11institutetext: Machine Learning Group, EISLAB, Luleå Tekniska Universitet,
Luleå, Sweden 11email<EMAIL_ADDRESS>22institutetext: Optimation
Advanced Measurements AB, Luleå, Sweden 22email<EMAIL_ADDRESS>33institutetext: Human Interface Laboratory, Kyushu University, Fukuoka, Japan
33email<EMAIL_ADDRESS>
*Corresponding author -<EMAIL_ADDRESS>
# Depth Contrast: Self-Supervised Pretraining on 3DPM Images for Mining
Material Classification

Prakash Chandra Chhipa 11** Richa Upadhyay 11 Rajkumar Saini 11 Lars Lindqvist
22 Richard Nordenskjold 22 Seiichi Uchida 33 Marcus Liwicki 11

###### Abstract

This work presents a novel self-supervised representation learning method to
learn efficient representations without labels on images from a 3DPM sensor
(3-Dimensional Particle Measurement; estimates the particle size distribution
of material) utilizing RGB images and depth maps of mining material on the
conveyor belt. Human annotations for material categories on sensor-generated
data are scarce and cost-intensive. Currently, representation learning without
human annotations remains unexplored for mining materials and does not
leverage on utilization of sensor-generated data. The proposed method, Depth
Contrast, enables self-supervised learning of representations without labels
on the 3DPM dataset by exploiting depth maps and inductive transfer. The
proposed method outperforms material classification over ImageNet transfer
learning performance in fully supervised learning settings and achieves an F1
score of 0.73. Further, The proposed method yields an F1 score of 0.65 with an
11% improvement over ImageNet transfer learning performance in a semi-
supervised setting when only 20% of labels are used in fine-tuning. Finally,
the Proposed method showcases improved performance generalization on linear
evaluation. The implementation of proposed method is available on
GitHub111https://github.com/prakashchhipa/Depth-Contrast-Self-Supervised-
Method.

###### Keywords:

computer vision, material classification, self-supervised learning,
contrastive learning

##  1 Introduction

Figure 1: The proposed approach comprises three steps: (1) Visual data
collection of material on the conveyor belt through 3DPM sensor. It captures a
depth map (height of material) and corresponding pixel-mapped reflectance
data, the amount of light reflected from the imaged material registered by the
camera sensor. (2) Self-supervised pre-training on unlabeled pair of the depth
map and reflectance visual data using proposed method Depth Contrast
exploiting depth of material as supervision signal from data, thus enabling
self-supervised representation learning beyond RGB images. (3) Performing the
downstream task of material classification using the pretrained encoder where
input is formulated by combining depth map and reflectance visual data. This
work describes pixel-mapped reflectance data as reflectance image and depth
maps as raw image in further sections.

Identifying and classifying materials on the conveyor belt is a fundamental
process in the mining industry. It is essential to properly sort the materials
before forwarding it for stockpiling or further processing. There is a need
for real-time monitoring of the materials on the conveyor belt at mine sites
for determining the destination for the material accurately and instantly. The
traditional methods employed to identify materials or rock minerals are based
on the physical and chemical properties of the material. Also, based on human
vision (basically human experience). In the recent past, advancement in the
field of Artificial Intelligence (AI) and Machine Learning (ML) has made it
possible to successfully classify materials using data driven methods, more
precisely intelligent computer vision methods [7], [14], [9]. This work aims
to classify the materials using images from the 3DPM sensor [17] and transfer
learning [23], chapter 15 of [10], and employing Deep Learning (DL)
architectures. The deep Convolutional Neural Networks (CNNs) like Efficient-
net [19], DenseNet [13], ResNeXt [22] etc, are pretrained on large datasets
such as ImageNet [8] and used to extract meaningful representations from new
data. These high level representations are further used for classification.

This work proposes a self-supervised representation learning (SSL) method
Depth Contrast, to learn rich representations without human annotations to
showcase the capabilities to significantly reduce the need for human
supervision for downstream tasks, e.g., material classification. The Depth
Contrast self-supervised representation learning method employs the
temperature scaled cross-entropy loss for contrastive learning based on the
SimCLR method [4]. The proposed pretraining method Depth Contrast exploits
supervision signal from data, e.g., depth information of material, thus
enabling to learn self-supervised representations on pixel-mapped reflectance
data and depth maps from 3DPM sensor, which is beyond the typical RGB visual.
Learned representations through SSL pretraining enable downstream tasks, e.g.,
material classifications with fewer human-annotated labeled examples, by
leveraging domain-specific unlabeled data. Results of detailed experiments on
downstream task material classification show that 1) It achieves benchmarked
performance in mining material classification employing deep CNNs with
supervised ImageNet [8] transfer learning on the combined representation of
reflectance and raw images 2) Proposed Depth Contrast method further improves
the performance of material classification in a fully supervised setting and
showcases the capabilities to reduced the needs of human annotation in a semi-
supervised setting. The result section describes the detailed, quantified
outcomes.

###  1.1 Measurement system

3-Dimensional Particle Measurement (3DPM®) [17] is a system that estimates the
particle size distribution of material passing on a conveyor belt. 3DPM can
also determine particle shape, bulk volume flow and identify abnormalities
such as the presence of boulders or rock bolts. Some benefits of online
particle size distribution monitoring of bulk material on the conveyor are new
control and optimization opportunities for grinding, crushing, and
agglomerating. The system can be configured to individually estimate particle
size distribution for a large variety of materials such as limestone, coke,
agglomerated materials, metal ores, etc. In applications where different
materials are transported on the same conveyor belt, the current material must
be determined accurately for automated system configuration. First part of the
Fig. 1 shows the schematic demonstration of the 3DPM system based on laser
line triangulation, which produces 3D data with known real-world coordinates.
The data used in this study comprises a depth map and corresponding pixel-
mapped reflectance data. Reflectance data is the amount of light reflected
from the imaged material registered by the camera sensor. The 3DPM data can be
visualized as images but are different from RGB/gray images; however, they can
be treated in similar ways. Table 1 shows the reflectance (left) and depth-map
(right) images of cylindrical shaped material in first row, respectively.

###  1.2 Related work

Many studies focused on similar material type or rock type identification
using computer vision and machine learning techniques. In the past 5-6 years,
the DL algorithms were used for material or rock classification using images,
which yielded some remarkable results without the use of image pre-processing
and feature extraction. The article [7] exploits deep CNNs for identification
of rock images from Ordos basin and achieves an accuracy of 98.5%. In [14], a
comparison of Support Vector Machine (SVM), a histogram of oriented gradient
based random forest model, and comprehensive DL model (i.e., Inception-V3 +
Color model), for mineral recognition in rocks indicates that the DL model has
the best performance. A faster R-CNN model along with VGG16 for feature
extraction is used in [15] for identifying nine different rock types and also
hybrid images of multiple rocks. The designed model gave an excellent accuracy
of 96% for independent rock types and around 80% for hybrid rock type images.
Similar work in [9] employs transfer learning methods using two light-weighted
CNNs SqueezeNet and MobileNets for classifying 28 types of rocks from images.
These networks provide quick and accurate results on the test data; for
example, SqueezeNet’s accuracy is 94.55% with an average recognition time of
557 milliseconds for a single image. Since all these studies were carried out
for different datasets and a different number of classes, it is not possible
to compare them. Also, a few of the above studies focus on images of ores,
some on rocks, mineral rocks, and many other related variants.

Most of the previous works for ore type or material classification have used
2-dimensional imaging systems that work with RGB images or grayscale images.
The works which employ ML or DL are majorly carried out in supervised settings
and do not exhibit much progress in utilizing the unlabeled data in either
unsupervised or self-supervised settings. Self-supervised learning in computer
vision attempts to learn representations from visuals without the need for
annotations. There has been several approaches for self-supervised
representation learning as (i) contrastive joint embedding methods (PIRL [16]
SimCLR [4], SimCLRv2 [5], and MoCo [12]), (ii) quantization (SwAV [3] and
DeepCluster [2]), (iii) knowledge distillation (BYOL [11] and SimSiam [6]),
and (iv) redundancy reduction (BT [24] and VICReg [1]). This work specifically
focuses on self-supervised methods based on contrastive learning (CL). The
state-of-the-art contrastive learning methods SimCLR [4], [5] and MoCo [12]
learn by minimizing the distance between representations of different
augmented views of the same visual example (‘positive pairs’) and maximizing
the distance between the representations of augmented views from different
visual examples(‘negative pairs’). However, applying self-supervised learning
to leverage on utilization of unlabeled data is not explored beyond the
natural images. Therefore, the current work proposes contrastive learning
based novel self-supervised pretraining method Depth Contrast for learning
representations on visual data (raw and reflectance images) from 3DPM sensor
and further improving the performance of downstream task, online material type
classification model from the 3DPM images while material passes on the
conveyor belt. Many DL based models are investigated, and transfer learning is
used to improve the task performance.

The rest of the paper is organized as follows. Section 2 discusses the dataset
used in this study. Methodology and experiments are discussed in Section 3.
Section 4 presents the results of the proposed work. Finally, we conclude in
Section 5.

##  2 3DPM Dataset

For material classification, there are two modalities of data that are
acquired using the 3DPM sensor. First are the reflectance images, which are 2D
grayscale images of the material on the conveyor belt taken in red laser light
(680 nm). Lighting conditions, color, and distance between the sensor and the
conveyor belt i.e., base depth may affect the 2D imaging system [20]. The
second modality is the 3D depth map of the bulk material, i.e., the distance
between the material and the sensor. As the material is passed on the conveyor
belt, data of multiple laser lines are collected at regular intervals, thereby
creating a 3D depth image. 2D imaging systems have scale or perception bias,
which is resolved in this 3D data as it is unaffected by the change in light
and color of the material [21]. The 3DPM dataset is prepared for this work by
collecting the data from sensors under similar lighting conditions. Further,
the challenge of variable base depth, which is an issue for the depth map, is
solved by subtracting the conveyor depth from all the data. Therefore, every
reflectance image has a corresponding raw image (i.e., depth maps). Table 1
shows the sample 3DPM images of all the categories of material in the 3DPM
dataset. In order to feed these images to the CNNs three arrangements were
made, only raw images, only reflectance images, and respective reflectance and
raw images are merged, forming a three-channel image. The experiments proved
that combining the reflectance and raw images led to higher performance, refer
to Table 3.

The 3DPM dataset has seven classes corresponding to the categories of mining
material available on the conveyor belt. These classes are Cylindrical, Ore1,
Ore2, Ore3, Mixed1, Mixed2, and Agglomerated (Aggl.). Some of the material
categories belong to a specific type of material e.g., Cylindrical, Ore1,
Ore2, Ore3, and Agglomerated, whereas the remaining categories, such as Mixed1
and Mixed2, represent the mixture of several materials present on the conveyor
belt. Identification of Mixed categories remains challenging with manual
visual inspections. The class distribution is shown in Table. 2.

Table 1: Classwise raw and reflectance image pairs

Material | Reflectance Image | Raw Image | Material | Reflectance Image | Raw Image
---|---|---|---|---|---
Cylindrical |  |  |  Mixed1 |  |
Ore1 |  |  |  Aggl. |  |
Ore2 |  |  |  Mixed2 |  |
Ore3 |  |  |  |  |

Table 2: Types of materials and their distribution Material name | Total images
---|---
Mixed 1 | 164
Mixed 2 | 122
Ore 1 | 860
Ore 2 | 698
Ore 3 | 503
Agglomerated (Aggl.) | 616
Cylindrical | 45

##  3 Methodology and Experiments

This work aims to investigate the classification of materials using supervised
and self-supervised learning methods. For faster and more efficient training
with the limited (insufficient) data which is available at hand, transfer
learning [9] is employed to derive essential features to achieve better
classification performance. This section discusses transfer learning and the
supervised and self-supervised techniques used in this work.

###  3.1 Transfer Learning

Transfer learning [18] is a method in ML that exploits the existing knowledge
of a network to learn a distinct but relevant task efficiently. In transfer
learning, the network is first well-trained on a very large dataset to solve a
specific problem (maybe classification, regression, etc.). This mechanism is
referred to as the source task. For another task i.e., target task, which has
lesser data than the source task, the knowledge acquired by the source task is
shared in network parameters (or weights) to accomplish the target task. The
transfer of information can be carried out in two ways; the first is when the
learned network parameters of the source task, act as a good starting point
for the target task, and the complete network can further be fine-tuned while
training on the target data, refereed as ‘fine-tuning’ in this article. The
second is when the source network is used as it is to extract features for the
target task, referred to as ‘linear evaluation’. In this work, transfer
learning is applied in both supervised and self-supervised settings. Already
trained networks on ImageNet [8], which is a substantial multi-label image
database, are utilized here for material type classification. These are
further discussed in section 3.2 and section 3.3.

###  3.2 Supervised Downstream Task

Supervised learning [10] is a type of ML technique that uses human-annotated
labels to predict the outcome of the learning problem. As the 3DPM dataset has
labels along with the reflectance and raw images containing depth maps of the
materials, thus applying supervised learning methods for downstream tasks of
classification is reasonable to be applied in both supervised transfer
learning section 3.1 as well as self-supervised Depth Contrast learning
section 3.3. This work considers three pretrained networks i.e., Efficient-net
b2[19], DenseNet-121[13] and ResNeXt-50 (32$\times$4d)[22] for ImageNet[8]
transfer learning method and EfficientNet-b2[19] for self-supervised method
for representation learning using Depth Constrast method. Since the downstream
task of material classification on the 3DPM dataset has seven classes
corresponding to 7 categories of materials thus, the above-mentioned CNN
networks are extended with a fully connected (FC) layer module having two FC
layers, one hidden layer of 512, and one output layer of 7 units.

###  3.3 Depth Contrast - Self-supervised learning

With a moderate amount of data availability in terms of reflectance and depth
images as pair, we propose a method, “depth contrast”, based on normalized
temperature-scaled cross-entropy loss from SimCLR [4]. It models the two
transformed views of input images from a pair of reflectance and depth images,
respectively, and intends to maximize the agreement between the stated views
of the same data example through contrastive loss. Derived from SimCLR [4],
following are the components for Depth Contrast, mentioned in Figure 2.

  * •

A domain specific prior and stochastic transformation based module that
transforms the synchronously yet independently generated pair of reflectance
and depth views of the same example through uniform transformation of random
cropping operation, denoted as $\tilde{x}_{ref}$ and $\tilde{x}_{dep}$ which
are considers as positive pair. Both, reflectance and depth views are 32 bit
images and depth view specifically captures the 3D depth of the material.

  * •

A neural network base encoder f(·) which yields representations from
transformed reflectance and depth views of data examples. Specifically, this
work uses Efficient-net b2 [19] as base encoder based on empirical analysis of
CNNs in transfer learning based supervised learning method and further obtains
obtain $h_{ref}$ = f($\tilde{x}_{ref}$) = Efficient-net($\tilde{x}_{ref}$) and
$h_{dep}$ = f($\tilde{x}_{dep}$) = Efficient-net($\tilde{x}_{dep}$) where
$h_{ref}$, $h_{dep}$ $\in$ & $\mathbb{R}^{d}$ are the output after the average
pooling layer respectively.

  * •

A small-scale multi-layer perceptron (MLP) network projection head g(·) that
maps representations to the latent space where contrastive loss is applied. A
MLP having three hidden layers of 2048, 2048, and 512 neurons and output layer
with 128 neurons to obtain $z_{ref}$ = g($h_{ref}$) =
$W^{(2)}$$\sigma$$(W^{(1)}{h_{ref})}$ and $z_{dep}$ = g($h_{dep}$) =
$W^{(2)}$$\sigma$$(W^{(1)}{h_{dep})}$ where $\sigma$ is a ReLU non-linearity.

  * •

A contrastive loss function, normalized temperature-scaled cross entropy loss
(NT-Xent) from SimCLR [4] is defined for a contrastive prediction task. For
given a set $\tilde{x}_{k}$ including a positive pair of examples
$\tilde{x}_{ref}$ and $\tilde{x}_{dep}$ , the contrastive prediction task
intend to identify $\tilde{x}_{dep}$ in {${\textbf{$\tilde{x}_{k}$}}\\}_{k\neq
ref}$ for a given $\tilde{x}_{ref}$.

Figure 2: Depth Contrast method. An uniform data augmentation operator is
sampled from one random-crop transform (t $\sim$ T), applied to each pair of
both views, reflectance and depth image from 3DPM sensor, considering
correlated views. A base encoder network f(·) which is Efficient-net b2 and a
projection head which is perceptron network g(·) are trained to maximize
agreement using a normalized temperature-scaled cross entropy loss from SimCLR
[4]. Upon completion of pre-training, encoder network f(·) and representation
h used for downstream classification task

The loss function for a positive pair of examples (ref, dep) is defined as

$L_{ref,dep}=-log\dfrac{exp(sim(\boldsymbol{z}_{ref},\boldsymbol{z}_{dep})/\tau)}{\sum_{k=1}^{2N}1_{[k\neq
ref]}exp(sim(\boldsymbol{z}_{ref},\boldsymbol{z}_{k})/\tau)}$ (1)

In equation 1, where $1_{[k\neq ref]}\in{0,1}$ is an indicator evaluating to 1
if $k\neq i$. Equations 2 and 3 define dot product between $l_{2}$ normalized
respective quantities, and $\tau$ defines the temperature parameter. During
pre-training, a randomly sampled minibatch of N examples is randomly sampled.
The contrastive prediction task is defined on pairs of reflectance and depth
views derived from the minibatch, resulting in 2N data points. A sampling of
negative examples is not performed explicitly. Instead, given a positive pair,
the other 2(N $-$ 1) augmented examples within a minibatch are considered
negative examples. The loss value is computed across all positive pairs of
reflectance and depth views, both
$(\boldsymbol{z}_{ref},\boldsymbol{z}_{dep})$ and
$(\boldsymbol{z}_{dep},\boldsymbol{z}_{ref})$, in each mini-batch.

###  3.4 Experiments

The experiments are designed for in-depth analysis of both types of input
images, CNNs architectures, and comparative analysis of proposed self-
supervised representation learning method Depth Contrast with ImageNet[8]
pretrained models on a different level of labeled data availability. Broadly,
training of material classification tasks is defined in two arrangements,
fine-tuning and linear evaluation, respectively.

Table 3: Performance comparison between ImageNet pretrained and Depth Contrast pretrained models fine-tuned on 3DPM dataset in semi and fully supervised setting  Exp. No. | Input | Model | Dataset split (in %) | Performance (in F1 score)
---|---|---|---|---
|  |  | Train | Val. | Test | Train | Test
| ImageNet pre-trained
1 | Raw images | EfficientNet | 60 | 20 | 20 | 0.31 ± 0.0142 | 0.30 ± 0.0061
2 | Reflectance images | EfficientNet | 60 | 20 | 20 | 0.68 ± 0.0081 | 0.69 ± 0.0235
|  | 3.1 EfficientNet | 60 | 20 | 20 | 0.73 ± 0.0077 | 0.72 ± 0.0294
3 | Raw + Reflectance | 3.2 ResNeXt | 60 | 20 | 20 | 0.75 ± 0.0321 | 0.67 ± 0.0841
|  | 3.3 DenseNet | 60 | 20 | 20 | 0.74 ± 0.0297 | 0.72 ± 0.0411
4 | Raw + Reflectance | EfficientNet | 10 | 10 | 20 | 0.65 ± 0.0616 | 0.54 ± 0.0231
| Depth Contrast pre-trained (60% unlabelled data)
5 | Raw + Reflectance | EfficientNet | 60 | 20 | 20 | 0.73 ± 0.0152 | 0.73 ± 0.0135
6 | Raw + Reflectance | EfficientNet | 10 | 10 | 20 | 0.71 ± 0.0399 | 0.65 ± 0.0263

In fine-tuning training task, all the layers of Convolutional Neural Network
(CNN) architecture and fully connected layers are trained on 3DPM dataset
(refer to Table 3 whereas in the linear evaluation training task mentioned in
Table 4, only fully connected layers are trainable and CNN architecture serve
as a feature extractor.

Table 4: Performance comparison between ImageNet pretrained and Depth Contrast pretrained models linear evaluation on 3DPM dataset in semi and fully supervised setting Exp. No. | Input | Model | Dataset split (in %) | Performance (in F1 score)
---|---|---|---|---
|  |  | Train | Val. | Test | Train | Test
| ImageNet pre-trained
7 | Raw + Reflectance | EfficientNet | 60 | 20 | 20 | 0.74 ± 0.0825 | 0.69 ± 0.0431
8 | Raw + Reflectance | EfficientNet | 10 | 10 | 20 | 0.67 ± 0.0364 | 0.52 ± 0.0380
| Depth Contrast pre-trained (60% unlabelled data)
9 | Raw + Reflectance | EfficientNet | 60 | 20 | 20 | 0.74 ± 0.0273 | 0.72 ± 0.0854
10 | Raw + Reflectance | EfficientNet | 10 | 10 | 20 | 0.71 ± 0.0624 | 0.64 ± 0.0147

Comparative study of these two types of tasks allows for analyzing
representation learning capabilities of the proposed method Depth Contrast in
a more detailed manner. This work uses a 5-cross stratified validation
technique in which each fold comprises 20% data ensuring class distributions
to ensure robustness in performance. In general 60% data, equal to three folds
used as the train set, 20%, one fold for the validation set, and the remaining
20%, one fold for the test set. This procedure is repeated five times to test
each fold at once, and variations in results are reported in terms of standard
deviation alongside the mean F1 score.

Fine-tuning experiments mentioned in Table 3, Experiment 1, 2, and 3.1 are
focused on investigating the effectiveness of input image type for material
classification and chooses Efficient-net b2 as base architecture based on
preliminary analysis on several CNN architectures. Further, experiments 3.2
and 3.3 focus on exploring different CNN architectures in which input types
remain a combination of raw and reflectance images, based on performance
analysis of previous experiments. Based on preliminary empirical analysis, the
combination of raw and reflectance images is composed of three-channel images
and raw-reflectance-raw channels. Specifically, experiment 3.2 uses DenseNet
121 [13] and experiment 3.3 uses ResNeXt (31 $\times$ 4d) [22] architecture.

The purpose of experiment 4 in Table 3 is to benchmark the material
classification performance in a limited labeled data setting while using the
Efficient-net network over a combination of raw and reflectance images based
on the performance of previous experiments. This experiment uses a single fold
where 10% data for training and the remaining 10% data for validation.
However, the test set remains the same for all folds. It is worth noticing
that experiments 1 to 4 uses ImageNet[8] pretrained models.

Finally, Experiments 5 and 6 in Table 3 are focused on evaluating the effect
of the proposed self-supervised representation learning method, Depth
Contrast, in semi and fully supervised settings, respectively. Before these
experiments, the Efficient-net b2 model is pretrained using the Depth Contrast
method over training data without using labels. This pretraining allows the
model to learn domain-specific representations in a self-supervised manner.
Experiment 5 uses training data the same as previous experiments 1 to 3.
Another side, experiment 6 evaluates the performance in a limited labeled data
set to compare the effectiveness of Depth Contrast pretraining with experiment
4, while both the experiments use weights initialization from the Depth
Contrast method

Experiments dedicated to linear evaluation training tasks are mentioned in
Table 4. Experiment 7 and 8 investigates the performance on ImageNet [8]
pretrained model corresponds to fine-tuning experiments 3.1 and 4. Similarly,
experiments 9 and 10 correspond to fine-tuning experiments 5 and 6 to
investigate the performance of the Depth Contrast pretrained model. In a
nutshell, a comparative analysis of the aforementioned experiments can analyze
the effectiveness of different transfer learning mechanisms and the leverage
of unlabelled sensor-generated data to improve performance in typical
industrial settings.

All the fine-tuning experiments mentioned in Table 3 and linear evaluation
experiments in Table 4 for material classification follow the learning rate of
0.00001, Adam optimizer, batch size of 16, input image size of $224\times
224$, and dropout regularization of $0.3$ for the hidden layer of FC layer
module. Images are 32 bit, so current work only uses random crop as an
augmentation technique. Further, Depth Contrast pretraining method uses the
same input image size with uniform random crop to both input views, batch size
of 256, a learning rate of 0.00005, temperature parameter value of 0.1, and
the MLP projector head comprises three hidden layers with 2048-2048-512
neurons with ReLU and a batch normalization layer. The output layer of the
projector head consists of 128 neurons during Depth Contrast pre-training. The
architecture of the MLP projection head is chosen based on preliminary
empirical analysis. Further, the F-score evaluation metric is used to
accurately measure the performance of models while having class imbalance
presents. The empirical analysis of network architectures and training
parameters are confined by limited human & computing resources. Methodological
development for Depth Contrast and its investigation remains the main focus.

##  4 Result and Discussion

Table 5: Class-wise train and test performance for ImageNet pretrained and fine-tuned on 3DPM dataset in fully supervised setting |  | Experiment No. 3.1
---|---|---
S.No. | Classes | Train | Test
|  | Precision | Recall | F1 | Precision | Recall | F1
1 | Mixed 1 | 0.31 ± 0.0235 | 0.63 ± 0.1522 | 0.41 ± 0.0457 | 0.31 ± 0.0589 | 0.61 ± 0.1846 | 0.40 ± 0.0643
2 | Agglomerated | 0.65 ± 0.0755 | 0.84 ± 0.0166 | 0.73 ± 0.0539 | 0.64 ± 0.0499 | 0.84 ± 0.0425 | 0.72 ± 0.0203
3 | Mixed 2 | 0.70 ± 0.2032 | 0.23 ± 0.0405 | 0.34 ± 0.0488 | 0.63 ± 0.3924 | 0.22 ± 0.1996 | 0.29 ± 0.2164
4 | Ore 1 | 0.89 ± 0.0185 | 0.72 ± 0.0527 | 0.79 ± 0.0320 | 0.89 ± 0.0113 | 0.72 ± 0.0537 | 0.80 ± 0.0294
5 | Ore 2 | 0.89 ± 0.0721 | 0.72 ± 0.0433 | 0.79 ± 0.0371 | 0.89 ± 0.0841 | 0.71 ± 0.0284 | 0.79 ± 0.0300
6 | Ore 3 | 0.69 ± 0.0768 | 0.71 ± 0.0450 | 0.70 ± 0.0528 | 0.69 ± 0.0744 | 0.70 ± 0.0584 | 0.69 ± 0.0610
7 | Cylindrical | 0.75 ± 0.1912 | 0.58 ± 0.0859 | 0.64 ± 0.0908 | 0.84 ± 0.1570 | 0.62 ± 0.2558 | 0.67 ± 0.2046
Table 6: Class-wise train and test performance for Depth Contrast pretrained and fine-tuned on 3DPM dataset in fully supervised setting |  | Experiment No. 5
---|---|---
S.No. | Classes | Train | Test
|  | Precision | Recall | F1 | Precision | Recall | F1
1 | Mixed 1 | 0.30 ± 0.0509 | 0.48 ± 0.1288 | 0.36 ± 0.0630 | 0.26 ± 0.0393 | 0.56 ± 0.2023 | 0.35 ± 0.0675
2 | Agglomerated | 0.64 ± 0.0295 | 0.87 ± 0.0270 | 0.74 ± 0.0172 | 0.66 ± 0.0586 | 0.85 ± 0.0552 | 0.74 ± 0.0311
3 | Mixed 2 | 0.70 ± 0.1256 | 0.32 ± 0.1026 | 0.43 ± 0.1033 | 0.63 ± 0.3049 | 0.20 ± 0.1086 | 0.29 ± 0.1546
4 | Ore 1 | 0.93 ± 0.0226 | 0.71 ± 0.0198 | 0.80 ± 0.0193 | 0.90 ± 0.0330 | 0.73 ± 0.0380 | 0.81 ± 0.0179
5 | Ore 2 | 0.88 ± 0.0555 | 0.72 ± 0.0391 | 0.79 ± 0.0278 | 0.90 ± 0.0361 | 0.74 ± 0.0404 | 0.81 ± 0.0250
6 | Ore 3 | 0.68 ± 0.0577 | 0.78 ± 0.0307 | 0.73 ± 0.0333 | 0.73 ± 0.0365 | 0.74 ± 0.0510 | 0.73 ± 0.0193
7 | Cylindrical | 0.96 ± 0.0359 | 0.45 ± 0.1523 | 0.60 ± 0.1421 | 0.89 ± 0.1535 | 0.56 ± 0.2940 | 0.62 ± 0.2551
Table 7: Class-wise train and test performance for Depth Contrast pretrained and fine-tuned on 3DPM dataset in semi supervised setting using only 20% of labelled data |  | Experiment No. 6
---|---|---
S.No. | Classes | Train | Test
|  | Precision | Recall | F1 | Precision | Recall | F1
1 | Mixed 1 | 0.35 ± 0.1273 | 0.51 ± 0.0632 | 0.41 ± 0.0763 | 0.30 ± 0.0816 | 0.44 ± 0.0785 | 0.34 ± 0.0340
2 | Agglomerated | 0.56 ± 0.0657 | 0.90 ± 0.0470 | 0.69 ± 0.0469 | 0.52 ± 0.0757 | 0.85 ± 0.0548 | 0.64 ± 0.0575
3 | Mixed 2 | 0.44 ± 0.5110 | 0.09 ± 0.0673 | 0.11 ± 0.0694 | 0.17 ± 0.3249 | 0.07 ± 0.0758 | 0.07 ± 0.0924
4 | Ore 1 | 0.87 ± 0.0761 | 0.76 ± 0.0467 | 0.81 ± 0.0221 | 0.83 ± 0.0810 | 0.73 ± 0.0481 | 0.77 ± 0.0374
5 | Ore 2 | 0.87 ± 0.0645 | 0.65 ± 0.1050 | 0.73 ± 0.0587 | 0.87 ± 0.0423 | 0.64 ± 0.1256 | 0.73 ± 0.0870
6 | Ore 3 | 0.77 ± 0.1103 | 0.56 ± 0.1603 | 0.63 ± 0.1199 | 0.76 ± 0.1011 | 0.52 ± 0.1292 | 0.61 ± 0.1029
7 | Cylindrical | 0.74 ± 0.4333 | 0.31 ± 0.2556 | 0.41 ± 0.2570 | 0.64 ± 0.4165 | 0.22 ± 0.2222 | 0.30 ± 0.2547

This section analyzes the results on downstream tasks of material
classifications while comparing the effect of the proposed pretraining method.
It also extends the analysis of the learning capabilities of models concerning
labeled data quantity and different training strategies, including fine-tuning
and linear evaluation.

Results for experiments 1, 2, and 3.1 mentioned in Table 3 provides clear
insights about input mode that combined representation of raw and reflectance
image obtains higher performance on train and test set for fine-tuning on
material classification. Commonly used Efficient-net b2 [19] model with the
combined representation of raw and reflectance image input achieves an F1
score of 0.71 on the test set whereas the model with only reflectance image
remain lower F1 score of 0.69 and model with only raw images performs
significantly poor. These experiments direct the current work to use the
combined representation of raw and reflectance images for further experiments
to evaluate different CNN architectures and the proposed self-supervised
method.

Further, the explorations of DenseNet 121 [13] and ResNeXt (31x4d) [22] CNN
architectures obtains F1 score of 0.67 and 0.72 in experiments 3.2 and 3.3
respectively. It shows that Efficient-net b2 [19] in experiment 3.1 remains
competitive concerning classification performance on the test set, lower
standard deviation, and less prone to overfit on the train set. It is
important to note that Efficient-net b2 [19] being a lightweight model with
lesser learning parameters, is a good fit for the 3DPM dataset. Analysis from
experiments 1 to 3.3 indicates that the combined representation of raw and
reflectance image with Efficient-net b2 [19] architecture obtains benchmarked
results and is a suitable candidate for further investigation on the proposed
Depth Contrast method. The Depth Contrast pretrained model, which is fine-
tuned in a fully supervised setting in experiment 5, outperforms other models.
It not only achieves the highest F1 score of 0.73 with minimal standard
deviation but also depicts no overfitting with the same F1 score on the train
set.

More specifically, while comparing the performance of this model with ImageNet
[8] pretrained model in the same fully supervised settings, it shows an
improvement of 1% on the test set. This improvement in the downstream material
classification task showcases the leverage of unlabeled data used by the
proposed Depth Contrast pretraining method to learn efficient representations
without human annotations.

Interestingly, The Depth Contrast pretrained model, which is fine-tuned in a
semi-supervised setting using only 20% of labeled data in experiment 6,
achieves a comparable F1 score of 0.65. The proposed method, Depth Contrast,
clearly outperforms by 11% on ImageNet [8] pretrained model in the same semi-
supervised settings mentioned in experiment 4. This comparative study
showcases the representation learning ability of the Depth Contrast method to
yield performance generalization on unseen data even when trained on
significantly reduced labeled data.

A similar performance is followed for linear evaluation tasks when pretrained
CNN serves as a feature extractor, and only fully connected layers are
trained. Table 4 showcases a comparative analysis of the Depth Contrast
pretrained model with the ImageNet pretrained model in fully and semi-
supervised settings. Depth Contrast pretrained and linear evaluated model in
experiment 9 obtains F1 score 0.72, which is 3% higher than ImageNet
pretrained model in experiment 7 for same fully supervised setting. Similarly,
Depth Contrast pretrained model from experiment 10 obtains F1 score of 0.64,
which is 12% higher than the ImageNet model in the same semi-supervised
setting. While linear evaluation clearly shows that ImageNet pretrained model
suffers high overfitting in limited labeled data availability, whereas Depth
Contrast leverages domain-specific unlabeled data and learns efficient
representations for performance generalization.

Detailed class-wise results are mentioned in Table 5 and Table 6 for ImageNet
and Depth Contrast pretrained model respectively in fully supervised setting.
It is observed that material categories compounded by multiple materials,
Mixed1 and Mixed2, perform poorly since their texture characteristics are not
uniform, and the sample count is also low in the 3DPM dataset. A similar trend
is followed in Depth Contrast pretrained model in the semi-supervised setting
mentioned in Table 7. However, the recall and precision of other classes are
better for the Depth Contrast pretrained model. Further, current work shares
the following conceptual findings.

Figure 3: Performance comparison of models pretrained on ImageNet and Depth
Contrast Efficient-net in semi and fully supervised settings

###  4.1 Raw image of depth maps scales representations and improves learning

Depth maps of the material on conveyor belts are directly associated with the
shape and size of the material; thus, depth details are valuable information
addition for learning representation. However, alone depth maps are not
sufficient to define the material. It provides the reason that the combined
representation of raw (depth details) and reflectance images yield optimal
performance. This fact also forms the backbone of the Depth Contrast
pretraining method for view pair modeling.

###  4.2 CNN with reduced parameters performs better

The architecture of Efficient-net b2 [19] offers adaptive properties for
width, depth, and resolution of convolutional layers based on input image
size. It seems that the model adapts conveniently based on dataset size and
texture details, making it a suitable CNN architecture even with fewer
learning parameters.

###  4.3 Self-supervised method Depth Contrast significantly improves
downstream task performance and reduces human annotations

As Depth Contrast constructs input pair view using reflectance image and depth
map of the raw image, which allows learning representation comprehensively
using both types of details textures from reflectance view and depth maps.
During contrastive mechanism, it learns correlation between texture and depth
of material, whereas negative pairs allow learning dissimilarity among texture
and depth details across material categories. Performance on downstream tasks
supports the fact about learning representations in the self-supervised manner
as the method outperforms in fully and semi-supervised labeled data settings.
Specifically, in limited labeled data scenarios, performance remains
statistically significant (p <0.05).

###  4.4 Self-supervised method Depth contrast encourages performance
generalization

Comparative analysis of fine-tuning and linear evaluation task in Figure 3
shows that gap in classification performance between ImageNet pretrained and
Depth Contrast pretrained model becomes significant when moving from fine-
tuning to linear evaluation. It indicates the rich representation learning
capabilities of the model due to Depth Contrast that when CNN model is used as
only feature extractor, then also a performance on unseen data remain
competent whereas the ImageNet pretrained model starts suffering in
performance generalization. It also shows the potential of the self-supervised
methods in the visual domain beyond the natural visual concepts that are
challenging to understand and annotate by humans.

##  5 Conclusion and Future Scope

Current work explores the computer vision methods and deep CNNs on mining
material classification on 3DPM sensor images. It proposes the self-supervised
learning method Depth Contrast to improve the representation learning by
leveraging sensor-generated data without human annotation. This work
contributes the following:

  * •

Obtains benchmark results of F1 score 0.72 on 3DPM dataset for mining material
classification employing ImageNet [8] transfer learning in a fully supervised
setting

  * •

Contributes to a novel self-supervised pretraining method, Depth Contrast,
which improves performance for mining material classification by obtaining an
F1 score of 0.73 in a fully supervised setting. It obtains F1 score 0.65 semi-
supervised setting which shows improvement of 11% over ImageNet [8] transfer
learning. The proposed method depicts consistent performance improvement on
fine-tuning and linear evaluation. It shows the applicability of self-
supervised learning beyond the natural visual concept domain.

  * •

The Depth Contrast method showcases the utilization and leverage of sensor-
generated visual data to learn representations, significantly reducing the
need for human supervision, thus making industrial AI automation more robust,
cost-effective, and serving as lifelong learning. The proposed method’s main
idea is based on multiple input views from different sensors, which has
potential possibilities to apply the method in different automation scenarios
where views are in terms of video frames, visual captures from different
angles, environment, etc.

The potential of self-supervised methods in the work indicates the well-versed
possibilities to utilize the machine-generated unlabeled data to reduce the
need for human supervision beyond natural visual concepts, reducing the cost
and increasing efficiency. The proposed method is adaptable in all the domains
where depth information is significant. Future work is subtle to investigate
further the field of contrastive joint embedding and other self-supervised
methods based on knowledge distillations and bootstrapping. Exploring more
network architectures, including transformers, is also essential to elevate
supervised performance with increased data.

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  *[3DPM]: 3-Dimensional Particle Measurement
  *[AI]: Artificial Intelligence
  *[ML]: Machine Learning
  *[DL]: Deep Learning
  *[CNNs]: Convolutional Neural Networks
  *[SVM]: Support Vector Machine
  *[CNN]: Convolutional Neural Network


# Lifetimes and Oscillator Strengths for Ultraviolet Transitions in Neutral
Chlorine

R.B. Alkhayat  Department of Physics and Astronomy, University of Toledo,
Toledo, OH 43606  R.E. Irving  S.R. Federman D.G. Ellis  S. Cheng

###### Abstract

We present lifetime measurements using beam-foil techniques for radiative
transitions from the 3$p^{4}$(${}^{1}S$)4$s$ ${}^{2}S_{1/2}$,
3$p^{4}$(${}^{3}P$)5$s$ ${}^{2}P_{1/2,3/2}$, and 3$p^{4}$(${}^{3}P$)3$d$
${}^{2}F_{5/2}$ levels in Cl I and the corresponding results of the oscillator
strengths for transitions at 1004.68, 1079.88, 1090.73, and 1094.77 Å,
respectively. We compare our experimental results with available theoretical
calculations and astronomical observations in an effort to resolve
discrepancies among them.

##  1 Introduction

Neutral chlorine plays an important role in understanding the structure of
diffuse interstellar clouds. A small fraction of the chlorine in diffuse
clouds is in the form of HCl, while most of the chlorine converts to HCl in
dense clouds because of the reaction of Cl with H${}_{3}^{+}$ (Dalgarno et
al., 1974). Knowledge of various ionization states of chlorine (Jura & York,
1978; Moomey et al., 2012) allows a better understanding of the processes
affecting diffuse cloud chemistry (Jura, 1974; Neufeld & Wolfire, 2009). Cl I
is an effective way of tracing the molecular fraction of H2 (Sonnentrucker et
al., 2002). Furthermore, Cl I has over $50$ transitions between 920 and 1390 Å
(Morton, 2003), but few of the most prominent ones have reported experimental
lifetimes.

The oscillator strengths of the Cl I lines are difficult to compute from ab
initio theory because there is strong configuration interaction and spin-orbit
mixing, especially between the levels of the $3p^{4}$ 3$d$ and $3p^{4}$ 5$s$
configurations. For this reason, LS-coupling or any other coupling scheme
seems not to describe the states very well. This creates a situation where the
calculation of the oscillator strengths is quite challenging and leads to
confusion in state designations.

Few theoretical and experimental data of transition probabilities and
lifetimes are available for Cl I. Ojha & Hibbert (1990) performed a
configuration interaction calculation using CIV3 on Cl I to compute a large
number of transitions. However, they recommend caution when using their
results due to the strong mixing between $3p^{4}$ $(^{3}P)$ 3$d$ and $3p^{4}$
$(^{3}P)$ 5$s$. Biémont et al. (1994) reported oscillator strengths for Cl I
by considering the most important interaction and relativistic effects. They
suggested additional elaborate work, especially for weaker transitions. The
early theoretical work of Ojha & Hibbert (1990) and Biémont et al. (1994)
shows significant discrepancies in oscillator strengths with astronomical and
experimental results (Federman, 1986; Schectman et al., 1993), particularly
the lines $\lambda\lambda$1088, 1097 for the reasons mentioned earlier. Singh
et al. (2006) calculated oscillator strengths using configuration interaction
wavefunctions, but their results show differences in the length and velocity
forms. Astronomical observations were described by Sonnentrucker et al. (2006)
for the Cl I lines at 1004.68, 1079.88, 1090.73, and 1094.77 Å. All quoted
wavelengths are given in vacuum. [NIST wavelengths as well as designations for
energy levels (Kramida et al., 2018) are used in this paper, except for the
changes in designation suggested by Oliver & Hibbert (2007) noted below.]
However, their resulting oscillator strengths are different from theoretical
predictions (Biémont et al., 1994) by factors 3.1, 1.2, 2.4, and 0.42,
respectively. Oliver & Hibbert (2007, 2008, 2013) published a set of large-
scale calculations for neutral chlorine in an attempt to understand the causes
for the continuing discrepancies between theory and observation or experiment;
they point to the strong mixing between the $J=5/2$ levels of the $3p^{4}$
3$d$ and $3p^{4}$ 5$s$ configurations.

The main plan of this paper is to provide experimental results for lifetimes
and oscillator strengths through beam-foil spectroscopic techniques and to
resolve the existing conflicts between theory versus observations and
experiment. No previous experimental values have been reported to estimate the
oscillator strengths for the lines of interest to Sonnentrucker et al. (2006).

##  2 Experimental Details

The experimental lifetime measurements were executed at the Toledo Heavy Ion
Accelerator (THIA). More details about the experimental techniques and the
facility were described in earlier published papers (e.g., Federman et al.,
1992; Haar et al., 1993; Schectman et al., 2000). Chlorine ions were produced
by heating sodium chloride in a high-temperature oven at the THIA accelerator
using a Danfysik Model 911A Universal Ion Source and then selected by a
bending magnet. The ion beam was accelerated to final kinetic energies of 130
or 170 keV. Chlorine ions were steered toward carbon foils with thicknesses
ranging from 2.2 to 2.4 $\mu$g cm-2 by an electrostatic switchyard. Typical
beam currents were set to be around 90 to 100 nA to reduce foil breakage. An
Acton 1 m normal-incidence vacuum ultraviolet monochromator with a 2400 line
mm-1 grating blazed at 800 Å was used for the transitions for the various
charges and excited states produced when ions passed through a carbon foil. A
Galileo Channeltron detected the emitted radiation at the exit slit of the
monochromator. The spectrometer has a resolution of approximately 0.2 Å.

In this study, the lifetimes and corresponding oscillator strengths of lines
at 1004.68, 1079.88, 1090.73, and 1094.77 Å were obtained. Because the lines
under investigation are relatively weak, only forward decay curves were
acquired by moving the carbon foils upstream away from the monochromator slit.
The error bars associated with the lifetimes take into account both
experimental and statistical uncertainties. The fluctuation in signals present
in spectra and decay curves is less than 20%. All decay curves and spectral
data were normalized using an optical monitor signal from a photomultiplier
tube. Possible systematic effects such as nuclear scattering, foil thickening,
and beam divergence were studied at two different energies (see Federman et
al., 1992) in the forward direction, and the spread among the results for a
transition yielded the value for the systematic uncertainty (typically 5$\%$).
The statistical uncertainties (about 6$\%$) were inferred from the random
noise in a specific measurement. The systematic errors were added in
quadrature to the statistical errors to determine uncertainties in the
lifetime measurements.

Using the line at 1004.68 Å, the decay curve for the 3$s^{2}$3$p^{4}4s$
${}^{2}S_{1/2}$ level was affected by a line at 1005.28 Å due to Cl III. To
account for blending from this line, we took decay curves at two settings,
namely 1004.53 Å and 1005.00 Å. Analysis and comparison of these two decay
curves confirmed the influence of the blending with the Cl III line and gave
results consistent with its previously measured meanlife of 7.87 ns (Schectman
et al., 2005). With this information, we performed a two-exponential fit, as
shown in Figure 1, to extract the desired meanlife for the 3$s^{2}$3$p^{4}$
4$s$ ${}^{2}S_{1/2}$ level.

A single exponential fit was adequate to obtain the lifetime from decay of the
3$s^{2}$3$p^{4}$5$s$ ${}^{2}P_{1/2}$ level seen via $\lambda$1079.88. To the
precision of our measurements, this transition was not affected by cascades,
nor by the presence of the nearby strong line of Cl II at 1079.08 Å whose
lifetime is 9.14 ns (Schectman et al., 2005). The fitted decay curve appears
in Figure 2.

The situation was more complicated for the decay of the 3$s^{2}$3$p^{4}$5$s$
${}^{2}P_{3/2}$ level from the line at 1090.73 Å. The cascades from higher
levels could impact our lifetime measurements by affecting the population of
the level of interest. The results from Oliver & Hibbert (2013) suggest that
decays from many upper states may populate this level. The common cascades
involving 3$p^{4}$4$p$ ${}^{2}D_{3/2,5/2}^{\rm o}$ levels with a typical
lifetime of 30 ns were observed in our decay curve. Evidence for other
cascades was not apparent; those with lifetimes greater than 30 ns are beyond
the capabilities of THIA. We applied the method of Arbitrarily Normalized
Decay Curves (ANDC; Curtis et al. (1971)) to remove the effect of cascades
from the primary mean lifetime. Because the lifetimes of the possible cascades
were significantly longer than the primary decay, the cascades played a minor
role and affected the primary lifetime by less than 16$\%$. A semi$-$log plot
for the 5$s$ ${}^{2}P_{3/2}$ decay curve is shown in Figure 3 using the
$\lambda$1090.73 transition.

A short-lived decay component from the fit to a transition in Cl V at 545.11 Å
(3$s$3$p$ ${}^{4}P^{\rm o}_{5/2}$) was seen in second order. We only saw the
effect of Cl V in the decay curve at an energy of 170 keV (see Figure 3)
because (1) measurements at higher energy produce higher charge states and (2)
the slight difference in wavelength setting between the measurements at 130
and 170 keV could have included more intensity from the Cl V line at 170 keV.
Schectman et al. (2005) found contaminating lines from highly-ionized chlorine
(Cl IV and V) in their THIA data on Cl II, too. The same situation was
observed by Brown et al. (2018) in their work on P II. Further measurements at
170 keV were produced on the Cl V line at 545.11 Å to establish its short
lifetime.

For the line at 1094.77 Å, resulting from decay of the 3$s^{2}$3$p^{4}$3$d$
${}^{2}F_{5/2}$ level, the decay curve may be affected by contamination from
adjacent lines. The possible contaminating intensity that may be coming from
Cl I lines at 1095.14 and 1095.66 Å was studied by moving the grating
position. One setting at 1094.53 Å was far away from any blending, while a
setting at 1095.43 Å was where the most significant amounts of contamination
were expected. The fits yielded indistinguishable differences in lifetimes,
indicating there was no detectable contamination from other Cl I lines. The
best single-exponential fit is shown in Figure 4 for the $\lambda$1094.77
transition.

We attempted to measure branching ratios from the ratio of intensities for the
pairs of lines, 1079.88 versus 1090.27 Å and 1090.73 versus 1103.34 Å.
However, our spectral measurements were not precise enough for any meaningful
results because the blending and contamination from Cl IV and V seen in second
order, and the resulting limited signal to noise during the attempt to remove
the contamination, prevented us from making accurate branching fractions from
the intensity ratios. As a result, we adopted the branching ratios for
$\lambda\lambda$1079.88, 1090.73 from the calculations of Oliver & Hibbert
(2013) when inferring oscillator strengths from our experimental lifetimes.
The decays associated with the other two transitions at 1004.68 and 1094.77 Å
represent the dominant channel according to Oliver & Hibbert (2013).

##  3 Results and Discussion

Our results for lifetime measurements, as well as comparison with earlier
theoretical calculations, are shown in Table 1. The weighted average of the
lifetimes reported in Table 1 are obtained from experiments acquired at beam
energies 130 and 170 keV. Our lifetime measurements are in very good agreement
with theoretical calculations by Singh et al. (2006) and Oliver & Hibbert
(2013), considering our 2$\sigma$ uncertainties lead to differences of less
than 15$\%$. These theoretical calculations are based on configuration
interaction wavefunctions and relativistic effects. The earlier effort by Ojha
& Hibbert (1990) yielded much longer lifetimes due to the heavy mixing among
Cl I levels encountered in their less extensive calculations.

Our lifetime for the 3$s$3$p$ ${}^{4}P^{\rm o}_{5/2}$ level of Cl V is
$0.27\pm 0.01$ ns. Our value does not agree with theoretical results of
approximately 0.11 ns obtained by several methods (Fawcett, 1987; Choudhury et
al., 2003; Froese Fischer et al., 2006). Perhaps our measurements were
affected by cascades, yielding a longer lifetime for 3$s$3$p$ ${}^{4}P^{\rm
o}_{5/2}$. In any case, its approximate value helps us to extract the primary
lifetime of interest.

Finally, we compare results for oscillator strengths derived from experimental
lifetimes with those published previously, as shown in Table 2. Generally, our
experimental values for oscillator strengths are in very good agreement with
those of Sonnentrucker et al. (2006), Singh et al. (2006), and Oliver &
Hibbert (2013), again with differences less than about 15$\%$. The
correspondence is less satisfactory with the calculations of Ojha & Hibbert
(1990) and Biémont et al. (1994).

A reason for the poorer agreement with the results from Ojha & Hibbert (1990)
and Biémont et al. (1994) may be the smaller scale of the computations
compared with what is possible with today’s servers. Ojha & Hibbert (1990)
predicted oscillator strengths with smaller values than other $f$-values shown
in Table 2. The less extensive set of calculations leads to fewer terms in the
eigenfunction expansions, causing the amount of mixing between the fine
structure levels in the 3$p^{4}(^{3}P)$ 3$d$ and 3$p^{4}(^{3}P)$ 5$s$
configurations to be underestimated. This is likely the cause for the
significant differences between the length and velocity results in their
calculations. The same explanation may apply to the results from Biémont et
al. (1994) because the level of mixing could produce both smaller and larger
$f$-values. The $\lambda$1094.77 transition is more complicated theoretically
because the 3$p^{4}$(${}^{3}P$) 3$d$ configuration mixes with
3$p^{4}$(${}^{3}P$) 5$s$ to produce 22 even parity levels. Oliver & Hibbert
(2007) changed the designation of the heavily mixed level ($J=5/2$) to be
(${}^{3}P$)3$d$ ${}^{2}F_{5/2}$ and that improved their theoretical
calculations. Since Biémont et al. (1994) kept the term classification given
in the NIST tables (Kramida et al., 2018), some of the difference between
their $f$-value for the line at 1094.77 Å and ours may arise from the
classification scheme used.

While our results generally agree with the $f$-values given by Sonnentrucker
et al. (2006), that is not the case for $\lambda$1090.73. Sonnentrucker (2019,
private communication) noted that this portion of the spectrum contains
substantial amounts of blending from a combination of stellar features and the
wing of a strong H2 line. The line blends likely affected their placement of
the stellar continuum when measuring this relatively weak Cl I line.

##  4 Conclusions

We presented experimental lifetimes and the corresponding $f$-values based on
beam-foil spectroscopic techniques that are needed in studies of interstellar
Cl I. Our results agree very well with the most recent theoretical predictions
of Singh et al. (2006) and Oliver & Hibbert (2013), and are generally
consistent with the $f$-values obtained from astronomical spectra
(Sonnentrucker et al., 2006). The resulting $f$-values are in quite good
agreement with those given by Singh et al. (2006), Sonnentrucker et al.
(2006), and Oliver & Hibbert (2013), except the $f$-value for the line at
1090.73 Å that does not agree with Sonnentrucker et al. (2006). In particular,
these transitions provide important information on the structure of diffuse
gas because Cl I is a good tracer of molecular components. On the other hand,
our $f$-values differ substantially from the theoretical calculations
presented by Ojha & Hibbert (1990) and Biémont et al. (1994). The results of
our lifetime measurements and oscillator strengths are the only available
experimental measurements for these levels to date. Since our results agree so
well with the latest theoretical efforts, future analyses can incorporate
these additional Cl I transitions for improved self-consistency.

We thank Paule Sonnentrucker for useful comments and Robert Snuggs for
technical assistance.

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Table 1: Cl I Lifetimes $J_{u}$ | $\lambda_{ul}$ |  $\tau$ (ns)
---|---|---
| (Å) | Present | OHaaOjha & Hibbert (1990) $-$ configuration interaction using CIV3. | SJMbbSingh et al. (2006) $-$ configuration interaction using CIV3. | OccOliver & Hibbert (2013) $-$ configuration interaction using CIV3.
1/2 | 1004.68 | $1.04\pm 0.08$ | $\ldots$ | $1.06$ | $1.11$
1/2 | 1079.88 | $5.83\pm 0.36$ | $21.26$ | $\ldots$ | $6.26$
3/2 | 1090.73 | $8.98\pm 0.72$ | $17.77$ | $\ldots$ | $8.07$
5/2 | 1094.77 | $6.28\pm 0.18$ | $29.23$ | $6.21$ | $7.50$
Table 2: Cl I Oscillator Strengths $\lambda_{ul}$ (Å) | $J_{l}$ | $J_{u}$ |  $f$-value ($\times 10^{-2}$)
---|---|---|---
|  |  | Present | OHaaOjha & Hibbert (1990). | BGZbbBiémont et al. (1994) $-$ configuration interaction using SUPERSTRUCTURE. | SFYccSonnentrucker et al. (2006) $-$ astronomical observations. | SJMddSingh et al. (2006). | OeeOliver & Hibbert (2013). |
1004.68 | 3/2 | 1/2 | $4.73\pm 0.36$ | $\ldots$ | $\ldots$ | $5.14^{+0.58}_{-0.51}$ | 4.69ffBased on length formalism. | 4.43ffBased on length formalism. |
| $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | 3.99ggBased on velocity formalism. | 4.25ggBased on velocity formalism. |
1079.88 | 3/2 | 1/2 | $0.47\pm 0.03$ | 0.065ffBased on length formalism. | 0.70ffBased on length formalism. | $0.56^{+0.13}_{-0.12}$ | $\ldots$ | 0.44ffBased on length formalism. |
| $\ldots$ | $\ldots$ | $\ldots$ | 0.13ggBased on velocity formalism. | 0.69ggBased on velocity formalism. | $\ldots$ | $\ldots$ | 0.40ggBased on velocity formalism. |
1090.73 | 3/2 | 3/2 | $0.95\pm 0.08$ | 0.25ffBased on length formalism. | 0.68ffBased on length formalism. | $0.28^{+0.04}_{-0.04}$ | $\ldots$ | 1.07ffBased on length formalism. |
| $\ldots$ | $\ldots$ | $\ldots$ | 0.46ggBased on velocity formalism. | 0.61ggBased on velocity formalism. | $\ldots$ | $\ldots$ | 0.97ggBased on velocity formalism. |
1094.77 | 3/2 | 5/2 | $3.85\pm 0.11$ | 0.11ffBased on length formalism. | 1.66ffBased on length formalism. | $3.96^{+0.42}_{-0.38}$ | 3.72ffBased on length formalism. | 3.22ffBased on length formalism. |
| $\ldots$ | $\ldots$ | $\ldots$ | 0.045ggBased on velocity formalism. | 1.52ggBased on velocity formalism. | $\ldots$ | 3.94ggBased on velocity formalism. | 3.04ggBased on velocity formalism. |

Figure 1: Decay curve for the line at 1004.68 Å for a beam energy of 170 keV.
The post-foil velocity of 0.941 mm ns-1 was used to convert the foil position
into a time. The foil was moved relative to the monochromator entrance slit in
increments of 0.1 mm until it was displaced 3.7 mm; then the increments were
increased to 0.5 mm. The curvature beyond about 3 ns in the fitted decay curve
(blue line) arises from the presence of decays in Cl III as noted in the text.
Figure 2: Decay curve for the line at 1079.88 Å for a beam energy of 130 keV.
The post-foil velocity of 0.818 mm ns-1 was used to convert the foil position
into a time. Figure 3: Decay curve for the line at 1090.73 Å for a beam energy
of 170 keV utilizing a three-exponential fit as shown by the solid curve. At
the shortest time, the decay from Cl V is seen, and the portion between 22 and
35 ns reveals cascades of about 30 ns. The step size furthest from the slit
was 4 mm. Figure 4: Decay curve for the line at 1094.77Å for a beam energy of
130 keV.