND Vis/NIR, and a blank to
accommodate high dynamic range of acquiring bright and faint stars.

Figure 5: (Left) Acquisition camera procured from Basler. (Right) Quantum
efficiency more than 65% for wavelengths $0.4-0.8\mu$m.

###  2.2 Alignment strategy

The alignment of optics is automated in several systems. Table 2 presents the
alignment strategy, motor or actuator selection, and controller driving the
motor or actuator.

Table 2: Opto-mechanical alignment configuration and motor/actuator types. Optics | Motion type | Precision | Repeatability | Motor and controller
---|---|---|---|---
ADC1 | Rotational | Yes | No | Stepper, MAXnet driver
ADC2 | Rotational | Yes | No | Stepper, MAXnet driver
K-Mirror | Rotational | Yes | Yes | Stepper, MAXnet driver
VPyWFS fold | Linear | Yes | Yes | Stepper, MAXnet driver
VPyWFS Lens | XY Linear | Yes | No | PI P-625.2CD, E-727 controller
PI Modulation | Tip/Tilt | Yes | Yes | PI S-331.2SH, E-727 controller
Dichroic 1 Periscope | Tip/Tilt | Yes | Yes | Stepper, MAXnet driver
Dichroic 2 Periscope | Tip/Tilt, Linear | Yes | Yes | Stepper, MAXnet driver
Acquisition Filter Wheel | Rotational | No | No | Stepper, MAXnet driver
Acquisition Fold Filter Wheel | Rotational | No | No | Stepper, MAXnet driver

###  2.3 Instrument control software

####  2.3.1 Computer hardware

The MAPS computers are COTS products. Three computers are used for the MAPS AO
control (See Figures 6 and 7): the AO cameras (aocameras), the AO
Reconstruction Computer (aorc) and the AO server computer (aoserv). These
computers are identical, i.e., use the same motherboard, processor, and RAM.
These computers each are Intel Xeon with four cores and have 32 GB RAM. The
advantage of using the COTS parts is that they allow managing aged or non-
working parts with replacements likely available for some time in the future.
They also allow easy installation of software upgrades on the replacement
hardware.

The software architecture is based on INDI - Instrument Neutral Distributed
Interface (Elwood 2007). An example application of this architecture is the
Large Binocular Telescope Interferometer instrument[19, 20]. In this
architecture, servers communicate with the hardware, publish relevant
information, and appropriate web-based interface clients to subscribe to the
information. We do not have a central database system. All the server software
is implemented in C/C++, and web-based Graphical User Interfaces (GUIs) are
implemented in Java and HTML5.

Figure 6 presents the architecture of the low-latency real-time WFS loop and
DM loops. These processes use high priority, locked-down memory, and fixed
processor affinity for the low time-delay control loop performance. The
aocameras is the computer where all the frame grabbers of the CCID75 and
SAPHIRA cameras are installed. The INDI drivers, ao_cam_viswfs and
ao_cam_irwfs, which are installed on the aocameras read frames from the CCID75
and SAPHIRA detectors. These INDI drivers also compute slopes and send them to
aorc over a dedicated Ethernet socket in a “WFS loop”, operated at the WFS
frame rate, 1kHz. The aorc server computer runs a second loop, “ASM loop”,
independent of the WFS loop and converts the WFS slopes to the ASM commands.
These commands are sent to the ASM actuators to apply corrections.

Figure 6:  Computer architecture of MAPS AO system. The frame grabbers of the
VPyWFS-CCID75 and the IRPyWFS-SAPHIRA and the RJ45 Ethernet of the acquisition
camera are installed on the aocameras server computer. The INDI instrument
drivers, ao_cam_viswfs, ao_cam_irwfs and ao_cam_acq, which are installed on
aocameras computer, read frames from all the cameras. The ao_cam_viswfs and
ao_cam_irwfs compute slopes from the detector images and then send to aorc
over a dedicated Ethernet socket in a “WFS loop” operated at the WFS frame
rate, 1kHz. ao_dm_operate driver works on the aorc computer runs a second loop
“ASM loop” independent of the WFS loop and converts the WFS slopes to the ASM
commands and send to the ASM actuators to apply correction. The ao_dm_actuator
allow engineering with actuators and the ao_dm_housekeeper does house keeping
and safety.

The non-real-time input and output (I/O) devices such as alignment motors and
actuators (See Table 2), web GUIs, and telemetry storage are implemented on
the aoserv computer.

CCID75 is controlled by SciMeasure’s Little Joe readout electronics and
controller. The readout frames from the SciMeasure controller are grabbed
using a low-latency optimized software from EDT Vision Link F4 frame grabber.
The EDT frame grabber software is installed on a CentOS Linux 7.8 with kernel
running 3.10.0. The pixels read from the sensor are deinterlaced to
reconstruct the correct frame. The software works in Linux, CentOS 7, and is
developed in our lab in the INDI framework in C/C++. The camera link cables
are extended several meters using a noiseless VisionLink camera-fiber-link
extender system using LC/LC duplex multimode fiber optic patch cables between
the CCID75 camera (will be inside the telescope) and the data acquisition
computer (will be placed in the computer control room) for the data
acquisition. (see Figure 9).

Two threads run in the ao_cam_viswfs or ao_cam_irwfs process. One thread runs
the “WFS loop” – reads frames from the camera frame grabber and computes
slopes from the detector image and sends the computed slopes to the aorc
computer. Second loop runs a INDI communication thread responding to user
requests such as changing camera configuration, change frame rate and gain.

Acquisition camera is a GigE industrial camera, and we use Pylon SDK from
Basler for the data acquisition. The camera control and grabbing of frames are
implemented over a TCP protocol using an RJ45 Ethernet cable.

Fast steering tip-tilt modulator software is implemented in Linux using E-727
library and works over a TCP protocol using an RJ45 Ethernet cable.

Telemetry of all the systems and all the time are recorded, including all
wavefront sensors images, slopes, and reconstruction matrix. We plan to use
this information to improve AO performance – for gain estimation[21] and
predictive control[22], the experiments in post-processing to correlate the
telemetry data with science data.

Figure 7:  The aoserv computer handles non-real-time Input and Output devices
such as motors and actuators, web Graphical User Interfaces (GUI) and
telemetry storage. For example, lighttpd is web socket server. The indimaxnet
is an INDI driver for controlling motors. The ao_dm_adm is an INDI driver
allows to play with ASM administrative states. Figure 8:  Expected performance
of MAPS compared to legacy MMT AO system. Reproduced from Hinz et al. 2018[5].
The performance of legacy MMT AO was limited with residual error of 450 nm due
to a low number 55 of corrected modes and a slow temporal response 2.7 ms
delay. The new design will correct 220 modes with a faster temporal response
of 1 ms delay. These efforts will push the residual wavefront error down to
$<$200 nm, i.e., $>70\%$ and $60\%$ Strehl ratios at K and H-bands.

###  2.4 Expected performance of MAPS

The legacy MMT adaptive optics system was optimized for higher wavelengths
with 75% at M-band and delivered poor Strehl ratios for lower wavelengths, 20%
at H-band. The performance was limited due to a low number 55 of corrected
modes and a slow temporal response 2.7 ms delay. For the median seeing at the
MMT of $0.8^{\prime}\prime$, the residual wavefront error is approximately 450
nm RMS, i.e., Strehl ratio of 75% at M-band and $<20$% at H-band. In the new
design, we aim several improvements to the AO control aiming to reduce the
residual wavefront error and increase the Strehl ratio:

  * •

The legacy MMT AO system control was developed by Microgate, and the code was
not open to making modifications to improve the performance. In MAPS, we have
full freedom as we develop the control system for the ASM and wavefront
sensor. We will deploy an optimal PID controller[23], higher spatial mode
correction, and vibration reduction using the accelerometer feed-forward to
reduce residual wavefront error further and increase the Strehl ratio. This
new system will correct 220 modes with a faster temporal response of 1 ms
delay. MAPS is expected to deliver two times better performance – residual
wavefront error of approximately 200 nm RMS. These efforts will push the
residual wavefront error down to $<$200 nm, i.e., $>70\%$ and $60\%$ Strehl
ratios at K and H-bands (See Figure 8).

  * •

The software is carefully designed by leveraging recent advances in the field
to make it reliable and efficient to maximize scientific output. We use very
advanced algorithms for the slope estimation and accurate alignment of camera
triplet lens – from the experience of LBTI[19] and MagAO-X[24]. Simplified
operational interfaces are implemented leveraging the INDI protocol aiming at
improving the observational efficiency.

  * •

Since the deformable mirror being the secondary mirror of the telescope, there
is no artificial calibration source allowing to measure an interaction matrix
as done in classical AO systems. We will use a pseudo-synthetic interaction
matrix reconstructor tweaked from synthetic and on-sky interaction matrices
[25](lead: Masen Lamb).

Figure 8 shows the MAPS estimated Strehl ratio as a function of residual
wavefront error and wavelength.

Figure 9:  (a) A laboratory setup to characterize the CCID75 and tip-tilt
modulation mirror. (b) A E-727 PI controller is used to control the tip-tilt
modulation mirror. (c) The camera link cables are extended several meters
using a noiseless VisionLink camera-fiber-link extender system using LC/LC
duplex multimode fiber optic patch cables between the CCID75 camera (will be
inside the telescope) and the data acquisition computer (will be placed in the
computer room) for the data acquisition.

##  3 Characterization and results

To characterize the performance of the CCID75 camera, PI fast steering tip-
tilt modulation mirror and its E-727 controller, and the Basler acquisition
camera are installed in the MAPS laboratory (see Figure 9) at the Steward
Observatory, University of Arizona.

###  3.1 CCID75 wavefront sensor camera

The CCID75 is characterized for its readout noise, system gain, and linearity
from the Photon Transfer Curve (PTC)[26]. Figures 10 show the images of CCID75
that were recorded using a scene in front of the camera and bias by closing
the shutter. The bias images were stable when tested by power cycling the
camera and the SciMeasure controller. However, the expected temperature-
dependent controller bias characterization has not been done yet.

  * •

For the PTC measurement, the CCID75 is exposed to a precisely controlled laser
source of light and illuminated uniformly flat on the detector. Once the noise
at each illumination level is calculated, a PTC is generated by plotting the
camera’s output RMS noise vs mean signal level on a log-log curve (see Figure
11).

  * •

Read noise is directly available from this PTC by recording the noise level at
zero illumination.

  * •

The camera gain is obtained by fitting a line to the variance vs mean signal
curve in the shot noise limited region and by measuring the slope of that
line. The gain of camera systems is typically expressed in ADU/e-, that is,
the number of analog to digital units per signal electron (see Figure 11).

  * •

The readout noise in ADU/px is divided by the system’s gain to yield the noise
in e-/px.

Table 3 presents various RCL programs of CCID75 and corresponding ROI, system
gain, readout noise, dynamic range, and frame rates. The measured readout
noise is more or less matches with the expected readout noise numbers from the
company[17]. There is a small difference in the readout noise measurement
frame to frame, and that is shown in Figure 12. Furthermore, we measured
quantum efficiency by using a calibrated black-body integrated sphere, and the
measured quantum efficiency matches with Schuette et al. 2014[17] with $\pm
5\%$ deviation.

We need $80\times 80$ pixels ROI for no binning mode, and we will use RCL3 as
it offers the best results required for our specifications: $160\times 96$
pixels ROI, 2.5e-/px readout noise at 2kHz frame rate. We trim the unused
pixels in the VPyWFS software and make final $80\times 80$ ROI. For $2\times
2$ binning, we have optional readout $80\times 80$ ROI, e.g., RCL12 with
readout noise 3e-/px. For $4\times 4$ binning, we have optional $40\times 40$
ROI, e.g., RCL14 with readout noise 2e-/px.

Table 3: CCID75 characterization results. RCL3 will be selected for no-binning readout mode case. Program | Readout | Gain | $\sigma^{\rm mes}_{\rm R}$ | $\sigma^{\rm exp}_{\rm R}$ | Dynamic range | Frame rate | Pixel Rate
---|---|---|---|---|---|---|---
| size | ADU/e- | e-/px | e-/px | ADU/px | Hz | MHz
RCL 0 | $160\times 160$ | 13.8 | 3.69 | 4.4 | 60455 | 2151 | 4.54
RCL 1 | $160\times 128$ | 13.6 | 4.04 | 3.9 | 62262 | 2287 | 3.85
RCL 2 | $160\times 160$ | 15.8 | 2.86 | 2.7 | 62675 | 1441 | 2.78
RCL 3 | $160\times 96$ | 14.6 | 2.49 | 2.7 | 62395 | 2303 | 2.78
RCL 4 | $160\times 128$ | 12.3 | 3.60 | 2.1 | 63261 | 1014 | 1.47
RCL 5 | $160\times 96$ | 15.8 | 2.54 | 2.1 | 62948 | 1332 | 1.47
RCL 6 | $160\times 96$ | 17.6 | 2.94 | 2.0 | 62932 | 931 | 1.01
RCL 7 | $160\times 128$ | 11.0 | 5.63 | 5.9 | 42685 | 3083 | 5.56
RCL 8 | $160\times 160$ | 8.23 | 3.73 | 4.4 | 35103 | 2151 | 4.54
RCL 16 | $160\times 160$ | 0.94 | 7.45 | 4.4 | 4999 | 2151 | 4.54
RCL 24 | $160\times 160$ | 0.73 | 6.30 | 4.4 | 4815 | 2151 | 4.54

Figure 10: Scene and bias images. The bias image show 20 readout outputs with
each output associated with an array of 16 (Horizontal) $\times 80$ (Vertical)
imaging pixels. The bias voltages are adjusted to make them even. The
wavefront sensor images will be subtracted with median bias. The bias can be
dependent on the temperature fluctuations, we plan to a bias image for each
target slew.

Figure 11:  (Left) PTC curve is a log‑log plot of noise versus signal. In this
method, the gain and readout noise of the CCID75 are calculated by using a
linear range of plot and slope where photon shot noise dominates. PTC shows
various noise regions (readout noise, shot-noise, and saturated region). The
RMS value of shot noise is equal to the square root of the photon incident’s
mean number on a given pixel. Thus, the shot noise profile becomes a straight
line with a slope of 0.5 on the log-log curve. Keep in mind that shot noise is
inherent in the nature of light itself and has nothing to do with the camera
design. (Right) The camera gain, ADU/e-, is obtained by fitting a line to the
variance vs. mean signal curve in the shot (photon) noise limited region and
measuring the slope of that line.

Figure 12: Readout noise, $\sigma_{\rm R}$ for various frames.

The pyramid wavefront sensor images need to be synchronized with the modulator
motions – the camera integration period should be an integer multiple of the
modulation period. We are currently working on the synchronization of the
CCID75 wavefront sensor camera images with the PI E-727 modulator tip-tilt
motions. The SciMeasure controller of the CCID75 camera generates an output
signal for each frame, and this external trigger is used in the PI E-727
controller to move the tip-tilt modulator mirror.

###  3.2 Tip-tilt modulation mirror

The fast steering tip-tilt modulation system is characterized for its
frequency response – checking the peak-to-valley modulation amplitude at
several operational frequencies. We verified the modulation amplitude
physically by installing a laser source, reflected the laser beam on the tip-
tilt modulation system, and recorded a circular modulation on the CCID75. Our
requirement of $2\times 10\lambda/D$ modulation is equivalent to peak-to-
valley of $1428\mu$rad. The system is capable of delivering more than two
times our required modulation amplitude (i.e., $3000\mu$rad). Figure 13 shows
the frequency response and recorded circular modulation.

The circular modulation is created by applying sine-wave-generators to the two
tip-tilt axes and a 90-degree phase-shift between them (see Figure 14). The
factory-built sine-wave-generator is not sampled very well, and that caused
limitations in: (i) making a perfectly circular modulation; (ii) making
modulation for all frequencies and amplitudes we wanted. To fix this, we
generate sin-wave data in our software and write that to the firmware of the
E-727 controller.

Figure 13:  (Left) Bode plot – frequency response of modulation system showing
modulation amplitude for various modulation frequencies. The system is capable
of delivering modulation two times the requirement. (Right) $3000\mu$rad
amplitude and 1000 Hz modulation circle recorded on the CCID75 camera using a
laser beam reflected on the modulation system. Figure 14:  A circular
modulation with $3000\mu$rad at 1000 Hz is created with the tip-tilt
modulation stage by applying 90-degree phase-shift between two axes moving
with sine wave.

##  4 Summary and Future work

We presented an overall design of the MAPS visible pyramid wavefront sensor.
The final design of the wavefront sensor is post-PDR. The optics is under
procurement, and they are expected to deliver by the end of 2020. Once the
optics arrive, we will machine mechanical parts. Then we will start the
integration of optics on the VPyWFS optical bench at the Steward Observatory
and test the optics and verify the software, which is already working with
simulated wavefront sensor images.

An AO system’s success depends on lots of testing the cameras and modulation
devices and with the software, and we have carried out all possible tests. We
have already installed and characterized the critical components of the VPyWFS
system: the Basler acquisition camera, PI fast steering tip-tilt modulator,
and CCID75 wavefront sensor camera in the lab. All these systems are within
the specifications.

The MAPS-ASM development is finished and almost ready for usage with the
wavefront sensor. On sky-tests and commissioning on the MMT is planned for
summer 2021. We will use a pseudo-synthetic interaction matrix reconstructor
that is tweaked from simulations and an on-sky interaction matrix. MAPS
exploits the low thermal emissivity of ASM, ARIES, and MMTPol and delivers
unique astronomical capabilities.

###### Acknowledgements.

The MAPS project is primarily funded through the NSF Mid-Scale Innovations
Program, programs AST-1636647 and AST-1836008.

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