# Convolutive Block-Matching Segmentation Algorithm
with Application to Music Structure Analysis

###### Abstract

Music Structure Analysis (MSA) consists of representing a song in sections
(such as “chorus”, “verse”, “solo” etc), and can be seen as the retrieval of a
simplified organization of the song. This work presents a new algorithm,
called Convolutive Block-Matching (CBM) algorithm, devoted to MSA. In
particular, the CBM algorithm is a dynamic programming algorithm, applying on
autosimilarity matrices, a standard tool in MSA. In this work, autosimilarity
matrices are computed from the feature representation of an audio signal, and
time is sampled on the barscale. We study three different similarity functions
for the computation of autosimilarity matrices. We report that the proposed
algorithm achieves a level of performance competitive to that of supervised
state-of-the-art methods on 3 among 4 metrics, while being fully unsupervised.

Index Terms—  Music Structure Analysis, Audio Signals, Barwise Music
Processing

##  1 Introduction

Citing Paulus et al. [1], “[…] it is the structure, or the relationships
between the sound events that create musical meaning”. Following that
statement, the Music Structure Analysis task (MSA) was developed, focusing on
the retrieval of the structure in a song [2], which can be seen as retrieving
a simplified description of the organization of a song at the macroscopic
scale111This work focuses on a “flat” estimation, i.e. a single-level
estimation, as opposed to a hierarchical level of structure.. This paper
specifically studies the subtask of structural segmentation of audio signals,
consisting of estimating the boundaries between different sections, i.e.
estimating the time instances which separate consecutive sections on the basis
of an audio recording.

This task is generally solved focusing on one or several criteria among four:
homogeneity, novelty, repetition and regularity [2]. The homogeneity criterion
assumes that musical elements (notes, chords, tonality, timbre, …) should be
similar to constitute a section. Novelty is the counterpart of homogeneity,
considering that boundaries must be placed between consecutive musical
elements that are highly contrastive. Both are generally studied jointly.
Repetition does not consider segments locally, but rather relies on a global
approach of the song, to catch recurring motifs (for instance a melodic line).
The rationale is that motifs, which may be individually heterogeneous,
constitute segments when they are repeated. Finally, the regularity criterion
assumes that, within a song, segments should be of comparable sizes.

In this article, we introduce a new algorithm to perform unsupervised music
segmentation. Our contribution is the design of a cost function which relies
on homogeneity and regularity, which can be optimized using dynamic
programming. This results in an efficient unsupervised segmentation technique,
as supported by a comparison with state-of-the-art unsupervised and supervised
methods. The algorithm is implemented in the open-source as_seg toolbox [3]

This article is organized as follows: Section 2 presents the autosimilarity
matrix, on which the CBM algorithm detailed in Section 3 is applied, and
Section 4 presents experimental results, conducted on both RWC Pop and SALAMI
datasets [4, 5].

###  1.1 Related work

Music structure is frequently estimated using an “autosimilarity matrix”,
presented in Section 2. In a nutshell, an autosimilarity matrix is a square
matrix presenting the similarity between each pair of time instances in the
song. For instance, the kernel of Foote [6] uses autosimilarity matrices, and
exploits the homogeneity/novelty criteria, estimating boundaries as points of
high dissimilarity between the recent past and the near future.

Jensen [7] developed an optimization problem minimizing the average self-
dissimilarity (in an autosimilarity matrix) of each segment, as a way to
account for the homogeneity of each segment. This optimization problem is
solved by dynamic programming. Sargent et al. [8] later extended this
optimization paradigm by adding prior knowledge on the segment sizes in the
form of constraints.

McFee & Ellis [9] developed an algorithm based on spectral clustering,
interpreting the repetition of musical content as principally connected
vertices in a graph. The structure is then obtained by studying the
eigenvectors of the Laplacian of this graph, forming cluster classes for
segmentation.

Serrà et al. [10] developed “Structural Features”, which, by design, encode
both repetitive and homogeneous parts. The rationale of these features is to
account for the musical content of several consecutive frames, then used to
compute the similarity. Boundaries are obtained as points of high novelty
between consecutive structural features.

The most recent techniques often make use of neural networks, e.g. [11, 12,
13]. In particular, the work of Grill & Schlüter [11], based on a
Convolutional Neural Network (CNN), may be considered as state-of-the-art in
the structural segmentation task.

##  2 Autosimilarity Matrix

###  2.1 Barwise TF Matrix

We consider that bars are well suited to express patterns and sections in
Western modern music (our case study). In particular, we assume that musical
sections start and end on downbeats, which is experimentally confirmed by
works such as [14, 15] where the use of structural information improves the
estimation of downbeats. The direct consequence is the need for a powerful
tool to estimate bars, in our case the madmom toolbox [16].

Thus, we decide to represent music as barwise spectrograms, with a fixed
number of time frames $T$ per bar. In practice, following [17], this article
focuses on the Barwise TF matrix, consisting of a matrix of size $B\times TF$,
$B$ being the number of bars in the song (i.e. a dimension accounting for the
barscale), and $TF$ the vectorization of both time (at barscale) and frequency
dimensions into a Time-Frequency dimension. Following the work of Grill &
Schlüter [11], in what follows the frequency dimension corresponds to the Log
Mel feature, i.e. the logarithm of Mel coefficients.

###  2.2 Similarity Function

Given a Barwise TF matrix $X\in\mathbb{R}^{B\times TF}$, an autosimilarity of
$X$ is defined as a matrix $A(X)\in\mathbb{R}^{B\times B}$ where each
coefficient $A(X)_{ij}$ represents the similarity between two bars $X_{i}$ and
$X_{j}$, such that $A(X)_{ij}=s(X_{i},X_{j})$, subject to a similarity
function $s()$. Three similarity functions are studied here:

  * •

Cosine similarity, the normalized dot products between two vectors:
$s^{cos}(X_{i},X_{j})=\frac{\left\langle
X_{i},X_{j}\right\rangle}{\|X_{i}\|_{2}\|X_{j}\|_{2}}$.

  * •

Covariance similarity, the Cosine similarity of the centered matrix $X$, i.e.
denoting as $\bar{x}\in\mathbb{R}^{TF}$ the average of all bars in the song:
$s^{cov}(X_{i},X_{j})=\frac{\left\langle
X_{i}-\bar{x},X_{j}-\bar{x}\right\rangle}{\|X_{i}-\bar{x}\|_{2}\|X_{j}-\bar{x}\|_{2}}$.

  * •

The Radial Basis Function (RBF), a kernel function where
$s^{RBF}(X_{i},X_{j})=\exp\left(-\gamma\left\|\frac{X_{i}}{\|X_{i}\|_{2}}-\frac{X_{j}}{\|X_{j}\|_{2}}\right\|^{2}_{2}\right)$.

Parameter $\gamma$ is set relatively to the standard deviation of the pairwise
Euclidean distances, i.e. denoting as $\sigma=\underset{1<i,j<B,i\neq
j}{\text{std}}\left(\left\|\frac{X_{i}}{\|X_{i}\|_{2}}-\frac{X_{j}}{\|X_{j}\|_{2}}\right\|^{2}_{2}\right)$,
we set $\gamma=\frac{1}{2\sigma}$.

These three autosimilarities are presented in Figure 1. Note that the self-
similarity of a vector is equal to one in these similarity functions, and
corresponds to the main diagonal of the autosimilarity matrix.

Fig. 1: Cosine, Covariance and RBF autosimilarities on the song POP01 from RWC
Pop [4].

##  3 Convolutive “Block-Matching” Algorithm

Formally, given a musical song sampled in time as $B$ bars, structural
segmentation can be defined as finding a set of boundaries (located on
downbeats) $Z$ representing the start of all segments, i.e.
$Z=\\{\zeta_{i}\in\llbracket 1,B\rrbracket,\,i\in\llbracket 1,E\rrbracket\\}$,
with $E\leq B$ the number of estimated boundaries. The $i$-th segment $S_{i}$
is exactly the interval composed of the bars between two consecutive
boundaries, i.e. $S_{i}=\llbracket\zeta_{i},\zeta_{i+1}\llbracket$.

Starting from an autosimilarity matrix, structural segmentation is obtained
using the Convolutive “Block-Matching” segmentation algorithm (CBM). In a
nutshell, the CBM algorithm is based on the definition of a score function
$\gamma()$ applied on segments, and the segmentation of the song results in
the maximum total score of the segments, i.e. denoting as $\Theta$ the set of
all possible segmentations:

$\vspace{-5pt}Z^{*}=\underset{Z\in\Theta}{\operatorname*{arg\,max}}\sum\limits_{i=1}^{E-1}\gamma(\llbracket\zeta_{i},\zeta_{i+1}\llbracket).\vspace{-5pt}$
(1)

###  3.1 Dynamic Programming - Fundamentals

The optimization problem defined in Equation 1 can be solved using dynamic
programming [18, Chap. 9]. In particular, following [7], by considering each
bar as a vertex and each segment between two bars as an edge, a segmentation
can be reinterpreted as a path in a Directed Acyclic Graph. By assigning the
segment score as the weight of the associated edge, the optimal segmentation
can be reframed as the problem of finding the longest path in the graph.
Precisely, the solution is computed as presented in the “Single-Source
Shortest Paths in Directed Acyclic Graphs” problem (for a critical path) [18,
Chap. 24], as the graph is topologically sorted (due to the chronological
order of bars in the song), and composed of a single vertex as origin (the
first bar of the song).

###  3.2 Score function

The score function in the CBM algorithm, defining the optimization problem to
be solved, is inspired from the work of Sargent et al. [8], which extended the
score function of Jensen [7] in order to take into account both the
homogeneity and the regularity criteria. For a segment $S_{i}$ of size $n$,
this results in a mixed score function:

$\gamma(S_{i})=\gamma^{K}(S_{i})-\lambda p(n).$ (2)

In details, Equation 2 is the weighted sum of two terms: $\gamma^{K}(S_{i})$,
evaluating the homogeneity of the segment using convlution kernels (Section
3.2.1), and $p(n)$, a penalization term related to the regularity of the
segment (Section 3.2.2). Parameter $\lambda$ is a weighting parameter.

####  3.2.1 Convolution Kernels

Given an autosimilarity matrix $A(X)$, the convolution score
$\gamma^{K}(S_{i})$ of segment $S_{i}$ is computed by evaluating the
autosimilarity values restricted to that segment, denoted as $A_{S_{i}}(X)$,
and represents (to some extent) the inner similarity of this segment. In
practice, this is obtained by weighting the different values in the
autosimilarity, in a convolution operation between the autosimilarity and a
(fixed) “convolution” kernel matrix $K$ of the size of the segment, such as:

$\gamma^{K}(S_{i})=\frac{1}{\nu\,n}\sum\limits_{k=1}^{n}\sum\limits_{l=1}^{n}A_{S_{i}}(X)_{kl}K_{kl}.$
(3)

The convolution is normalized by the size of the segment222The normalization
by the size of the segment is meant to adjust the squared dependence to the
size of the segment in the number of autosimilarity values ($n^{2}$ values in
the autosimilarity) into a linear dependence. $n$ and by a parameter $\nu$,
scaled on the convolution values in this particular song333Parameter $\nu$ is
set as the maximal convolution value obtained by sliding a kernel of size 8 on
this autosimilarity, i.e. the highest score among all possible segments of
size 8..

In the CBM algorithm, the design of the convolution kernel defines how to
translate bar similarities into segment homogeneity, which is of particular
importance. A very simple kernel is a kernel matrix full of ones, i.e.
$K=\mathds{1}_{n\times n}$, resulting in the sum of all the values in the
autosimilarity. Still, we consider that the main diagonal in the
autosimilarity is not informative regarding the overall similarity in the
segment, as its values are normalized to one, thus $K_{ii}=0,\,\forall i$.
Hereafter are presented two ways for designing kernels.

Full Kernel: The first kernel is called the full kernel, and corresponds to a
matrix full of 1 (except on the diagonal where it is equal to 0). The full
kernel captures the average value of similarities in this segment (without the
self-similarity values). Practically, denoting as $K^{f}$ the full kernel,
$K^{f}_{ij}=\begin{cases}1&\text{if }i\neq j\\\ 0&\text{if }i=j\end{cases}.$

Band Kernel: The second kernel design, called band kernel, emphasize on short-
term similarity: the score is computed on a few bars in the segment only,
depending on their temporal proximity (only the closest bars are considered).
In practice, this is obtained setting every entry to 0, except for some upper-
and sub-diagonals, where they are set to 1. The number of upper- and sub-
diagonals is a parameter, corresponding to the maximal number of neighbouring
bars considered to evaluate the similarity. Denoting as $v$ the number of
bands, the $v$-bands kernel $K^{vb}$ is defined as:
$\begin{array}[]{crl}K^{vb}_{ij}=\begin{cases}1&\text{if }1\leq|i-j|\leq v\\\
0&\text{if }i=j\text{ or }|i-j|>v\end{cases}.\end{array}$

Figure 2 represents a full, a 3-bands and a 7-bands kernel of size 10.

(a) Full kernel $K^{1b}$.

(b) 3-bands kernel.

10 (c) 7-bands kernel.

Fig. 2: Different kernels, of size 10

####  3.2.2 Penalty Function

The regularity function is based on prior knowledge, and aims at enforcing
particular sizes of segments, which are known to be common in a number of
music genres, notably Western modern music. In particular, as presented in [8,
17], some sizes of segments are most common in the annotations. In particular,
in the SALAMI dataset [5], as presented in Figure 3, most segments are of size
8, and the remaining segments are generally of size 4, 12 or 16. Finally, even
segments are more common than segments of odd sizes. Hence, the regularity
function models this distribution, as:

$\vspace{-5pt}p(n)=\begin{cases}0&\text{if }n=8\\\ \frac{1}{4}&\text{else if
}n\equiv 0\pmod{4}\\\ \frac{1}{2}&\text{else if }\text{if }n\equiv
0\pmod{2}\\\ 1&\text{otherwise}\end{cases}\vspace{-10pt}$ (4)

Fig. 3: SALAMI annotations, at bar level (coarse level, test subset defined in
[11]).

##  4 Experiments

(a) $F_{0.5}$.

(b) $F_{3}$.

Fig. 4: F-measures according to the different autosimilarity matrices and
kernels (RWC Pop dataset).

(a) $F_{0.5}$.

(b) $F_{3}$.

Fig. 5: F-measures according to the different autosimilarity matrices and
kernels (SALAMI test subset, defined in [11]).

The CBM algorithm being a segmentation algorithm, it is evaluated on the
structural segmentation task on both RWC Pop and SALAMI datasets [4, 5]. The
SALAMI dataset is restricted to the test subset defined in [11]. The remainder
of the dataset is used to fix parameter $\lambda$, in a learning scheme. On
the RWC Pop dataset, $\lambda$ is fitted in a 2-fold cross-validation scheme,
by splitting the dataset in two subsets: songs with odd vs. even numbers, as
in [17].

We evaluate the algorithm on the Hit-Rate metrics, comparing a set of
estimated boundaries with a set of annotations. In particular, an estimated
boundary $\zeta^{e}_{i}\in Z^{e}$ is considered to be correct if it is close
(with respect to a tolerance $t$) to an annotated boundary $\zeta^{a}_{j}\in
Z^{a}$, i.e. $|\zeta^{e}_{i}-\zeta^{a}_{j}|\leq t$. Tolerances are set to 0.5s
and 3s, following the standards in MSA [2]. The segmentation is finally
evaluated with Precision, Recall and F-measure. Only F-measures are shown here
($F_{0.5}$ and $F_{3}$).

The autosimilarity matrices are computed with the three similarity functions
(Cosine, Covariance and RBF), and computed with the full, 3-bands, 7-bands and
15-bands kernels. Segmentation results are presented in Figures 4 and 5 for
the RWC Pop and SALAMI datasets respectively.

These results exhibit a clear advantage of using the Covariance and RBF
similarity functions compared to the Cosine similarity function. The best
results on both datasets are obtained with the RBF similarity function. The
design of the kernel is also largely impacting the segmentation results. In
these experiments, the 7-bands and the 15-bands are respectively the best-
performing kernels on the RWC Pop and SALAMI datasets.

Table 1 compares the best results obtained with the CBM algorithm with those
of the state-of-the-art. In this comparison, the CBM algorithm largely
outperforms the unsupervised segmentation methods, and is competitive with the
global (supervised) State-of-the-Art [11] in all metrics, except on the
$F_{0.5}$ for the SALAMI dataset.

Method | RWC Pop | SALAMI
---|---|---
$F_{0.5}$ | $F_{3}$ | $F_{0.5}$ | $F_{3}$
CBM | 66.52% | 81.16% | 44.94% | 63.18%
Foote [6] | 34.48% | 55.01% | 32.70% | 54.23%
Spectral [9] | 45.01% | 60.30% | 33.69% | 48.44%
Clustering
Structural | 42.96% | 62.15% | 33.84% | 53.72%
Features [10]
CNN [11] | 69.70% | 79.34% | 54.09% | 62.28%
Table 1: Comparison of the best-performing CBM with state-of-the-art
algorithms. Following [17], results for the unsupervised algorithms are
computed with the MSAF toolbox [19], and realigned on downbeats. Results for
the CNN [11] are extracted from the 2015 MIREX contest.

##  5 Conclusions

This article has presented different autosimilarity matrices, computed at the
barscale, hence studying several distinctive ways to represent similarities
between pairs of bars in a song. These autosimilarities are then processed by
the CBM algorithm, estimating boundaries between structural sections.

The CBM algorithm achieves levels of performance outperforming the current
unsupervised state-of-the-art [6, 9, 10] and comparable to those of the global
(supervised) state-of-the-art [11].

Overall, the design of the kernel clearly impacts the segmentation results.
Hence, future work could focus on studying alternative types of kernels, and,
in particular, using normalized values in the kernel (as in [20]) and
normalizing the score associated with each kernel by the number of nonzero
values instead of the size of the kernel.

Convolution kernels studies in this article focus on the homogeneity of each
segment, but different kernels, in particular considering those of Shiu et al.
[20], could be considered in order to account for the repetition criterion.
The kernel values could depend on the particular song or dataset considered.
Of particular interest could be the learning of such kernels instead of an
(empirical) definition.

Penalty values for the different cases were set quite empirically, and would
benefit from further investigations.

This work opens new paths towards future progress in structural segmentation
methods, for which we hope that the open-source as_seg toolbox [3] provided
with this work, will contribute.

## References

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# Formats over Time: Exploring UK Web History

Andrew N. Jackson

The British Library  Boston Spa, Wetherby  West Yorkshire, LS23 7BQ, UK
<EMAIL_ADDRESS>
###### Abstract

Is software obsolescence a significant risk? To explore this issue, we
analysed a corpus of over 2.5 billion resources corresponding to the UK Web
domain, as crawled between 1996 and 2010. Using the DROID and Apache Tika
identification tools, we examined each resource and captured the results as
extended MIME types, embedding version, software and hardware identifiers
alongside the format information. The combined results form a detailed
temporal format profile of the corpus, which we have made available as open
data. We present the results of our initial analysis of this dataset. We look
at image, HTML and PDF resources in some detail, showing how the usage of
different formats, versions and software implementations has changed over
time. Furthermore, we show that software obsolescence is rare on the web and
uncover evidence indicating that network effects act to stabilise formats
against obsolescence.

###### category:

H.3.3 Information Storage and Retrieval Information Search and Retrieval

###### keywords:

Information filtering, Selection process

###### category:

H.m Information Systems Miscellaneous

##  1 Introduction

In order to ensure that our digital resources remain accessible over time, we
need to fully understand the software and hardware dependencies required for
playback and re-use. The relationship between bitstreams and the software that
makes them accessible is usually expressed in terms of data ‘format’ - instead
of explicitly linking individual resources to individual pieces of software,
we attach identifiers like file extensions, MIME types and PRONOM IDs to each
and use that to maintain the link. These identifiers can also be attached to
formal format specifications, if such documentation is available.

Successful digital preservation therefore requires us to fully understand the
relationship between data, formats, software and documentation, and how these
things change over time. Critically, we must learn how formats become
obsolete, so that we might understand the warning signs, choices and costs
involved. This issue, and the arguments around the threat of obsolescence, can
be traced back to 1997, when Rothenburg asserted that “Digital Information
Lasts Forever—Or Five Years, Whichever Comes First.” [1]. Fifteen years later,
Rothenberg maintains that this aphorism is still apt [2]. If true, this
implies that all formats should be considered brittle and transient, and that
frequent preservation actions will be required in order to to keep our data
usable. In contrast, Rosenthal maintains that this is simply not the case,
writing in 2010 that “when challenged, proponents of [format migration
strategies] have failed to identify even one format in wide use when
Rothenberg [made that assertion] that has gone obsolete in the intervening
decade and a half.” [3]. Rosenthal argues that the network effects of data
sharing act to inhibit obsolescence and ensure forward migration options will
arise. Similarly, Rothenburg remains skeptical of the common belief that
different types of content are normalising on HTML5 and so reducing the number
of formats we need to address [2]. If these assertions are true, then format
migration or emulation strategies become largely unnecessary, leaving us to
concentrate on storing the content and simply making use the available
rendering software.

The fact that the very existence of software obsolescence remains hotly
disputed therefore undermines our ability to plan for the future. To find a
way forward, we must examine the available evidence and try to test these
competing hypotheses. In this paper, we begin this process by running
identification tools over a suitable corpus, so that we can use the resulting
format profile to explore what happens when formats are born, and when they
fade away. Working in partnership with JISC and the Internet Archive (IA), we
have been able to secure a copy of the IA web archives relating to the UK
domain, and host it on our computer cluster. The collection is composed of
over 2.5 billion resources, crawled between 1996 and 2010, and thus gives us a
sufficiently long timeline over which some reasonable conclusions about web
formats might be drawn.

Determining the format of each resource is not easy, as the MIME type supplied
by the originating server is often malformed [4]. Instead, we apply two format
identification tools to the content of each resource \- DROID and Apache Tika.
Both use internal file signature (or ‘magic numbers’) to identify the likely
format of each bitstream, but differ in coverage, complexity and granularity.
In particular, DROID tuned to determine different versions of formats, while
Apache Tika returns only the general format type, but augments it with more
detailed information gleaned from parsing the bitstream. Thus, by combining
both sets of results, we can come to a more complete understanding of the
corpus. Furthermore, by comparing the results from the different
identification tools, we can also uncover inconsistencies, problematic formats
and weak signatures, and so help drive the refinement of both tools.

##  2 Method

The test corpus is called the JISC UK Web Domain Dataset (1996-2010), and
contains over 2.5 billion resources harvested between 1996 and 2010 (with a
few hundred resources dated from 1994), either hosted on UK domains, or
directly referenced from resources hosted under ‘.uk’. This adds up to 35TB of
compressed content held in 470,466 arc.gz and warc.gz files, now held on the a
50-node HDFS filesystem. As the content is hosted on this distributed
filesystem, we are able to run a range of tools over the whole dataset in a
reasonable time using Hadoop’s Map-Reduce framework.

Due to it’s prominence among the preservation community and the fine-grained
identification of individual versions of formats, DROID was chosen as one of
the tools. To complement this, we also chose to use the popular Apache Tika
identification tool, which has been shown to have much broader format coverage
[5]. Unfortunately, both tools required some modification in order to be used
in this context. DROID was particularly problematic, and we were unable to
completely extract the container-based identification system in a form that
made it re-usable as a Map-Reduce task. However, the binary file format
identification engine could be reused, and the vast majority of the formats
that DROID can identify are based on using that code (and the DROID signature
file it depends upon - we used signature file version 59). Herein, we refer to
this as the ’DROID-B’ tool. Both tools were run directly on the bitstreams,
rather than being passed the URLs or responses in question, and so the
identification was based upon the resource content rather than the name or any
other metadata. For this first experimental scan, we decided to limit the
identification process to the top-level resource associated with each URL and
crawl time - archive or container formats were not unpacked.

In order to compare the results from DROID-B and Apache Tika with the MIME
type supplied by the server, the identification results are normalised in the
form of extended MIME Types. That is, where we know the version of a format as
well as the overall MIME Type, we add that information to the identifier using
a standard type parameter, e.g. “image/png; version=1.0”, corresponding to
PUID fmt/11. In this way, extended MIME types can act as a bridge between the
world of PRONOM identifiers and the standard identification system used on the
web. Broad agreement between tools can be captured by stripping off the
parameters, but their presence lets more detailed information be collected and
compared in simple standard form. A number of formats also embed information
about the particular software or hardware that was using in their creation -
PDF files have a ‘creator’ and a ‘producer’ field, and many image formats have
similar EXIF tags. As we are also interested in the relationship between
software and formats, we have attempted to extract this data and embed it in
the extended MIME type as software and hardware parameters. The full
identification process also extracted the year each resource was crawled, and
combines this with the three different MIME types to form a single ‘key’.
These keys were then collected and the total number of resources calculated
for each. Overall, the analysis was remarkably quick, requiring just over 24
hours of continuous cluster time.

##  3 Results

###  3.1 The Format Profile Dataset

The primary output of this work is the format profile dataset itself111To
download the dataset, see http://dx.doi.org/10.5259/ukwa.ds.2/fmt/1.. Each
line of this dataset captures a particular combination of MIME types (server,
Apache Tika and DROID-B), for a particular year, and indicates how many
resources matched that combination. For example, this line:

image/png image/png image/png; version=1.0 2004 102

means that in this dataset there were 102 resources, crawled in 2004, that the
server, Tika and DROID-B all agreed have the format ‘image/png’, with the
latter also determining the format version to be ‘1.0’. Due disagreements over
MIME types and the number different hardware and software identifiers the
overall profile is rather large, containing over 530,000 distinct combinations
of types and year. Below, we document some initial findings drawn from the
data. However, there is much more to be gleaned from this rich dataset, and we
have made it available under an open licence (CC0) in the hope that others
will explore and re-use it.

Figure 3.1: Identification failure rates for Apache Tika and DROID-B.

###  3.2 Comparing Identification Methods

####  3.2.1 Coverage & Depth

The identification failure rates for both tools are shown in Figure 3.1, as a
percentage of the total number of resources from each year. Overall, Apache
Tika has significantly lower failure rate than DROID-B - 1% versus around 10%.
There also seems to be a significant downward trend in the DROID-B curve,
which would indicate that DROID copes less well with older formats. However,
initial exploration indicate that this is almost entirely due to the
prevalence of pre-2.0 HTML, which was often poorly formed.

####  3.2.2 Inconsistencies

By comparing the simple MIME types (no parameters) we were able to compare the
results from both tools, revealing 174 conflicting MIME type combinations. For
example, some 2,957,878 resources that Apache Tika identified as ‘image/jpeg’
we identified as ‘image/x-pict’ by DROID. The PRONOM signature for this format
is rather weak (consisting of a single byte value at a given offset) and can
therefore produce a large number of false positives when run at scale
222Indeed, it appears that this signature has been removed from the latest
version of the DROID binary signature file (version 60, published during
preparation).. Another notable class of weak signatures correspond to text-
based formats like CSS, JavaScript, and older or malformed HTML. Apache Tika
appears to perform slightly better here - for example, the HTML signature is
much more forgiving than the DROID-B signature.

More subtle inconsistencies arose for the Microsoft Office binary formats and
for PDF. In the former case, a full implementation of DROID would probably be
able to resolve many of the discrepancies. The picture for PDF is more
complex. The results were mostly consistent, but DROID-B failed to recognise
1,340,462 resources that Apache Tika identified as PDF. This appears to be
because the corresponding PRONOM signature requires the correct end-of-file
marker (‘%%EOF’) to be present, whereas many functional documents can be
mildly malformed, e.g. ending with ‘%%EO’ instead. Also, the results for
PDF/A-1a and PDF/A-1b were not entirely consistent, with Tika failing to
identify many documents that DROID-B matched, but matching a small number of
PDF/A-1b documents that DROID missed. A detailed examination of the signatures
and software will be required to resolve these issues.

###  3.3 Format Trends

Figure 3.2: Number of resources of each format versus its lifespan. Formats
identified using Apache Tika.

As mentioned in the introduction, one of the core questions we need to
understand is whether formats last a few years and then die off, or whether
(on the web at least) network effects take over and help ensure formats
survive. We start to examine this question by first determining the lifespan
of each format - i.e. the number of years that have elapsed between a format’s
first and last appearance in the archive. This lifespan is plotted against the
number of resources that were found to have that format, such that young and
rare formats appear in the bottom-left corner, whereas older and popular
formats appear in the top-right, as shown in figure 3.2. Due to the extreme
variation in usage between formats, the results are plotted on a logarithmic
scale.

If popularity has no effect on lifespan, we would expect to see a simple
linear trend - i.e. a format that has existed for twice as long as another
would be found in twice as many documents. Due to the logarithmic vertical
axis of figure 3.2, would be shown as a sharp initial increase followed by an
apparent plateau. However, in the presence of network effects we would expect
a much stronger relationship, and indeed this is what we find - a format that
has been around longer is exponentially more common that younger formats (an
exponential fit appears as a straight line in figure 3.2). A large number of
formats have persistent for a long time (47 formats have been around for 15
years), and that since 1997, roughly six new formats have appeared each year
while fewer have been lost (roughly 2 per year). While this confirms the
presence of the network effects Rosenthal proposed, proving that these formats
are more resilient against obsolescence will require a deeper understanding of
obsolescence itself.

Figure 3.3: Selected popular image formats over time. Formats identified using
Apache Tika.

As a first step in that direction, we examine how format usage changes over
time. Figure 3.3 shows the variation in usage of some of the most common image
formats. Unsurprisingly, JPEG has remained consistently popular. In contrast,
the PNG and ICO formats have become more popular over time, and the GIF, TIFF
and XBM formats have decreased in popularity, with the drop in usage of the
XBM format being particularly striking.

Figure 3.4: HTML versions over time. Formats identified using DROID-B. Figure
3.5: PDF versions over time. Formats identified using DROID-B and Apache Tika.

###  3.4 Versions & Software

Figures 3.4 and 3.5 show how the popularity of various versions of HTML and
PDF has changed over time. In general, each new version grows and dominates
the picture for a few years, before very slowly sinking into obscurity. Thus,
while there were just two active versions of HTML in 1996 (2.0 and 3.2), all
six were still active in 2010. Similarly, there were three active versions of
PDF in 1996 (1.0-1.2) and eleven different versions in 2010 (1.0-1.7, 1.7
Extension Level 3, A-1a and A-1b, with 1.2-1.6 dominant). In general, it
appears that format versions, like formats, are quick to arise but slow to
fade away.

Figure 3.6: PDF software identifiers over time. Formats and software
identified using Apache Tika.

Finally, figure 3.6 shows the popularity of different software implementations
over time and the dominance of the Adobe implementations (although later years
have seen an explosion in the number of distinct creator applications, with
over 2100 different implementations of around 600 distinct software packages).
Similarly, the JPEG data revealed over 1900 distinct software identifiers and
over 2100 distinct hardware identifiers. We speculate that the number of
distinct implementations can be taken as an indicator for the maturity,
stability and degree of standardisation of a particular format, although more
thorough analysis across more formats would be required to confirm this.

##  4 Conclusions

We have made a rich dataset available, profiling the format, version, software
and hardware data from large web archive spanning almost one and a half
decades. Our initial analysis supports Rosenthal’s position; that most formats
last much longer than five years, that network effects to appear to stabilise
formats, and that new formats appear at a modest, manageable rate. However, we
have also found a number of formats and versions that are fading from use, and
these should be studied closely in order to understand the process of
obsolescence. Furthermore, we must note that every corpus contains its own
biases, such as crawl size limits or scope parameters333Even the crawl time
itself can be quite misleading, as a newly discovered resource may have been
created or published some years before. Therefore, we recommend that similar
analyses be performed on a wider range of different corpora in order to
attempt to confirm these trends.

We used two different tools (DROID-B and Apache Tika) that perform the
essentially the same task (format identification), and ran them across the
same large and varied corpus. In effect, each can be considered a different
‘opinion’ on the format, and by uncovering the inconsistencies and resolving
them, we can improve the signatures and tools in a very concrete and
measurable way, and more rapidly approach something like a ‘ground truth’
corpus for format identification.

Future work will examine whether the underlying biases of the corpus can be
addressed, whether we can reliably identify resources within container
formats, and whether the raw resource-level data can be made available. This
last point would allow many more format properties to be exposed and make it
easier to resolve inconsistent results by linking back to the actual
resources.

##  5 Acknowledgments

This work was partially supported by JISC (under grant DIINN06) and by the
SCAPE Project. The SCAPE project is co-funded by the European Union under FP7
ICT-2009.4.1 (Grant Agreement number 270137).

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Present address: ]Applied Materials, Inc., Santa Clara, CA 95054, USA

# Measurement of DC and AC electric fields inside an atomic vapor cell with
wall-integrated electrodes

Lu Ma  [  Department of Physics, University of Michigan, Ann Arbor, Michigan,
48109, USA  Michael A. Viray  Department of Physics, University of Michigan,
Ann Arbor, Michigan, 48109, USA  David A. Anderson  Rydberg Technologies Inc,
Ann Arbor, Michigan, 48103, USA  Georg Raithel  Department of Physics,
University of Michigan, Ann Arbor, Michigan, 48109, USA  Present address:
Applied Materials, Inc., Santa Clara, CA 95054, USA

###### Abstract

We present and characterize an atomic vapor cell with silicon ring electrodes
directly embedded between borosilicate glass tubes. The cell is assembled with
an anodic bonding method and is filled with Rb vapor. The ring electrodes can
be externally connectorized for application of electric fields to the inside
of the cell. An atom-based, all-optical, laser-spectroscopic field sensing
method is employed to measure electric fields in the cell. Here, the Stark
effect of electric-field-sensitive rubidium Rydberg atoms is exploited to
measure DC electric fields in the cell of $\sim 5$ V/cm, with a relative
uncertainty of 10%. Measurement results are compared with DC field
calculations, allowing us to quantify electric-field attenuation due to free
surface charges inside the cell. We further measure the propagation of
microwave fields into the cell, using Autler-Townes splitting of Rydberg
levels as a field probe. Results are obtained for a range of microwave powers
and polarization angles relative to the cell’s ring electrodes. We compare the
results with microwave-field calculations. Applications are discussed.

††preprint: APS/123-QED

##  I Introduction

The introduction of DC and AC electric fields into vapor-cell-based quantum
devices currently is of considerable interest. For instance, DC Stark-tuning
of Rydberg transition frequencies broadens the frequency range of Rydberg-
atom-based microwave field detectors [1, 2, 3, 4, 5]. Auxiliary radio-
frequency (RF) fields for heterodyne RF field sensing in vapor-cell devices
enhance sensitivity [6] and allow RF phase sensing [7, 8, 9]. Further, a range
of quantum devices that require accurate control of in-vacuum electric fields
could, potentially, be implemented inside miniaturized glass cells. These
include Paul [10, 11], Penning [12, 13, 14] and cusp [15] traps for ions,
electrons and plasmas, and Faraday-shielded magneto-optical-traps (MOTs) [16,
17] for applications requiring controlled electromagnetic boundary conditions
or a well-defined black-body radiation environment [18, 19, 20].

DC and low-frequency electric-field control inside glass vacuum cells using
electrodes placed outside of the cells is challenging due to cell-internal
photo-electric charging effects [21]. While such effects can be controlled in
order to enable all-optical generation of cell-internal electric fields [22],
physical electrodes inside the cell provide improved electric-field control
with greater flexibility in field geometry. Here, we seek structures that are
directly integrated into the glass cell wall, simultaneously serving as
electrodes and as through-connects.

Figure 1: Images of glass vapor cell with wall-integrated electrodes for
application of DC and AC electric fields. (a) Picture of the actual cell. The
black rings are anodically-bonded conducting-Si rings. (b) Illustration of the
testing setup, showing the cell, the rubidium $5S_{1/2}\rightarrow 5P_{3/2}$
EIT probe laser (780 nm, red), the $5P_{3/2}\rightarrow\,Rydberg$ EIT coupler
laser (480 nm, blue), and the microwave-emitting horn. The lead wires to the
Si rings are only connected for DC field measurements. The setup allows
variation of the microwave polarization angle $\theta$. The displayed case is
for maximum microwave transmission into the cell.

To incorporate electrodes directly into the body of a glass vacuum cell, the
electrodes must be attached to the glass in a way that yields a seal between
the two materials with sufficiently low leak rates and outgassing levels for
use in high vacuum. This places limits on both the electrode material and the
possible bonding processes. We have found that the integration of highly
conductive doped-Si parts into borosilicate glass walls via an anodic-bonding
technique [23, 24, 25, 26] enables the fabrication of high- and ultra-high-
vacuum devices. The Si electrodes afford electric-field control inside the
cell directly through the cell wall. The electric fields can have complex
geometry, and the cells can be integrated onto electronic circuit boards. One
cell structure we have fabricated is shown in Fig. 1(a). The cell is mostly
made of borosilicate glass (pyrex) and features eight evenly-spaced ring
electrodes along the length of the body. Application of different voltage
combinations to the eight electrodes allows the realization of a variety of
electric-field geometries. The rings also serve a secondary, serendipitous use
as a partial polarizer for microwave radiation, thanks to the small 6 mm
spacing between them.

We utilize laser spectroscopy of an atomic vapor to analyze the electric
fields in the cell. Atom-based electric field sensing is currently an active
field of research, drawing interest from both researchers studying fundamental
science, and engineers working on integrated quantum metrology systems. This
technique uses atoms in Rydberg states (states with high principal quantum
number $n$) as electric ($E$)-field probes. Though electromagnetically-induced
transparency (EIT) [27, 28], the atoms yield narrow laser-spectroscopic lines
that mark the optical excitation energy of the Rydberg levels. Rydberg-level
Stark shifts can be observed via EIT line shifts. From measured line shifts
and splittings one can determine the strength of the $E$-field in the laser-
probe region. This technique, which takes advantage of the large
susceptibilities of Rydberg atoms to DC and AC electric fields [29, 30], has
previously been used to observe a variety of electric fields, including radio
HF and VHF fields [31, 32, 33], monochromatic [1, 2, 3, 4] or modulated [34]
microwave radiation, plasma electric fields [35, 36], and DC electric fields
[31, 37, 22].

We first study a DC electric-field configuration by applying a variable DC
voltage to one of the Si ring electrodes, with the others grounded. In the
second configuration, a microwave field is injected into the cell by radiating
microwaves of variable intensity and polarization from a microwave horn into
the cell. In each configuration, we analyze Rydberg-EIT signals to deduce the
electric field.

##  II Experimental Setup

###  II.1 Cell Fabrication

In the late 1960s, G. Wallis and D. I.Pomerantz (P. R. Mallory & Co. Inc.)
demonstrated a glass-metal sealing method with the assistance of a static
electric field [38], which became known as anodic bonding [39, 40, 41]. We
employ anodic bonding of borosilicate glass tubes and highly-doped Si rings to
create buffer-gas-free Rb vapor cells with wall-integrated electrodes. Glass
surfaces are prepared with a standard Chemical-Mechanical-Polishing (CMP)
process. The Si rings are fabricated from double-side polished Si wafers. The
bonding process is performed at a temperature of about 300∘C. The bonding
voltage applied to the Si rings ranges from 600 to 900 V, limited by sparking
at higher voltages.

In order to minimize the number of thermal cycles, our multi-surface anodic
bonding is performed in one step using a custom-designed, compact bonding jig
shown in Fig. 2. The circular bonding pieces, which all have equal diameters,
are assembled and aligned along a common axis on top of two supporting ceramic
tubes. To ensure contact across the 16 bonding surfaces, the pieces are
clamped between spring-loaded caps with setscrews for force adjustment. The Si
rings and glass parts are wrapped with thin wires, which are connected to
metal rails that pass through the centers of the slotted ceramic tubes. The
bonding voltages are applied via the rails. During the bonding, the jig is
heated on a hot plate and covered with an Al sheet-metal lid. After bonding,
the cell is filled with Rb vapor at high-vacuum pressure and sealed.

Figure 2: Bonding apparatus used for simultaneous anodic bonding of 9
borosilicate glass parts with 8 highly-conductive Si rings. Bonding voltages
are applied through thin wires connectorized with solid-wire buses.

###  II.2 Optical and Electric-Field Setup

Figure 1b shows the optical and microwave / DC electric-field setup. We use a
two-photon EIT ladder configuration in which the uppermost state is a Rydberg
level. The two counter-propagating EIT lasers are overlapped along the cell
axis, as illustrated in Fig. 1 (b). The first laser drives the
$5S_{1/2}\rightarrow 5P_{3/2}$ EIT probe transition and has a wavelength of
$\lambda_{p}=780$ nm (red), a power of 11 $\mu$W, and a diameter of
$w_{0}=464$ $\mu$m. The second laser (EIT coupler), runs at $\lambda_{c}=480$
nm (blue) and 46 mW, has a diameter of $w_{0}=268$ $\mu$m, and drives the
$5P_{3/2}\rightarrow 49D_{5/2}$ (AC field measurements) or the
$5P_{3/2}\rightarrow 32S_{1/2}$ (DC field measurements) Rydberg transitions.
The EIT signal is obtained by scanning the coupler laser across the Rydberg
resonances. The probe beam is sent into a photodiode connected to a
transimpedance amplifier. The EIT signal, displayed on and acquired with an
oscilloscope, exhibits Rydberg transitions whose quadratic DC and linear AC
Stark effects reveal the electric fields present in the cell.

The DC electric fields are applied by mounting the cell on a small piece of
circuit board and connectorizing the Si rings to external voltage-control
lines, as shown in some detail in Figs. 3(a) and (b).

In the microwave measurements, the vapor cell is mounted stem-down on a thin
anti-static acetal rod, which is held in place by a post holder. The Si rings
are floating, with no wires attached. The microwave radiation is emitted from
a 15-dBi standard gain microwave horn (Pasternack PE9852/2F-15) connected to a
synthesizer. We set the microwave frequency to 18.149805 GHz to resonantly
drive the $49D_{5/2}\rightarrow 50P_{3/2}$ Rydberg transition. The horn is
attached to a rotating mount to allow for a variation of the microwave
polarization angle $\theta$ (see Fig. 1 (b)) over a range of 360∘, with a
resolution of 1∘. The microwaves are incident on the side of the vapor cell,
which is in the horn’s far field, at a distance of 15 cm.

##  III Experimental Analysis

###  III.1 DC electric field

First, we test our device for DC electric field injection capability using the
cell setup shown in Fig. 3(a). The strength of the DC field inside the cell is
monitored through the DC Stark shift of the Rydberg EIT signal. In this test,
the 32S1/2 Rydberg state, which has a DC polarizability $\alpha$ of 2.214
MHz/(V/cm)2, is used. The shift in a DC field $E_{DC}$ is given by $-\alpha
E_{DC}^{2}/2$.

When the voltage $V$ applied to the center Si ring is increased (Fig. 3(b)), a
new EIT peak starts to emerge on the red side of the strongest EIT resonance
(Fig. 3(c)). This new peak arises from DC Rydberg level shifts in the region
around the center Si ring, where the applied voltage $V$ induces DC electric
fields. The maximum frequency separation between the shifted peak (“New peak”
in Fig. 3(c)) and the main peak is ($32.3\pm 5$) MHz, corresponding to a
measured DC electric-field maximum of $E_{DC}=(5.4\pm 0.5)$ V/cm. We note that
in Fig. 3(c) there are several copies of the same Rydberg spectrum near $0$
MHz, $-75$ MHz and $-115$ MHz that belong to the $F=4$, $F=3$ and $F=2$
hyperfine states of the intermediate $5P_{3/2}$ level, respectively. The
hyperfine splittings are reduced by a factor $\lambda_{p}/\lambda_{c}-1$ due
to EIT Doppler shifts in the cell.

In Fig. 4 we show calculated distributions of the DC electric field, $E_{DC}$,
along the cell axis and compare modeled with experimentally measured Stark-
shifted EIT spectra. In an initial model, we compute the electric-field
distribution in the cell without any surface charges on the class walls (Fig.
4 (a)). We then compute an average of Stark-shifted EIT spectra of the
$33S_{1/2}$-level, with the average taken over the computed distribution of
$E_{DC}$ along the cell axis. The initial model predicts a quadratic Stark
shift that is about a factor of ten larger than measured. A global attenuation
of $E_{DC}$ by a factor of $\approx 3$, as visualized in Fig. 4 (b), results
in a simulated spectrum (red line in Fig. 4 (c)) that closely resembles the
measured one (black line). In light of this finding, we then calculate the
$E_{DC}$-distribution for a physical model in which the voltage-carrying Si
ring is straddled by two grounded rings (orange sheaths in Fig. 4 (e)) on the
inner cell wall. The grounded rings simulate the field-reducing effect of
surface charges accumulated on the inner glass surfaces near the voltage-
carrying Si ring. The resultant simulated spectrum in Fig. 4 (f) (red line)
closely approaches the measured spectrum (black line), without any additional
field attenuation needed for agreement.

Future spatially-resolved Rydberg-EIT DC electric-field measurements may
reveal more detail as to how exactly the field reduction by a factor of
$\approx 3$ occurs. The electrode structure as well as the overall cell
symmetry suggest that $E_{DC}$ should have a leading quadrupole term, as is
also evident in the field simulations. The ability to create such fields,
using one or more of the wall-integrated electrodes, will be valuable for
confining charged particles in vapor-cell Penning or cusp traps, which would
require an additional longitudinal magnetic field, or Paul traps, which would
utilize voltage drives in the HF and VHF radio-frequency regimes.

Figure 3: (a) Picture of the cell setup used for spectroscopic DC electric-
field measurement in the cell. Individual voltages are applied to the highly-
conductive Si ring electrodes through the ribbon cable and thin wires glued

to the outer rims of the Si rings with conductive glue. (b) Wiring diagram
used for the data in (c). (c) Rydberg-EIT spectra of Rb $31S_{1/2}$ for the
indicated voltages $V$ vs detuning of the coupler laser from the $5P_{3/2}$,
$F=4$ $\rightarrow$ $31S_{1/2}$ transition. The “new peak”, most clearly
visible on the main line near $0$ MHz, is due to DC Stark shifts near the
voltage-carrying Si ring.

Figure 4: Calculated DC electric fields for an unshielded (a) and a shielded
(d) case for $V=10$ V. Simulated DC Stark spectra are plotted in red in (c)
and (f), respectively, measured spectra are plotted in black. The calculated
unshielded DC field from (a) must be scaled down by a factor of $\approx 3$,
as visualized in (b), to arrive at a reasonable match between simulated and
measured spectra in (c). In a simulation of a physical field-reducing
mechanism, we add two grounded metal sheaths (orange parts in (e)) on both
sides of the voltage-carrying Si ring. This leads to reasonable agreement
between simulated and measured spectra (f), without any further field
attenuation.

###  III.2 Injected microwave electric fields

####  III.2.1 Varied Microwave Power at Fixed Polarization Angle

Figure 5: EIT signals vs coupler laser detuning for the indicated microwave
powers. For these data, the microwave polarization angle is set for maximum
transmission ($\theta=0$).

In a first set of microwave measurements, the horn is kept at
$\theta=0^{\circ}$ (see Fig. 1 (b)), the microwave polarization angle of
maximum transmission. The Si rings are on floating DC potentials and are not
connected to any wires. We measure resonant Autler-Townes (AT) splittings of
the $49D_{5/2}\rightarrow 50P_{3/2}$ Rydberg transition at 18.149805 GHz, for
microwave powers injected into the horn of $P_{horn}=$-3.7, -6.2, -9.0, -11.9,
and -14.9 dBm, as measured by a power meter. Additionally, we record a control
measurement where the microwave is turned off. In Fig. 5 we show the EIT
spectra recorded at these values of $P_{horn}$. Since this measurement
qualitatively differs from earlier work due to the presence of the Si rings,
in the following we analyze the data in some detail.

In Fig. 6 we plot the AT splitting in MHz as a function of
$\sqrt{P_{horn}/1~{}{\rm{mW}}}$. The black data points are the measured EIT
line splittings, denoted $\Delta_{meas}$. The splittings are due to several
effects. The microwave electric field, $E_{MW}$, induces an AT splitting that
ideally is proportional to $E_{MW}$ and that represents the dominant
contribution to $\Delta_{meas}$ at the higher powers in Fig. 6. Further, Fig.
5 shows that there is a residual splitting of several MHz, denoted $b$, even
when the microwave is turned off. The residual splitting is indicative of DC
stray electric fields from the cell walls, and possibly a Zeeman splitting due
to stray magnetic fields. We empirically quantify the splitting effects by
applying a fit to the black data points of the form
$\Delta_{meas}=\sqrt{(ax)^{2}+b^{2}}$, where $x=\sqrt{P_{horn}/{\rm mW}}$. The
term $ax$ accounts for the microwave-induced ideal AT splitting of the Rydberg
line, which is dominant at higher microwave powers $P_{horn}$. The $b$-term
accounts for the stray-field-induced splitting, which is dominant at zero and
low values of $P_{horn}$.

The fit result is shown in Fig. 6 in solid red. The $a$ and $b$ values from
the fit are:

$\displaystyle a$ $\displaystyle=(31.9\pm 1.7)\textrm{
MHz}/\sqrt{P_{horn}/{\rm mW}}$ $\displaystyle b$ $\displaystyle=(3.54\pm
0.90)\textrm{ MHz}$ (1)

The dashed blue line in Fig. 6 shows the ideal microwave-induced AT splitting,
$ax$, that the Rydberg line would exhibit in a Doppler-free cold-atom
measurement [42] with no DC fields present. The magenta data points are
corrected line splittings, $\Delta_{corr}$, in which we subtract off the
splitting contribution due to the DC stray field according to:

$\Delta_{corr}=\sqrt{\Delta_{meas}^{2}-b^{2}}\approx ax$ (2)

The value of $\Delta_{corr}$ has an improved linear relationship with the
microwave field $E_{MW}$.

Figure 6: Autler-Townes splitting of the EIT signal in MHz vs
$x=\sqrt{P_{horn}/1~{}{\rm{mW}}}$. The black data points are measured peak
separations, $\Delta_{meas}$. The solid red curve is a fit for $\Delta_{meas}$
of the form $y=\sqrt{(ax)^{2}+b^{2}}$ with fit parameters $a$ and $b$ (see Eq.
III.2.1). The dashed blue line shows $y=ax$. The magenta data points are
corrected peak separations, $\Delta_{corr}$ (see Eq. 2).

The corrected splitting, $\Delta_{corr}$, approximately equals the Rabi
frequency, $\Omega_{0}$, of the resonantly driven microwave transition (in
Hz). The following equation applies,

$E_{MW}d/h=\Omega_{0}=ax\approx\Delta_{corr}\quad.$ (3)

Here, $d$ is the transition dipole moment, and $h$ is Planck’s constant. Our
applied microwave field drives the $49D_{5/2}\rightarrow 50P_{3/2}$ Rydberg
transition, which has a known transition dipole moment of $d=1.16\times
10^{-26}$ Cm. Equation 3 and the corrected splittings $\Delta_{corr}$ then
allow us to calculate the electric field $E_{MW}$.

$\sqrt{P_{Horn}/1\textrm{mW}}$ |  $\Delta_{meas}$ [MHz] |  $E_{MW}$ [V/m] |  $x/E_{MW}$ [m/V]
---|---|---|---
0.18 $\pm$ 0.01 | 6.3 $\pm$ 1.5 | 0.36 $\pm$ 0.09 | 0.50 $\pm$ 0.12
0.25 $\pm$ 0.01 | 7.7 $\pm$ 1.5 | 0.44 $\pm$ 0.09 | 0.58 $\pm$ 0.12
0.36 $\pm$ 0.01 | 10 $\pm$ 1.5 | 0.58 $\pm$ 0.09 | 0.62 $\pm$ 0.09
0.49 $\pm$ 0.02 | 16 $\pm$ 1.5 | 0.93 $\pm$ 0.09 | 0.53 $\pm$ 0.05
0.65 $\pm$ 0.02 | 23 $\pm$ 1.5 | 1.3 $\pm$ 0.09 | 0.50 $\pm$ 0.04
Table 1: The columns show $x=\sqrt{P_{Horn}/1\textrm{mW}}$, the measured
splittings $\Delta_{meas}$, the electric fields $E_{MW}$ calculated from Eqs.
2 and 3, and the ratio $x/E_{MW}$, which should ideally be constant.

A summary of results is shown in Table I. Overall, the data series shows that
$E_{MW}$ can be measured in our cell with wall-integrated Si electrodes using
established methods for atom-based microwave electric-field sensing [1, 2, 3,
4, 42]. The field injected into the cell is only about $60\%$ of the field
that would be present without the cell (see details in Sec. IV). In view of
anticipated electron-, ion- and plasma-trapping applications of this cell, it
mostly is important to conclude that microwave field injection into the cell
for plasma diagnostics and charged-particle-drive will be efficient. A
detailed evaluation of the cell for the purpose of microwave field metrology
is not part of the present work.

####  III.2.2 Varied Polarization Angle at Fixed Microwave Power

Figure 7: EIT signals vs coupler-laser detuning for the indicated values
$\theta$ of the incident microwave polarization. The power is fixed at
$P_{horn}=-3.7$ dBm, the highest value in Fig. 5.

In our second set of microwave measurements we use a fixed power
$P_{horn}=-3.7$ dBm and the horn is rotated. We take measurements of the AT
splitting from $\theta=0^{\circ}$ (maximum transmission) to
$\theta=90^{\circ}$ (minimum transmission), going in increments of about 10∘.
In Fig. 7 we show the AT splitting of the EIT signal at selected angles, and
in Fig. 8 the measured (black) and corrected (red) splittings in MHz for all
angles. We see that, as expected, the splitting decreases as the polarization
of the microwave-field direction becomes aligned parallel with the conducting
rings.

It is instructive to compare the observed polarization dependence with that of
an ideal microwave polarizer (such as one formed by a large, planar grid of
parallel wires with a wire separation much less than the microwave
wavelength). The transmission behavior of the ideal microwave polarizer
follows Malus’s law [43], i. e. the transmitted electric field, $E_{MW}$,
would be

$E_{MW}=E_{0}\cos(\theta)\quad.$ (4)

There, $E_{0}$ is the field without polarizer, and the angle $\theta$ is
defined such that maximum transmission occurs at $\theta=0^{\circ}$. For
comparison, we have added a blue, dashed curve in Fig. 8 that represents the
behavior of an ideal microwave polarizer.

Figure 8: Splittings $\Delta_{meas}$ (black) and $\Delta_{corr}$ (pink) vs
polarization angle of the incident microwave radiation, with the relation
between $\Delta_{meas}$ and $\Delta_{corr}$ established in Eq. 2. For
reference, the dashed blue curve represents Malus’s law, as it would apply for
an ideal microwave polarizer.

Comparing the measured and corrected separations, $\Delta_{meas}$ and
$\Delta_{corr}$, with the Malus’s-law curve, we see that the separations not
only decrease faster with $\theta$ for $\theta\lesssim 30^{\circ}$, but they
also level out at about 25$\%$ of the $\theta=0$-splitting when $\theta$
approaches 90∘. Evidently, the cell electrodes do not act as a perfect
microwave polarizer, as explained more in the following paragraph. In view of
applications that require external microwave injection, the results show that
microwave fields polarized transversely relative to the cell axis still
transmit at about 25$\%$. This is relevant, for instance, if one intended to
drive the electron cyclotron motion in a vapor-cell Penning trap formed with
the cell. This trap would have a strong magnetic field along the cell axis,
and the cyclotron motion would be transverse, requiring a transversely
polarized ($\theta=90^{\circ}$) microwave field to drive it.

There are several reasons for why the cell is not an ideal microwave
polarizer. Mostly, the cell structure - finite conductive-Si rings embedded in
a dielectric with large dielectric constant - exhibits a microwave response
that differs substantially from that of a grid of parallel wires in vacuum.
This is shown in the microwave field simulations below. The simulations also
bear out that the field polarization inside the cell may have some
ellipticity. A minor effect that may contribute to the measurement result is
that, while the microwave horn is perfectly polarized at our level of
precision, reflections of microwaves from parts of the setup may be polarized
differently from the incident wave and may enter into the cell. We can discard
another potential cause for non-ideal polarizer behavior, namely that the skin
depth in the Si could, in principle, be too large. For the wafer grade we use
(resistivity 0.001 to 0.005 $\Omega$cm), we estimate a skin depth $\lesssim
10~{}\mu$m at 18 GHz, which is 1/50 of the wafer thickness. Hence, the Si
rings behave as near-ideal conductors, as confirmed in our microwave
simulations.

##  IV Microwave Simulations

To gain more insight into the microwave experiment discussed in Sec. III.2, we
simulate the horn plus cell system using Ansys HFSS software for the geometric
parameters used in the experiment. The model further uses accurate dielectric
constants and resistivities. Here we show results for $\theta=0^{\circ}$ and
$90^{\circ}$. We also run simulations without the cell present to calibrate
the in-cell microwave fields relative to the cell-free case.

Figs. 9(a) and (b) show the geometries for $\theta=0^{\circ}$ and
$90^{\circ}$. The coloring inside the cell indicates the microwave electric-
field magnitude at the temporal phase when the field is greatest, on a color
scale ranging from green (weak) to red (strong field). Fig. 9(c) and (d) show
the field magnitude along the cell axis at the temporal phases of maximal
(red) and minimal (black) fields. The green curve shows the maximal field
without cell present. (The field minimum without cell present is practically
zero, because the incident field is linearly polarized).

Since the experimental data represent an average of the microwave field along
the length of the cell, we look at the behavior of the simulated-field
averages. Fig. 9(a) and (c) ($\theta=0$, corresponding to largest transmission
overall), show that the electric-field transmission, averaged along the cell’s
axis, is about $60\%$ of what it would be if no cell were present. Fig. 9(b)
and (d) ($\theta=90^{\circ}$, corresponding to lowest transmission overall),
indicate a transmission of about $25\%$. The simulated average-field ratio
been the two cases therefore is about 2.5:1, whereas in the experiment it is
about 3:1. We therefore see good qualitative agreement between the simulated
and measured field ratios. Deviations are mostly attributed to fabrication
uncertainties in the cell geometry.

While the experiment in its present form only yields a field average, the
simulation has sub-mm spatial resolution. The electric field distributions in
Figs. 9(a) and (c) show that for $\theta=0^{\circ}$ (high transmission) the
field tends to be larger in the spaces between the rings and weaker in the
planes of the rings. For $\theta=90^{\circ}$ (low transmission; Figs. 9(b) and
(d)), the opposite trend is observed. Another noteworthy detail is that the
field minima (black curves) are substantial ($5\%$ to $10\%$ of the cell-free
field, in both cases of $\theta$). This is indicative of a slightly elliptical
character of the field’s polarization inside the cell. The ellipticity is
attributed to the fact that the cell components are neither infinitely long
parallel wires, nor is the space between the rings filled by vacuum (as it
would be for a parallel-wire microwave field polarizer). It is therefore
plausible to assume that the structural parts scatter the field into
directions orthogonal to the incident field, with material-related phase
shifts. This can lead to elliptically polarized net fields on the cell axis,
as suggested by the black and red curves in Figs. 9(c) and (d).

Figure 9: Results of an Ansys HFSS simulation of the microwave experiment
described in Subsec. III.2. a) and b) show horn and cell geometries, as well
as the calculated electric-field distributions on planes containing the cell
axis (colors explained in text). c) and d) show the field-strength magnitudes
on the cell axis at temporal phases of maximal (red) and minimal (black) field
strength, and for the case that the cell is absent (green).

##  V Conclusion

Using an anodic-bonding method, we have fabricated a vapor cell that
incorporates conductive Si electrodes directly into the body of a high-vacuum
Rb vapor cell. DC electric fields applied via the electrodes and microwave
electric fields radiated into the cell from a horn antenna were measured using
atomic field sensing methods. Measurement results were compared with
simulations, and reasonable agreement was found. From the perspective of cell
characterization, the main remaining issue is how exactly does the observed
reduction of the DC electric field by about a factor of 3 occur. Future
position-resolved spectroscopic field measurements may be helpful to address
this issue.

Cells with wall-integrated electrodes present opportunities in science and
technology. For instance, the DC quadrupole electric field investigated in the
present work, as well as variations of it that employ all electrodes instead
of only one electrode, combined with a longitudinal magnetic field, will
enable studies of vapor-cell-based electron, ion and plasma Penning, cusp and
Paul traps. Rydberg-EIT can be used to measure the electric fields in and
around such charged-particle traps. HF and VHF radio-frequency signals
directly applied via the wall-integrated electrodes may enable novel designs
for Paul traps and mass spectrometers, and may become useful in advanced RF
field sensing applications.

###### Acknowledgements.

This work was supported by NSF Grant Nos. PHY-1707377 and PHY-1806809 and
Rydberg Technologies Inc. The cell was made in the Lurie Nanofabrication
Facility at the University of Michigan. We thank Dr. Pilar Herrera-Fierro and
her team for their technical support while developing the cell.

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