figure table

# The Keck Planet Imager and Characterizer: A dedicated single-mode fiber
injection unit for high resolution exoplanet spectroscopy

Jacques-Robert Delorme  Department of Astronomy, California Institute of
Technology, Pasadena, CA 91106, USA  W. M. Keck Observatory, 65-1120 Mamalahoa
Highway., Kamuela, HI 96743, USA.  Nemanja Jovanovic  Department of Astronomy,
California Institute of Technology, Pasadena, CA 91106, USA  Daniel Echeverri
Department of Astronomy, California Institute of Technology, Pasadena, CA
91106, USA  Dimitri Mawet  Department of Astronomy, California Institute of
Technology, Pasadena, CA 91106, USA  Jet Propulsion Laboratory, California
Institute of Technology, Pasadena, CA 91109, USA  J. Kent Wallace  Jet
Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109,
USA  Randall D. Bartos  Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA 91109, USA  Sylvain Cetre  W. M. Keck Observatory,
65-1120 Mamalahoa Highway., Kamuela, HI 96743, USA.  Peter Wizinowich  W. M.
Keck Observatory, 65-1120 Mamalahoa Highway., Kamuela, HI 96743, USA.  Sam
Ragland  W. M. Keck Observatory, 65-1120 Mamalahoa Highway., Kamuela, HI
96743, USA.  Scott Lilley  W. M. Keck Observatory, 65-1120 Mamalahoa Highway.,
Kamuela, HI 96743, USA.  Edward Wetherell  W. M. Keck Observatory, 65-1120
Mamalahoa Highway., Kamuela, HI 96743, USA.  Greg Doppmann  W. M. Keck
Observatory, 65-1120 Mamalahoa Highway., Kamuela, HI 96743, USA.  Jason J.
Wang  Department of Astronomy, California Institute of Technology, Pasadena,
CA 91106, USA  Evan C. Morris  U.C. Santa Cruz, 1156 High Street, Santa Cruz,
Ca 95064, USA.  Jean-Baptiste Ruffio  Department of Astronomy, California
Institute of Technology, Pasadena, CA 91106, USA  Emily C. Martin  U.C. Santa
Cruz, 1156 High Street, Santa Cruz, Ca 95064, USA.  Michael P. Fitzgerald
Department of Physics & Astronomy, University of California, Los Angeles, CA
90095, USA  Garreth Ruane  Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA 91109, USA  Tobias Schofield  Department of
Astronomy, California Institute of Technology, Pasadena, CA 91106, USA  Nick
Suominen  Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA 91109, USA  Benjamin Calvin  Department of Astronomy, California
Institute of Technology, Pasadena, CA 91106, USA  Eric Wang  Department of
Physics & Astronomy, University of California, Los Angeles, CA 90095, USA
Kenneth Magnone  Department of Physics & Astronomy, University of California,
Los Angeles, CA 90095, USA  Christopher Johnson  Department of Physics &
Astronomy, University of California, Los Angeles, CA 90095, USA  Ji Man Sohn
Department of Physics & Astronomy, University of California, Los Angeles, CA
90095, USA  Ronald A. López  Department of Physics & Astronomy, University of
California, Los Angeles, CA 90095, USA  Charlotte Z. Bond  W. M. Keck
Observatory, 65-1120 Mamalahoa Highway., Kamuela, HI 96743, USA.  Jacklyn
Pezzato  Department of Astronomy, California Institute of Technology,
Pasadena, CA 91106, USA  Jorge Llop Sayson  Department of Astronomy,
California Institute of Technology, Pasadena, CA 91106, USA  Mark Chun
Institute for Astronomy, University of Hawaii, 640 N. Aohoku Place, Hilo, HI
96720, USA.  Andrew J. Skemer  U.C. Santa Cruz, 1156 High Street, Santa Cruz,
Ca 95064, USA.

###### Abstract

The Keck Planet Imager and Characterizer (KPIC) is a purpose-built instrument
to demonstrate new technological and instrumental concepts initially developed
for the exoplanet direct imaging field. Located downstream of the current Keck
II adaptive optic system, KPIC contains a fiber injection unit (FIU) capable
of combining the high-contrast imaging capability of the adaptive optics
system with the high dispersion spectroscopy capability of the current Keck
high resolution infrared spectrograph (NIRSPEC). Deployed at Keck in September
2018, this instrument has already been used to acquire high resolution spectra
($R>30,000$) of multiple targets of interest. In the near term, it will be
used to spectrally characterize known directly imaged exoplanets and low-mass
brown dwarf companions visible in the northern hemisphere with a spectral
resolution high enough to enable spin and planetary radial velocity
measurements as well as Doppler imaging of atmospheric weather phenomena. Here
we present the design of the FIU, the unique calibration procedures needed to
operate a single-mode fiber instrument and the system performance.

###### keywords:

Instrumentation, W. M. Keck Observatory, Exoplanets, High contrast imaging,
High dispersion coronagraphy, High resolution spectroscopy

* Corresponding author: Jacques-Robert Delorme<EMAIL_ADDRESS>
##  1 Introduction

Since the first exoplanet detections almost three decades ago [1, 2],
thousands have been detected and confirmed using various indirect and direct
observing strategies. Each technique provides access to specific planet
populations and allows the observer to retrieve specific parameters of the
systems observed. Characterization of these planetary systems is critical to
understanding their properties, formation and evolution. Photometric and
spectroscopic data are particularly valuable as they give access to multiple
parameters (orbital parameters, spin, temperature, atmospheric composition,
cloud coverage…). High dispersion spectroscopy (HDS) has quickly been
recognized as a powerful way to characterize exoplanet atmospheres and some
strategies has been developed to spectrally characterize exoplanets detected
using indirect methods [3, 4]. However, these measurements were challenging
until more advanced observing strategies became available and used with stable
infrared spectrographs such as Keck/NIRSPEC [5] or VLT/CRIRES [6]. The first
molecular detections in exoplanet atmospheres allowed observers to constraint
orbital parameters and retrieve new information such as wind flow and molecule
mixing ratios [7].

In parallel, the adaptive optic (AO) system and the infrared detectors of
VLT/NACO [8, 9] have been used to image the first exoplanet in 2004 [10]
followed in 2008 by the detection of the first three companions to HR 8799
[11], using the high contrast imaging (HCI) capabilities of both Keck and
Gemini telescopes. These high HCI techniques have since been improved and many
new observing strategies developed. Today most of the large telescopes have
HCI capabilities, which enabled the detection of a few dozen companions.
Photometric and spectroscopic data have slowly been collected on all the
companions imaged using low to medium resolving power instruments
(R$\sim$10–5,000) such as Keck/OSIRIS [12], Keck/Nirc2, LBT/LMIRcam [13],
Palomar/P1640 [14], VLT/Sphere [15], Gemini/GPI [16] or Subaru/CHARIS [17].

The next step in the field is to push to higher resolving power (R$>$30,000)
in order to collect spectral data where absorption and emission lines begin to
be resolved by using the high dispersion coronagraphy (HDC) technique [18, 19,
20, 21, 22]. This technique optimally combines HCI and HDS and provides the
ability to do species-by-species molecular characterization (e.g. water,
carbon monoxide, methane,…), thermal (vertical) atmospheric structure,
planetary spin measurements (length of day), and potentially Doppler imaging
of atmospheric (clouds) and/or surface features (continents versus oceans)
[20]. As none of the current facility instruments at large telescopes offers
both HCI and HDS capabilities together, several projects recently commenced to
combine the HCI capabilities with the HDS capabilities of various instruments
at those observatories. Among them the Fiber Injection Unit (FIU) part of the
Keck Planet Imager and Characterizer (KPIC) project presented in this paper,
the Rigorous Exoplanetary Atmosphere Characterization with High dispersion
coronography instrument (REACH) [23, 24] and High-Resolution Imaging and
Spectroscopy of Exoplanets (HiRISE) [25]. The first two projects are both
transitioning from commissioning to early science at the time of writing of
this article and offer complimentary wavelength coverage across the near-IR
(NIR) on Mauna Kea (REACH operates from Y-H and the KPIC-FIU operates in K and
L bands), while HiRISE is still in the development stage.

In this paper, we present a detailed overview of the design and performance of
the dedicated FIU for the Keck II telescope. In Sect. 2 we briefly introduce
the KPIC demonstrator in which the FIU is contained and presents its goals and
the requirement who must be satisfied to reach them. In Sect. 3, we present
details of the design of the FIU, a quick description of the key components of
NIRSPEC and our studies into the two key properties of the FIU: background and
throughput. In Sect. 4, we describe the main calibration procedures performed
to prepare the FIU for science observations. Section 5 presents the
acquisition sequence used during the night to acquire science data and we
present some example data acquired on one of our first test targets (HR 7672 B
[26]). In Sect. 6 we demonstrate the sorts of information that can be extract
from HDC data. Finally, Sect. 7 rounds out the paper with some concluding
thoughts.

##  2 Keck Planet Imager and Characterizer

The Keck Planet Imager and Characterizer is a demonstrator deployed at the W.
M. Keck Observatory. Located downstream of the Keck II adaptive optic system
[27], the goal of this platform is to demonstrate multiple new concepts to
image and characterize exoplanets on-sky. In order to reduce the complexity of
such a project, the project is broken into phases. Phase I, deployed at the
summit of Maunakea in fall 2018, contains an infrared pyramid wavefront sensor
(PyWFS) [28] and the modules and components critical for the demonstration of
the FIU. Figure 1 presents several pictures of the KPIC optomechanics before
their deployment. The vertical aluminum plate (unanodized) is the FIU plate.
It supports optics commons to both the FIU and PyWFS as well as the components
for the FIU. The black anodized plate is the PyWFS plate. It supports all the
optics of the PyWFS. The horizontal plate located under the two previous
plates is a kinematic platform to simplify co-alignment between the two
vertical plates. The orange module supported by 3 struts is a SAPHIRA detector
used by the PyWFS.

---
Figure 1:  Pictures of KPIC before its deployment.

The second phase, planned to deploy in late 2021 will contain extra modules:
an atmospheric dispersion compensator, phase induced amplitude apodization
optics, a high order deformable mirror and coronagraphs, whose goal will be to
improve the overall throughput for the planet light, while reducing star light
leakage to reduce overall integration times[29, 30, 31]. In this paper, we
present a detailed overview of the first phase FIU and its performance.

###  2.1 FIU phase I goals and requirements

The first version of the FIU presented in this paper has been designed as a
prototype. The design has been driven by the space available in the Keck II AO
bench, the existing science instruments available at Keck (i.e. NIRC2 and
NIRSPEC) and the science goals. Its main goal was to demonstrate the concept
by acquiring high resolution spectral data on a variety of targets. We wanted
the instrument to be able to observe of all known substellar companions
accessible to Keck, which sets most of the requirements as shown in Table 1.

To achieve this goal, the target or its host star must be observable by the
Keck II AO system. Although the FIU can be used in combination with the
visible Shack Hartmann wavefront sensor, we mainly use it with the IR PyWFS.
Since its deployment, this wavefront sensor, which operates in H band, has
been consistently used to observe targets up to $12^{th}$ magnitude. The
Strehl ratio measured in K band is 65% in 0.5 arcsec seeing and 45% in 1
arcsec seeing when the H magnitude of the star observed is $\leq 6$. Above
this magnitude performance progressively decreases. The performance of this
wavefront sensor has been described in detail in Ref. 28. It is currently not
possible to close the AO loop on a system with two or more components if they
have a similar H magnitude and a separation between 0.5 and 2 arc-seconds.
This issue will be addressed when the second phase will be deployed. Because
the PyWFS is using most of the H band light and the targets of interest are
brighter in the K and L bands, the first version of the FIU was designed to
collect spectral data in those photometric bands.

Once the AO loop is closed, the main challenge is to precisely align the
object of interest with a single mode fiber (SMF) with a precision of less
than one fifth of a $\lambda/D$ ($\leq$ 10 mas in K band) to achieve and
maintain high coupling. To align the object of interest with a SMF, we image
the system on a detector. Usually not visible on this detector, the object of
interest is aligned with a SMF by tracking the position of its host star at a
relatively low frequency ($<1$Hz). This camera is sensitive to both J and H
bands. However, we permanently installed a H band filter in front of it. In
the second phase of this project we will installed it in a filter wheel with
multiple filter options.In order to observe all known substellar companions
accessible to Keck, we must be able to track the position of object with a
H-mag up to 12 and have a capture range of $\pm 2.5$ arcsec.

The use of SMFs makes the observation with such a system more challenging than
observations with conventional AO-fed slit spectrographs such as Keck/NIRSPEC
or VLT/CRIRES. However, they provide multiple benefits. Specifically, the SMF
has a small solid angle on sky minimizing thermal background leaking into the
spectrograph, which is critical in K and L band. They can also help filter out
unwanted speckle (star light) [32] and they make future wavefront control
relatively simple in that only a few spatial frequencies need to be addressed
[33], which allows the bandwidth to be increased with these algorithms [34].
Finally, they allow the use of compact fiber-fed spectrographs that can be
located of the telescope in a more stable environment. If fed by an SMF, the
position and shape of the beam inside a fiber-fed spectrograph is agnostic of
input conditions and greatly simplifies the spectral calibration by making the
line spread function, a Gaussian profile in this case, which is extremely
stable.

In order to reduce the cost and the time needed for this project, we designed
the FIU as an interface to connect the AO bench to NIRSPEC. Because NIRSPEC
was not designed as a fiber-fed spectrograph, it constrained the design in
multiple ways (shape of the cold stop, injection outside of the cryostat, size
and shape of the slits available, etc) described later in this paper.NIRSPEC
sets the resolving power to 35,000 if we maintain a sampling of at least 2
pixels at all wavelengths across the bands observed (K or L band). The data
collected are compared to models by computing the cross correlation function
(CCF). To be usable, we must be able to detect the spectral signature of the
object of interest with a signal-to-noise ratio (S/N) greater than 3 after two
hours of integration. The table 1 summarizes all the baseline requirements for
the KPIC FIU.

Tracking and acquisition
---
Specifications | Value | Notes
Scale of optical fibers | $\sim\lambda/D$ | SMF optimally matched to PSF
Capture range |  $\pm 2.5$ arcseconds | Covers most high contrast targets
Alignment accuracy | $<0.2\lambda/D$ | —
Tracking speed |  $<1$ Hz | Tracking, not tip/tilt correction
Tracking stability |  $<0.2\lambda/D$ RMS | —
Tracking bands | J or H band | —
Limiting magnitude |  $>12$ in H-mag | PyWFS limitation
Spectroscopy
Specifications | Value | Notes
Spectral Range | K & L band | Not simultaneously
Resolving Power | $\geq 30,000$ | NIRSPEC limitation
Sampling |  $\geq 2$ pixels | At all wavelengths
Overall performance
Specifications | Value | Notes
Total Peak Efficiency | $\geq 2\%$ | From top of atmosphere
Pt sources sensitivity |  $\geq 16$ K-mag | S/N $\geq$ 3 in CCF in $\approx$ 2h.
Table 1:  FIU Phase I requirements.

##  3 Fiber injection unit design

The FIU deployed at Keck is based on three modules: an injection module, a
bundle of fibers and an extraction module. This section describes these
modules, the NIRSPEC instrument used to acquire the data and the expected
performances of the overall instrument. The interaction between these
components and the way we are using them to achieve our goals is described in
the following sections of this paper.

###  3.1 Injection module

Located downstream of the Keck II AO system the goal of the injection module
is to inject the light of faint companions (exoplanets, brown dwarf, etc) into
one of the single-mode fibers (SMFs) of a bundle described in Sect. 3.2.
Figure 2 shows a schematic of the KPIC optical layout. This diagram is not to
scale and the orientation of the optics is not correct. In this paper, we only
describe the optical layout of the FIU.

---
Figure 2:  Diagram of the KPIC optical layout. The scale and the orientation
of the optics are not correct. The FIU and PyWFS plates as well as the Saphira
detector are visible in the first figure of this paper.

To direct the light to the FIU, the converging beam coming from the AO bench
is reflected by the three optics constituting a field steering mirror module
(FSM - See Fig. 2). The first optic of this FSM (A) is the KPIC pick off. It
consists of an actuated dichroic and a static flat mirror installed on a
translation stage. When neither optic is in the beam, all the light goes to
the facility infrared imager NIRC2. If the dichroic is in the beam, 90% of the
J and H band light goes to KPIC while the rest goes to NIRC2 . If the flat
mirror is in the beam, all the light goes to KPIC.

After the FSM, the converging beam is directed to the FIU plate. This plate is
visible in the images presented in Fig. 1 (unanodized), and supports all the
components of the injection module. After going through two optical relays
(D-J in Fig. 2), comprised of simple reflective optics in phase I, the light
is collimated by a 168.31 mm focal length off axis parabola (OAP, K) made of
Zerodur and coated with protected gold (Nu-Tek). The two optical relays are
based on four identical OAPs to the one used for collimation (Nu-Tek \- D, G,
K, J) and two flat mirrors (Newport \- E and I). All these optics are made of
Zerodur and coated with protected gold. The F# of the input and output focal
plane are the same as the F# of the telescope (13.66). The diameter of the
collimated beams in these relays is 12.32 mm. In the first optical relay, the
static pick off dichroic of the PWS (Asahi Spectra \- F) reflects 90% of the J
and H band light in the direction of the sensor while the rest of the light is
transmitted (K and L band). These two optical relays mostly empty during the
first phase of the project will be populated in the phase two [30, 31].

After the two relays, a tip-tilt mirror (TTM) is situated in the pupil plane
of the instrument for aligning the target with the fiber as well as fine
tuning the pointing onto the fibers (L). The TTM (Physik Instrumente,
S-330.8SL) is a piezo mechanism, which offers a field steering of $\pm$ 2.4
arc-second in two axes. An off-the-shelf protected gold flat mirror (Thorlabs,
19 mm diameter) is attached to the platform using a custom made, flexure-based
mirror holder. Made of Invar and titanium, this mirror holder has been
designed to minimize the forces applied to the flat mirror in order to
minimize distortions and to be as light as possible in order to optimize the
response of the overall TTM module.

A custom dichroic (Asahi Spectra, M) is used to split light and direct it to
the camera for tracking purposes while allowing science light to pass through
to the injection unit. It reflect 90% of the J and H band light while longer
wavelength light ($\geq$K and L) is transmitted.

The reflected path towards the camera contains a H band filter (Asahi Spectra,
P), an air-spaced achromatic doublet (Thorlabs, Q), a plano-concave lens
(Edmund Optics, R) and a low noise InGaAs detector (First Light Imaging,
Cred-2 [35]), which offers a 4.125 $\times$ 5.125 arc-second field-of-view
(FOV, 512 x 620 pixels, with an $\approx$ 8.06 mas/pixel sampling). When KPIC
is used as a FIU, this detector is used to track the position of the science
targets. For this reason, we refer to it as the “tracking camera”. A stage can
be used to translate the plano-concave lens in/out of the beam. When out of
the beam, a pupil image of the Keck primary is formed. When in the beam, a
focal plane image is formed. The FOV of this detector has been carefully
selected to be able to observe the targets of interest selected for this
project. It limits the maximum separation between the objects of the systems
observed. However, this FOV allows us to observe most of the exoplanets
already imaged and visible from Maunakea. The K and L band light is next
incident on the injection optic (N): a 35 mm focal length OAP (Nu-Tek). Made
of Zerodur and coated with protected gold, this optic is the last of the FIU
module before the fiber bundle (O) described in the following section. The
bundle is carefully positioned at the focus (F# = 2.8) and on the optical axis
of the OAP. The effective focal length of the OAP is the one which maximizes
the injection into the fiber for both K and L bands.

To aid in aligning the incoming beam with the bundle, a corner cube (T) is
located beneath the dichroic. Its role will be explained in the calibration
procedures of the system (see Sect. 4.1.1 ).

###  3.2 Fiber bundle

The fiber bundle has several key roles: 1) it is used to route the science
light to the spectrograph and 2) it has peripheral fibers that light can be
reverse injected into to aid with alignment optimization. The layout of the
bundle used in KPIC is shown in Fig. 3. On the input end, the fiber bundle is
connected to the injection module (see Sect. 3.1) located inside the Keck AO
bench. On the output side, the fiber bundle is connected to the extraction
module (see Sect. 3.3) located in the calibration unit of NIRSPEC [36] a
facility class high spectral resolution spectrograph of the W. M. Keck
Observatory.

---
Figure 3:  Diagram the first KPIC-FIU fiber bundle.

Manufactured by Fiber Guide Industries this critical component of the FIU is
based on ZBLAN 6.5/125 fluoride fibers (Le Verre Fluoré) and SMF-28-ULTRA
silica fibers (Corning). The bundle contains five ZBLAN 6.5/125 science fibers
going from the input to the output connectors (note, this indicates the fibers
have a $6.5~{}\mu$m diameter core and $125~{}\mu$m cladding). These are
indicated in red on the diagram. This part of the bundle is 5 m long, a length
necessary to connect the injection and extraction modules. The science fibers
are surrounded by six SMF-28-ULTRA calibration fibers at the input connector
end and two ZBLAN 6.5/125 calibration fibers on the output connector end,
represented in blue and orange in the figure respectively. These alignment
fibers are contained within the furcation tubing of the main bundle for about
$50$ cm before they are broken out into individual fibers with FC/PC
connectors. The input and output connectors also contain dummy fibers which
act as scaffolding to locate the science and calibration fibers during
manufacturing. Represented in black in the diagram, these fibers are segments
of SMF-28-ULTRA terminated within the package.

The custom input and output connectors were manufactured using two different
approaches compatible with the specific needs of each connector. The input
connector contains three layers of fibers where the position of each fiber is
not critical. In this connector, the fibers are butted cladding-to-cladding
and their position is maintained by an outer metallic structure. The cladding-
to-cladding construction maintains the core separation of two adjacent fibers
to $\approx 125\>\mu$m which corresponds to $\approx 800$ mas in K band.

The output connector contains only one layer of fibers but these fibers must
be aligned with a high precision to make sure they pass through the mechanical
slit of NIRSPEC downstream. For this reason, the fibers are supported using a
V-groove on this side. The pitch of the V-groove used set the core-to-core
separation between two adjacent fibers to $127\>\mu$m. On the input side, four
of the input calibration fibers, labeled $C_{1}$, $C_{2}$, $C_{4}$ and $C_{6}$
in the diagram, are connected to a 1550 nm laser source. The two other input
calibration fibers ($C_{3}$ and $C_{5}$) were connected to two high speed
InGaAs photo-detectors. On the output side, the two calibration fibers
($C_{A}$ and $C_{B}$) were connected to two broadband infrared light sources
(tungsten lamps, Thorlabs, SLS202L). In section 4 we describe how and when
these elements are used.

Figure 4 shows a picture of the fiber bundle currently used by KPIC (left) and
a picture of the input connector (right). For reference, the diameter of the
connector is 7 mm. The gold coating visible on the input connector is an anti-
reflection (AR) coating to optimize the throughput of the bundle in K and L
bands, and is used at the output as well. The overall throughput of the bundle
in K band was measured in the laboratory to be $95.3\%$ in K band. According
to the manufacturer, the attenuation of the ZBLAN fiber varied between 2.6 and
5.3 dB/km across the K-band which corresponds to a throughput $\geq 99.4\%$
for 5 meters of fiber. The rest of the throughput loss is due to the Fresnel
reflections which occur at both ends of the bundle due to imperfect AR
coatings. The L-band throughput has not been measured because of a lack of
equipment in those bands. However, some preliminary observations in L-band
indicate that the throughput of the bundle in this band is close to
expectation.

---
Figure 4:  Left: Picture of the bundle. Right: Picture of the input connector
of the bundle.

The minimum number of fibers needed to acquire HDC data is three: one for the
target of interest, one for its host star and one for the sky background. The
final number of science fibers was chosen as a trade off between the price of
the bundle and various technical constraints. For instance, the shape and size
of the NIRSPEC slit limits the number of fibers on the output connector and
imposes a linear arrangement of fibers. We decided to use a design with five
science fibers to cover most science cases and to have redundancy in case one
of the science fibers was damaged. Regarding the calibration fibers, the
bundle has been designed to be functional even if one of the calibration
fibers of each set is damaged (one fiber connected to the laser, one to the
photo-detector and one to the broadband light source). The position of the
fibers on the input connector was not critical. We required the arrangement of
fiber relatively to be compact in order to image most or all of them on the
tracking camera if needed. To keep the system simple and efficient, we chose
to maintain a coarse separation between the fibers. The minimum separation
between two fibers is $\approx 800$ mas and the maximum is $\approx 4000$ mas.
Because the star is usually brighter than the companion by several magnitudes,
we can collect stellar light even if the star is not aligned with a fiber
(light from the speckle field). We can adjust the amount of stellar light
injected into a science fiber using the rotator of the telescope by bringing
the star closer to a science fiber or moving it away. If the host star cannot
be brought close enough to a science fiber when data are collected on the
companion, we can collect spectral data on the host star before or/and after
by aligning it with one of the science fibers. Finally, because the separation
between the first and last science fiber is $\approx 4$ arcsec, one of the
fibers will always be far enough from the star to acquire background data.

###  3.3 Extraction module

The extraction module, known as the fiber extraction unit (FEU) is the
interface between the fiber bundle and NIRSPEC. Its goal is to reshape the
light coming from the different fibers of the bundle and optimally inject this
light into the high-resolution spectrograph, which was originally designed to
work in the seeing limit. The left panel of Figure 5 shows a picture of the
FEU installed in the calibration unit of NIRSPEC, and the right panel is the
computer-aided design (CAD) model.

---
Figure 5:  Left: picture of the FEU installed in NIRSPEC’s calibration unit.
Right: a CAD model view of the FEU.

A custom made brass part visible in the right panel of Fig. 5 (labeled 2)
guides the output connector of the bundle (labeled 1) and aids in aligning it
with an air-spaced doublet collimating lens mounted in the same part. This
part has been made of brass mainly because this material is relatively soft
and easy to machine. On the doublet side, we built a custom barrel to match
the diameter of the lenses and to adjust the distance between the lenses if
needed. For the bundle, we chose the material of the barrel to be softer than
the material of the bundle (aluminum) to minimize the risk of galling when the
bundle slides in the barrel. The doublet is composed of a germanium and
silicon lens (Rocky Mountain Instrument). The effective focal length of this
doublet is 10.84 mm and the throughput in K and L bands was measured to be
$>92\%$. The numerical aperture of the science fiber has been measured in
laboratory to be 0.175 at 2 $\mu$m. After the air-spaced doublet, the
$1/e^{2}$ diameter of the collimated Gaussian beam is 3.8 mm. Close to its
output connector, the stainless steel mono-coil jacket of the bundle is
attached to a motorized translation stage (labeled 4) using a custom made
kinematic interface (labeled 3). The translation stage is used to move the
bundle along the optical axis guided by the brass part, which corresponds to
the focus axis of the bundle/lens system. The brass piece prevents the bundle
from moving in the axes perpendicular to the optical axis and constrains the
pitch and yaw of the output connector while the bundle is being focused. The
rotation of the bundle about the optical axis is constrained by a clamp and
kinematic interface. This simple kinematic interface combined with the brass
holder have proved reliable when it comes to returning the fiber bundle to the
same position and orientation each time it has been connected. This assembly
is mounted on two motorized translation stages, labeled 5, used as a pupil
steering mechanism to move the fiber bundle and the air spaced doublet in the
plane perpendicular to the optical axis. This mechanism is used each time the
bundle is connected to align the beam coming from the bundle to the NIRSPEC
field stop located into the cryostat. The next and last optical element of the
fiber extraction unit is a TTM (labeled 6) held by a custom made bracket
(labeled 7). Based on a Newport CONEX-AG-M100D, this element reflects the
light in the direction of NIRSPEC calibration unit. This TTM is located in a
pupil plane and is used to align the images of fibers with the slit of the
spectrograph.

###  3.4 NIRSPEC

Figure 6 presents a diagram of the optical layout of NIRSPEC (not to scale).
For more information regarding the NIRSPEC optical layout please consult: Ref.
36, 37 and 38. NIRSPEC’s calibration unit located to the left side of this
diagram contains the FEU described in the previous section.

---
Figure 6:  Diagram of the NIRSPEC optical layout with the FEU installed in its
calibration unit. This diagram is not to scale and does not show the optics in
the correct orientation.

A fold mirror (labeled D) installed in the calibration unit of NIRSPEC was
motorized using a flip mechanism (OWIS,KSHM 65-LI-MDS). It is used to select
the input of the calibration unit. When in the beam, the mirror directs light
coming from the calibration sources of NIRSPEC’s integrating sphere (and an
air-spaced collimating triplet) to the slit in order to calibrate the
spectrograph. When out of the beam, the light from the FEU is directed to
NIRSPEC. After this optical element, the light is focused by an air-spaced
triplet (E - EFL = 152.4 mm) and reflected by a motorized fold mirror (F)
before it enters into the NIRSPEC cryostat. When KPIC is in use, this fold
mirror is in the beam. After this mirror, the beam goes through the uncoated
CaF2 window of the NIRSPEC cryostat before being reflected by the three
mirrors of the rotator. The second optic of this rotator (I) is an OAP (EFL =
400 mm). After the rotator the collimated Gaussian beam ($1/e^{2}$ diameter of
10.0 mm) passes through two filter wheels (K) before being focused by an OAP
(M) onto the selected slit located in a slit wheel (O). All NIRSPEC slits are
reflective. The light passing through the slit is dispersed and imaged on the
science detector named ‘Spec’ (Teledyne, science grade Hawaii-2RG detector).
The light reflected by the slit is imaged by a slit-viewing camera named
‘Scam’ (Teledyne, engineering grade Hawaii-2RG detector).

Figure 7 presents a combination of images acquired with the slit-viewing
camera. This image has been obtained by combining images acquired with light
injected into each fiber of the output connector of the bundle (see Sect.
3.2). This image presents the case where the PSFs associated with the fibers
has been offset from the slit. This mode is mainly used during the calibration
of the instrument. Indeed, unlike the science detector, the light coming from
the fiber is not dispersed in the focal plane of the slit-viewing camera,
which allows quick flux measurements. To align the PSFs and the slit, we use
the FEU TTM (C). If the fibers contained in the bundle are not properly
oriented with respect to the slit, we use the internal NIRSPEC rotator to make
small adjustments.

---
Figure 7:  A composite image with all fibers illuminated acquired with the
slit-viewing camera. In this case, the seven PSFs are offset from the slit.
The seven PSFs visible on this image are respectively associated to (from left
to right): CA, S1, S2, S3, S4, S5 and CB. The slit (dark blue) used in this
case was the 0.0407”x1.13”.

Figure 8 presents two of the nine orders visible on the science detector when
configured for K band observations. This image is also a combination of images
obtained by combining images acquired with light injected into each fiber of
the output connector of the bundle. Each order contains seven spectra. The
five central spectra are associated with the five science fibers of the bundle
while the two lateral spectra are associated with the two calibration fibers.
Depending on the slit selected (short or long), the light from the calibration
fibers is reflected in the direction of Scam or transmitted to Spec. The
separation between the spectra is fixed ($\approx 19$ pixels) and set by the
separation between the fibers in the output connector of the bundle. The width
of the trace can be adjusted by moving the bundle along the optical axis using
the focus actuator (labeled 4 in Fig. 5). We adjust the position of this
actuator during a calibration procedure of the FEU (see Sect. 4.2) to properly
sampled the data.

---

Figure 8:  Two of the nine orders visible on the science detector when
configured for K band observations. Each order of this patchwork of images
contained seven spectra. The upper and lower spectra of each order are
associated with the two calibration fibers contained in the output connector
of the bundle while the five other spectra are associated with the science
fibers. This image is a composite image with all fibers illuminated

.

###  3.5 Expected performance

Because the FIU module of KPIC aims to spectrally characterize faint objects
with a high resolution ($R>$30,000), the background seen by the science
instrument and the overall throughput are the key properties that need to be
understood. In this section we present our estimations and measurements of
these parameters in K band. Although, the phase I version of the instrument
has been designed to allow science observations in K and L bands, we have
mainly focused our work on the K band to date. We will start to work in L
bands once most of the other challenges of this project will be overcome.

####  3.5.1 Background

For a fiber-fed spectrograph, the background seen by the science instrument
can be decomposed into four components: the background injected into the
science fibers of the bundle (sky background and upstream optical elements),
the emissivity of the fiber itself, the background emitted between the fiber
bundle and the cold stop of NIRSPEC and the background emitted in the
cryostat.

The first component of the background is relatively small. SMFs are extremely
efficient at rejecting upstream background from sky, telescope and FIU because
of their relatively small solid angle projected on sky (45 mas2 in K band).
For reference, the average sky brightness in K band at zenith during dark
times and during a clear night at the summit of Maunakea is equal to 12.6
mag/arcsec2 (http://www.cfht.hawaii.edu/). The second component of the
background is the emissivity of the fiber itself. We have not quantified this
component yet. However, KPIC uses a relatively short (5 m) SMF with very high
transmission and with a very small core diameter ($6.5~{}\mu$m). We can
compute the background emitted based on the energy absorbed by the material of
the fiber ($\leq 0.6\%$ in K band). However, it is difficult to estimate the
fraction of this background transmitted to the FEU side of the bundle.

The third component of the background is the sum of the emissivities of all
the warm optics used to project the light from the fiber onto the NIRSPEC slit
(labeled A-G in the Fig. 6). To reduce this component of the background, we
use a cold stop, named ”FEU stop”, located in both filter wheels of NIRSPEC
(labeled K on the Fig. 6). These stops have been installed in both wheels in
order to be able to use them with all the NIRSPEC filters available. The stops
consist of a hole in a metallic plate, which has been black painted. The hole
diameter has been optimized to maximize the signal-to-noise ratio (SNR) seen
by the science detector. The radius of the cold stop which maximizes the SNR
‘$R_{\text{max}}$’ is:

$R_{\text{max}}\approx 1.5852\sigma\approx 0.6731\text{FWHM}$

where $\sigma$ and FWHM (Full Width Half Maximum) characterize the Gaussian
profile’s
width111https://wise2.ipac.caltech.edu/staff/fmasci/GaussApRadius.pdf. By
using the ratio between the $1/e^{2}$ diameter and the FWHM
($2\sqrt{2ln(2)}\approx 1.7$), we can compute the optimal diameter for the
cold stop. Because the mode field diameter of the science fibers as well as
the effective focal length of the air-spaced doublet and triplet (labeled B
and E on Fig. 6) are wavelength dependent, the optimal diameter is also
wavelength dependent. Moreover, the diameter of the beam at the location of
the stop can be affected by the defocus applied to the bundle to optimize the
size of the PSF on the slit (see Sect. 4.3). At 2 $\mu$m, we computed the
optimal diameter of the stop to be $\approx$7.9 mm. We decided to use a
slightly larger cold stops (8.1 mm diameter) because the optical elements of
the NIRSPEC calibration unit were never calibrated (as it wasn’t needed) and
because the K and L bands go beyond 2 $\mu$m. Moreover, the impact of
increasing the thermal background sightly is not as severe as restricting the
light from the companion.

These stops are used in addition to a blocking filter, which suppresses the
science and background light outside of K band to prevent order overlap.
Several filters are available in each filter wheel. Thus far, we have mainly
observed in K band (1.9 to 2.5 $\mu$m). In this case, we are using the filter
named “Thin” located in the first filter wheel. It consists of a substrate of
PK-50. This material is a thermal-IR flux blocker opaque for wavelengths
$>2.8\mu$m. At wavelengths $<1.9~{}\mu$m the background is negligible and the
light coming from the target is absorbed by the germanium lens of the air
spaced doublet located in the FEU (labeled B in Fig. 6). The few observations
made in L band have been made using the broad ’KL’ filter.

The last component of the background is the internal background of the
spectrograph itself. In the case of NIRSPEC, a recently discovered light leak
currently adds to the instrument thermal background [39].

Figure 9 shows the central section of one of the orders visible on a Spec
frame (left panel) acquired by pointing at a dark region of the sky (no
visible target). The left half of the image is not reduced while the right
side is reduced by removing a background acquired during the day (no light
injected into the fibers) and correcting for hot pixels. The graphic on the
right side of the figure presents a vertical line profile of the same order.
This profile is the median of the profiles associated to all the wavelengths
of the order. The profile computed from the raw data is represented in blue
while the profile computed from the reduced data is represented in red.

---
Figure 9:  Left: Central section of order 33 of a Spec frame acquired with no
object in the tracking camera FOV (exposure time = 599 sec, Nirspec setup for
K band observation, clear sky, elevation = 54.2∘ and no moon). The left side
of this image has not been reduced while the right side has been reduced by
subtracting a background acquired during the previous night with the same
settings and by removing the bad pixels. The horizontal lines of each side
indicate the position of the fibers. From top to bottom: CA, S1, S2, S3, S4,
S5, CB (see Fig. 3). The slit induced background is visible in the raw data
(bright band around the 5 science fibers). Right: Line profiles across order
33. This profile is the median of the profiles associated to all the
wavelengths of the order. The profile computed from the raw data is
represented in blue while is computed from the reduced data is represented in
red.

The two first components of the background (sky and fiber emissivity) are not
visible in the Fig. 9. If they were visible, we would see small peaks at the
locations of the fibers in the red trace. Because we do not use exposure times
longer than those used to acquire this data during science observations (599
seconds), we can consider these two components as negligible in standard
observing conditions. More tests need to be done to determine if the
conclusion will be the same in L band, with the telescope pointed at lower
elevation or during a night with the moon visible.

The third component, emitted by warm optomechanical components located in the
calibration unit of NIRSPEC (see Fig. 6), is visible in the raw data (bright
band around the 5 science fibers) but can be removed efficiently by reducing
the data. This contribution to the background is not dependent of the
observing conditions but can probably be affected by variation of temperature
in the AO room. In this case for an AO room temperature of 6.1∘C, we measured
an average of 0.5 counts per second for the reddest order (order 39 –
$\lambda\in[2440:2484]$ nm) and less than 0.05 counts per second for the
bluest order (order 31 – $\lambda\in[1943:1977]$ nm).

Regarding the last background component, the thermal background of the
instrument, it is combined with all the noise and offsets of the science
detectors. This component affects the entire image. Visible as an offset below
and above the bright green band on the left side of the image presented by the
Fig. 9, the sum of these effects contributes 180 counts on the reddest side of
the detector and 90 counts on the bluest side. As the temperature inside the
cryostat is controlled, we can consider this to be constant. As shown by the
Fig. 9, this component can be removed efficiently. The optical leak discussed
previously is not visible is the sub-image presented in this paragraph.

####  3.5.2 Throughput

Figure 10 presents the throughput of the overall system (sky to detector
included) as a function of the wavelength measured on July the 3rd 2020 on the
star Kappa Andromedae. The throughput is the ratio between the number of
photon expected and the number of photons detect by the science detector. Nine
orders are visible on this plot. The left one is the 31st order of NIRSPEC
while the right one is the 39th order. For this measurement, the light was
injected into the second science fiber (labeled $S_{2}$ in Fig. 3). This set
of data has been acquired during a clear night. according to the Canada France
Hawaii Telescope, the MASS seeing was $\leq 0.2$ arc second and a DIMM seeing
of $\approx 0.6$ arc second (both measured for a wavelength of 0.5 $\mu$m).
During this measurement the target was at a 64.5∘ elevation.

---
Figure 10:  Throughput as a function of the wavelength from sky-to-detector
measured on July the 3rd 2020 on the star Kappa Andromedae. For this
measurement, the light was injected into science fiber $ScF_{2}$ of the
bundle.

It can be seen that the peak throughput in K band reaches 3% (well above our
2% requirement). The data in the figure represents one of the best results
achieved to date. Multiple parameters can affect the throughput: seeing,
weather, AO performance, calibration quality. Despite this, over the last few
observing runs, we have consistently measured a throughput between 1.5 and 2.5
% over the K band.

Neither the Keck II AO system nor the KPIC instrument contains an atmospheric
dispersion compensator (ADC). As such, the light of the target is slightly
dispersed in the focal plane of the input connector of the bundle for non-zero
Zenith angles. For this reason the injection is not uniform across the K band.
In the case presented in Fig. 10, the injection was optimized for a selected
wavelength (center of the K band). This effect is a function of the elevation
of the telescope. To optimize the overall throughput of the system for all the
wavelengths, an ADC will be deployed in the phase II of the KPIC project.

We also measured the throughput in L band using Kappa Andromeda at the end of
the same night. We measured a preliminary throughput of up to $6\%$ between
3.7 and 3.8 $\mu$m.

The peak throughput measured on-sky of $3.2\%$ in K band is consistent with
the expected value of $3.4\%$, computed assuming 200 nm RMS of residual
aberration and taking into account the performance of each of the optics. We
have identified several ways to improve the overall performance of the system,
which should result in an increase in the quality of the science data in the
near future. The following table presents the throughput budget computed for
the FIU in both K and L bands.

Throughput budget
---
Components | K-band | L-band | Description
Sky | 98% | 85% | —
Telescope | 90% | 90% | 3 reflective optics
Keck II AO optics | 63% | 63% | 7 reflective & 1 transmissive optics
Fiber Injection Unit | 77% | 77% | 12 reflective & 2 transmissive optics
Strehl | 72% | 90% | Assuming 200 nm RMS wavefront error
Dispersion & Pointing loss | 95% | 95% | At 30 degrees zenith angle
Fiber injection efficiency | 60% | 60% | Keck pupil geometry and NA mismatch
Bundle | 95% | 97% | Material absorption & Fresnel reflections
FEU + Calibration unit | 89% | 89% | 2 reflective & 5 transmissive optics
NIRSPEC throughput | 30% | 30% | Diffraction efficiency & optic throughput
Filter and background stop | 80% | 80% | —
H2RG Quantum efficiency | 95% | 95% | —
Total | 3.4% | 3.7% | From top of atmosphere
Table 2:  Throughput budget computed for the FIU in both K and L bands.

##  4 Calibrations

Injecting light into a SMF, which subtends a very small solid angle on-sky,
requires precise calibration of the instrument. In this section, we describe
the various calibrations performed before and during the observations.

###  4.1 Fiber injection unit calibrations

####  4.1.1 Science fibers position

The science fibers are not visible on any sensors, so their positions are
unknown at first. The tracking camera is integral to finding the position of
the science fibers and optimizing the coupling of a target. By virtue of the
dichroic beamsplitter before the tracking camera (M in Fig 2), J and H band
light can be used to determine the location of a target. To determine the
position of the science fibers on the tracking camera, we follow a two step
calibration process. The first one is quick but not highly accurate while the
second one is time consuming but very accurate.

The first calibration procedure relies on light to be retro-fed through the
peripheral calibration fibers in the bundle. An infrared laser is used and
injected into four of the six fibers and emitted from the input connector of
the bundle (see Sect. 3.2). The light coming from those fibers is collimated
by the focusing OAP of the injection module (H in Fig. 2). A fraction of this
light is reflected by the dichroic (M) in the direction of the corner cube
(T), which reflects the light in the direction of the dichroic. The light
transmitted forms an image on the tracking camera composed of four PSFs (one
per retro-fed calibration fiber). By retro-feeding an asymmetric pattern of
calibration fibers and by knowing the geometry of the bundle, we can determine
the position of the other fibers (science fibers) in the input connector of
the bundle. The image presented in Fig. 11 is the output automatically
generated by the algorithm used to perform this calibration procedure. It
takes only a few seconds to get a result but the estimated positions are not
highly accurate (usually a couple of pixels) for multiple reasons: the shape
of the PSFs for the four calibration fibers are altered by the OAP and the
corner cube, which makes the position measurement of these fibers inaccurate,
even if the geometry of the bundle is precisely known, we do not take into
account field distortions at the detector, and the corner cube is not perfect
so the incident and reflected beams are not parallel, to name a few.

---
Figure 11:  Output figure automatically generated by the algorithm used to
roughly determine the position of each fiber of the bundle. The ”X” shape of
the PSFs is due to the corner cube

In order to maximize the throughput of the instrument, we use a second
calibration procedure based on a direct measurement of the light injected into
the fibers. For this step, we turn on the calibration source of the Keck II AO
bench to create a PSF on the tracking camera and then use the TTM of the fiber
injection unit (labeled L on Fig. 2) to align this PSF with one of the science
fibers. Then we scan the TTM across the expected location of the fiber and
record the flux on the slit viewing camera of NIRSPEC, Scam (see Fig. 6) as
well as the tracking camera. The SCAM images are used to measure the flux
injected into the science fiber while the tracking camera images are used to
measure the flux variation of the light source and track the PSF position
associated with each flux measurement. In this way, we can build and injection
map through the fiber and by fitting the peak, we can determine the TTM
position of optimum coupling very accurately and the corresponding PSF
position that yields this optimum alignment on the tracking camera at the same
time. The left image presented in Fig. 12, is the injection map obtained by
performing such a scan. The position of each pixel of this injection map
correspond to a position of the PSF on the tracking camera and the value
associated with each pixel is the flux measured by using Scam normalized by
the flux of the calibration source measured by the tracking camera. This
calibration method is time consuming. We are currently limited by the minimum
exposure time of the Scam detector ($\approx 600$ ms) and its read-out
($\approx 1200$ ms). We tried multiple scan patterns to reduce the time needed
to perform this calibration but for the moment, the grid scans are the most
accurate and reliable. As shown by the injection map radial profile presented
on the right side of Fig. 12, knowledge of the position of each fiber is
critical if we want to maximize throughput. An offset of one pixel on the
tracking camera (8.06 mas) corresponds to a loss of 10% of throughput, two
pixels (16.12 mas) corresponds to a loss of 30% and three pixels (24.18 mas)
to a loss of 55%. An offset of 50 mas which correspond to the angular
resolution of the Keck telescopes at 2$\mu$m correspond to a loss of 97% of
the throughput. This is why we take the time to perform these calibrations
properly and why we perform these calibration before each science night even
if the bundle has not be disconnected between two observations.

---
Figure 12:  Left: injection map obtained by performing a 25 by 25 grid scan.
The pitch of the grid is 5 mas in both direction. Right: Radial profile
computed from the injection map.

During the calibrations, the PSFs in H, K and L bands are superimposed. As
neither the Keck II AO system nor the first phase of the KPIC project contains
an atmospheric dispersion corrector, when on-sky the PSFs of the target in H,
K and L bands are superimposed only when observing at Zenith. Therefore, when
observing away from Zenith, the location of the PSF on the tracking camera,
which operates in H band, will not correspond to the location of the K and L
band PSFs in the focal plane of the injection OAP. As such, an additional step
is taken during the acquisition sequence, whereby the PSF is offset with the
TTM along the elevation axis by the calculated offset expected from the
differential atmospheric refraction between the H and science bands (K or L).
This offset is a function of the elevation of the target and the refractive
index of the air versus wavelength. To compute the latter, we use an
analytical approximation of the refractive index which depends on the
temperature, pressure and relative humidity of the air above the primary
mirror [40]. The tracking loop used to align the target with the fiber
computes this value and applies the offset at each iteration of the loop (see
Sect. 5).

####  4.1.2 Tracking camera

The calibration of the tracking camera is critical because we use it as a
reference to inject the light of the target of interest into one of the
science fibers. Key to calibrating the camera is understanding the plate
scale, the orientation and the field distortion map. We use two different
methods to calibrate the tracking camera. The first one can be performed
during the day by using NIRC2 as a reference. The plate scale, the orientation
and the distortion map of this detector is regularly calibrated and can be
considered as reliable. By using a dichroic like the KPIC-pick off (labeled A
on Fig. 2) we can image the PSF of the calibration unit of the Keck II AO
bench on both NIRC2 and the tracking camera at the same time. We translate the
calibration source in both the X and Y axis and acquire images for each
position with both detectors. We compute the position of the PSF in each
image. A set of two positions can be used to determine the plate scale of the
tracking camera and a set of three positions forming an asymmetric pattern can
be use to determine the orientation of the tracking camera with respect to
NIRC2. The more sets of data available the more accurate the plate scale and
the orientation. The variation as a function of x/y on the detector of plate
scale and orientation between those sets of data is used to compute the
distortion map of the tracking camera. To model the distortion in X and Y on
the detector, we use the methodology of Service et al. 2016 [41] and use a 5th
order bivariate Legendre polynomial. A second calibration method performed
during the night is routinely used to refine this. This method consists of
observing an object with multiple components (a binary star for example).
Because the astrometry of such an object (position angle and separation) is
stable during the calibration, we can use images of this object acquired on
different parts of the detector to calibrate the distortion map of the
tracking camera. To move the object around the detector we steer the TTM in
the FIU. Indeed, in the presence of local field distortions, the position
angle and separation vary across the detector. The average separation of this
target can be used to determine the plate scale and the orientation of the
detector. In order to mitigate orbital motion uncertainties of the system
observed to perform this calibration, we image the system with NIRC2 and the
Cred2 in parallel. We also tried to observe known fields of stars, like M92.
However, the FOV of the tracking camera (4.5 x 5.5 arc-second) is too narrow
to image many bright stars at the same time (H-mag $\leq$ 10).

The offsets computed from the calibrations outlined above, are applied to the
tracking loop (see Sect. 5) to align the science target with the selected
science fiber. We verify at the beginning of each run that we can align the
PSF with a sub-pixel resolution to confirm the validity of the tracking camera
calibrations.

####  4.1.3 Coupling Optimization

To optimize the coupling, we must reduce the wavefront error in the system in
order to maximize the image quality in the focal plane of the input connector
of the fiber bundle. However, this plane is not easily accessible and cannot
be imaged with a detector so we cannot use any standard focal plane wavefront
sensing strategy in this case. The solution found to overcome this problem is
to use two calibration procedures. The first one is used to optimize the image
quality on the tracking camera while the second one is used to calibrate the
non-common path aberrations (NCPA) between the two paths of the FIU (tracking
camera and injection module).

To optimize the image quality on the tracking camera we use a phase diversity
algorithm called “image sharpening”. This is used in the calibration procedure
for some of the Keck facility instruments. This procedure can be run before
each science night as it takes only a few minutes to complete. Indeed, even if
the version used is not fully automated yet, we never start from a very
deformed PSF. We usually start with less than 100 nm RMS of wavefront
aberration in the system and consistently reach wavefront errors $<20$ nm RMS
by using this procedure.

Once the wavefront error is reduced to maximize the image quality on the
tracking camera, we use a Zernike optimization strategy which measures the
flux transmitted through the fiber bundle to indirectly reduce the NCPA
between the two paths of the FIU. We first select a Zernike mode (we usually
start with the defocus). Then we scan this mode in amplitude by using the Keck
AO DM. For each amplitude we perform a tip-tilt scan in order to build an
injection map (see Sect. 4.1.1). This is done incase the PSF move laterally
while being defocus (i.e. in case there is cross-coupling between modes). By
fitting a 2D Gaussian to each injection map we obtain the optimal injection
for each Zernike amplitue. The optimal amplitude for the selected Zernike mode
is determined by fitting a second order polynomial on the optimal injection
values measured for each amplitude of the selected Zernike mode. We then apply
this value to the DM and continue the calibration procedure by scanning the
next Zernike mode. This calibration procedure is completed once all the
Zernike modes selected have been scanned. Because we currently only scan one
mode at a time, we assume the modes in the system are orthogonal, which is a
reasonable assumption. In addition, most of the NCPA is in the lowest order
modes so we typically dont need to scan beyond 15 Zernike modes.

Figure 13 presents some of the injection maps obtained while optimizing the
defocus for the first three science fibers. Each row is associated to a fiber
(top row to S1, central row to S2, and bottom row to S3) and each column to a
defocus amplitude (from left to right: -180, -90, 0, +90 and +180 nm RMS). In
this figure, we can see that the NCPA are not the same for each fiber of the
bundle. Indeed, the elongation in the injection maps hints at the presence of
astigmatism in the PSF at the location of some of the fibers. Because this
calibration is time consuming and because we mainly use the second science
fiber of the bundle on sky, we only run the calibration for this fiber
routinely.

---
Figure 13:  Measured injection maps from data collected on three fibers: S1
(top row), S2 (central row), S3 (bottom row) and five defocus amplitudes
centered on the initial defocus. From left to right: -180, 90, 0, +90 and +180
nm RMS. The flux of the injection map has been normalized by the maximum of
all the injection maps measured for those three fibers (63 total).

By using this calibration procedure, we have been able to improve the
injection by $\sim 13\%$. This result has been obtained by scanning eight
Zernike modes (Noll index $\in[4:11]$). The results presented in this
paragraph have been obtained by connecting the bundle to a photo-detector
using a simple optomechanical assembly. The use of the photo-detector allows
us to run the calibration faster but prevents us from running the calibration
when the bundle is connected to NIRSPEC. In the future we aim to be able to
run this calibration, by using Scam and/or Spec. In addition, we need to
improve the algorithm to converge faster. We also want to characterize the
NCPA and determined how it has evolved over time in order to determine how
often this calibration has to be performed.

###  4.2 Fiber extraction unit calibrations

NIRSPEC can be used on both Nasmyth platforms of the Keck II telescope. As
such, the bundle has to be reconnected to the FEU each time the instrument is
transported. Even if the re-positioning of the bundle (focus and orientation)
is repeatable and the FEU stable over time, we perform basic calibrations of
this module before each science night in order to optimize the performance of
the instrument.

The first calibration is used to co-align the fibers contained in the output
connector of the bundle with the slit selected for the observation. To move
the fibers with respect to the slit, we use the FEU-TTM (labeled C on the Fig.
6). To rotate the fibers with respect to the slit we use the rotator mirror
contained inside the NIRSPEC cryostat. Usually the rotator does not need to be
rotated by more than a degree, because the bundle were clocked to
approximately the right orientation by hand initially.

The second calibration is used to co-align the beam coming from the fiber
bundle with the stop used to reduce the background (see Sect. 3.4). This stop
is in the pupil plane of the fore-optics. To move the beam with respect to the
stop, we translate the bundle in the planes perpendicular to the optical axis
using two of the motorized translation stages contained in the FEU (see Sect.
3.3).

The third calibration is used to focus the bundle and adjust the size of the
PSFs coming from each fiber of the bundle on the slit. Because NIRSPEC has not
been designed to be diffraction-limited, the PSF is smaller than the slit when
the bundle is perfectly in focus. In this case, the spectrum acquired by the
science detector of NIRSPEC is undersampled. To overcome this problem, we have
the capability to defocus the bundle in order to optimize the sampling of the
science data. We adjust the focus of the bundle using one of the motorized
translation stages contained in the FEU (see Sect. 3.3). At the shortest
observed wavelength in a given band, we adjust the focus of the bundle to get
2.4 pixels/FWHM and this produces an R$\sim$35k.

These three calibration procedures are relatively rapid to perform due to the
stability of the FEU (usually less than one hour). The adjustments between two
consecutive nights are typically minor.

###  4.3 NIRSPEC calibrations

KPIC uses NIRSPEC in non-standard ways, so additional calibration steps on top
of the standard ones, are necessary. The days before the observation we take
the standard backgrounds and darks with multiple instrument set ups we are
likely to use during the science nights. We have the possibility to take extra
calibration data after the night if needed but calibration data acquired
before the science night can be used to quickly reduce the data during the
night to verify if everything is working as expected.

During the days before the observation, a wavelength solution calibration of
the science detector is performed by using NIRSPEC’s calibration sources (see
Fig. 6). The different arc lamp sources available in this unit have known
emission spectra, that enable wavelength calibration of the instrument. The
calibration unit also contains an extended white light source. We use this
source to acquire flats for every configuration we plan to use during the
night.

The next step of the NIRSPEC calibrations consist on determining where the
traces associated with each fiber in the bundle is located on the science
detector. The position of these spectra must be known to extract the spectral
information of each target observed. In the case of a bright object, the
location of the spectra is obvious but this is not the case for faint objects,
and so determining where to look for the traces with a calibration source off-
sky can be beneficial. To perform this calibration, we set up NIRSPEC, align
the fibers of the output connector with the slit using the position determined
previously (see Sect. 4.2) and inject the light of the calibration source of
the Keck II AO bench in each science fiber, one at a time. For each science
fiber, we acquire an image with the science detector. Because the calibration
source of the Keck II AO bench is bright and its emission spectra continuous,
we can extract the position of the traces associated with each science fiber,
across all the orders visible on the detector. Because the position of the
spectrum on the science detector and the wavelength solution are dependent on
the position of all the opto-mechanical elements located downstream of the
bundle, we need to perform this calibration for each instrument configuration
we plan to use during the science nights.

When we observe a target with at least one bright component (K or L magnitude
$<$ 10), we repeat this calibration on-sky. By acquiring such a data set on-
sky, we can insure that our calibrations were not affected by long term
thermal variations as the calibration is taken close to when the science data
is acquired. In addition, we can observe the target of interest and perform
the calibration by keeping all the opto-mechanical elements located downstream
of the bundle fixed, which yields a superior wavelength solution. Finally, the
data collected on the main star of the system can be used in the reduction of
the science data.

##  5 Science data acquisition

The FIU can be used to observe different kinds of targets. In this section we
only described the data acquisition procedure followed to acquire high-
resolution spectra of exoplanets and brown dwarfs. In most cases, we cannot
image the exoplanet using the tracking camera during an observation. So, in
order to blindly align the PSF of an exoplanet with one of the science fibers
of the bundle, we need to have an accurate knowledge of the astrometry of the
system being observed (position angle and separation). For companions with
well-characterized orbits such as the HR 8799 planets for example [42], we can
use the predicted relative astrometry or use data collected during the most
recent observation to measure the position. To predict the position of a
planet we use the algorithm used by the website
”http://whereistheplanet.com/”. If the information is not available or not
reliable, we can observe the target with NIRC2 at the beginning of our
observing run to measure the astrometric parameters of the companion.

During the observation, the first step of the acquisition sequence consists of
aligning the star with the selected science fiber. To achieve this, we use a
tracking loop. Its goal is to align the science target or its host star with a
science fiber by controlling the TTM in the FIU (labeled L , on Fig. 2). It
uses as inputs the image from the tracking camera as well as multiple
parameters provided by the telescope, the calibration procedures as well as
the user.

The algorithm uses tracking camera images to determine the position of the
host star on the detector. Using the position of the science fibers determined
during the calibration (see Sect. 4.1), the algorithm determines the FIU-TTM
offset needed and applies the command. As described in Sect. 4.1, we need to
take into account the atmospheric dispersion. This effect is automatically
compensated by the tracking loop at each iteration. For a given Zenith angle,
temperature, pressure and relative humidity, the offset in the differential
atmospheric refraction between H, where the camera tracks and K, where science
is conducted, is calculated and applied along the elevation axis (axis of
refraction). At this point we usually acquire data using the science detector
of NIRSPEC on the host. These data are used to measure the throughput of the
instrument and to reduce the science data acquired later in this sequence.
Figure 14 presents data acquired with the star of the HR7672 system aligned
with the second science fiber (labeled S2 on Fig. 3) on July 3rd, 2020. The
left panel presents the central section of the order 33 ($\lambda\in$
[2047:2083] nm) before and after reduction. The graph presented on the right
side of the figure presents the median line profile of this order. The blue
curve is the line profile computed from the raw data while the red one is
computed from the reduced data. The spectra of the star, aligned with the
second science fiber of the bundle, is clearly visible on both the Spec frame
and the graph presented by this figure.

---
Figure 14:  Left: Central section of order 33 of a Spec frame acquired with
the star of the HR 7672 system align with the second science fiber (exposure
time = 29.5 sec). The left side of this image has not been reduced while the
right side has been reduced by subtracting the background and removing the bad
pixels. The horizontal lines of each side indicate the position of the fibers.
From top to bottom: CA, S1, S2, S3, S4, S5, CB (see Fig. 3). Right: Profiles
of order 33. This profile is the median of the profiles associated across all
the wavelengths of the order. The profile computed from the raw data is
represented in blue while the line profile computed from the reduced data is
represented in red.

After aligning the star with the selected science fiber and the spectral data
collected, we use the relative astrometry of the companion to offset the star
in order to align the science target with the fiber. This offset is applied by
providing the astrometric parameters of the target (position angle and
separation) to the tracking loop. After correcting the astrometric parameters
to take into account the field distortion of the tracking camera, the tracking
loop computes the offset needed and sends a command to the FIU-TTM to apply
the offset. We verify at the beginning of each run that we can apply such
offsets with a sub-pixel accuracy by observing several binary stars with both
components visible on the tracking camera. At this point, integration on the
science target (the companion) begins. In the case of faint targets (K or L
magnitude $\geq$ 13), we acquire multiple 10 min exposure frames with the
science detector of NIRSPEC. Figure 15 presents, on its left side, a section
of order 33 extracted from one of the science frames acquired the HR7672b
system aligned with the second science fiber. The graph presented on the right
side of the figure presents the median profiles of this order. The blue curve
is the profile computed from the raw data while the red one is computed from
the reduced data. Three peaks are visible in the line profile, which indicate
the position of the fiber traces. The one associated with the second science
fiber contains a combination of the light coming from the science target, the
speckle field of the star and the multiple backgrounds described in Sect.
3.5.1. The line associated with the third and fourth science fiber contains
the light of the the speckle field of the star and the multiple backgrounds
(see Sect. 3.5.1). We cannot adjust the intensity of the light coming from the
speckle field of the star in the science fiber aligned with the companion as
the separation between the companion and its host start is constant. However,
it can be adjusted for the other fiber by moving the star around the science
target using the rotator of the telescope. The offset applied to the rotator
is automatically taken into account by the tracking loop.

---
Figure 15:  Left: Central section of the order 33 of a Spec frame acquired
with the companion of the HR 7672 system align with the second science fiber
(exposure time = 599 sec). The left side of this image has not been reduced
while the right side has been reduced by subtracting the background and
removing the bad pixel. The horizontal lines of each side indicate the
position of the fibers. From top to bottom: CA, S1, S2, S3, S4, S5, CB (see
Fig. 3). Right: Profiles of the order 33 computed by averaging the profile
associated to each wavelength of the order. The profile computed from the raw
data is represented in blue while the profile computed from the reduced data
is represented in red.

During the observation of a faint target, we regularly acquire data with the
star of the system aligned with the selected fiber (every hour or 6 science
frames) in order to get enough calibration data and to make sure the injection
into the fiber is high and stable by measuring the throughput of the system.

##  6 On sky performance and first results

To demonstrate the science capabilities of the system, we observed HR 7672 B
on September 28 2020, a bright ($K=13$ mag) early L-type brown dwarf that is
expected to have a similar spectral signature as many of our more challenging
targets [26]. Residing 0.64 arcsec from the star at the epoch of observation
[43], the companion also resides at comparable separations from the star as
our exoplanet targets. We obtained ten 600 seconds exposures of the brown
dwarf placed on science fiber S2, resulting in a total integration time of 100
minutes. The data were reduced using a preliminary version of the KPIC data
reduction pipeline. The thermal background of the instrument was subtracted
using 8 hours of backgrounds taken during the day with the same instrument
setup. The A0 standard star ups Her was observed at the start of the night to
calibrate the position and width of all of the fiber traces. We used this
trace information to extract spectra from all of the science fibers of the HR
7672 exposures, resulting in on-axis observations of both HR 7672 A and B on
S2. The extracted spectra were then averaged in time, removing bad pixels due
to cosmic ray contamination. The M-giant HIP 81497 was observed in each fiber
to compute the wavelength solution of each fiber. The A0 star zet Aql was
observed immediately before the HR 7672 observations to measure the total end-
to-end spectral response, including the telluric absorption profile.

The spectral response, wavelength solution, on-axis observations of S2, and
planetary atmosphere models were used to construct forward models of the on-
axis spectra of the brown dwarf companion. We used a BT-SETTL atmosphere model
with an effective temperature of 1800 K and a $\log(g)=5.0$ for the planet
spectrum [44]. We varied the radial velocity of the planet, rotational
broadening, and overall flux of the planet in fitting the forward model to the
data. A more detailed description of the data extraction and fitting technique
will be discussed in a subsequent paper. Figure 16 presents the best-fit model
and data from order 37 of the spectrum of HR 7672 B. The best-fit forward
model matches the data very well, as can be seen in visual inspection. To
better visualize the detection, we show the cross correlation function
detection of HR 7672 B in the top row of Fig. 17. There is a clear detection
of the brown dwarf and is consistent with previous $R\sim 1400$ spectra at the
same wavelength [26]. The posterior distributions for the radial velocity of
the planet and its rotational broadening are shown in the bottom row of Fig.
17. The vsin(i) measured is (42.6$\pm$0.8) km/s, and is the first detection of
rotational broadening for this companion. The detection and spin measurement
of a companion just 0.64 arcsec from its host star demonstrates the HDC
capabilities of KPIC.

---
Figure 16:  Spectrum of HR 7672 B (37th NIRSPEC order). The middle panel
includes the extracted spectrum of the science fiber including its 1-$\sigma$
uncertainties (orange contours). The spectra were high-pass filtered but
plotted with an offset corresponding to the continuum median value. The best-
fit forward model of the data is shown as a black line. Because the spectrum
of the companion is contaminated by the glare of the star, we jointly fit an
on-axis starlight spectrum with a model of the planet. Both components of the
model, which include telluric lines, are shown separately as dashed lines. The
companion is modeled with a BT-SETTL template assuming a $1800\,\mathrm{K}$
temperature and a $\log(g)=5.0$ surface gravity. The top panel features
spectral templates that can be used to identify spectral lines in the data.
The system transmission includes: the transmission of the atmosphere and the
instrument. The BT-Settl model includes spin broadening of the companion,
while the molecular template is only broadened to the resolution of the
instrument. The lower panel shows the residuals of the fit.
---
Figure 17:  Detection of HR 7672 B using the four reddest NIRSPEC orders
(Order 36-39). The top left panel is a type a cross correlation analysis. It
is calculated using the forward model framework illustrated in Figure 16 as
the estimated flux and associated uncertainty of the brown-dwarf companion as
a function of the radial velocity (RV) shift of the model assuming a null spin
for the companion. Fictitious fibers that only include background and dark
flux are also analyzed with the same model as a way to sample the noise. The
top right panel is the signal to noise (S/N) of the detection as a function of
RV assuming the best fit spin ($v\sin(i)=42.6\,\mathrm{km/s}$) for the model.
The S/N is calculated as the estimated amplitude of the companion divided by
its estimated uncertainty featured in the top right panel. The bottom two
panels are the marginalized posteriors for the radial velocity and the spin of
the companion respectively. The estimated radial velocity of the companion is
consistent with the prediction from relative astrometry measurements of the
companion and the radial velocity of the host star.

##  7 Conclusion

The fiber injection unit, part of the KPIC demonstrator, is a powerful tool to
acquire high spectral resolution data on faint objects surrounding stars,
faint isolated objects and close binaries. Deployed at the summit of Maunakea
in the fall 2018, the FIU has completed commissioning and has begun regular
science operations earlier this year. Numerous known stellar systems have been
imaged already and science data acquired. These data, currently being reduced
and analyzed, will be published in subsequent papers. After multiple months of
science exploitation, the second phase of the project will be deployed in
order to improve the overall performance of the instrument. The hardware,
software and observing strategies developed, tested and used by both phases of
this project will help to prepare future instruments on both ground and space
based telescopes.

###### Acknowledgements.

This work was supported by the Heising-Simons Foundation through grant
#2019-1312. It has been previously submitted as an SPIE proceeding [45]. W. M.
Keck Observatory is operated as a scientific partnership among the California
Institute of Technology, the University of California, and the National
Aeronautics and Space Administration (NASA). The Observatory was made possible
by the generous financial support of the W. M. Keck Foundation. The authors
wish to recognize and acknowledge the very significant cultural role and
reverence that the summit of Mauna Kea has always had within the indigenous
Hawaiian community. We are most fortunate to have the opportunity to conduct
observations from this mountain.

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