# High Efficiency Echelle Gratings for the Far Ultraviolet

Nicholas Kruczek1  Drew M. Miles2,3  Brian Fleming1  Randall McEntaffer2,3
Kevin France1,4  Fabien Grisé2  Stephan McCandliss5  1Laboratory for
Atmospheric and Space Physics, University of Colorado, 600 UCB, Boulder, CO
80309, USA
2Pennsylvania State University, University Park, PA, USA
3RFD Optics, LLC, University Park, PA, USA
4Center for Astrophysics and Space Astronomy, Boulder, CO, USA
5Department of Physics and Astronomy, The Johns Hopkins University, Baltimore,
MD, USA<EMAIL_ADDRESS>
###### Abstract

Modern grating manufacturing techniques suffer from inherent issues that limit
their peak efficiencies. The anisotropic etching of silicon facilitates the
creation of custom gratings that have sharp and atomically smooth facets,
directly addressing these issues. We describe work to fabricate and
characterize etched silicon echelles optimized for the far ultraviolet (FUV;
90 – 180 nm) bandpass. We fabricate two echelles that have similar parameters
to the mechanically ruled grating flown on the CHESS sounding rocket. We
demonstrate a 42% increase in peak order efficiency and an 83% decrease in
interorder scatter using these gratings. We also present analysis on where the
remaining efficiency resides. These demonstrated FUV echelle improvements
benefit the faint source sensitivity and high-resolution performance of future
UV observatories.

††journal: osajournal††articletype: Research Article

##  1 Introduction

Echelles used in the far ultraviolet (FUV; 90 – 180 nm) bandpass historically
have been fabricated using mechanical ruling techniques. This process uses a
diamond stylus drawn across the face of a substrate to cut and trace the
grooves, producing sharp angled facets with high diffractive efficiency for
select wavelengths. Traditional high-resolution FUV spectrographs (e.g.,
$HST$-STIS; [1]) use mechanically ruled echelles, but instrumental
efficiencies are low due to scatter and loss of light to off-blaze orders.
Holographic ruling is not suited for these high resolution applications due
its inability to rule the required low groove densities.

There are several sources of error that contribute to the efficiency losses of
mechanically ruled gratings. The two sources of interest to this work arise
from stylus wear and groove non-uniformities. Stylus wear, which results in a
slightly different groove shape at the beginning than at the end of the set
and rule process, is particularly problematic for large-area gratings. Groove
non-uniformities can be periodic, from the periodic mechanisms that drive the
ruling engine, or random, from surface and tip irregularities or from
variations in the ruling conditions [2, 3, 4]. The resulting rounded edges and
imprecise groove locations shift power into adjacent orders, scattered light,
and diffraction ghosts, reducing the instrument throughput [5, 6]. For
example, the echelle modes of $HST$-STIS scatter up to 20$\%$ of the power in
each order across $\gtrsim$ 400 pixels in the cross-dispersion direction,
which, when compounded over tens of orders with mixed scattered emission and
absorption lines, amounts to prohibitive, non-uniform backgrounds for
observing faint sources [7, 8].

Current work on X-ray reflection gratings leverages the inherent crystalline
structure of silicon to produce X-ray gratings with diffraction efficiencies
within 90$\%$ of the theoretical maximum [9]. This same process can be
extended to the FUV, where groove efficiencies on the order of 80% have been
demonstrated for low-order gratings [10]. The technique produces gratings with
atomically-smooth facets, resulting in more light diffracted into the blaze
order and reduced scatter relative to state-of-the-art ruling methods. The
technique relies on a free-form electron-beam (e-beam) patterning process that
enables the creation of custom groove traces. This pattern is then transferred
into Si using an anisotropic KOH etch, producing sharp and atomically smooth
grating facets at custom blaze angles. A description of the recording process
is presented in Section 2. For additional details see, e.g., Refs. [9], [11],
and references therein.

To demonstrate the gains provided by this technique, we fabricated two new
versions of the echelle flown on the Colorado High-resolution Echelle Stellar
Spectrograph (CHESS) sounding rocket payload [12]. The payload was designed to
operate from 100 – 160 nm. CHESS used a replica of a mechanically ruled
grating, fabricated by Richardson Gratings [13, 14]. This optic had a groove
density of 89 grooves mm-1, an angle of incidence ($\alpha$) of 63∘, and a
ruled area of 102 $\times$ 102 mm. The optic was operated in Littrow
configuration with a tilt ($\gamma$) of $\sim$6∘ to redirect the incoming beam
to the cross dispersing grating. As a part of the CHESS flight program a spare
gold coated echelle was ordered and this is the optic we use for comparison to
the new etched gratings.

The layout of the paper is as follows: Section 2 describes the fabrication
process for the echelles studied in this work. Section 3 provides details on
the efficiency measurement procedure, with efficiency results presented in
Section 3.2. Section 4 describes our efforts to characterize the full
diffraction arc produced by these new gratings. We discuss aperture
diffraction effects observed in the diffracted spot in Section 4.2. We then
compare the CHESS in-instrument performance of an etched echelle to that of
the mechanically-ruled flight echelle in Section 5, where we also demonstrate
the gains provided by this new technology to a future large UV/O/IR mission.
We summarize our results and discuss future work, including plans for the
fabrication of gratings with holographic solutions, in Section 6.

##  2 Echelle Fabrication

Figure 1: Scanning electron microscope images of an example KOH-etched
echelle. The yellow arrows in both figures show the vector of the incoming
beam. (a) Top view, labeled for reference are the period, blazed facets, and
an Si plateau. (b) Side view, showing the groove profile with the plateau,
illuminated facet, and blaze angle labeled. Obtaining the side view images
requires that the grating gets cleaved, so the grating shown in these images
is a test echelle. The specks on the facets in the image are KOH crystals that
are removed from the grating surface prior to coating.

Fabrication begins with the acquisition of crystalline Si substrates with the
appropriate crystal orientation; the {111} planes of crystalline Si define the
grating facet angle because they etch at a significantly slower rate than any
other Si plane. Substrates can therefore be cut from a Si boule with the {111}
planes oriented to match the desired grating blaze angle. The procured
substrates are then coated with a layer of Si3N4, which serves as a hard mask
for the KOH etch process, and a resist that provides a reactive layer for the
e-beam. The coated substrate is then installed in the e-beam writer and the
writer is programmed to expose the traces of the grooves. After e-beam
exposure, the substrate is developed so that either the resist that was
exposed to the e-beam is removed (for a positive-tone resist) or remains on
the substrate surface (for a negative-tone resist). In both cases, the final
result is a grating pattern defined by the remaining resist and the exposed
nitride. The resulting pattern is then dry-etched into the nitride itself,
forming the hard mask, and any residual resist is stripped. Finally, the
substrate is etched in the bath of KOH, forming the blazed facets defined by
the {111} planes for the grooves traced in the nitride hard mask.

Of particular importance to this process is that some residual nitride is
necessary to define the grating groove pattern after the dry etch, otherwise
the entire Si surface would be etched when exposed to KOH. While the nitride
is ultimately removed in a process step after KOH exposure, narrow
($\sim$5-10% of the period), flat Si plateaus remain at the top of the groove
facets, representing the areas that were masked by the nitride. These plateaus
do not contribute to the blazed diffraction pattern and set an upper limit on
groove efficiency; fabrication optimization often focuses on minimizing the
width of these plateaus to reduce their impact on grating performance. As a
demonstration of these features, top-down and side views of an etched grating
are shown in Fig. 1.

Figure 2: The gold coated V1 (a; 1.5 $\mu$m wide Si plateaus) and V2 (b; 0.4
$\mu$m wide Si plateaus) echelle gratings fabricated by RFD Optics, LLC.

Two echelles were fabricated by RFD Optics, LLC for this work (Fig. 2). Both
have a 60 $\times$ 60 mm ruled area, which was selected to optimize
fabrication time to fit within the project schedule. They were etched from 100
mm diameter by 1 mm thick Si wafers oriented such that the {510} crystal plane
faced upwards to set the {111} plane at 62.2 $\pm$ 1.0∘. This degree level
error on the blaze angle is set by the dicing accuracy of the vendor. This was
less than a degree off from the CHESS blaze angle while having the benefit of
being an off the shelf wafer, saving cost and lead time on procurement. Both
gratings fabricated in this work were made from phosphorus-doped Cz substrates
with a resistivity $>$1 ohm-cm. The wafers were polished by the vendor to have
a surface roughness of 1 nm and a bow $<$40 $\mu$m.

The first grating (V1) directly adapted processes used for X-ray grating
fabrication and relied on a positive-tone e-beam resist, ZEP520A [15]. As with
other positive e-beam resists, the ZEP520A that was exposed during e-beam
lithography processing was removed in the resist development step, leaving
behind the unexposed regions to define the grating groove trace. The desired
Si orientation required an off-axis cut to the Si that produced a narrow
groove "pillar" on top of a broader base, as seen in Fig. 1(a). The depth of
the "pillars" etches more quickly than the width, causing the groove aspect
ratio (the ratio of the groove width to the groove depth) to decrease to the
point of mechanical instability when subject to extended KOH exposure. To
limit the effects on groove structure from extended KOH etching, a higher
ratio of exposed:unexposed area was pursued during e-beam exposure. When the
ratio of exposed:unexposed grating regions grows too large, e-beam fogging can
affect the resist, modifying the ultimate size of the groove features after
development and degrading the fidelity of the residual resist [16]. To both
minimize the over-etching effects from the KOH exposure and avoid resist
fogging, an exposed:unexposed ratio of $\sim$6:1 was used along with a
controlled KOH etch, resulting in $\sim$1.5 $\mu$m Si plateaus at the apex of
each groove in the 11.2 $\mu$m groove period.

A second version (V2) of the CHESS grating was produced with smaller Si
plateaus to provide a performance comparison to the V1 grating. The V2 grating
used a negative e-beam resist, hydrogen silsesquioxane (HSQ) [17], to
circumvent the fogging issues encountered with the positive resist; the
negative e-beam resist allowed the ratio of exposed:unexposed regions to be
inverted during the e-beam write. Using HSQ, the V2 grating achieved a
$\sim$20:1 ratio of groove period to feature width after e-beam exposure and
resist development. The groove pattern was then transferred through the
nitride layer and exposed to the KOH bath in the same manner outlined for the
V1 grating.

When the unexposed HSQ was removed after e-beam exposure, the remaining
exposed HSQ formed an SiO2-like material. This SiO2-like residual resist
etched more quickly than pure SiO2 when exposed to KOH. Early test samples for
the V2 grating demonstrated that the residual HSQ broke down quickly during
the KOH exposure and potentially re-deposited on the sample during the etch
process, resulting in a thin, anisotropic layer that adhered to the Si wafer
surface. This layer did not significantly affect diffraction performance (see
Section 3.2), but was visible as a “scum” layer on the grating surface that
persisted through oxide removal and metal coating.

The HSQ development also removed the unexposed resist across the entire wafer
surface, including the wafer regions outside of the patterned area. The
unmasked Si3N4 outside the patterned area was subsequently removed during dry-
etch processing, leaving an unmasked Si surface during KOH etching. To
minimize the excess etching of the unmasked Si outside the grating area and
the physical area available for re-deposition of the developed HSQ during KOH
etching, the V2 grating was diced down to a 70 mm $\times$ 60 mm rectangle
prior to KOH exposure, leaving only the active grating area and a small
unruled region to be used as a reflectivity sample (see Fig. 2(b)). This piece
was submounted onto a new 100 mm diameter by 1 mm thick wafer afterwards,
which facilitates handling and mounting during testing. Both gratings received
a gold coating deposited on top of a chromium adhesion layer. These layers
were 30 nm Cr with 100 nm Au for V2 and 10 nm Cr with 50 nm Au for V2. This
reduction in coating thickness minimizes the impact the coating has on grating
performance after additional study indicated that a 50 nm thick coating was
sufficient for achieving a reflective layer with little to no pitting.

##  3 Efficiency Characterization

###  3.1 Measurement Procedure

Efficiency measurements are performed in the University of Colorado Square
Tank Chamber [12, 18], the layout of which is shown in Fig. 3. The echelle
gratings are mounted on a goniometer. This goniometer is attached to a
horizontal translation stage that slews the grating in and out of the incoming
beam, as well as a rotation stage. Two types of detectors are used to cover
the entire bandpass - microchannel plate (MCP) detectors for $\lambda$ = 90 –
120 nm and a photomultiplier tube (PMT) for $\lambda$ = 115 – 160 nm. The PMT
is a Hamamatsu R6836. Two different MCP detectors are used for different parts
of the study: A Quantar 3391A and a custom MCP from Sensor Sciences LLC. The
Quantar MCP is used for the peak order efficiency measurements. It reached the
end

Figure 3: The inside of the CU Boulder Square Tank with the V1 echelle
installed. The PMT detector is shown on the swing arm and the swing arm and
translation stage are located in the ‘reflected’ position, where the incoming
beam diffracts off of the grating. To sample the incoming beam, the swing arm
is moved to the ‘incident’ position, as indicated by the green box in the
image, and the translation stage is used to move the grating and goniometer
out of the path of the beam. The inset image in the top right shows the
definitions of the grating $\alpha$ (Inset (a)), $\gamma$ (Inset (b)), and the
grating coordinate frame. In the chamber, $\alpha$ is set by the goniometer,
tilting the grating about the axis parallel to the grooves. $\gamma$ is set by
the rotation stage, which rotates the grating azimuthally, disentangling the
incoming and reflected beams.

of its life after that test was completed. The Sensor Sciences detector was
purchased as a replacement but is still undergoing commissioning. In
particular, it experiences high levels of ion backgrounds that arise when the
swing arm stage is moved between the incident and reflected positions. This
ion contamination has a significant decay time after motion and exists at
levels that limit its accuracy for reflectivity measurements ($\sim$10% of the
reflected signal). The design and implementation of an ion repeller grid is in
progress. This detector is used for follow up efficiency measurements and
diffraction arc characterization. The light sources used for the measurements
are an H-Ar fed hollow cathode discharge lamp for $\lambda$ = 90 – 120 nm and
a Hamamatsu X2D2 deuterium lamp with an MgF2 window for $\lambda$ = 115 – 160
nm. These lamps feed an Acton VM-502 monochromator that is scanned across the
bandpass to sample the grating efficiency at wavelengths of interest.

To facilitate the discussion on grating alignment and efficiency measurements,
we have included an inset figure and additional pointers in Fig. 3. The
detector is mounted on the “swing arm” stage that scans azimuthally about the
chamber center between the ‘incident’ and ‘reflected’ beams. The incident
position allows the detector to directly measure the incoming beam without the
grating in the optical path. This position is indicated by the green box in
Fig. 3. In the reflected position, the translation stage is used to move the
grating into the optical path. The detector measures the diffracted beam by
moving the swing arm around the chamber to this reflected position. This
configuration is the one shown in Fig. 3.

Several alignment steps are taken prior to starting efficiency measurements to
ensure that the grating is in the correct geometric configuration. The inset
of Fig. 3 provides context for the definition of the angles optimized during
this alignment procedure. The inset (a) shows a side-on view of the grating,
with the local axes defined having the y-axis parallel to the grooves and the
z-axis aligned with grating normal. The y-axis is also labeled on the grating
itself in the square tank image to assist in visualizing the alignment. We
define $\alpha$ as the inclination angle between the incoming beam and grating
normal, as shown in the inset figure. $\alpha$ is controlled in the chamber
using the goniometer. For an echelle in Littrow, $\alpha$ is equal to the
blaze angle of the facets (62.2∘ for the Si gratings).

Inset (b) shows a top-down view of the grating, in a similar orientation to
the square tank image, with the same axes defined. In this image, the dashed
red line shows the projection of the incoming beam onto the grating surface.
The angle between this projection and the x-axis defines $\gamma$. In Littrow,
$\gamma$ = 0∘ results in the diffracted beam being directed back towards the
incoming beam. Therefore, a $\gamma$ is introduced to disentangle the two,
allowing the diffracted beam to be measured without blocking the incoming
light. $\gamma$ is controlled in the chamber by moving the rotation stage.

A grating is first visually aligned in the chamber using visible light fed
through the monochromator, with the rotation stage set to $\gamma$ = 0∘. The
grating is adjusted within its mount until the diffracted beam runs vertically
and is coincident with the incoming beam aperture, putting the grating into
Littrow and confirming that the grating facets are properly aligned relative
to the mount. Once aligned, the swing arm is used to position the detector
such that it is as close to the incoming beam as possible without vignetting
(placing it in the reflected position), and then the rotation stage is moved
to the point where the diffracted beam is centered on the detector setting
$\gamma\approx$ 6∘.

With $\gamma$ defined, we proceed to vacuum alignments to refine $\alpha$. The
Si substrate used for the echelles has an angular uncertainty of $\pm
1^{\circ}$. While we can set the grating to our desired $\alpha$, it may not
be correct due to this uncertainty combined with uncertainties in our mount
and alignment and that difference can impact grating performance. To ensure
that we are illuminating the facets at the ideal angle for our setup, we first
maximize the peak efficiency over a single order. The reflectivity across a
1.5 nm range is measured at several different $\alpha$’s and the angle with
the highest peak reflectivity is selected for the remainder of

Figure 4: A demonstration of peak $\alpha$. Each curve shows a single order
with a different $\alpha$, measured as an offset from the center peak value by
the amount listed in the legend.

the efficiency study (Fig. 4). We found that deviations from the expected
$\alpha$ were at most 0.2∘ relative to the nominal $\alpha$ = 62.2∘. A
perfectly aligned grating would have a diffraction arc running vertically. As
a check to our alignment, we can observe several echelle orders using the MCP
detector and measure a tilt based on their positions. We find values on the
order of 0.2 – 0.3∘, we do not expect offsets of that magnitude to impact
efficiency significantly.

To check that we are sampling the peak order efficiency over the entire
bandpass, we repeat the 1.5 nm wide scans at three different wavelength
regions. We assume the maxima of these peaks correspond to the blaze
wavelength for integer order solutions to the grating equation and use their
values to produce an equation consistent with the observed distribution.
Performing 1.5 nm wide scans across the entire bandpass is a time consuming
process. Instead, we use this analytic grating equation fit to generate a list
of the remaining peak wavelengths, which we then sample when measuring the
peak order grating efficiency.

To obtain an efficiency, we scan across 16 wavelengths in total (four for the
MCP, 13 for the PMT, with one wavelength overlapping) spanning 97 - 160 nm. A
dark wavelength is included at the beginning and end of these scans. This
wavelength is chosen to be a value where the monochromator efficiency drops
below the backgrounds, serving as a proxy for the monochromator scatter and
detector noise. We measure count rates at the incident and reflected
positions, the ratio of these values provides the grating efficiency. The
grating is then removed from the setup and reinstalled in a configuration
where the reflectivity of the gold coating can be measured at the same
$\gamma$. For the Si gratings, the coating reflectivity is measured from an
unruled portion of the grating substrate. The CHESS echelle received a 50 nm
thick gold coating, which was applied by the vendor. We do not have the
benefit of an unruled portion of the grating to use to test reflectivity and
so we instead infer this value by measuring the reflectivity of an unruled
substrate that is otherwise identical to the grating and that received the
same coating prescription. Differences could exist between these coatings but
based on results presented in this work (Section 5.1) we do not expect that
this possible discrepancy is driving the efficiencies measured in this work.

###  3.2 Efficiency Results

The resulting peak order groove efficiencies of both lithographic gratings as
well as the mechanically ruled CHESS grating are shown in Fig. 5. When
comparing the groove efficiencies between the gratings, we find a significant
improvement in the performance of the Si gratings. In particular, the V2
grating demonstrates a $\sim$50% increase in efficiency (20% absolute change)
across the bandpass. The short wavelength measurements were taken using the
Quantar MCP prior to it being decommissioned. The declining performance of
this detector lead to severe gain sag during the measurements. This effect is
evident in the systematic variability of measurements below 120 nm. These
values do vary about a mean that is consistent with the long wavelength
results.

Figure 5: The groove efficiency of the 0.4 $\mu$m-wide plateau echelle (V2;
black), the 1.5 $\mu$m-wide plateau echelle (V1; blue), and the mechanically
ruled CHESS echelle (green). Peak order groove efficiencies are not continuous
functions, they are discreet points at the apex of each individual order.
Lines have been included for each set of points to aid in clarity only, not to
imply a continuous distribution in wavelength. Off peak wavelengths reach
similar, or larger, groove efficiencies only after including contributions
from two orders. The corresponding orders for a selection of points for the V2
echelle have also been included. The dashed lines show the theoretical
efficiencies for the two lithographic gratings assuming only geometric losses.
We demonstrate how the groove efficiency of the V2 grating improves as the
second (square points) and third (triangle points) brightest orders are
included in the efficiency measurement.

The square and triangle points in Fig. 5 show the theoretical maximum
efficiency of the Si gratings assuming only geometric losses to their
plateaus. These values are equal to 86.7% for the V1 grating and 96.5% for the
V2 grating. Ideally, all of the remaining light would be directed to a single
order, achieving the maximum possible groove efficiency. As discussed in
Section 1, natural imperfections and nonidealities in all grating fabrication
methods and coating processes result in gratings that deviate from this
idealized performance, directing light away from the blaze order into
neighboring orders and interorder scatter. It is helpful to characterize how
this light is distributed for several reasons including providing a baseline
metric as this technology continues to develop and to inform instrument
design, since light diffracted into neighboring orders can still be imaged on
the detector if designed properly.

We provide a brief demonstration of this using the V2 grating installed in the
same configuration. We measure the two brightest neighboring orders about the
peak, and add them onto the peak order groove efficiency. Additional orders
would have been included but the geometry of the square tank limited the range
the detector could cover. These measurements took place after we had installed
the new MCP detector (Section 3.1) and the grating had been removed from the
chamber. Therefore, we treat them as a demonstration of the evolution of total
groove efficiency. This MCP detector has a CsI photocathode, improving its red
sensitivity. We ran this test at longer wavelengths because the D2 lamp has a
higher signal, which helps reduce the impact of the ion backgrounds.

The result of this measurement is shown in Fig. 5, demonstrating the change in
the groove efficiency as the additional orders are included in the diffracted
counts. While a vast majority of the light does reside in the peak order, the
addition of these neighboring orders results in a non-negligible increase in
the overall efficiency. With proper instrument design and detector selection,
groove efficiencies on the order of 80% could be achievable with these new
echelles in their current state. The remaining $\sim$20% between the three
order line and the theoretical maximum is expected to reside in additional
outer orders, given the predicted low scatter performance of these gratings.
We can explore this in more detail by studying the complete diffraction arc.

##  4 The Diffraction Pattern

###  4.1 Diffraction Arc Scans

Figure 6: (a) A top down view of the square tank in the configuration used for
the diffraction arc scans. In this orientation, the dispersion axis runs along
the swing arm’s path so that the detector can scan along the entire
diffraction arc. (b) An image of the V1 grating mounted in this configuration.
The dispersion axis runs horizontally in this image. This is a 90∘ rotation
about grating normal relative to the orientation in Fig. 3. We have labeled
the grating’s y-axis as a reference to the grating coordinate system in that
figure.

To quantify the KOH-etched echelle diffraction arc, we remove the goniometer
from the square tank chamber and mount the grating to a vertical plate in a
new configuration (Fig. 6). In this orientation, the grating is rotated 90∘
about grating normal from the original setup, such that $\alpha$ now runs
azimuthally about the chamber, meaning the diffraction arc runs along the same
axis as the swing arm stage and the swing arm can be used to scan the full
diffraction pattern. With the grating hard-mounted to the plate, the grating
is fixed at $\gamma$ = 0. We are unable to operate the grating in Littrow in
this configuration because the detector would block the incoming beam when
trying to measure the blaze order. To avoid this, we increase $\alpha$ by
$\sim$9∘, which was the smallest angle where we can scan all of the observable
orders without vignetting the beam. While this change impacts the diffraction
pattern, the changes are slight and our goal with this process is to quantify
where the light is diffracting in general, not compare efficiency levels in
specific orders.

Four diffraction arc scans are shown in Fig. 7, normalized to the peak counts.
All scans are at 150 nm. The scans were primarily taken using the PMT
detector, with imaging of the individual diffraction peaks taken using the
Sensor Sciences MCP. For each grating, we find both a high order diffraction
pattern just out of Littrow (150∘–170∘ from incident) and a second diffraction
pattern closer to the incident position (20∘–60∘). This second pattern arises
from diffraction off of the flat Si plateaus, which have the same groove
density and therefore generate a secondary grating that is effectively
optimized for m = 0 (specular reflection) with a non-zero efficiency in nearby
orders. Two PMT scans of the V2 grating are included. These were taken before
and after the gold coating was applied. We attempted to measure the groove
efficiency of the V2 grating pre-coating but did not have a usable sample of
unruled substrate to reliably measure a reflectivity. The V1 grating has the
largest plateaus. This results in it having the largest fraction of total
power diffracted into low orders relative to the peak high order counts. The
application of the gold to the V2 gratings widens the plateaus slightly,
resulting in more power being directed to low orders. While this trend is
visible in Fig. 7(a), as the amount of power in the low orders increases
across the three measurements, the comparison is not perfectly 1:1 due to
differences in substrate reflectivities.

Figure 7: The diffraction arcs of the Si gratings for the low (a) and high (b)
order diffraction arcs. The curves in both plots are normalized to the peak
high order value (near 162∘). The blue line shows the observed pattern for the
gold coated V1 grating. The V2 grating is shown both before (orange) and after
(black) the gold coating was applied. The gray line shows the scan of the gold
coated V2 grating taken with the new MCP. The x-axis tracks the swing arm
angle relative to the incident position. In that coordinate system, the blaze
order would be at 180∘ if the grating was in Littrow. The observed peak orders
are seen at $\sim$162∘ due to our rotation out of Littrow to cover the entire
diffraction arc. A selection of orders have been labeled in both plots for
reference.

For all three PMT scans of the high orders, we see a primary peak near 162∘
and additional ringing at lower angles (158∘ and 153∘). Similar to the low
orders, this ringing is most pronounced in the V1 grating and the least
pronounced in the bare V2 grating. This trend presumably results from coating
differences, as the application of a coating will round out the otherwise
sharp Si facets, resulting in more power diffracted into off-blaze orders. As
expected from the efficiency measurements, the MCP scan of the coated V2
grating shows four individual echelle orders that all have appreciable
efficiencies. The peak order is evenly split between two of those orders,
which is expected given that the wavelength for this scan (150 nm) has a non-
integer order solution to the grating equation in this geometry.

The ringing seen in the high order curves occurs in the direction favored by
the out of Littrow orientation, it is likely that the ringing asymmetry is
present due to this rotation and that, in Littrow, the profile would look
symmetric. The combined efficiency of the two peak orders in the MCP scan is
$\sim$70%, in good agreement with Fig. 5. This indicates that the grating
orientation is not significantly impacting the efficiency of the peak
order(s). Therefore, while the asymmetry we see in the diffraction pattern is
likely due to the grating orientation, we do not expect that this power would
be redirected to the blaze order in Littrow. Instead, we would expect to see
this power shared between symmetric orders at the same angular spacing on
either side of the blaze order.

We confirm the geometric predictions shown in Fig. 5 by calculating a total
groove efficiency from the PMT scans for these low and high orders. We measure
a total grating efficiency using the total counts in each region as well as
the reflectivity of the gold coating at the corresponding $\alpha$’s for the
two regions. Table 1 lists the measured groove efficiencies for the low and
high orders of the gold coated V1 and V2 gratings. These values include light
present as interorder scatter. The table also lists the expected groove
efficiency based off of the geometry and the total efficiency, which serves as
a check that we are accounting for all of the light. The error bars on these
total efficiency measurements come from standard error propagation methods for
combining the errors present in the diffraction arc scans and gold
reflectivity measurements. We find total efficiencies consistent with 100% to
within the error bars for both gratings. This demonstrates that, while we may
not have a sub-percent accuracy in our light accounting procedure, we can rule
out that our observed discrepancy between the measured and geometrically-
predicted efficiencies is not due to missing light in the system, in line with
the expectation that the discrepancy lies in scatter and the off-peak orders.

For both gratings, we find that the measured low order groove efficiency is
larger than the geometric expectation. For the V1 grating, this discrepancy
can be explained by a widening of the plateaus due to the application of the
gold coating. Assuming the worst case, where 0.13 $\mu$m of material is added
to either side of the plateau, we would expect the V1 plateaus to reflect
15.7% of the light after coating. This is compared to the measured 14.5%,
showing that this increase is consistent with some amount of widening due to
the coating. For the V2 grating, this same issue would exist but we observe a
larger shift in power towards these low orders than would be expected if an
additional 0.12 $\mu$m is added to the total plateau width. In this case, the
additional width would only lead to 4.6% of light reflecting off the plateaus,
below the observed value of 5.7%. The cause for this increase is not currently
known and will require a more detailed study of how the application of a
coating impacts the shape and size of the facets.

Table 1: Total Groove Efficiencies [%] Grating | Low Orders | Low Orders | High Orders | Total
---|---|---|---|---
(Geometric)
V1 | 14.5 $\pm$ 0.2 | 13.3 | 85.1 $\pm$ 1.5 | 99.6 $\pm$ 1.5
V2 | 5.7 $\pm$ 0.1 | 3.6 | 95.1 $\pm$ 1.6 | 100.7 $\pm$ 1.6

Despite the observed redistribution of light to low and off-blaze orders,
these KOH-etched gratings still outperform traditional mechanically ruled
gratings. Continued development of this technology could further improve this
performance and concentrate the outlying energy more centrally about the blaze
order. Table 1 shows that the observed diffraction arc is consistent with the
geometrically predicted distribution to within 1-2% and a majority of that
light is concentrated within one or two peak orders. While it looks like a
most of the light outside of the peak order is concentrated in outer orders,
it’s difficult to separate scatter from square tank noise and spot structure.
We can better understand scatter and demonstrate the benefits of this new
technology through in-instrument comparisons.

###  4.2 Spot Structure

Preliminary observations of the diffracted spot off of the Si gratings using
the MCP detector showed the presence of streaks running along the dispersion
axis and repeating along the cross dispersion axis (Fig. 8(a)). The size of
these features is consistent with the e-beam tool write field size and visual
inspection of the surface at multiple angles reveals a grid pattern that
matches this effect (Fig. 8(b)). Observing these boundaries under a microscope
shows that the grid manifests as narrow dark features (Fig. 8(c)). These
features likely arise due to small discontinuities between neighboring write
areas.

Figure 8: (a) The streaked pattern observed in the square tank spot, in this
case at 150 nm. The lines run along the dispersion direction and repeat across
the cross dispersion direction. (b) The write area grid effect observed along
the surface of the V2 grating. A similar pattern is seen on the V1 grating.
(c) Four of these write area cells observed under a microscope, where the
narrow write area edges are observable as faint black lines. (d) The observed
grid pattern using the laser beam in the bench-top setup. In this case a full
grid pattern is seen.

The microscope image shows features that subtend a smaller area than might be
expected based on the size of the features observed in the square tank
exposure. We use a bench-top setup to study this in more detail, illuminating
the grating with a red laser ($\lambda$ = 635 nm) with a spot large enough to
subtend a roughly 4 $\times$ 4 grid of the square regions on the grating
surface. Near the grating, the spot shows lines similar to what was observed
in the square tank (Fig. 8(d)). In this case, the pattern is seen in both the
dispersion and cross dispersion directions. We likely did not see the
horizontal gaps in the square tank image due to the nonzero $\Delta\lambda$
bandpass of the monochromator. Having a small range of wavelengths would smear
the diffracted spot and hide these features.

Further from the grating surface, the Si gratings show the typical echelle
diffraction profile, but each individual order additionally contains a
secondary diffraction pattern. This is shown in Fig. 9 for the three gratings
studied in this work. The mechanically ruled grating acts as a control for the
V1 and V2 gratings. The write area cells on the V1 grating run diagonally
relative to the grooves, this results in an X-shaped pattern relative to a
diffracted spot that otherwise looks similar to the mechanically ruled
grating. The V2 grating has write area cells that run parallel/perpendicular
to the grooves resulting in a secondary diffraction pattern that runs
perpendicular to and along the grating dispersion axis.

Figure 9: (a) The peak order diffracted spot from the CHESS echelle, showing
the expected profile for an echelle grating. (b) The peak order diffracted
spot from the V1 echelle. Here the e-beam write areas run diagonally relative
to the grooves, so an X-shaped square aperture diffraction profile is observed
superimposed on the grating spot. (c) The peak order diffracted spot from the
V2 echelle. Here the e-beam write areas run parallel/perpendicular to the
grooves, so a cross-shaped square aperture diffraction profile is observed
superimposed on the grating spot.

This secondary pattern matches that of a square aperture, indicating that
these individual write regions act as independent apertures. At FUV
wavelengths, the grating-to-detector distance in the square tank falls in the
near field diffraction regime. The near field diffraction pattern of a square
aperture can be solved analytically. Following the notation of Goodman [19],
the intensity of a 1D square aperture of width $l$ at a distance $z$ from the
aperture is:

$I(z)=\frac{1}{\sqrt{2}}\left[C\left(\sqrt{2N_{F}}(1-2z/l)\right)+C\left(\sqrt{2N_{F}}(1+2z/l)\right)\right]\\\
+\frac{j}{\sqrt{2}}\left[S\left(\sqrt{2N_{F}}(1-2z/l)\right)+S\left(\sqrt{2N_{F}}(1+2z/l)\right)\right]$
(1)

Where C and S are the Fresnel integrals and NF is the Fresnel number, which is
the metric used to roughly delineate the near and far field regimes. When
observing light with wavelength $\lambda$ , NF is defined as:

$N_{F}=\frac{(l/2)^{2}}{\lambda z}$ (2)

NF $\gtrsim$ 1 is typically considered the near field. At square tank
distances, NF = 3 – 5 across the CHESS bandpass. A simulated idealized
diffraction pattern for five square apertures is shown in Fig. 10(a),
calculated using Equation 1. Note, this assumes a perfectly coherent spherical
wavefront is incident on the apertures and is only meant to demonstrate that
the effect can generate notable periodic gaps in the imaged spot, like we see
in the square tank. The square tank image is generated from a less ideal light
source so will not agree exactly. This analysis, along with Table 1, indicate
that the write region boundaries do not cause a significant loss of light
($\lesssim$ 1%). Instead, the observed gaps only appear large because of these
diffraction effects. Their impact will be more important on instrument
performance, where bright lines could display the effects shown in Fig. 9 if
NF is sufficiently small.

The Fresnel number for these square apertures in the CHESS instrument range
from 1.53 (at 100 nm) to 0.96 (at 160 nm). Again using Equation 1 to generate
the combined intensity profile for 100 square cells, which is the number that
would exist across a full echelle in the instrument, we estimate the impact
this effect would have on the performance of CHESS (Fig. 10(b)). For the
idealized instrument, a feature that is 50 $\mu$m away from the edge of a spot
on the detector will overlap with either a neighboring order in the cross
dispersion direction or lie beyond the CHESS resolving power requirement (R
$\sim$ 120,000) in the dispersion direction. 50 $\mu$m in image space is
equivalent to 50 mm in echelle space. At this distance, the collective write
area diffraction effects are expected to be at most 1.0 $\times$ 10-4I0, where
I0 is the peak line intensity. In both directions, this diffraction effect
would only have a modest, if any, impact on the CHESS results, given that its
targets lack bright emission lines. A study concerning particularly bright
emission features may need to consider these effects. Nonetheless, the
presence of this diffraction pattern warrants further study to better
understand its impact. Additionally, multiple square apertures will
collectively exhibit a grating like behavior. We would not expect this pattern
to negatively impact performance given that the efficiency envelope of the
grating would be defined by the aperture diffraction geometry of a single
square aperture "groove" [20].

Figure 10: (a) The 1D near field diffraction pattern for five square apertures
for NF = 4.0 (black line), which is the average value for the square tank in
the FUV. The five colored rectangles show the initial square apertures, which
have effectively no edge separation between their neighbors. This near field
diffraction pattern forms periodic troughs like we observe in the square tank
spot (Fig. 8(a)). (b) The falloff of the total diffraction profile for an
assembly of 100 square apertures, simulating the observed edge effects from
the side of the echelle grating. The apertures run from x = -100 to 0 mm and
only the peak at x = 0 is shown.

##  5 In-instrument Performance

###  5.1 CHESS Demonstration

We can further demonstrate the gains provided by the KOH etching process by
comparing how these new echelles perform in the CHESS instrument relative to
the original mechanically ruled grating. The V1 grating was chosen over the V2
grating due to damage present on the surface of the V2 grating that we were
concerned could impact the analysis. The CHESS payload was reassembled from
storage, using the same flight cross disperser and flight MCP detector. The
payload was aligned in the CU Boulder Long Tank facility, which is a large
vacuum collimator. See previous CHESS references for complete details about
Long Tank operation, payload alignment, and instrument operating principles
[21, 13, 14]. Both the mechanically ruled and V1 gratings are installed using
the same mount. A base plate is used to ensure that the V1 grating sits at the
same height within the mount as the CHESS echelle. The payload is initially
illuminated with visible light to align the V1 grating by hand, prior to
vacuum operations.

The cross disperser is mounted on a set of actuators, which are primarily used
for focusing the instrument but can also position the spectrum on the
detector. We use this second capability to generate a map of the echelle
diffraction arc for both gratings over the cross disperser’s range of motion.
The resulting images are shown in Fig. 11. Each circle in that image is an
individual detector exposure. The central circle in each image contains the
peak orders, this is the ‘flight-like’ alignment of the instrument. The cross
disperser is scanned in both directions along the dispersion axis to capture
the neighboring orders. Each exposure is stitched together to form the final
image. The most prominent feature in each image is the string of Lyman
$\alpha$ (Ly$\alpha$; 121.6 nm) orders, which are contained within the orange
lines in the stitched V1 grating echellogram.

Figure 11: Stitched echellograms of the mechanically ruled echelle (a) and V1
grating (b). Each circle in the image is an individual detector exposure,
generated by tilting the cross disperser along the echelle dispersion axis to
cover the range of echelle orders. The orange lines shown in the lower image
contain the band of Ly$\alpha$ orders. The region between these lines was used
to generate the 1D extracted spectrum shown in Fig. 13. The peak order
efficiency gains from Fig. 5 and the improved scatter performance of the KOH-
etched grating can be clearly seen here, where a majority of the light is
concentrated in the central two orders. This is compared to the more numerous
bright orders and prominent scatter feature seen for the mechanically ruled
grating in (a).

We are unable to properly focus the V1 grating, which is evident in the larger
order widths and the lack of obvious emission lines outside of the brightest
features, since the signal from dimmer lines is spread over a larger area.
Subsequent analysis using a Fizeau interferometer found that this is due to a
curvature in the grating substrates (Fig. 12). The V2 grating was also tested
and demonstrated a similar curvature and so we do not plan on testing it in-
instrument. Diagnosing and correcting this behavior is planned as a future
point of study, with the likely solution simply requiring the use of thicker
substrates. Despite this issue, we can see the benefits provided by the
lithographic fabrication process. The first benefit is the previously
discussed improved peak order efficiency of the Si echelle, which is evident
in the concentration of the spectrum towards the center of the stitched
echellogram. The second benefit is observed in the interorder scatter. Echelle
interorder scatter follows a unique path across the detector, linking
diagonally between two identical wavelengths in two neighboring orders [8].
This form of scatter is noticeably more prominent in the mechanically ruled
echellogram. The defocus of the V1 echellogram could complicate this
interpretation.

To confirm these observations, we perform 1D extractions of the Ly$\alpha$
diffraction profiles for each grating. For both gratings, an extraction region
is defined that runs along the echelle dispersion direction. This region is
shown as the orange lines in Fig. 11(b). A similar region is defined for the
mechanically ruled echelle but we chose to omit it from the plot to provide
better clarity of the scatter profile. We generate a 1D spectrum by collapsing
each extracted region vertically. A coarse background correction is performed
by defining identically sized regions above and below the extracted profile.
These regions are individually summed and then averaged together before being
subtracted from the 1D Ly$\alpha$ spectrum. This is an imperfect method given
the presence of small emission features within the selected background
regions, but it is the only process capable of removing the effects of
instrument and cross disperser scatter from the echelle scatter signal.
Therefore, we expect that our final scatter measurements are likely lower
limits on the true value due to the larger contribution from these emission
features.

The two 1D Ly$\alpha$ spectra are shown in Fig. 13. While the in-instrument
echelle diffraction profile has useful parallels to the echelle profile
measured in the square tank, we caution against directly comparing specific
order efficiencies between the two given the potential differences in echelle
orientation and the unaccounted for contribution of the cross disperser on the
observed

Figure 12: The measured curvature of the V1 grating, taken with a Fizeau
interferometer using a 632.8 nm laser. This surface shape induces the defocus
that we see for the grating in Fig. 11(b). The dark regions show patches that
were either too low signal or fall out of the measurement range of the
interferometer. This image serves as a qualitative demonstration of the
grating curvature and these regions do not impact that interpretation.

profile. When comparing the spectra of the two gratings, we find that 92.7% of
all of the light captured in the extracted region is confined to the two
brightest orders of the V1 grating, compared to 60.7% for the mechanically
ruled grating. This demonstrates how the 50% increase in peak order efficiency
shown in Fig. 5 propagates down to the instrument level, specifically, more
light is falling on the detector in its flight configuration. We additionally
confirm the expected low interorder scatter levels of the V1 grating, finding
that $\sim$1% of the light is scattered between the orders. This is a
significant improvement over the 6% measured for the mechanically ruled
echelle, although we note that this value is also much smaller than we had
expected at this wavelength. For comparison, Landsman and Bowers measured a
peak scatter of 20% on the STIS E140M echelle grating. This could reflect
improvements in modern day mechanical ruling techniques [8].

The introduction of a defocus by the Si grating hides further spectral
performance enhancements provided by the Si gratings. If the warping was not
present, we would additionally expect the Si gratings to produce narrower
spectral features in Fig. 13. This is equivalent to a higher resolving power
brought about by the improved groove positional accuracy and blaze angle
consistency that can be achieved using this fabrication process. That would be
in addition to the previously described improvements to grating groove
efficiency. Future work of this type will be aided by the use of a thicker
substrate to prevent the warping of the KOH-etched echelles. We could also
gain a more detailed look at how the diffraction effects discussed in Section
4.2 impact the instrument.

Figure 13: The extracted Ly$\alpha$ diffraction profiles from Fig. 11 for the
mechanically ruled (a) and V1 (b) echelles. The percent of light in each order
is shown next to the corresponding peak. This value is relative to the sum of
the light in the entire profile. An estimated interorder scatter is also
provided in the top right, measured using the same metric.

###  5.2 Gains Provided to Flagship Missions

The Astro2020 Decadal survey recommended a large UV/visible/IR telescope
capable of achieving resolving powers in the FUV of 120,000. Utilizing these
new gratings could significantly improve the performance of the spectroscopic
channels of this next generation instrument compared to past flagship
missions. We can use the LUVOIR/LUMOS-B channel as an example to demonstrate
this improvement. This instrument originally had a high resolution channel
designed that would utilize gratings similar to those studied in this work
[22]. The effective area of LUMOS-B with a conventional grating is
$\sim$30,000 cm2 at 1250 Å and we assume a STIS-like echelle scatter profile.
Observing a faint quasar with F = 1 $\times$ 10-15 erg cm-2 s-1 Å-1 for five
hours results in an observation with SNR = 17.2. The introduction of the KOH-
etched grating, with its increased efficiency and decreased scatter, could
achieve an SNR = 22.9 across the same observing time assuming only the peak
orders are included. This demonstrates a potential 33.5% increase in SNR
through the use of Si gratings, which can be further improved upon if more
orders can be captured by the detector. This analysis does not include the
effects of the write area diffraction pattern discussed in Section 4.2, which
would require additional considerations particularly in terms of achievable
resolving powers.

##  6 Conclusions

Leveraging a process developed for X-ray diffraction gratings, we have
fabricated echelles for the FUV that demonstrate a $\sim$50% increase in
groove efficiency over traditional mechanically ruled echelles (Fig. 5). In-
instrument comparisons (Figs. 11 and 13) show how the improved peak efficiency
propagates down to the instrument level. We additionally found the KOH-etched
gratings had an 83% decrease in interorder scatter compared to the
mechanically ruled grating. With the proper instrument design and detector
selection, echelle groove efficiencies approaching 80% with minimal interorder
scatter are possible when KOH-etched echelle gratings are used.

To support the continuing development of these gratings, we underwent a
detailed accounting of the light budget across the full diffraction arc of the
grating. We find that our deviation from the geometrically predicted
efficiencies is not due to missing light in the system. We instead find that
the remainder of the light resides in neighboring orders distributed around
the blaze order. We observed that the individual e-beam write areas introduce
a square aperture diffraction effect to each order. We expect that this would
not significantly impact the performance of CHESS but could not confirm this
due to the substrate curvature preventing a focused in-instrument spectrum. A
multipass e-beam exposure, where each region is progressively patterned
multiple times but with a small positional offset, could potentially be
utilized to smooth out the write field boundaries and eliminate this effect at
the cost of doubling the e-beam write time. The feasibility of this process
and alternative solutions is still under study.

Future work on KOH echelles will focus on further driving more power into the
blaze order. While the rounding out of the otherwise sharp grating facets by
the coating could be driving our observed efficiency distribution, our limited
data on the pre- vs post-coating V2 grating demonstrates only a modest impact
on the diffraction profile (Fig. 7) but does require further study. Fully
diagnosing the observed diffraction arc of KOH-etched echelle gratings will
require a combination of modeling, fabrication, and characterization efforts.
Previous simulations of echelle gratings demonstrate that achieving a
perfectly blazed diffraction profile can be complicated, indicating that our
geometric models are likely too simplified [23, 5]. Additional efficiency
gains can be realized through minimizing or removing the Si plateaus. One
option to circumvent the plateaus is to replicate the grating, see [9] for
complete details. This process has the benefit of removing the plateaus but
does impact the blaze profile, which must be accounted for in the grating
design.

Beyond echelles and high resolution spectroscopy, anisotropically etched Si
gratings hold potential for a variety of UV gratings. The atomically smooth
facets should be comparable to the performance of holographically ruled
gratings while simultaneously achieving a blazed profile without requiring
post-processing. The blaze angle can be customized, including angles below
what is typically achievable for holographic gratings. The groove trace is
also free form, so holographic solutions can be reproduced on Si with the
added benefit of reducing the restriction on available recording wavelengths,
widening the recording geometry parameter space. To support the fabrication of
such gratings, we have developed a methodology for translating holographic
solutions into an e-beam readable format, which was demonstrated on an EUV
grating sample as a part of the ESCAPE Phase A study [24, 25].

We plan on leveraging these benefits through the fabrication of several
gratings of increasing complexity, ranging from a spherical grating with a
uniform line density to an ellipsoid with variable groove spacing [26, 27, 28,
29]. As in this work, these gratings will be modeled after ones that have
flown on sounding rocket missions to provide a baseline point of comparison.
For the sounding rocket payloads that are still active, we additionally plan
to flight test the fabricated gratings. Combined, this work is a crucial step
in our ability to meet the efficiency goals of future large UV observatories.

## Acknowledgements

Part of this work was carried out in the PSU Materials Research Institute and
PSU Nanofabrication Lab and the authors would like to thank the staff that
supported the grating development efforts that were undertaken there. NK would
like to thank Nicholas Nell and Patrick Behr for their support in CHESS
alignment and operation. This work was supported by NASA grants NNX16AG28G,
80NSSC19K0450, and 80GSFC20C0087 to the University of Colorado.

## Disclosures

Randall McEntaffer and Drew M. Miles have a financial interest in RFD Optics,
a company which could potentially benefit from the results of this research.
This interest has been reviewed by the University in accordance with its
Individual Conflict of Interest policy, for the purpose of maintaining the
objectivity and the integrity of research at The Pennsylvania State
University.

## Data Availability

Data underlying the results presented in this paper are not publicly available
at this time but may be obtained from the authors upon reasonable request.

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