J Infrared Milli Terahz Waves (2018) 39:561–572
https://doi.org/10.1007/s10762-018-0482-6

Real-Time Amplitude and Phase Imaging of Optically
Opaque Objects by Combining Full-Field Off-Axis
Terahertz Digital Holography with Angular
Spectrum Reconstruction
Masatomo Yamagiwa 1,2 & Takayuki Ogawa 3 &Takeo Minamikawa 1,2 & Dahi Ghareab Abdelsalam 1,2,4 &Kyosuke Okabe 5 & Noriaki Tsurumachi 5 &Yasuhiro Mizutani 2,6 & Testuo Iwata 1,2 &Hirotsugu Yamamoto 2,7 & Takeshi Yasui 1,2

Received: 13 January 2018 / Accepted: 12 March 2018 /Published online: 3 April 2018
# Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract Terahertz digital holography (THz-DH) has the potential to be used for non-destructive
inspection of visibly opaque soft materials due to its good immunity to optical scattering andabsorption. Although previous research on full-field off-axis THz-DH has usually been performed
using Fresnel diffraction reconstruction, its minimum reconstruction distance occasionally preventsa sample from being placed near a THz imager to increase the signal-to-noise ratio in the hologram.

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10762-0180482-6) contains peer-reviewed but unedited supplementary material, which is available to authorised users.

* Takeshi Yasui
yasui.takeshi@tokushima-u.ac.jp

1

Graduate School of Technology, Industrial and Social Sciences, The Tokushima University, 2-1,
Minami-Josanjima, Tokushima 770-8506, Japan

2

JST, ERATO, MINOSHIMA Intelligent Optical Synthesizer Project, 2-1, Minami-Josanjima,
Tokushima 770-8506, Japan

3

Graduate School of Advanced Technology and Science, The Tokushima University, 2-1,
Minami-Josanjima, Tokushima 770-8506, Japan

4

Engineering and Surface Metrology Lab, National Institute of Standards, Tersa St., El Haram, El
Giza 12211, Egypt

5

Faculty of Engineering, Kagawa University, 2217-20, Hayashicho, Takamatsu, Kagawa 761-0396,
Japan

6

Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan

7

Center for Optical Research and Education, Utsunomiya University, 7-1-2, Yoto, Utsunomiya,Tochigi 321-8585, Japan562

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In this article, we apply the angular spectrum method (ASM) for wavefront reconstruction in fullfiled off-axis THz-DH because ASM is more accurate at short reconstruction distances. We
demonstrate real-time phase imaging of a visibly opaque plastic sample with a phase resolution
power of λ/49 at a frame rate of 3.5 Hz in addition to real-time amplitude imaging. We also perform
digital focusing of the amplitude image for the same object with a depth selectivity of 447 μm.
Furthermore, 3D imaging of visibly opaque silicon objects was achieved with a depth precision of
1.7 μm. The demonstrated results indicate the high potential of the proposed method for in-line or inprocess non-destructive inspection of soft materials.
Keywords Terahertz . Digital holography . Phase image . Off-axis . Angular spectrum method

1 Introduction
Digital holography (DH) [1] is a technique that acquires a hologram of an object by a digital
imaging device and numerically reconstructs the optical wavefront based on the acquired
hologram to obtain both the amplitude and phase images of the sample object. Furthermore,
the phase image can be used for three-dimensional (3D) imaging of geometrical shapes or optical
thicknesses in an object with a sub-wavelength depth resolution, whereas digital focusing of theamplitude image [2] enables 3D imaging with a wavelength depth resolution over a wide
dynamic range of depths without changing the optical system. Until now, visible light has been
widely used for DH with a variety of light sources and digital imaging devices, namely, VIS-DH.
The 3D shape of a visibly transparent object can be visualized by VIS-DH in a transmission
configuration [3]. Furthermore, the VIS-DH reflection configuration enables 3D imaging of
surface shapes in a visibly opaque object [4]. Due to its real-time, quantitative, 3D-imaging
capability, VIS-DH has been widely used in various applications in science and industry.
However, if the object surface is visibly rough, strong scattering and/or phase wrapping
ambiguity will be problematic in VIS-DH. Additionally, transmission VIS-DH cannot beapplied to a visibly opaque object. If DH is performed using other electromagnetic radiation
with good immunity to optical scattering and good penetration of visibly opaque objects, theapplications of DH will be further expanded; for example, non-destructive inspection of soft
materials, such as plastics, semiconductor, ceramics, rubber, wood, and concrete, will be
realized.
One promising radiation for this purpose is terahertz (THz) radiation (freq. = 0.1~10 THz,
wavelength = 30~3000 μm) [5, 6]. Due to its existence at the boundary between optical andelectric radiation, THz radiation has both characteristics, i.e., good penetration of visibly
opaque, non-metallic materials, less scattering by visibly rough surfaces or visible scattering
objects, good beam coherence, low invasiveness, and multiple spectral fingerprints. Fortunately, the recent progress of continuous-wave (CW) THz laser sources and THz digital imagers
allows full-field DH to be easily performed in the THz region [7–16]. For example, thecombination of a gas far-infrared laser with a pyroelectric array detector was applied for
Garbor-type in-line transmission THz-DH to acquire the phase image of cancerous tissues[12]. While in-line THz-DH can be performed in a simple optical configuration without theneed of a two-arm interferometer, it is hampered by the spatial overlap of unnecessary zeroorder-diffraction-light and conjugate first-order-diffraction-light images on the necessary firstorder-diffraction-light image. To overcome this problem, off-axis full-field THz-DH [13] wasperformed in a transmission or reflection configuration using a THz quantum cascade laser

J Infrared Milli Terahz Waves (2018) 39:561–572

563(THz-QCL) [17, 18] and uncooled, bolometer-type 2D focal plane array [19]; in this case, theunnecessary zero-order-diffraction-light and conjugate first-order-diffraction-light images were
spatially separated and then filtered in the spatial frequency domain. By using the Fresnel
diffraction method (FDM) [20, 21] for the numerical reconstruction of the THz wavefront, theTHz amplitude and phase imaging of the samples was demonstrated in real time. While FDM
performs only one Fourier transform, its use is limited under certain conditions, e.g., theminimum distance (reconstruction distance z) between the object plane and the hologram
plane. In many cases of actual full-field THz-DH, the output power of a THz-QCL is notalways enough to achieve a high signal-to-noise ratio (SNR) in a real-time hologram acquisition by a THz digital imager; in this case, the object must be placed near the imager to reduce
the signal loss in the lens-less configuration of DH. Such an experimental configuration may
not satisfy the requirement for the minimum z in FDM. An angular spectrum method (ASM)[20, 21] is another hologram reconstruction method and is more accurate for short reconstruction distances; however, a Fourier transform is performed twice. ASM has been used for pointscanning THz-DH systems [7, 15], but no attempt has been made to use ASM in full-field
THz-DH equipped with THz-QCL and THz digital imagers.
In this article, we acquired a THz digital hologram using a full-field off-axis THz-DH
system equipped with THz-QCL and uncooled, bolometer-type 2D focal plane arrays andthen, performed the numerical reconstruction of the wavefront based on ASM. Furthermore,
we evaluated the phase noise in the reconstructed phase image, which limits the precision of
the phase imaging and the 3D imaging of a sample. Finally, we demonstrated the quantitative
phase imaging of visibly opaque objects in real time and the 3D shape measurement of avisibly opaque, stepped structure.

2 Method
2.1 Experimental Setup
Figure 1 illustrates a schematic diagram of a full-field off-axis THz-DH system in a transmission configuration. The CW-THz radiation was generated by a THz-QCL (EasyQCL,LongWave Photonics LLC, center frequency = 3 THz, center wavelength = 100 μm, average
power = 1.78 mW). The THz-QCL was kept at 50 K in a cryostat using a Stirling cycle cooler
without the need for cryogenic cooling. After passing through an optical chopper (OC, 3501,
New Focus, modulation frequency = 7.5 Hz), the CW-THz radiation was collimated at adiameter of 7 mm by an off-axis parabolic mirror (OA-PM, off-axis angle = 90°, diameter =25.4 mm, focal length = 50.8 mm) and was fed into a Mach-Zehnder interferometer. In theinterferometer, the object beam passed through a silicon beam splitter (BS, diameter =101.6 mm, thickness = 500 μm, reflection = 54%, transmittance = 46%) and a sample, whereas
the reference beam was reflected by BS and an aluminum mirror (M). Both beams wereincident onto an uncooled, 2D micro-bolometer array, namely, the THz imager (IRV-T0831,
NEC Inc., sensor area = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, pixel
size = 23.5 μm × 23.5 μm, frame rate = 7.5 frames per second, exposure time = 66.7 ms, digital
output resolution = 14 bit) at an off-axis angle of 40°. This results in the generation of verticalinterference patterns of CW-THz radiation on the THz imager, namely, the THz digitalhologram. To improve the image SNR, we adopted a dynamic subtraction technique bysynchronizing the THz imager with the CW-THz radiation. To this end, the CW-THz radiation

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was chopped with the OC. We performed alternating acquisitions of the image with andwithout the CW-THz radiation and subtracted successive images, thereby suppressing thebackground noise. The minimum sampling spacing in the THz hologram is 47 μm from thesampling theorem for a THz imager with a 23.5-μm pixel pitch.

2.2 Hologram Reconstruction
ASM is a method to directly calculate the diffraction integral. Since the details of ASM aregiven elsewhere [20, 21], we briefly describe the main characteristics of this method. In thescalar diffraction theory, the diffracted field, ψp(x, y; z), is given by the incident field, ψp0(x, y),as follows:
 



ψp ðx; y; zÞ ¼ F −1 F ψp0 ðx; yÞ  H k x ; k y ; z ;ð1Þ
where H(kx, ky; z) is the spatial frequency transfer function (SFTF). As shown in Eq. (1), ASM
requires two Fourier transform (FT) calculations. Assuming that the sampling period along thex-axis is Δx with a total of M samples and the sampling period along the y-axis is Δy with a totalof N samples, the discrete form of Eq. (1) is given by:




ð2Þ
ψp ½m; n ¼ IDFT 2D DFT 2D ψp0 ðm; nÞ  H ½p; q :In Eq. (2), the discrete form of SWTF, H[p, q], is given by:
rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
22
ðpΔk x Þ − ðqΔky Þ−jk 0 z 1−
k0 2
k0 2
H ½p; q ¼ e;

ð3Þ

where Δkx and Δkx are the frequency resolution corresponding to sampling periods, Δx and Δy,along the x- and y-directions, respectively. The sampling period of the reconstructed image isequal to that of the hologram regardless of the reconstruction distance.

3 Results
3.1 Amplitude and Phase Imaging of a Plastic Object
We first measured a plastic object, i.e., a visibly opaque sample with a 3D shape. In thissample, two letters, BP^ and BS,^ were impressed in a convex manner (height = 228 μm)
Fig. 1 Experimental setup. THzQCL THz quantum cascade laser(center frequency = 3 THz,
average power = 1.78 mW); OC
optical chopper (modulation
freq. = 7.5 THz); OA-PM off-axis
parabolic mirror (off-axis angle =90°, diameter = 25.4 mm, focal
length = 50.8 mm); M aluminum
mirror; BS silicon beam splitter(diameter = 101.6 mm, thickness =500 μm)J Infrared Milli Terahz Waves (2018) 39:561–572

565

on a polystyrene plate (thickness = 0.8 mm, refractive index = 1.67), as shown in Fig. 2a.
Figure 2b shows the acquired hologram (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, number of image integrations = 128). We confirmed theinterference pattern with a spacing of ≈ 80 μm. This spacing was in good agreement withthe expected value based on the CW-THz radiation wavelength of 100 μm and the offaxis angle of 40°. To avoid aliasing in the reconstruction, we added null data to the areaaround the hologram to increase the number of pixels to 640 pixels × 640 pixels. Then,
we reconstructed the amplitude and phase images of the sample at a reconstruction
distance, z, of 7 mm using ASM, as shown in Fig. 2c, d. The two letters BP^ and BS^
were clearly confirmed in both images. In the amplitude image, the image contrast is
given by the edges of the letters due to the reflection and scattering losses of CW-THz
radiation. However, the contrast in the phase image is due to the differences in the
optical thickness in the letter and no letter regions. The phase image has a better contrast
than the amplitude image in the limited SNR of the hologram.
We next demonstrated the digital focusing of the amplitude image in the same plastic
sample (see Fig. 2a) by changing the reconstruction distance, z. Figure 3 and Video 1
show a series of amplitude images as z was changed at intervals of 1 mm (image size =7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, number of image integrations = 128). The letters BP^ and BS^ were in focus at z = 7 mm, but they were out offocus at z ≥ 8 mm and ≤ 6 mm. The depth resolution of the digital focusing was estimatedby the depth of the focus, DF, of the optical system as follows:

Fig. 2 a Optical photograph of a visibly opaque, plastic sample with two impressed letters, BP^ and BS.^ b THz
digital hologram (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, number of image
integrations = 128). Reconstructed images of the c amplitude and d phase (image size = 7.52 mm × 5.64 mm,
pixel number = 320 pixels × 240 pixels) by ASM

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DF ¼

λ100  10−6¼¼ 447 Ëcm:
0:4732NA2

ð4Þ

This depth resolution is reasonably reflected in Fig. 3 and Video 1. Because digital focusing
does not require any changes in the optical setup, it is a powerful modality for 3D imaging overa wide dynamic range of depths. For example, if another object is placed at a different depth
position, digital focusing allows us to individually separate and visualize them.
We also obtained a real-time movie of the amplitude and phase when the plastic sample (seeFig. 2a) was screened by a paper sheet. A hologram was acquired over 11.4 s at a frame rate of
3.5 Hz, as shown in the left panel of Video 2. Figure 4a shows a snapshot of the hologram
movie (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, no image
integration). The interference pattern was still observed in the single-shot hologram. By
applying ASM to the full movie of the hologram, we obtained movies of both the amplitude
and phase, as shown in the center and right panels of Video 2, respectively. Figure 4b, c shows
snapshots of the amplitude and phase movies (image size = 7.52 mm × 5.64 mm, pixel
number = 320 pixels × 240 pixels, reconstruction distance z = 7 mm) before the sample wasscreened by the paper sheet (t = 0.285 s). The two letters BP^ and BS^ were confirmed in both
images. Next, Fig. 4d, e shows snapshots of the amplitude and phase movies when the sample
was partially screened by the paper sheet (t = 1.710 s). Good contrast was still maintained in
the phase image, whereas the two letters almost disappeared in the amplitude image due to thedecreased amplitude caused by the paper sheet. These movies and figures reflect the change in
the amplitude and phase caused by inserting the paper sheet in front of the sample. Furthermore, the phase image is more powerful than the amplitude image in the low SNR. The realtime imaging capability of both the amplitude and phase has the potential to expand theapplications of THz-DH.

3.2 3D Imaging of a Semiconductor Object Based on a Phase Image
We measured a semiconductor object, i.e., a visibly opaque sample with known 3D
dimensions to demonstrate the potential for 3D imaging of visibly opaque objects. A
checker pattern was carved on a silicon substrate (n-type, thickness = 300 μm, electric
resistivity > 1 Ω•cm) by a photolithography method. Figure 5a shows the optical photograph and schematic drawing of the checker-patterned sample (grid size = 1 mm by 1 mm).
The depth of the sample was determined to be 21.11 ± 0.03 μm by a 3D optical microscope
based on white light interferometry (Veeco, Wyko NT9100, depth resolution < 0.1 nm,
lateral resolution > 0.5 μm).
We acquired the THz digital hologram (see Fig. 5b, image size = 7.52 mm × 5.64 mm, pixel
number = 320 pixels × 240 pixels, number of image integrations = 128) of the sample. By
applying ASM to the acquire hologram, we reconstructed the amplitude image and phase
image of the sample (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels ×240 pixels)
at a reconstruction distance, z, of 7 mm, as shown in Fig. 5c, d. In the amplitude image,although the edge of the grid pattern was confirmed, the checker pattern with different
thicknesses was not as clear due to the small differences in the THz attenuation between the
checker patterns. However, the phase image clearly shows the checker pattern due to the large
difference in the optical thicknesses of the top and bottom surfaces.

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567

Fig. 3 Digital focusing of the amplitude image (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels ×
240 pixels, number of image integrations = 128) for visibly opaque, plastic sample (see Fig. 2a) by ASM. The
reconstruction distance, z, was changed at intervals of 1 mm within a range of 15 mm. The corresponding movie
is Video 1

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Fig. 4 Real-time movie of a visibly opaque, plastic sample. a Snapshot of a THz digital hologram (image size =7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, frame rate = 3.5 Hz). Snapshots of the reconstructed b amplitude and c phase movies (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels)
by ASM before the sample was screened by a paper sheet (t = 0.285 s). Snapshots of the reconstructed damplitude and e phase movies (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels) by
ASM after the sample was screened by a paper sheet (t = 1.710 s). The corresponding movie is Video 2

We reconstructed a 3D image of the sample from the phase image, ϕ(x, y). The 2D
distribution of the relative thickness, t(x, y), was given by:tðx; yÞ ¼λ
 ϕðx; yÞ;
2π nsample −nairð5Þwhere λ is the wavelength of the CW-THz radiation and nsample and nair are the refractive
indices of the samples and air, respectively. nsample was determined to be 3.1 by ourasynchronous-optical-sampling terahertz time-domain spectrometer [22]. Figure 5e shows
the t(x, y) of the sample calculated from the phase image in Fig. 5d. The 3D contour of thesample was clearly visualized. Because the relative thickness was 13.4 ± 1.6 μm for the top

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Fig. 5 a Optical photograph and schematic diagram of a visibly opaque, silicon sample with a checker pattern. b
THz digital hologram (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, number ofimage integrations = 128). Reconstructed images of the c amplitude and d phase (image size = 7.52 mm ×5.64 mm, pixel number = 320 pixels × 240 pixels) by ASM. e 3D image calculated by the phase image in Fig. 5dsurface and − 9.0 ± 1.8 μm for the bottom surface, the difference in the geometrical thickness
was 22.4 ± 1.7 μm. This value is in good agreement with the value (21.11 ± 0.03 μm) obtainedby 3D optical microscopy. The unevenness of the phase value in each pattern was due to thephase noise discussed later rather than the surface roughness of the sample. The expectedvalues for the spatial resolution of the horizontal and vertical directions are given by:
SRx ¼

λz
100  10−6  14  10−3¼
¼ 186 μm
MΔx
320  23:5  10−6

ð6Þ

SRy ¼

λz
100  10−6  14  10−3¼
¼ 248 μm:
N Δy240  23:5  10−6

ð7Þ

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Fig. 6 a Thz digital hologram, b reconstructed amplitude image, and c reconstructed phase image without the
sample (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, number of image integrations = 128). d THz digital hologram, e reconstructed amplitude image, and f reconstructed phase image without
the sample (image size = 7.52 mm × 5.64 mm, pixel number = 320 pixels × 240 pixels, no image integrations).
Spatial distribution of the phase noise in g 128-hologram-integrated and h no-hologram-integrated phase images.
i Phase resolution and amplitude SNR with respect to number of image integration

4 Discussion
Phase resolution is an important performance of THz-DH to determine the depth precision of 3D imaging based on the phase image. Here, we discuss the phase resolution in
the present phase image because the phase resolution is directly related to the depth
resolution. The phase resolution is defined as the fluctuation of the phase value between
different phase images, which depends on the robustness of the optical system to external
disturbance (vibration, air turbulence, etc.) and/or SNR in the phase image. Figure 6a–cshows a typical hologram without the sample (image size = 7.52 mm × 5.64 mm, pixel
number = 320 pixels × 240 pixels, number of image integrations = 128) and the corresponding amplitude and phase images (image size = 7.52 mm × 5.64 mm, pixel number =320 pixels × 240 pixels), respectively. Also, Fig 6d–f shows the hologram, amplitude
image, and the phase image when no image integrations were performed. Amplitude

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images in Fig. 6b, e shows an uneven distribution of the amplitude value due to the beamprofile of THz-QCL, which is in reasonable agreement with the bright distribution ofholograms in Fig. 6a, d. In contrast, phase images in Fig. 6c, f shows significantly
different profile from amplitude images in Fig. 6b, e. The mean and standard deviation of
the spatial phase distribution were 1.44 ± 0.81 rad in Fig. 6c and 1.12 ± 0.75 rad in
Fig. 6f, respectively.
We next evaluated the phase resolution using the phase image. To this end, we
repeated 10 acquisitions of 128-hologram-integrated phase image and no-hologramintegrated phase image. Then, we calculated the standard deviation of the phase values
at each pixel in 10 phase images to provide the phase resolution. Figure 6g, h shows thespatial distribution of the phase resolution for 128-hologram-integrated and nohologram-integrated phase images (image size = 7.52 mm × 5.64 mm, pixel number =320 pixels × 240 pixels). The spatial dependence of the phase resolution was relatively
flat, and is related to the amplitude image because a decreased amplitude and theresulting low SNR increase the phase noise. The mean of the phase resolution in thewhole image region of Fig. 6g was 0.10 rad, corresponding to a phase resolving power of
λ/62; in the center region with a high SNR, as indicated by the black dashed box in
Fig. 6g, the mean phase resolution and the corresponding phase resolving power were0.071 rad and λ/91, respectively. From these values, the depth resolution in the 3D
imaging was estimated to be 1.6 μm for the whole region and 1.1 μm for the centerregion. These estimated values are in reasonable agreement with the experimental values
in Fig. 5e. On the other hand, the mean phase resolution and the corresponding phaseresolving power in Fig. 6h were 0.071 rad and λ/91 for the whole region and 0.071 radand λ/91 for the center region, respectively. These values determined the precision of thereal-time phase imaging in Fig. 4 and Video 2. Finally, red plots in Fig. 6i shows
dependence of the phase resolution on number of image integration. For comparison,blue plots in Fig. 6i shows a relation between amplitude SNR and number of image
integration. These plots clearly indicate that the phase resolution depends on the amplitude SNR.

5 Conclusions
We constructed an off-axis THz-DH system equipped with THz-QCL and an uncooled, 2D
micro-bolometer array, applied ASM to the acquired THz digital hologram, and performed
real-time amplitude/phase imaging and digital focusing of visibly opaque objects. The
quantitative phase imaging was confirmed by taking 3D imaging of these objects andevaluating the phase noise. The demonstrated real-time and precise 3D imaging capability
will be a powerful tool for the non-destructive inspection of optically opaque soft materials.
Acknowledgements This work was supported by grants for Exploratory Research for Advanced Technology(ERATO) MINOSHIMA Intelligent Optical Synthesizer (IOS) Project (JPMJER1304) from the Japanese Scienceand Technology Agency and Research Grant 2015 from Mitutoyo Association for Science and Technology,
Japan. The authors gratefully acknowledge Prof. Qing Hu of Massachusetts Institute of Technology for his help
in preparation of the THz-QCL device and the Kagawa University Nanotechnology Supporting Office as part ofthe BNanotechnology Project^ in the Ministry of Education, Culture, Sports, Science and Technology (MEXT),
Japan, for its help in the preparation and evaluation of the semiconductor sample. We also wish to acknowledge
Ms. Natsuko Takeichi of Tokushima University for her help in the preparation of the manuscript.

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