# Automatic Head Overcoat Thickness Measure with NASNet-Large-Decoder Net

Youshan Zhang, Brian D. Davison
Lehigh University
{yoz217<EMAIL_ADDRESS>Vivien W. Talghader, Zhiyu Chen, Zhiyong Xiao, Gary
J. Kunkel
Seagate Technology
{vivien.w.talghader, zhiyu.chen, zhiyong.x.xiao<EMAIL_ADDRESS>
###### Abstract

Transmission electron microscopy (TEM) is one of the primary tools to show
microstructural characterization of materials as well as film thickness.
However, manual determination of film thickness from TEM images is time-
consuming as well as subjective, especially when the films in question are
very thin and the need for measurement precision is very high. Such is the
case for head overcoat (HOC) thickness measurements in the magnetic hard disk
drive industry. It is therefore necessary to develop software to automatically
measure HOC thickness. In this paper, for the first time, we propose a HOC
layer segmentation method using NASNet-Large as an encoder and then followed
by a decoder architecture, which is one of the most commonly used
architectures in deep learning for image segmentation. To further improve
segmentation results, we are the first to propose a post-processing layer to
remove irrelevant portions in the segmentation result. To measure the
thickness of the segmented HOC layer, we propose a regressive convolutional
neural network (RCNN) model as well as orthogonal thickness calculation
methods. Experimental results demonstrate a higher dice score for our model
which has lower mean squared error and outperforms current state-of-the-art
manual measurement.

##  1 Introduction

Transmission electron microscopy (TEM) is a microscopy technique in which a
beam of electrons is transmitted through a specimen to form an image. TEM is
one of the premier tools to show microstructural characterization of materials
[6]. Differences in material density show up as contrast in a TEM image.

The hard disk drive industry uses TEM to measure head overcoat (HOC) thickness
on magnetic recording heads. In a bright-field TEM image, HOC appears as a
white layer sandwiched between two darker layers, a magnetic metal layer that
is part of the recording head and a capping layer deposited as part of TEM
sample preparation. This is because the HOC is comprised predominantly of
Diamond-like Carbon (DLC) which has relatively low density whereas the other
two layers are of much higher density.

Current state-of-the-art HOC thickness is sub-50A and its accurate and precise
measurement is critical for deposition process feedback since HOC thickness
has a direct impact on magnetic recording performance. There is currently no
automatic method to calculate the thickness of HOC from a TEM image, and
manual calculation is time-consuming and highly subjective. Therefore, there
is an industrial need to develop an efficient algorithm that can automatically
measure HOC thickness.

There are several issues in need of resolution to automatically measure the
HOC layer thickness. We do not have segmentation masks already defined for
HOC, and there is no standard rule to define the thickness of the HOC
layer—the boundary between the HOC layer and the sandwiching layers can be
fuzzy, making it challenging to consistently discern, whether by the same
operator or different operators. However, even if we have a clear mask of the
HOC layer, it is still difficult to determine the HOC thickness due to the
curvature and slope of the masked area. Hence, our challenges are: 1) how to
correctly generate a segmentation that separates the HOC from the surrounding
material; and, 2) how to accurately measure the thickness of the HOC layer.

Many traditional techniques have been proposed for segmentation, such as
threshold methods [21, 20, 24], region-based methods [5, 15], genetic methods
[8], level set methods [22, 13, 12] and artificial neural networks [17, 2, 1].

The threshold method is one of the most common and straightforward
segmentation methods. It is a region segmentation technique which divides gray
values into two or more gray intervals, and chooses one or more appropriate
thresholds to judge whether the region meets the threshold requirement
according to the difference between the target and the background, and
separates the background and the target to produce a binary image. Threshold
processing has two forms: global threshold and adaptive threshold. The global
threshold only sets one threshold, and the adaptive threshold sets multiple
thresholds. The target and background regions are segmented by determining the
threshold at the peak and valley of the gray histogram [10, 16]. Level set
methods are also widely used in the segmentation task. The basic idea of the
level set method for image segmentation is the continuous evolution of curve
motion. The boundary of the image is searched until the target contour is
found and then the moving curve is stopped. Curves are moved along every
three-dimensional section of images to slice different levels of the three-
dimensional surface. The level of the obtained closed curves of each layer
change over time, and finally get a corresponding shape extraction contour
[22]. In our tasks, the brightness is not consistent from image to image.
Therefore, the performance of traditional threshold-based and level-set based
methods are not good.

Deep neural networks have also been applied in segmentation and they supersede
many traditional image segmentation approaches. Garcia et al. presents an
overview of deep learning-based segmentation methods [7]. There are several
models to address the segmentation task. Fully convolutional networks (FCN)
[14] is one of the earliest approaches for deep learning-based image
segmentation which performs end-to-end segmentation. FCN is a type of
convolutional network for dense prediction that does not require an additional
fully connected layer. This method leads to the possibility of segmenting
images of any size effectively, and it is much faster than the patch
classification method (which divides images into several patches). Almost all
of the other more advanced methods follow this architecture. However, there
are several limitations of the FCN model, such as the inherent spatial
invariance causes the model to fail to take into account useful global context
information and its efficiency in high-resolution scenarios is worse and not
available for real-time segmentation. Another difficulty of using CNN networks
in segmentation is the existence of pooling layers. The pooling layer not only
enlarges the sensing field of the upper convolution layer but also aggregates
the background and discards part of the location information. However, the
semantic segmentation method needs to adjust the category map accurately, so
it needs to retain the location information abandoned in the pooling layer.

Later the encoder-decoder architecture becomes widely used in segmentation.
Segnet [3] and U-net [18] are representative encoder-decoder architectures.
This architecture first selects a classification network such as VGG-16, and
then removes its full connection layer to produce a low-resolution image
representation or feature mapping. This part of the segmentation network is
usually called an encoder. A decoder is a complementary part of the network
that learns how to decode or map these low-resolution images to the prediction
at the pixel level. The difference between different encoder-decoder
architectures is the design of the decoder. U-net uses a structure called
dilated convolutions and removes the pooling layer structure. Chen et al. [4]
proposed the Deeplab model, which used dilated convolutions and fully
connected conditional random field to implement the atrous spatial pyramid
pooling (ASPP), which is an atrous version of SPP [9] and can account for
different object scales and improve the accuracy.

After getting the segmented HOC layer from a segmentation network, we need to
predict the thickness of the HOC layer. Thickness measurement is a regression
problem, and deep networks have been developed to solve such tasks. Kang et
al. [11] proposed a convolutional neural network for estimating image quality,
but its architecture is simple, consisting of max pooling and two dense
layers. Zhang et al. [25] proposed a regressive neural network for electricity
prediction, but the input is a vector, not images. Rothe et al. [19] proposed
a regressive VGG-16 network for age prediction. However, a complex neural
network may not solve the problem due to overfitting, since the input to the
neural network here is the segmented HOC layer. Therefore, it is necessary to
design a robust regression convolutional neural network model for predicting
the thickness of the HOC layer.

Figure 1: The architecture of our NASNet-Large segmentation network. The
Encoder consists of the first 414 layers from NASNet-Large model. There are
four blocks in the decoder, and each block contains Upsampling, Conv+ReLu, and
BN layers. (Convolution (Conv), Batch normalization (BN), Rectified linear
units (ReLU).) The final decoder is fed into a softmax layer for HOC layer
prediction.

Our contributions are three-fold:

  1. 1.

We are the first to define a NASNet-Large-decoder network to segment TEM head
overcoat images;

  2. 2.

To remove irrelevant small segments, we are the first to propose a post-
processing layer which is able to filter out false segmented sections in
prediction images; and,

  3. 3.

We propose an orthogonal calculation method and a regressive convolutional
neural network to predict the thickness of the segmented head overcoat layer.
Experimental results demonstrate that the proposed model achieves the highest
dice and IoU score versus state-of-the-art methods.

This paper is organized as follows: in Sec. 2, the NASNet-Large-decoder
network, orthogonal distance calculation and regressive networks are
summarized; we present the segmentation results and the predicted thickness in
Sec. 3; in Sec. 4, we discuss the advantages and disadvantage of proposed
model and conclude in Sec. 5.

##  2 Methods

In this section, we first introduce the network to segment the TEM HOC images
and then describe the regressive network and concept of an orthogonal distance
to calculate the thickness of segmented HOC images.

###  2.1 NASNet-Large segmentation network

The NASNet-Large segmentation network contains an encoder and a decoder, which
is followed by a classification layer. The architecture is shown in Fig. 1.
There are two significant differences in our model comparing with Segnet,
which employs the pre-trained VGG16 network for the encoder. Our Nasnet-Large-
decoder net uses the first 414 layers of Nasnet-Large net (which is a network
well-trained for ImageNet classification) as the encoder to decompose images
[26]. We choose the first 414 layers because the size of the final layer is
close to the size of the original image, so it will not lose much information.
If we choose the last layer as the feature extraction layer, it will destroy
significant structural information of objects since the last layer will be
more suitable for classification, rather than segmentation. We do not use the
pre-trained weights but retrain the net using new data to fit Nasnet-Large in
our experiment since our dataset is significantly different from ImageNet. In
addition, the decoder is different and there are no pooling indices in our
model since Nasnet-Large net can produce detailed information for the decoder.

An appropriate decoder can upsample its input feature map using the max-
pooling layer. The decoding technique is illustrated in Fig. 1. There are four
blocks in the decoder. Each block begins with upsampling which can expand the
feature map, followed by convolution and rectified linear units. A batch
normalization layer is then applied to each of these maps. The first decoder,
which is closest to the last encoder can produce a multi-channel feature map.
This is similar to Segnet, which can generate a different number of sizes and
channels as their encoder inputs. The final output of the last decoder layer
is fed to a trainable soft-max classifier which produces a $K$ channel image
of probabilities where $K$ is the number of classes (two in our problem). The
predicted segmentation corresponds to the class with maximum probability at
each pixel.

###  2.2 Orthogonal calculation of HOC thickness

The current measurement technique for HOC layer thickness is a manually
labeled image with three lines as shown in Fig. 3. From the lengths of the
three lines, we calculate the mean thickness and standard deviation of the HOC
layer. However, there are two obvious shortcomings of this method. One is that
it only measures three lines, not all lines of the HOC layer. Secondly, the
three lines are horizontal, which may not measure the orthogonal distance of
HOC layer. If there is a slope in the HOC layer, the horizontal three-line
mean will produce a larger distance than the real thickness. Therefore, to
calculate thickness of the segmented HOC layer from Sec. 2.1, and capture the
physical meaning of the measurement, we also propose to calculate an
orthogonal distance. We need to give a formal definition of thickness of the
HOC layer. As shown in Fig. 4, ten black lines sample the thickness of the HOC
layer, and are perpendicular to the middle regression line. There are more
than one hundred orthogonal lines in the segmented HOC mask (i.e., one at each
pixel); we only show ten of them. The thickness of HOC is defined as the mean
of all lines which are perpendicular to middle regression line. The standard
deviation (SD) represents the variation in thickness across all orthogonal
lines.

Figure 2: The architecture of the thickness regression network. The input is
from the NASNet-Large segmentation network. The thickness regression network
primarily consists of two blocks, and each block includes Conv + ReLU and
Dropout layers. It is then followed by a Flatten layer. Finally, it ends with
a linear activation layer. The output is the thickness of the HOC layer.
Figure 3: The existing three-line thickness measurement of the HOC layer.
However, the three-line approach is manually labeled, and consists of
horizontal lines, which will overestimate the thickness if within a slope or
curve. Figure 4: The orthogonal distance of the HOC layer. Two red dashed
lines are the boundaries of the HOC layer; the middle red line consists of
midpoints of boundary points, and the blue dashed line is the regression line.
Several black lines are the orthogonal distance of the HOC layer. Lower right
shows magnified green box.

###  2.3 Regressive thickness prediction net

However, orthogonal calculation of thickness heavily depends on the boundary
of segmented mask. To alleviate this issue, we propose a regressive CNN (RCNN)
model, which is described in Fig. 2. The input is the segmented mask from Sec.
2.1, which contains all information about the HOC layer within the images
instead of simple boundary of the image, and the output is mean thickness of
HOC layer. There are two major blocks in the RCNN model. Each of them consists
of three convolutional layers and is followed by one dropout layer. After that
a flatten layer expands all features in its front dropout layer into a vector.
Two dense and activation layers follow. The regression network ends with a
linear activation to predict the thickness of the HOC layer. During the
training stage of the RCNN model, the labeled thickness is from the proposed
orthogonal calculation method.

There are two advantages of our RCNN model. First, the RCNN model is not
complex and easy to train. If the architecture is too complex, it may lead to
an overfitting problem. One reason is the input is the segmented HOC layer,
which does not contain too much information. Hence, a complex neural network
is unnecessary. Another advantage of the RCNN model is that it can give a
prediction with less error. In the training stage, the RCNN model is fed with
the segmented mask and outputs orthogonal calculation distance. The loss
function is mean squared error (MSE), which is defined in Eq. 1.

$\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(Y_{i}-\hat{Y_{i}})^{2},$ (1)

where $Y_{i}$ is the prediction value, and $\hat{Y_{i}}$ is the orthogonal
distance measurement as shown in Sec. 2.2. Therefore, we minimize the error
between orthogonal distance using the predicted HOC mask and the orthogonal
thickness. This further drives the prediction mean thickness to be close to
the orthogonal thickness.

Unfortunately, a deep network is often difficult to trust given its opacity.
Domain experts prefer a clear measurement. However, the proposed RCNN model
can be validated, if needed, by the orthogonal calculation.

##  3 Results

###  3.1 Datasets

Our modeling was trained with data, that are collected from three different
dates, differing in the composition of the HOC material. Due to a limited
sample size of 364 images, we use five-fold cross-validation to estimate the
performance of our model. We normalize pixel values of the image into a scale
between 0 and 1. Since we do not have ground truth for the mask of HOC layer,
the TEM image was first marked by an expert using thickness measurement
software (an internally developed package based on Zhang et al. [23]) to
manually segment the mask and output rough thickness. Fig. 5 shows four TEM
images with their corresponding segmentation labels. The middle two examples
in Fig. 5 cause difficulty with the HOC layer segmentation; there is a FOV
(field of view) sticker in the third image, and there is an extra horizontal
layer in the fourth image. Due to these reasons, the traditional threshold-
based methods failed in segmenting these three images.

Our experiments are implemented within Keras, and our network was trained on
an NVIDIA TITAN XP equipped with 12 GB of memory in order to exploit its
computational speed. The network parameters were set to: Batch size: 4, Step
size: 5, Number of epochs: 1000.

Figure 5: Four TEM HOC images and their corresponding HOC segmentations.

###  3.2 Segmentation results visualization

Fig. 6 compares the predicted segmented HOC image with the ground truth image
in the test dataset. The prediction image is close to the real mask, which
qualitatively demonstrates the high performance of our model.

Figure 6: Ground truth vs. prediction results. The first row is the ground
truth mask overlay with the raw image, and the second row is the prediction
result overlaid with the raw image.

###  3.3 Post-processing layer

However, there are some areas in the image which are not the true HOC layer in
the prediction result. We then propose a post-processing layer, which can
filter the irrelevant parts of the prediction. The first step of post-
processing layer is to classify the predicted image into several parts111The
major step of post-processing step is using the connectedComponentsWithStats
function in OpenCV., and we then simply select the largest areas (the HOC
area) as the final segmented HOC layer. As shown in the left image in Fig. 7,
the red box highlights erroneous predictions of the image (false negatives).
After post-processing, the red box is removed. Therefore, the prediction
result can be improved if we filter out such irrelevant parts.

Figure 7: The post-processing of prediction result. On the left is the
prediction result from the proposed network, and on the right is the result
after using our post-processing layer. The red box outlines an irrelevant
feature. Figure 8: Sample output image. Left: the predicted result of our
model; right: the original image. The segmented mask is perfectly overlapped
with the original image (MT: mean thickness, SD: standard deviation).

###  3.4 Metrics

To evaluate the performance of our NASNet-Large segmentation network, we use
the widely-used Dice coefficient index to indicate the goodness of the
segmentation results. Furthermore, we also report the IoU score. The two
metrics are defined in the following formulas:

$Dice=2\times\frac{|A\cap B|}{|A|+|B|},\ \ \ IoU=\frac{|A\cap B|}{|A\cup B|},$

where $A$ is ground truth mask, and $B$ is the prediction mask. We also
compare our results with performance of state-of-the-art methods.

Table 1: Five-fold cross-validation segmentation results Method | IoU | Dice score
---|---|---
U-Net | 0.80 | 0.85
Deep-Lab | 0.83 | 0.89
Segnet | 0.78 | 0.83
NastnetLarge-net | 0.86 | 0.92
NastnetLarge-net-post | 0.89 | 0.94

(a) Training with 0.0929 MSE

(b) Test with 0.0719 MSE

Figure 9: Comparison of the existing three-line method and our predication in
training and test datasets.

Tab. 1 lists the comparison results of different models (the metrics are only
reported on HOC layer and not the background area). Our NASNet-Large-Decoder
has a higher IoU and Dice score than other models. We also observe that the
method including post-processing outputs the highest scores, which illustrates
that the post-processing layer is useful in our segmentation task.

We use MSE to evaluate the performance of RCNN model and traditional
orthogonal distance calculation as defined in Eq. 1. As shown in Tab. 2, the
MSE of RCNN model is less than the other three methods, which implies that
RCNN model gives a closer prediction to orthogonal measurement than Segnet
RCNN and NASNet-Large RCNN. Differing from original Segnet and NASNet-Large
model, we replace the final softmax layer with a regressive layer to form the
Segnet RCNN and NASNet-Large RCNN model. Hence, these two models are able to
predict the thickness. Fig. 8 shows the final output of our thickness
measurement tool. The left image is the segmented HOC layer overlay with
original image, and it also shows orthogonal distance. We also add the file
name, mean thickness and standard deviation of the thickness on the top of the
image.

Table 2: Thickness prediction results comparison Methods |  MSE
---|---
Regressive CNN |  0.0089
Three-line measurement |  0.1524
Segnet RCNN |  0.1792
NASNet-Large RCNN |  0.2023

##  4 Discussion

In this section, we first analyze predicted HOC thickness and then discuss the
merits and demerits of our model.

###  4.1 Statistical analysis

(a) (2.40, 1.58)

(b) (4.29, 3.63)

Figure 10: Two outlier images, which correspond to the highlighted points in
Fig. 9(a). Labels are (X,Y) pairs. X-value is the thickness from three-line
measurement and y-value is the prediction value from orthogonal distance.
Figure 11: Linear regression fit of predicted thickness and the three -line
thickness (Different color represents data are collected from different
dates).

(a) Deep learning prediction

(b) Human measurement

Figure 12: TEM human 3-line measurement and TEM deep learning prediction
compared against measurements made with witness wafer metrology. Deep learning
prediction gives more accurate results than human three-line measurement.

As shown in Fig. 9, we compare the three-line measurements with orthogonal
distance from predicted HOC mask using linear regression in training and test
datasets, respectively. The blue dashed lines in the figure indicate the
desired line if prediction results are the same as the human three-line
measurements. The regression slope from training and test are 0.79968 and
0.99155, respectively, which demonstrate a strong linear correlation between
the human measurement and deep learning method. Especially noticable is the
test dataset, in which the prediction is almost the same as human measurement.
We also calculate the mean squared error (MSE) in Eq. 1 to indicate the error
between deep learning prediction and human measurement. Although there are
some outliers in Fig. 9(a), eg., (2.40, 1.58) and (4.29, 3.63) (the x-value is
three-line result and y-value is prediction results from our model), the
overall performance of the orthogonal measurement method is closer to human
measurement. The three-line method has a higher value than deep learning
prediction in these two off-line points. We further check the prediction mask
images of these two points as shown in Fig. 10. We observe that there is a
slope in these two prediction HOC layer. Remember, the three-line is measured
using horizontal lines, which will lead to a higher value than the real
distance if there is a slope in the boundary of mask images. However, we
calculate orthogonal distance, which represents the real thickness of the HOC
layer. Therefore, we can conclude that our method can be applied in thickness
measurements, and it will lead to better results than human three-line
measurement.

Fig. 11 describes overall performance in the training and test in terms of
three different data collection dates using the mean thickness and standard
deviation. We further compare the prediction thickness from our model and the
three-line approach with measurements made on witness wafers included in the
same HOC depositions as the product heads that were measured with TEM. The
witness wafers were measured using metrology calibrated using an amalgamation
of techniques, such as AFM (Atomic Force Microscopy), ellipsometry, and XRR
(X-Ray Reflectometry).

From Fig. 12, we can find that the deep learning-based model has slightly
worse results in sample set #1 since the slope is smaller than the three-line
measurement (0.98546 vs. 0.99119 ). However, the performance in sample set #2
is significantly higher than the three-line measurement (0.90861 vs. 0.8068).
Also, the overall prediction of our model is better than human measurement (as
shown in the green lines in Fig. 12 ). Therefore, we can conclude that our
model has a better performance than traditional manual measurement.

Figure 13: Two failures in NASNet-Large-Decoder model. The first row of image
is caused by the fuzzy boundary and the second row of image is caused by the
unusually dark HOC layer.

Although the RCNN model gives more accurate results than three-line
measurement (as shown in Tab. 2), we did not use it to predict thickness of
test datasets. The crucial reason is that customers require a comparison image
for thickness measure as shown in Fig. 8. But RCNN model cannot output images
with actual calculation of distance (i.e., cannot output an image as in the
left of Fig. 8). Hence it is not used on test datasets. However, RCNN model is
a back-up model if the orthogonal distance failed.

One of the distinct advantages of our model is that it achieves a higher Dice
and IoU score. And there are two reasons: the designed NASNet-Large
segmentation net is suitable for TEM image segmentation, and the post-
processing layer filters out the unnecessary parts in the image, which
improves the segmented results.

Although our model achieves a 0.94 Dice score, it still fails in some cases.
As shown in Fig. 13, we observe that segmentation results are worse in these
two situations. There are two reasons; one is that there is no similar image
in the training dataset, which leads to worse performance. Second is that our
model is not robust enough to deal with some unusual images. Comparing with
normal training images as shown in Fig. 5, two worse raw images (in Fig. 13)
are either too light (first row) or too dark (second row), and it is even
difficult for humans to distinguish the HOC layer and background. Also, our
model has limited sample size (less than 400 images), and so while in the
validation and test datasets the MSE is small, our model could not cover all
the cases, e.g., in Fig. 13. Therefore, including more samples in training
would help to get a more robust model. In addition, a limitation of the
NASNet-Large-Decoder network is that it needs a large memory to train the
model. Therefore, designing a more efficient architecture is a direction for
future work.

##  5 Conclusion

In this paper, we are the first to present a TEM HOC layer segmentation using
the NASNet-Large-decoder architecture, and we get an accurate segmentation
with 0.94 Dice score. A post-processing layer is employed to remove the
unnecessary part in the prediction map. We then propose an orthogonal
thickness calculation method as well as a regressive convolutional neural
network (RCNN) model to measure the thickness of the segmented HOC layer.
These advances enable manufacturers to replace a manual method with a much
more accurate automated process.

Our model can be further improved with a more robust encoder and decoder
model, to enable it to be applied in a wider variety of cases. The RCNN model
can also be enhanced by predicting both the mean thickness and the standard
deviation of the mean thickness.

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