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Abstract
Two diffractive optical elements are used to create a compact raster THz scanning setup in reflective configuration. The first one focuses the radiation into the small focal spot on the sample, while the second one collects reflected radiation and focuses it on the detector. To assure small size of the setup and large apertures of optical elements, structures work in the off-axis geometry. Thus, the focal spot is formed 100 mm after and 60 mm below the optical axis of the element, which measures 75 mm in diameter. The designed iterative algorithm allows further minimization of these values.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz radiation, ranging between infrared and microwaves, is most commonly placed within frequency range from 0.1 THz to 10 THz [1]. Due to the lack of effective, working in room temperature, compact and cost-efficient sources and detectors, it is one of the least studied ranges in the entire electromagnetic radiation spectrum and remained unexplored until the 1980s. THz radiation spectrum have drawn the researchers’ attention since the last few decades. The specific features of this range of radiation comprise non-ionization, noninvasiveness, high absorption and dispersion in water – the major component of biological tissues. THz radiation, in addition to defense applications [2,3] and detection of hazardous substances [4–6], can be very useful for medical diagnostics [7]. The most important property of sub-millimeter wavelengths is that no negative effect of its impact on human tissues has been found [8–11]. In medical applications, this type of radiation can be used to detect breast and skin cancer [12–16], study markers introduced into the blood circulation and even to analyze the cornea in the human eye [17,18]. Noninvasiveness of THz radiation is very important in case of developing a device that can be tested on a large population of patients, it is more cost efficient and safer diagnostics than conventional methods based on ionizing radiation.
Terahertz radiation is strongly attenuated by molecules of water, therefore investigated bio-samples have to either be thin or placed on the surface of material consisting water. Transmittive configuration is possible, however it requires preparation of the bio-samples analogous to histopathology, which is inadmissible in case of living patients. Thus, reflection configuration is necessary and the focus of our research shall be placed on the skin tissues. The main purpose of this work is to apply advanced diffractive optical elements (DOEs) to THz emitter and detector setup. Contrasting optical properties of healthy and cancerous skin could allow to distinguish life-threatening lesions. Due to limited resolution of THz scanning (relatively long wavelength), doctors’ inspection cannot be replaced, nevertheless such a device could be very useful in prevention care.
Our ambition is to design and manufacture thin DOEs, which would make THz skin scanner more compact and applicable. We propose an approach, novel in this field, based on utilization of iterative processes to optimize diffractive lenses, working in an off-axis focusing regime. The use of a classic diffractive lens with larger diameter, illuminated only partially, would result in very large focal spot, as it shown in Fig. 1(c). Furthermore, using refractive counterpart with the same parameters would result in lens having maximal thickness around 6 cm and adding a 7-cm-PA12 block to assure focusing 100 mm after the lens (simulations and optimizations of the refractive lens were carried out with Zemax software).
Fig. 1. Designed optical setup configuration (a) and scheme of iterative algorithm (b). Distances are in mm and red dashed line in (a) denotes the main optical axis of the setup. The intensity distributions corresponding to emitter lens plane (being illumination), after propagation through the classic diffractive lens – 1st iteration, after 2nd and 3rd iteration are given in (c).
2. Computer modeling and designing process
A set of diffractive optical elements has been numerically calculated by means of light propagation in the Fresnel region using modified convolution approach [19] and Gerchberg-Saxton algorithm [20–23]. The scheme of applied numerical procedure is presented in Fig. 1(b). All calculations have been conducted on 4096 × 4096 matrices of square pixels with sides of 117 µm for the design wavelength λ=576.5 µm, which corresponds to the frequency 520 GHz.
Initial light distribution imitates divergent Gaussian beam, emitted from quasi-point source, placed 75 mm before collimating lens, which gives Gaussian shape in the amplitude of the field but constant phase (quasi-plane wave). Additionally, this field is shifted 60 mm from the main optical axis of the setup, defined as the normal to the sample in the incidence point (marked with red dashed line in Fig. 1). To be able to minimize setup an off-axis focusing must be obtained with respect to the center of the first lens (and source of the radiation). Prepared initial light distribution is then multiplied by the transmittance of the converging lens and iterative Gerchberg-Saxton algorithm begins (as illustrated in Fig. 1(b)). Each step (number of steps was usually lower than 10) consists of 4 main operations – (1) propagation to the sample plane, (2) overwriting amplitude with desired distribution (spot with radius corresponding to the diffraction limit of light at a given wavelength), (3) back-propagation to the plane of the optical element, (4) overwriting amplitude with input light field distribution. Phase distribution after 3rd operation defines the shape of the diffractive lens, which is capable of off-axis focusing at designed distance a particular wavelength (hereafter ‘emitter lens’). In just a few iterations of the algorithm (4th does not differ from 3rd one), output light field distribution matches well with the assumed diffraction limited point and further steps do not introduce significant changes in both focal spot shape and DOE phase distribution. Detector lens is designed to conduct similar operation as emitter lens, but with reversed direction of propagation of the light (gathering light emerging from focal point, collimating it and focusing on the detector). Thus, it is formed as a mirror reflection of emitter lens, summed with simple off-axis converging lens to perform additional focusing.
The element has been manufactured using additive manufacturing (3D printing) by selective laser sintering (SLS) method [24]. During SLS, selected areas of the thin layers of powder material which are dispersed on the top of the build platform, are fused together by thermal energy of the focused laser beam to form a solid. The high-power laser heats the powder just below its boiling point. The uncured powder is removed and the final object is obtained. The method does not require usage of any additional supports to hold an object together while it is being printed, therefore is less time-consuming than other 3D printing methods. It provides the printing resolution of 0.05 mm, however, it should be underlined that the thinnest wall of the structure must have 0.8 mm in thickness to hold. Polyamide 12 (PA 12) [25,26] is a widely used material for SLS and was chosen as the material for diffractive structures. The refractive index for all frequencies in sub-THz range is equal to approximately 1.59 and the absorption coefficient corresponding to the frequency of 520 GHz is equal to 2.39 cm−1. These measurements have been conducted using Teraview Spectra 3000 spectrometer for the sample of 3D printing material before manufacturing. Manufactured lenses measure 75 mm in diameter and up to 0.98 mm in thickness (with additional 1 mm substrate), with focal length of 100 mm and focal point placed 60 mm below the optical axis of the lens (which also means, that it is placed outside lens aperture). It has to be noticed, that these dimensions derive strictly from the size of emitter and detector, available in the laboratory, not the properties of the setup itself. Thus, they can easily be minimized and adapted to the desired system.
3. Experimental evaluation
All measurements have been handled with Schottky diodes with frequency multipliers (VDI, Inc.) as source and detector of terahertz radiation. In order to achieve radiation at 520 GHz it multiplies base frequency 54 times. To ensure proper beam forming a diagonal horn antenna, with aperture diameter 2.4mm, is attached to a source output waveguide (WR-1.5). The radiation output power during experiment was about 0.05 mW, and full beam width at -3dB was 10 deg. Schottky diode in a WR-1.5 waveguide with a diagonal horn antenna has been used as a detector. Its aperture diameter was 2.4mm and responsivity was about 700V/W. First, both structures have been tested separately and then they have been combined into a single measurement setup. No additional screens, apertures or antireflective structures have been used.
3.1 Characterization of the structures
Performance of the designed diffractive structures has been tested by measurements of intensity distributions of the wavefronts formed by the structures after illumination expected in the final setup. Schemes of experimental setups are shown in Fig. 2. They differ only in additional collimating lens, used in emitter setup. In both cases, off-axis focusing with particular DOE has been performed and two-dimensional x-y scans in the plane of focus have been gathered together with x-z scans along propagation angle.
Fig. 2. Scheme of the setup used for characterization of emitter (a) and detector (b) structures. On the right a photograph of manufactured structure is presented and its designed phase delay map (where white and black corresponds to 0 and 2π phase shift introduced by the structure).
Both structures proved to be working as designed, focusing the radiation to spots presented in Fig. 3. For sake of clarity, intensity has been normalized to one and cross-sections along maximal values have been additionally plotted on corresponding axes. Full width at half maximum for emitter and detector focal spots for x and y axes respectively measured (1.33, 2.14) mm and (2.55, 2.15) mm. Eccentricity of ellipses fitted to full width at half maximum have been estimated to 0.61 and 0.29, respectively. Dotted line shows the Abbe diffraction limit for investigated lenses, which has been estimated to 2.8 mm (we took into account the size of the illuminating beam, not the total printed structure size, thus d = 50 mm). One can notice, that obtained focal spots are within theoretical diffraction limit, what can be considered as a satisfactory result, bearing in mind that the focal point lies outside the aperture of the lens. In case of emitter structure, stronger ellipticity of the focal point can be noticed, which most probably results from skewed detector plane. The structure has been calculated to form a circular focal spot in the sample plane (perpendicular to main optical axis). It has though been scanned in the plane, perpendicular to the beam (due to acceptance cone of the detector), which is tilted at an angle α from the main optical axis (Fig. 2).
Fig. 3. Intensity distributions in focal and propagation planes measured for the emitter (a), (c) and the detector (b), (d) structures, respectively.
3.2 Compact in-reflection inspection setup
Setup used for final verification of the structures is presented in Fig. 4. It consists of two Schottky diodes, operating at 520 GHz, as detector and emitter of THz radiation. Collimating lens is placed right after the emitter to obtain a plane wave, which illuminates designed DOE (emitter lens). Focused beam is then reflected from the sample (in the first experiments replaced with mirror) and focused again on the detector. Optical axes of emitter and detector are shifted 120 mm from each other, with the sample in the middle (located on the main optical axis). Size of the setup is dictated by laboratory convenience and can be easily replaced with mirror) and focused again on the detector. Optical axes of emitter and detector are shifted 120 mm from each other, with the sample in the middle (located on the main optical axis). Size of the setup is dictated by laboratory convenience and can be easily minimized even using the same DOEs, which can also be redesigned and further optimized to obtain shorter focal lengths and smaller diameters. Both structures could be identical, but a setup consisting of two different lenses has been chosen to verify the functioning of the iterated diffractive lens illuminated with a plane wave (emitter lens) and a divergent wave (detector lens). Moreover, additional space between emitter diode and emitter lens has been used to mount motorized stage, enabling scanning in the detector plane.
Detector has been mounted on a moving stage, allowing 3-axial scanning of the beam. Both x-y and x-z scans are presented in Fig. 5. As it can be seen, the diameter of obtained focal spot is close to 2 mm. Structures have been manufactured from PA12 material used for SLS printing. Each structure consists of 1-mm substrate and designed relief having maximal thickness of 0.98 mm – which results in 2 mm of attenuating material for each structure. According to Beer-Lambert’s law each structure will attenuate less than 38% of incident radiation, which means that both together will transmit over 52% of radiation (without Fresnel losses). Assuming reflection losses at each interface (four interfaces with change of refractive index between 1 and 1.59 resulting in 5.2% Fresnel losses each) and perfect mirror as a sample the whole system will transmit almost 43% of incident light. Moreover, the details of the structure are approaching the limitation of the resolution of SLS printing technique. Nevertheless, the structures work as intended, with satisfying transmission properties. For further minimization of losses, alternative methods of designing or manufacturing should be applied. We would suggest manufacturing lenses from paraffin-like material which are very transparent also for higher THz frequencies.
Fig. 5. Intensity distributions in compact in-reflection setup with the mirror as a sample recorded in the detector plane x-y (a) and x-z (b). Both distributions were normalized to the same value, thus they have the same intensity color bar.
3.3 Exemplary sample measurements
In the second part of this experiment, mirror has been replaced with the sample, consisting of PA12 and PMMA stripes (inset in Fig. 6). The PMMA cuboid has the dimensions 20 mm x 20 mm and is 10 mm thick. In the middle a 5-mm stripe of PA12 is inserted (it has thickness of 2 mm). Both materials have similar refractive indices and reflection coefficients (around 4-5%) at 520 GHz, nevertheless they could have been distinguished. Due to uncertainty of the manual placement of the sample, three scans (#1-3) have been performed with repositioning of the sample between them and are presented in Fig. 6. Measured voltage is proportional to the intensity of detected radiation. Highest reflections are observed, when THz beam is focused entirely on a single strip, independently from the material. Local minima have been measured on the boundaries between materials and zero values of voltage have been observed outside of the sample. These initial results verify operation of the setup in the reflective configuration, in the conditions comparable to real human skin rather than idealized mirror.
Finally, tests of spatial resolution of detection have been performed. For this purpose, HDPE plate has been covered with thick aluminum foil tape with 1 mm, 3 mm and 6 mm thick space left. Prepared samples have then been scanned in investigated setup and the results are presented in Fig. 7. Each slit scan has arbitrary values on horizontal axis due to the fact that sample was mounted each time at slightly different position. Reflection from solely aluminum foil produced 30-33 µV of voltage on the detector, which along with reflectivity of HDPE equal to ca. 5% allows to expect voltage to drop below 2 µV for polyethylene strip. It is, indeed, observed for 3 mm and 6 mm gaps, while for the smallest one the response is only halved. Following interpretation emerges - THz beam can be entirely focused on the details greater than 3 mm, allowing to direct measure their reflectivity. For smaller ones only part of the radiation reflects from the detail and while the detection of its presence is still possible, the intensity response corresponds to average reflectivity over certain area. It complies well with the measurements of the focal point size (Fig. 3), which have shown the diameter of the spot to be in the order of 2 mm. For both, 3-mm and 6-mm slits we can observe additional dips not related to the geometry of sample. The used foil was thick and probably these dips correspond to kneaded area for 3-mm and a small bending at the cut edge for 6-mm slit sample.
Fig. 7. Reflection from the sample - HDPE covered with aluminum foil with 1 mm, 3 mm and 6 mm thick space left.
Numerical simulations for shorter focal lengths have already been performed. Distance from the lens plane to the sample can be reduced even to 40 mm at the cost of doubling the size of the spot (for 50 mm spot size increases by 50%) and increasing its ellipticity.
4. Summary
We have designed, manufactured and tested diffractive off-axis optical elements, capable of focusing THz radiation on the sample, as well as gathering the reflected radiation and focusing it back on the detector. Lenses have been 3D-printed from polyamide with refractive index similar to silicate glass in visible light (around 1.5), but with relatively high absorption coefficient. We have proved, that manufactured DOEs work in the designed setup and allow to detect boundaries between two materials, similar in terms of reflectivity. Additionally, we have shown that details as small as 3 mm in width are fully recognizable, while smaller ones (like 1-mm slit) can be still partially detected. All presented results prove the concept of application of diffractive optical elements with off-axis focusing to non-invasive reflective THz scanning of human skin. However, some issues can be enumerated, showing possibilities of improvement. Firstly, the sample plane is not precisely defined in presented configuration, thus, it is planned to use a relatively thin window for repeatable placing of the sample. Secondly, the difference between healthy and cancerous skin could occur to be too small to differentiate it using proposed setup. Thus, the good solution would be using two or three different scanning frequencies to perform a quasi-multispectral imaging.
Funding
Narodowe Centrum Badań i Rozwoju (LIDER / 11/0036 / L-9/17 / NCBR / 2018).
Acknowledgments
The Authors would like to sincerely thank the Institute of Optoelectronics at Military University of Technology for help in realizing experimental evaluation and all fruitful discussions.
The Authors would also like to thank Orteh Company for providing LS 6.0 software used for designing and modelling of diffractive optical elements, which is accessible in the Laboratory of Optical Information Processing at the Faculty of Physics in Warsaw University of Technology.
Disclosures
The authors declare no conflicts of interest.
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