# PRMI: A Dataset of Minirhizotron Images for Diverse Plant Root Study

Weihuang Xu,1 Guohao Yu,1 Yiming Cui,1 Romain Gloaguen,2 Alina Zare,1 Jason
Bonnette,3 Joel Reyes-Cabrera,4 Ashish Rajurkar,4 Diane Rowland,5 Roser
Matamala,6 Julie D. Jastrow,6 Thomas E. Juenger,3 Felix B. Fritschi4

###### Abstract

Understanding a plant’s root system architecture (RSA) is crucial for a
variety of plant science problem domains including sustainability and climate
adaptation. Minirhizotron (MR) technology is a widely-used approach for
phenotyping RSA non-destructively by capturing root imagery over time.
Precisely segmenting roots from the soil in MR imagery is a critical step in
studying RSA features. In this paper, we introduce a large-scale dataset of
plant root images captured by MR technology. In total, there are over 72K RGB
root images across six different species including cotton, papaya, peanut,
sesame, sunflower, and switchgrass in the dataset. The images span a variety
of conditions including varied root age, root structures, soil types, and
depths under the soil surface. All of the images have been annotated with weak
image-level labels indicating whether each image contains roots or not. The
image-level labels can be used to support weakly supervised learning in plant
root segmentation tasks. In addition, 63K images have been manually annotated
to generate pixel-level binary masks indicating whether each pixel corresponds
to root or not. These pixel-level binary masks can be used as ground truth for
supervised learning in semantic segmentation tasks. By introducing this
dataset, we aim to facilitate the automatic segmentation of roots and the
research of RSA with deep learning and other image analysis algorithms.

## Introduction

Plant root systems play important roles in supporting our natural ecosystems,
adapting to changes in climate, and ensuring the sustainable production of
plants (Aidoo et al. 2016; Alexander, Diez, and Levine 2015; Ettinger and
HilleRisLambers 2017). Phenotyping RSAs is an important component of
understanding plant root systems to support and enhance these roles along with
advancing many aspects of plant science research (Pieruschka and Schurr 2019;
Trachsel et al. 2011; Wasson et al. 2012).

Figure 1: Illustration of a MR system. Before planting, transparent tubes are
inserted into the soil with the desired angle. A high-resolution camera slides
into the MR tubes to take images of the roots that happen to grow along the
surface of the tube at different depths over time.

Relative to above-ground plant phenotyping, below-ground field-based plant
root phenotyping is challenging. Many common approaches for field-based root
phenotyping, such as soil coring and “shovelomics” (Van Noordwijk and Floris
1979; Gregory 2008; Trachsel et al. 2011), are destructive, laborious, time-
consuming, and cannot be carried out in real-time or over-time. Minirhizotron
(MR) technology (Majdi 1996; Johnson et al. 2001) is one of the few most
widely-used approaches for phenotyping RSA non-destructively over time.
Generally, before planting, MR transparent tubes are installed in the field at
an angle (e.g. $45^{\circ}$) to the soil surface in locations that should
eventually be directly under or near to plants of interest. Then, as the
plant’s root systems grow, a high-resolution camera can be inserted along the
tube to capture root images at a variety of depths as shown in Figure 1. Since
the MR tubes remain in the soil during the entire growing period, the camera
is able to capture time-series RGB root images providing insight into RSA
development. In addition to the development of the whole root structure, MR
imagery can be used to observe changes of roots themselves throughout their
life cycle such as color, diameter, angle, and length changes.

Precisely segmenting roots from the soil background in MR imagery is a
critical step in studying root systems using MR technology. Traditionally, MR
images are manually annotated in which users trace along each individual root
to indicate the location and diameter. As can be imagined, manually tracing a
large number of thin, hard-to-see roots is incredibly tedious and time-
consuming. This annotation step is the primary bottleneck limiting the
effectiveness of MR technology for large-scale RSA studies. Given the
complexity of plant RSA, biological variation, and environmental- and
management- impacts on RSA, a huge amount of data is needed for comprehensive
RSA studies to lead to statistically reasonable conclusions. Thus, algorithms
for high-throughput automatic root segmentation tasks are essential.

Deep learning, and convolutional neural networks specifically, have shown
initial great success in plant root segmentation tasks (Yasrab et al. 2020;
Smith et al. 2020). The features learned by well-trained deep neural networks
are more representative and effective for segmenting roots as compared to
earlier image processing-based approaches (Das et al. 2015; Galkovskyi et al.
2012; Pierret et al. 2013; Haralick, Sternberg, and Zhuang 1987; Lobregt,
Verbeek, and Groen 1980). However, one limitation in applying these approaches
is the need for large MR image datasets for training that include the soil
characteristics and plant species of interest. Transfer learning has been
investigated to help alleviate the need for collecting and annotating enormous
MR image training sets for each soil type and plant species (Xu et al. 2020).
However, much of these investigations have been limited by the lack of public
sizeable public MR image datasets due to the fact that collecting and
annotating images are extremely tedious, time-consuming and often requires
some knowledge and expertise.

In order to help fill this gap and introduce the computer vision community to
this problem domain, we compiled a dataset, named PRMI (Plant Root
Minirhizotron Imagery), containing over 72 thousand MR RGB root images across
six different species, namely, cotton, papaya, peanut, sesame, sunflower, and
switchgrass. These images span a variety of conditions including varying root
age, root spatial structures, soil types, and depths under the soil surface.
We paired binary image-level labels for each image showing whether the image
contains roots along with meta-data such as crop species, collection location,
MR tube number, collection time, collection depth, and image resolution. In
addition, over 63 thousand of the images have been manually annotated to
generate pixel-level binary masks indicating whether the pixels correspond to
root or not. Annotating MR root images is challenging, so learning from weak
labels is essential, particularly when transitioning a trained method from one
location (i.e., soil type and properties) and one plant species (i.e., root
characteristics) to another. The primary use of the PRMI dataset is for
supervised/weakly-supervised semantic segmentation as well as transfer
learning. The RSA features (length, diameter, etc.) can be extracted for
scientific purposes after segmentation. We hope this dataset can make
contributions to facilitate the automatic segmentation of roots and the
research of RSA with deep learning. The dataset is publicly available:
https://gatorsense.github.io/PRMI/.

## Related Datasets and Annotation Tools

There are a few public MR image datasets available as summarized in Table 1.
However, these datasets are relatively small (e.g., the largest collection for
one species contains only 400 images) and only three of these datasets provide
pixel-level ground truth masks. These datasets have been used to develop image
processing-based approaches as well as deep-learning methods for root
segmentation tasks. For example, early work on the Peach1 dataset (Zeng,
Birchfield, and Wells 2006) proposed an image processing-based approach that
first extracted a collection of features using linearly-shaped spatial
filters. The soybean (Wang et al. 2019) and the chicory (Smith et al. 2020)
datasets have been used for developing deep learning segmentation approaches.

There are several annotation tools that have been used for manually tracing
roots. Zeng et. al., who provided the Peach1 dataset (Zeng, Birchfield, and
Wells 2006), developed Rootfly for root tracing. Le Bot et. al. developed a
software DART (Le Bot et al. 2010) to analyze RSA. Commercial tools are also
available such as RootSnap (CID Bioscience) and WinRHIZO Tron (Regent
Instrument) (Bauhus and Messier 1999). Furthermore, general image processing
software such as Photoshop and ImageJ have also been used for root tracing
(Abràmoff, Magalhães, and Ram 2004). Automated tools were also developed such
as EZ-RHIZO (Armengaud et al. 2009), RootNav (Yasrab et al. 2019), and
RootGraph (Cai et al. 2015).

Dataset | Num of images(Train/Test) | Label
---|---|---
Peach1∗ | 50/200 | Pixel label
Peach2∗ | 200/200 | Image Label
maple1∗ | 120/120 | Image Label
magnolia1∗ | 100/100 | Image Label
soybean§ | 39/13 | Pixel label
chicory‡ | 38/10 | Pixel label

  * •

∗ (Zeng, Birchfield, and Wells 2006); § (Wang et al. 2019); ‡ (Smith et al.
2020)

Table 1: Other Public MR Datasets

(a) Cotton

(b) Papaya

(c) Peanut

(d) Sesame

(e) Sunflower

(f) Switchgrass

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

Figure 2: Examples of selected raw root MR images for each species and
manually annotated ground truth masks. (a) Cotton, (b) Papaya, (c) Peanut, (d)
Sesame, (e) Sunflower, and (f) Switchgrass (rotated by $90^{\circ}$). 1st Rows
shows the images have no roots (only soil background). 2nd row shows the
images have roots. 3rd rows shows the paired binary masks.

## Image Collection

In our PRMI dataset, MR technology was used to collect root images across
cotton, papaya, peanut, sesame, sunflower, and switchgrass. For each species,
root images were captured from multiple plants and multiple MR tubes across a
variety of depths over different time periods and varying soil and
environmental conditions. Many of the root images are related to each others
in time or depth. For example, for a specific species, images were captured
from the same MR tube and the same depth across times (i.e., a time series of
MR imagery of particular plant root architectures). Thus, some of these images
will contain the same root portions at different ages, sizes, shapes and
colors. Although all the root images of different species were collected by MR
technology, the specifics of the MR technology were different for each sub-
collection. For example, the camera used for each species was distinct,
resulting in different image resolutions, dots per inch (DPI), and color
profiles. For each species, there were images containing plant roots as well
as images containing purely soil and background. Some example images for each
species are shown in the Figure 2.

The details of the sub-collections of each species are shown in Table 2,
including the dpi, resolution, number of locations, number of collection
tubes, number of root images, number of non-root images, the number of images
in train/val/test sets, and the total number of images. To maintain the
original appearance of the root images, we compiled the dataset using raw root
images in their original format without any pre-processing such as re-sizing
or any normalization.

Species | DPI | Size | Num of | Num of | Num of | Num of non- | Train | Val | Test | Total
---|---|---|---|---|---|---|---|---|---|---
locations | tubes | root images | root images
Cotton | 150 | $736\times 552$ | 1 | 12 | 918 | 1494 | 1271 | 564 | 577 | 2412
Papaya | 150 | $736\times 552$ | 2 | 6 | 487 | 59 | 282 | 131 | 133 | 546
Peanut | 120 | $640\times 480$ | 1 | 32 | 8508 | 8534 | 10087 | 3413 | 3542 | 17042
Peanut | 150 | $736\times 552$ | 2 | 24 | 11147 | 8478 | 11485 | 3347 | 4793 | 19625
Sesame | 120 | $640\times 480$ | 4 | 11 | 1460 | 700 | 1438 | 318 | 404 | 2160
Sesame | 150 | $736\times 552$ | 2 | 24 | 7923 | 6423 | 8637 | 2625 | 3084 | 14346
Sunflower | 120 | $640\times 480$ | 1 | 16 | 1646 | 2254 | 2211 | 722 | 967 | 3900
Switchgrass | 300 | $510\times 720$ | 3 | 72 | 3465 | 9072 | 11272∗ | 665 | 600 | 12537

  * •

∗ 2647 images in the training set have pixel-level annotation and the
remaining 8625 images only have image-level annotation.

Table 2: The summary of MR root images for each species in PRMI dataset.

## Image Annotation

Each MR image in this collection is paired with image-level annotations and
more than 63 thousand of the images are also paired with pixel-level
annotation. Next, we will introduce the annotation details.

### Image-level Annotation

To enable a more comprehensive understanding of the dataset, meta-data for
each MR image is recorded and provided in a JSON file (details can be found in
the appendix B). This meta-data includes crop species, collection location, MR
tube number, collection time, collection depth, and sensor DPI. More
importantly, we manually annotate each MR image with an binary image-level
label indicating whether the image contains roots. This image-level annotation
can be used in a weakly-supervised learning framework for plant root
segmentation tasks, which is one of the major proposed use of this data.

### Pixel-level Annotation

Each pixel-level annotation is a segmentation mask containing binary values
indicating the class (root/soil) for each pixel. Selected pixel-level
segmentation masks for each species are shown in Figure 2. All the pixel-level
masks were generated by technicians manually labeling pixels in the images.
However, different annotation methods were used to generate masks for
switchgrass and all the other species.

Pixel-level annotation for all species other than switchgrass. WinRHIZO Tron
software was used to manually trace the roots in images of cotton, papaya,
peanut, sesame, and sunflower. The pixel-level segmentation masks were
generated by drawing rectangular boxes to highlight the area of root pixels in
the software. To make the annotation as accurate as possible, multiple
rectangular boxes of different sizes were used for each single piece of root
to capture any variance in diameter. The coordinates of four vertexes of all
rectangular boxes were recorded for each root image. Then, the binary masks
were generated by reconstructing and aligning these boxes in a blank image of
the same size as the corresponding RGB root images.

Pixel-level annotation for the switchgrass. There are 3912 out of 12537
switchgrass images paired with pixel-level segmentation masks. Given the fine,
narrow switchgrass roots and the size of these images, it is extremely time-
consuming to manually annotate each pixel. To improve the efficiency of the
annotation process, two different annotation methods were used: a) technicians
annotated images on superpixels generated by running the Simple Linear
Iterative Clustering (SLIC) algorithm (Achanta et al. 2010) on raw images; and
b) technicians refined the predicted segmentation masks generated by passing
raw images to pre-trained U-net. Details can be found in appendix B.

## Dataset Split

For each species, the root images were collected from different locations,
dates, tubes, and depths. To ensure that the training, validation, and testing
data share a similar data distribution while ensuring that testing data does
not contain the same tubes and roots used for training, we split the data into
train, validation and test sets based on the tubes.

We randomly selected 60% of tubes for training, 20% for validation, and the
remaining 20% for test for each species other than switchgrass. In terms of
switchgrass root images, to ensure confidence in the accuracy of segmentation
masks in the test set, all the images with manually generated ground-truth
were placed in the test set. The training set was generated by randomly
selected 80% of tubes with AI-guided annotation with the remaining compiled in
the validation set. In addition, all the images with only image-level
annotations were placed in the training set to support weakly-supervised
segmentation. The total number of images for train, validation and test sets
are shown in Table 2.

The dataset could also be split according to other factors such as dates,
depths, and locations for specific research questions. For example,
researchers can split the dataset based on dates to study the changes of roots
over time. We paired image-level labels with meta-data for each image, which
can be easily used to sort and split dataset based on different attributes.

## Experiments and Results

The primary proposed use of this PRMI dataset is for root segmentation tasks.
To generate baseline benchmark results and show the challenges of this
dataset, we trained a U-net (Ronneberger, Fischer, and Brox 2015) for
supervised learning and IRNet (Ahn, Cho, and Kwak 2019) for weakly-supervised
learning on each sub-collection species to show the segmentation results. All
the models were trained on training set for 300 epochs using a single Nvidia
A100 GPU. For each sub-collection, the model performing best on the validation
set will be used to evaluate the segmentation performance on the test set. The
Intersection-Over-Union (IoU) and F1 score were calculated as evaluation
metrics. More details about training can be found in the appendix D.

Table 3 shows the F1 and IoU scores for each sub-collection. In general, the
dataset is quite challenging as the supervised model got around 35% average
IoU for all species. This dataset is even more challenging for CAM-based
weakly-supervised model since the CAM methods focus on the most different
parts in the images which could be complicated soil conditions underground
instead of roots when roots are rare and sparse. In addition, the number of
root pixels and the number of soil pixels are highly imbalanced resulting in
the fact that model could be easily biased towards soil features instead of
root features. Some species, such as cotton and sunflower, have relative less
images having roots compared with other species. With these facts, we believe
this dataset can be helpful for researchers to build and develop more robust
and advanced algorithms for automatic root segmentation tasks.

Species-DPI | U-net | IRNet
---|---|---
| IoU | F1 | IoU | F1
Cotton-150 | 4.8% | 0.092 | 0.8% | 0.016
Papaya-150 | 56.0% | 0.718 | 14.4% | 0.252
Peanut-150 | 36.8% | 0.538 | 2.6% | 0.055
Peanut-120 | 61.9% | 0.765 | 10.6% | 0.192
Sesame-150 | 20.6% | 0.341 | 4.4% | 0.084
Sesame-120 | 25.9% | 0.411 | 7.2% | 0.134
Sunflower-120 | 29.7% | 0.458 | 2.3% | 0.045
Switchgrass-300 | 40.2% | 0.574 | 2.2% | 0.043
Table 3: The IoU and F1 scores for each species in PRMI dataset.

## Conclusion

In this work, we present PRMI, a large-scale dataset of diverse plant root
images captured by MR technology across different species in a variety of
conditions. This dataset is very well suited to study supervised/weakly-
supervised semantic segmentation, transfer learning, one- or few-shot
learning, and data distribution shifts. Through this work, we hope the PRMI
dataset can bring more attention of computer vision community to this problem
domain and facilitate the research of weak-learning mechanisms and/or
transfer-learning mechanisms that can be applied with very limited data and
significant changes to the data distribution.

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##  Appendix A Appendix A: Image Collection

Although all the root images of different species were collected by MR
technology, the specifics and characteristics of the MR images were different
for each sub-collection. For each species, root images were captured from
multiple plants and multiple MR tubes across a variety of depths over
different time periods and varying soil and environmental conditions. For each
species, there were images containing plant roots as well as images containing
purely soil and background. To help better understand the varieties of root
images as well as different soil background, some example images for each
species are shown in the Figure 3. The top three rows show the images
containing roots, and the bottom three rows show non-root images with
different soil types and other background components (e.g., water bubbles and
condensation).

Different from other species, the raw switchgrass images were captured by a
high-resolution camera with a resolution of $2550\times 2160$. Due to the
drastically large size compared to the other sub-collections, we divided each
image into 15 sub-images of size $510\times 720$ without overlap. The row
index and column index for each sub-image are saved in both image names and
the image-level labels such that the original high-resolution images can be
reconstructed if needed. After dividing, the switchgrass sub-collection has
3465 sub-images with roots, 9072 sub-images without roots, resulting in a
total of 12,537 sub-images in total.

In addition, all of the images other than switchgrass were saved in JEPG
format and named using the following convention:
Species_tube_depth_date_time_location_DPI. For switchgrass images, all the
images were saved in PNG format and named using the following convention:
Species_tube_depth_date_time_location_DPI_row-index_column-index.

##  Appendix B Appendix B: Image Annotation

### Image-level Annotation

We provided meta-data for each image including crop species, collection
location, MR tube number, collection time, collection depth, and sensor DPI.
The image-level annotations are provided in a JavaScript Object Notation
(JSON) file with the following format:

  1. 1.

image_name (str): full name of MR image file with the data format extension

  2. 2.

crop (str): plant species of the MR image

  3. 3.

has_root (int): flag for whether image has roots (0 does not contain roots, 1
contains roots)

  4. 4.

binary_mask (str): variable indicating whether the image has a corresponding
pixel-level root segmentation mask. If so, the value is the full name of the
corresponding pixel-level segmentation mask. Otherwise, the value is ‘N/A’.

  5. 5.

location (str): abbreviation of the location where the image was collected

  6. 6.

tube_num (str): MR tube number where the image was collected

  7. 7.

date (str): date (Year-Month-Day) when the image was collected

  8. 8.

depth (str): depth at which the was image collected

  9. 9.

dpi (str): DPI of the collected image

In addition to the above, switchgrass MR annotations also contain the
following:

  10. 10.

row_idx (str): the row index of the image in the original spanning image

  11. 11.

col_idx (str): the column index of the image in the original spanning image

### Pixel-level Annotation for Switchgrass

The switchgrass dataset can be divided into three components: (a) 8625 images
only paired with image-level annotation (no pixel-level annotation masks); (b)
600 images paired with image-level and pixel-level annotation generated
manually by technicians; and (c) 3312 images paired with image-level and
pixel-level annotation which were generated by technicians refining the
segmentation results of a pre-trained U-net (Ronneberger, Fischer, and Brox
2015). The annotation methods for (b) and (c) are described below:

(b) Manual annotation by technicians for switchgrass MR images: The raw
switchgrass MR spanning images each have a size of $2550\times 2160$. Given
the fine, narrow switchgrass roots and the size of these images, it is
extremely time-consuming to manually annotate each pixel. To improve the
efficiency of the annotation process, we ran the Simple Linear Iterative
Clustering (SLIC) algorithm (Achanta et al. 2010) on raw images to segment
images into superpixels by clustering spatially-contiguous pixels into groups
according to color. Then, the technicians annotated the imagery on a
superpixel level such that all the pixels belonging to the same superpixel
share the same label. The fine roots are challenging to accurately delineate
and over-segment using SLIC due to their small size and, often, similarity in
color to the background. Thus, after annotating images on the superpixel
level, the technicians refined the masks by manually fine-tuned the labels on
a pixel-level for missing or inaccurate roots and root edges. This dataset
contains 600 switchgrass MR root images annotated using this method. Examples
of these switchgrass images and the corresponding manually annotated masks are
shown in Figure 5 (a) and (b), respectively.

(c) AI prediction aided annotation for switchgrass MR images: To further
improve the annotation efficiency, we also explored the possibility of using
the prediction results of a pre-trained U-net. Specifically, we used a U-net
model pre-trained on a large peanut root dataset and fine-tuned on a limited
switchgrass root dataset (Xu et al. 2020) to generate predicted segmentation
masks for cropped switchgrass images. Then, technicians refined the predicted
segmentation masks by manually adding or deleting the roots on the pixel-
level. There are 3312 switchgrass root MR images annotated using this method.
Examples of a spanning switchgrass image, the predicted segmentation mask
generated by U-net, and technician refined U-net-predicted mask are shown in
Figure 5 (c), (d) and (e), respectively.

##  Appendix C Appendix C: Intended Use of the Dataset

Supervised root segmentation. Semantic segmentation of plant roots from the
background is the first step before any further MR analysis. Generally,
training images with pixel-level annotation are required for this task.
Several models (e.g., fully convolutional networks(Long, Shelhamer, and
Darrell 2015), SegNet(Badrinarayanan, Kendall, and Cipolla 2015),
U-net(Ronneberger, Fischer, and Brox 2015), and DeepLab(Chen et al. 2018b))
have achieved success in segmentation of plant roots and leaves(Chen et al.
2018a; Zhu et al. 2018; Yu et al. 2020b, a). With this dataset, we expect to
boost the research of more advanced models and algorithms for plant root
segmentation applications given pixel-level labeled training data.

Weakly-supervised root segmentation. Generating pixel-level ground truth masks
for MR imagery is incredibly time-consuming and tedious. Thus, effort in
weakly-supervised semantic segmentation in which only image-level labels are
used to train a model would greatly boost MR segmentation efforts. Instead of
requiring a significant effort of labeling MR imagery for every new field and
plant species (with varying soil and root properties), images (or sub-images)
could be much more efficiently labeled with image-level labels.

Segmentation across location and species. Several MR segmentation approaches
have been developed in the literature. However, each of the approaches needs
to be re-trained to achieve adequate performance on any new plant species or
new location with different soil properties. One use of this dataset is to
develop approaches that can be effectively and efficiently transferred to new
locations and species.

Root feature analysis. For each species, we collected images at a different
depth, location over a period of time to capture the growth process of the
plant root system. The collection location, depth, and time information are
saved in the image-level label for each image. Root features such as root
color, root thickness, root length, root surface area, and the number of fine
roots, etc. can be extracted from root imagery. Given a specific location and
depth, the changes of young roots to old roots were recorded over time. This
dataset can be used in the time-series analysis of these root features, which
is valuable to identify the relationship between root age and root features.
The depth information plays an important role in terms of the structure of the
whole root system. This dataset can also be used for root alignment
applications to reconstruct the root system by combining imagery from a
different depth. Finally, this dataset covers $6$ different species. Comparing
and characterizing the root system across species can also be studied using
this dataset.

##  Appendix D Appendix D: Training Setup

We used U-net based model (Xu et al. 2020) and IRNet (Ahn, Cho, and Kwak 2019)
to benchmark the dataset for supervised learning and weakly-supervised
learning, respectively. The architecture of U-net model has five convolutional
blocks in encoder and four trans-convolutional blocks in decoder. The details
of architecture can be found in (Xu et al. 2020). Adamax optimizer was used
with learning rate 1e-4 and weight decay 5e-4. Binary cross-entropy loss was
used to calculate loss between predicted segmentation masks and ground truth
masks. The models are trained on suggested training set for 300 epochs. For
weakly-supervised learning using IRNet, we first trained the CAM step
(ResNet50 backbone) on training set using image-level label to classify the
root images vs. non-root images. We followed the training strategies in (Ahn,
Cho, and Kwak 2019). The pseudo ground truth masks are generated for both
training set and validation set by thresholding (0.9 as shown in (Yu et al.
2020b)) the attention map. Then, the U-net model were training on these pseudo
binary masks using the same training setup as the supervised learning. The
model with the smallest error on the validation set will be used to evaluate
the segmentation performance on test set.

(a) Cotton

(b) Papaya

(c) Peanut

(d) Sesame

(e) Sunflower

(f) Switchgrass

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

(t)

(u)

(v)

(w)

(x)

(y)

(z)

(aa)

(ab)

(ac)

(ad)

(ae)

(af)

(ag)

(ah)

(ai)

(aj)

Figure 3: Examples of selected raw root MR images for each species. (a)
Cotton, (b) Papaya, (c) Peanut, (d) Sesame, (e) Sunflower, and (f) Switchgrass
(rotated by $90^{\circ}$). Rows 1-3 show the images have roots and rows 4-6
show the images have no roots (only soil background).

(a) Cotton

(b) Papaya

(c) Peanut

(d) Sesame

(e) Sunflower

(f)

(g)

(h)

(i)

(j)

Figure 4: Examples of selected raw root MR images (top row) and manually
annotated ground truth masks (bot row) using WinRHIZO Tron software.

(a) Spanning Switchgrass Image

(b) Manually Annotated Mask

(c) Spanning Switchgrass Image

(d) U-net Predicted Mask

(e) Technician Refined Mask

Figure 5: Examples switchgrass root MR images and corresponding annotated
masks: (a) witchgrass MR image, (b) manually annotated ground truth masks, (c)
switchgrass MR image, (d) predicted segmentation masks generated by pre-
trained U-net, and (e) technician refined U-net-predicted mask. In (c), black
roots are unchanged, blue roots were added by the technician, and red roots
were deleted.


# Frequency conversion to the telecom O-band using pressurized hydrogen

Anica Hamer  Physikalisches Institut, Rheinische Friedrich-Wilhelms-
Universität Bonn, Bonn, Germany  Seyed Mahdi Razavi Tabar  Physikalisches
Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany
Priyanka Yashwantrao  Physikalisches Institut, Rheinische Friedrich-Wilhelms-
Universität Bonn, Bonn, Germany  Alireza Aghababaei  Physikalisches Institut,
Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany  Frank Vewinger
Institut für Angewandte Physik, Rheinische Friedrich-Wilhelms-Universität
Bonn, Bonn, Germany  Simon Stellmer<EMAIL_ADDRESS>Physikalisches
Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany

(December 23, 2023)

###### Abstract

Large-scale quantum networks rely on optical fiber networks and photons as so-
called flying qubits for information transport. While dispersion and
absorption of optical fibers are minimum at the infrared telecom wavelengths,
most atomic and solid state platforms operate at visible or near-infrared
wavelengths. Quantum frequency conversion is required to bridge these two
wavelength regimes, and nonlinear crystals are currently employed for this
process. Here, we report on a novel approach of frequency conversion to the
telecom band. This interaction is based on coherent Stokes Raman scattering
(CSRS), a four-wave mixing process resonantly enhanced in a dense molecular
hydrogen gas. We show the conversion of photons from $863\text{\,}\mathrm{nm}$
to the telecom O-Band and demonstrate that the input polarization state is
preserved. This process is intrinsically broad-band and can be adapted to any
other wavelength.

##  I Introduction

For quantum computing and communication purposes, state-preserving frequency
conversion of single photons is indispensable in hybrid architecture with
optical connections [1, 2, 3, 4, 5, 6, 7]. The most widely used method of
quantum frequency conversion is based on the $\chi^{2}$ nonlinearity of
crystals [1, 2, 4, 5, 6]. This approach has been developed towards near-unit
conversion efficiency and a drastically reduced incoherent background. In
related work, the $\chi^{3}$ nonlinearity of atomic gases has also been
employed in combination with short-pulse lasers [8, 9, 10].

Still, this crystal-based approach comes with a range of limitations,
including very narrow bandwidth, polarization-dependence of the conversion
process, crystal absorption, and inevitable background emission.

In recent work, a new approach to frequency conversion based on resonantly
enhanced nonlinear interaction in pressurized diatomic gases [7, 11] has been
demonstrated, based on a coherent anti-Stokes Raman scattering (CARS) “up-
conversion" process in the UV spectral range. It was shown that this process
is well suitable for single photon conversion in quantum information
processing due to its intrinsically broad bandwidth and insensitivity to the
input polarization. Furthermore, it is free of absorption losses, degradation,
or power limitations. A wide selection of molecules, isotopic compositions,
and transitions allows to cover a wide range of wavelengths.

Here, we present the extension of previous work to the corresponding
"upconversion" process, known as coherent Stokes Raman scattering (CSRS) [12],
which also relies on a four-wave mixing process that is resonantly enhanced in
the vicinity of a vibrational transition in a molecule.

In this letter, we demonstrate conversion from $863\text{\,}\mathrm{nm}$ to
$1346\text{\,}\mathrm{nm}$. These wavelengths are intentionally chosen to
prepare for the conversion of the two entangled photons of the biexciton
emission of indium arsenide (InAs)/gallium arsenide (GaAs) quantum dots [13,
14, 15, 16] to the telecom O-band. This band includes the zero crossing of the
dispersion in optical fibers and thus provides minimal signal distortion [17].
Connecting well-established solid-state platforms to optical fiber networks
paves the way towards long-distance quantum communication [18].

Figure 1: Experimental setup, showing the pump fields at
$1538\text{\,}\mathrm{nm}$ and $938\text{\,}\mathrm{nm}$ being overlapped with
the signal input at $863\text{\,}\mathrm{nm}$ via dichroic mirrors (DM) and
focused into the hydrogen cell. After the cell the input light and the
converted light are again separated via dichroic mirrors. The converted light
of $635\text{\,}\mathrm{nm}$ can be detected with one photomultiplier tube
(PMT) in the visible range and two avalanche photon detectors (APDs) in the
infrared. For the $1346\text{\,}\mathrm{nm}$ the combined PBS and APDs setup
allow for polarization-sensitive detection of the converted photons. The two
different coherent Raman scattering processes are shown schematically.

##  II Experimental setup

The concept of the experiment is shown in Fig. 1. The frequency conversion
process is based on two pump fields whose frequency difference at matched to
the vibrational level at $124\text{\,}\mathrm{THz}$ within the $Q_{1}(1)$
branch of molecular hydrogen. Here, the wavelengths of the two pump fields are
chosen to be $938\text{\,}\mathrm{nm}$ and $1538\text{\,}\mathrm{nm}$.

The $938\text{\,}\mathrm{nm}$ laser is an amplified diode laser and provides
$0.65\text{\,}\mathrm{W}$ to the experiment. The other pump laser at
$1538\text{\,}\mathrm{nm}$ is a diode laser, boosted to
$15\text{\,}\mathrm{W}$ through a fiber amplifier. These two lasers are
stabilized at the MHz-level by a wavelength meter.

The signal photons are derived from a diode laser operated near
$863\text{\,}\mathrm{nm}$ and attenuated to a typical power of a few
$\mathrm{\SIUnitSymbolMicro W}$. This wavelength is chosen to coincide with
the emission of InAs/GaAs quantum dots. The beams are overlapped using
dichroic mirrors, and focussed to waists of
$80\text{\,}\mathrm{\SIUnitSymbolMicro m}$ within the hydrogen cell. The beam
powers are monitored, and the polarization of the beams can be set
individually.

Our hydrogen cell is a home-built, cylindrical high-pressure vessel made from
stainless steel that can stand a pressure of up to $60\text{\,}\mathrm{bar}$.
The cell has a $12\text{\,}\mathrm{mm}$ bore and a length of
$140\text{\,}\mathrm{mm}$ and is capped by two uncoated sapphire windows.

Behind the cell, the converted photons at $635\text{\,}\mathrm{nm}$ and
$1346\text{\,}\mathrm{nm}$ are separated using dichroic mirrors from the pump
and signal light. Bandpass filters ($10\text{\,}\mathrm{nm}$ width and
$93\text{\,}\mathrm{\char 37\relax}$ transmission) provide further spectral
purification.

Photons converted to $1346\text{\,}\mathrm{nm}$ pass through a polarizing
beamsplitter (PBS) and are detected by two avalanche photodiodes (APD, ID Qube
NIR, dead time $100\text{\,}\mathrm{ns}$) with a quantum efficiency of
$12.5\text{\,}\mathrm{\char 37\relax}$. Photons at $635\text{\,}\mathrm{nm}$
follow a different path and are detected by a photomultiplier tube (PMT,
Hamamatsu model H10682-210) with a quantum efficiency of
$4.5\text{\,}\mathrm{\char 37\relax}$. Corresponding photon count rates are
measured with a single-photon counting module with a dead time of
$6\text{\,}\mathrm{ns}$.

##  III Frequency Conversion

###  III.1 Resonance

We scan the relative detuning of the pump fields around the molecular
resonance and observe frequency conversion simultaneously through the CRSR
process at $1346\text{\,}\mathrm{nm}$ and through the CARS process at
$635\text{\,}\mathrm{nm}$. Resonance lineshapes and efficiencies depend
strongly on the hydrogen pressure; see Fig. 2. By fitting resonances with
Lorentzian curves we obtain the pressure-dependent center positions and widths
are given in Fig. 3.

Figure 2: Pressure-dependence of the CSRS process (conversion to
$635\text{\,}\mathrm{nm}$, top) and of the CARS process (to
$1346\text{\,}\mathrm{nm}$, bottom) near the $Q_{1}(1)$ transition around
$124\text{\,}\mathrm{THz}$. Figure 3: Interpolation of the extracted center
positions of the Lorentzian curves depending on the pressure and separated for
the two frequency-converted wavelengths.

From our data, we derive a pressure (collisonal) shift of d$\nu$/dP =
$-94(1)\text{\,}\mathrm{M}\mathrm{Hz}\mathrm{/}\mathrm{bar}$ for the CARS
process and $-93(1)\text{\,}\mathrm{M}\mathrm{Hz}\mathrm{/}\mathrm{bar}$ for
the CSRS process, which are in the interval of all measured data sets reported
earlier [19, 20]. The uncertainty is entirely dominated in the uncertainty of
the pressure gauge. Extrapolating the curves to zero pressure gives an
unperturbed resonance frequency of $\nu(0)$ =
$124.571\,257(2)\text{\,}\mathrm{THz}$ (CARS) and $\nu(0)$ =
$124.571\,304(2)\text{\,}\mathrm{THz}$ (CSRS), in agreement with earlier data
[20]. Here, the uncertainty is dominated by the accuracy of the wavelength
meter.

Even for the smallest pressures evaluated here, the linewidth of the
unperturbed molecular resonance is narrowed dramatically through the Dicke
effect [19]. For pressures above about 1 bar, the linewidth increases
approximately linearly through density (pressure) broadening. The data shown
in Fig. 3 is approximated by the model described in Ref. [19] and yields a
pressure-dependent linewidth of
$42.7(5)\text{\,}\mathrm{MHz}\text{\,}{\mathrm{bar}}^{-1}$ for the CARS
process and $46.9(5)\text{\,}\mathrm{MHz}\text{\,}{\mathrm{bar}}^{-1}$ for the
CSRS process, compatible with earlier studies [19, 21].

###  III.2 Efficiency

As shown already in Fig. 2, the conversion efficiency is pressure-dependent.
This dependence is shown in Fig. 4. In the CARS process to
$635\text{\,}\mathrm{nm}$, a clear maximum near $8.0(2)\text{\,}\mathrm{bar}$
can be observed. For our experimental parameters stated above, the internal
conversion efficiency is $8.1\text{\times}{10}^{-10}\text{\,}$ and reduces to
an external efficiency of $1.5\text{\times}{10}^{-11}\text{\,}$, which takes
into account the transmission losses of the optics and the
$4.5\text{\,}\mathrm{\char 37\relax}$ efficiency of the detector.

The behaviour of the CSRS process to $1346\text{\,}\mathrm{nm}$ is strikingly
different. The efficiency does not show a pronounced maximum, but oscillates
around an internal efficiency of about $1.1\text{\times}{10}^{-9}\text{\,}$
for a pressure between about 5 and $20\text{\,}\mathrm{bar}$ (external
efficiency: $9.0\text{\times}{10}^{-11}\text{\,}$). We attribute the
oscillations to fluctuations in the experimental parameters during the
measurements, a behaviour we have already observed earlier, as each data point
corresponds to a measurement time of $2\text{\,}\mathrm{min}$ [11].

The noise level, i.e., the rate of undesired background photons originating
from the interaction of the pump fields, is compatible with zero within our
experimental uncertainty.

Figure 4: Conversion efficiency depending on the pressure of the hydrogen gas
based on the the phase mismatch between the light fields. The data is
normalized to its maximum value.

###  III.3 Preservation of polarization

Quantum frequency conversion requires a faithful preservation of the initial
photon state, namely its polarization. In contrast to a crystal, the hydrogen
gas itself is isotropic, and the reference frame is set by the light field. To
test the preservation of polarization, the output state is read out for two
polarization bases, namely linear and circular.

As the preservation of polarization in CARS processes has already been shown
[11], we only investigate the CSRS process here. The detection unit involves
waveplates at $1346\text{\,}\mathrm{nm}$, a polarization beamsplitter (PBS),
and detectors on the two outputs.

####  III.3.1 Linear polarization

Figure 5: Normalized measurement of the Stokes parameter set of linear and
diagonal with the highest values per each detector. Fitted via two sine
functions. Error bars for the y-axis are determined by the square root of the
count rate and are too small to be noticeable in this depiction.

To check for the preservation of the linear polarization, the pump
polarization is set to horizontal and the polarization of the signal photons
is rotated. The recorded polarization state of the converted photons shown in
Fig. 5 faithfully follows the input polarization.

Deviations can be attributed to imperfect waveplates and beamsplitters, as
well as leakage light from the pump fields.

####  III.3.2 Circular polarization

To check for preservation of the phase, the polarization of the signal photons
is turned from linear to circular. Correspondingly, the circularly polarized
signal photons at $1346\text{\,}\mathrm{nm}$ polarized diagonally before the
detectors.

The results are shown in Fig. 6. Again the output polarization faithfully
follows the input polarization, and the small deviations from an ideal
behaviour can be fully attributed to imperfect polarization optics.

Figure 6: Normalized measurement of the Stokes parameter set of linear and
circular with the highest values per each detector. Fitted via two sine
functions. Error bars for the y-axis are determined by the square root of the
count rate and are too small to be noticeable in this depiction.

####  III.3.3 Fidelity

We fit sine functions to the data sets presented in Figs. 5 and 6 and compute
the contrast for each measurement. The contrast for these four data sets
ranges between 79.1% and 99.3% and is limited by the background signal and
imperfect polarization optics, which are different for the two detectors and
which we do not correct for. Here, we determine the fidelity as the average of
the four contrast values and arrive at a fidelity of 0.904.

##  IV Conclusion

In this work, we have further developed our novel approach to frequency
conversion. While our previous work focused on a CARS process in the UV range
[11], we here presented a study on a CSRS process in the NIR range.

We have demonstrated frequency conversion from 863 nm to a telecom wavelength
and have shown the a photon’s polarization state is preserved. The poor
efficiency of this preliminary study can be readily increased though tighter
focusing of the beams, increase of the pump powers, and better mode overlap.
We anticipate an efficiency increase by orders of magnitude by employing
hydrogen-filled hollow-core fibers. Near-unit efficiency has recently been
shown in closely related work at comparable wavelengths [7]. Dedicated
polarization optics and improved spectral filters will reduce the background
and thereby increase the process fidelity.

##  V backmatter

###  V.1 Funding

We acknowledge funding by Deutsche Forschungsgemeinschaft DFG through grant
INST 217/978-1 FUGG and through the Cluster of Excellence ML4Q (EXC 2004/1 –
390534769), as well as funding by BMBF through the QuantERA project
QuantumGuide.

###  V.2 Acknowledgments

We thank all members of the Cluster of Excellence ML4Q, as well as Michael
Frosz from the MPI for the Science of Light, for stimulating discussions.

###  V.3 Data Availability Statement

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

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