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Improving depth-of field in broadband THz beams using nondiffractive Bessel beams Assaf Bitman,1,2,* Inon Moshe,1 and Zeev Zalevsky2 1
2
Applied Physics Division, Soreq NRC, Yavne 81800, Israel Faculty of Engineering, Bar Ilan University, Ramat-Gan 52900, Israel *Corresponding author:
[email protected]
Received August 6, 2012; revised September 2, 2012; accepted September 2, 2012; posted September 4, 2012 (Doc. ID 173884); published September 28, 2012 We report new results related to imaging using broadband Bessel-like beams at the terahertz (THz) domain that were generated by use of axicons and pulsed THz radiation emitting at a bandwidth 0.1 to 1 THz. Such Bessel-like beams exhibit an invariant line of focus with an extended length compared to Gaussian-beams Rayleigh range, which enables imaging through the extended length. We demonstrate this imaging property using a resolution target illuminated by broadband-THz beams and show an improvement by a factor of 3.5 in imaging depth while using Bessel-like beams over Gaussian beams. Our results highlight the potential in using broadband THz radiation together with nondiffractive Bessel beams to significantly improve spatial separation over deep view. © 2012 Optical Society of America OCIS codes: 110.6795, 220.3630, 070.7345, 110.6915.
Pulsed terahertz (THz) radiation imaging systems, such as time-of-flight (TOF) imaging systems, have the advantage of obtaining depth information in both transparent and opaque materials using transmission and reflection modes, respectively [1]. In conventional optical imaging systems there is a trade-off between axial and lateral resolution; hence both cannot be obtained in the same system. McLeod [2] showed that using axicon, one can extend the focal range with correlation to the input beam radius and the axicon’s base angle. Later it was Durnin [3] who gave exact propagation invariant solutions to the Helmholtz equation leading to an extended depth-of-field (DOF). The large variety of properties of nondiffractive beams, and especially Bessel beams, led to many applications and a wide range of optical-physical researches. Lloyd et al. [4] investigated the superluminal effects in a focus of an axicon integrated in a THz time-domain optical system. Yu and Dou [5] generated THz Bessel beams using binary axicons. Winnerl et al. [6] produced pulsed THz Bessel–Gauss beams with radial and azimuthal polarization, using microstructure antennas. Shaukat et al. [7] reported the spatial properties of a narrowband (2.8 THz) THz Bessel beam created using quantum cascade laser and axicons. Yu [8] also presented a microgenetic algorithm to design diffractive optical elements to construct arbitrary order Bessel beams. Recently, Liu et al. [9] reported DOF improvement in a THz imaging system using quasi-Bessel beams based on narrowband THz source (backward wave oscillator). Finally, Zhang and Buma [10] compared quasi-Bessel and Gaussian pulsed THz beams by the imaging of two pairs of needles in a dielectric media. Let us recall that an axicon produces a J 0 Bessel-like beam with a central peak radius that is propagation invariant along a distance Z max . This propagation distance can be geometrically estimated from the axicon apex to the point where the peak intensity of the J 0 beam sharply decays. This can be found by knowing the axicon base angle and the diameter of the incident Gaussian beam. 0146-9592/12/194164-03$15.00/0
The formation of Bessel beams in broadband radiation is not straightforward. For example, in the zero order Bessel function of the first kind (which is the case while using axicon) the central peak power is dependent on the wavelength [11]. Nevertheless, Fischer et al. [12] have proven that the key criterion in order to generate a Bessel beam in a low temporal coherence radiation source, i.e., broadband radiation, is a high spatial coherence. In this Letter we report, to the best of our knowledge, for the first time, the creation of Bessel-like beams in a pulsed THz imaging system using custom made axicons. The potential of using this type of “nondiffractive beam” in THz imaging systems is presented by using a resolution target that has been placed in several distances along the optical axis. A comparison to a broadband Gaussian beam using a biconvex lens is given. In a pulsed THz radiation source, based on photoconductive switch, all the frequencies of the wave packet emerge simultaneously from the origin antenna [13]. Therefore, we can assume that this source produces broadband THz radiation with highly spatial coherence, and one can generate Bessel beams, e.g., by using an axicon. In order to manufacture the axicon, we measured the refractive index of different materials, such as Teflon and high-density polyethylene. The refractive index measurements of these materials was made in a similar manner in previous studies [14,15]. From these materials we have chosen a Teflon rod to be used for the axicon fabrication because compared to other materials, it presented a low absorption coefficient. The refractive index was measured and it was found to the value of 1.3975 for frequencies between 0.15 to 1 THz. For this wavelength range, the Teflon is practically nondispersive. The images captured in our experiments are merely a convolution of the beam with the resolution target. This needs the crucial requirement that both the central lobe diameter of the J 0 Bessel-like beam (confined by the first zeros of the J 0 Bessel beam) and the Gaussian beam waist have the same diameter. Based on the knowledge of the broadband Gaussian beam size [16] and the averaged refractive © 2012 Optical Society of America
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broadband Bessel beams. It guarantees, once the collimation maintains, that whole THz wave-packet experiences the same Z max . Note that the definition of Z max of an axicon with base angle α, refractive index n, and an input beam radius R is Z max Fig. 1. (Color online) Setup sketch of the imaging system for scanning the resolution target with a broadband Gaussian beam. The source is imaged to plane B.
index, we designed a Teflon axicon with 26 base-angle degrees to meet the requirement of equal beam diameter. In order to compare the performances of the two types of beams we used a resolution target made of a metal plate with three rectangular slits 3 mm wide each (x direction) and 20 mm long (y direction). These apertures were separated in the x direction by 3 mm wide metal (duty cycle of 0.5). We scanned the slits, using x-y translation stage, locating them at a different distance from the lens/axicon each time (z direction). First, we scanned the resolution target with a broadband Gaussian THz beam (Fig. 1). We used the PICOMETRIX THz system TR 2000 in a transmission mode. The transmitter and receiver both have lenses with a focal length (FL) ( f 1 in Fig. 1) of 76 mm. Using two planoconvex Teflon lens with an FL (f 2 in Fig. 1) of 100 mm and a biconvex lens with FL ( f 3 in Fig. 1) of 40 mm (made of TSUROPICA), we imaged our source to plane B (through plane A), i.e., the objective-biconvex-lens focal-plane (see Fig. 1). This setup produced a Gaussian beam with a spot size diameter of ∼2.6 mm. Figure 2 shows the setup where we scanned the resolution target with a broadband J 0 Bessel-like beam. In this setup we replaced the three lenses with one planoconvex Teflon lens having FL ( f 2 in Fig. 2) of 300 mm; and two Teflon axicons. As mentioned before, the length Z max , where the central-lobe of a Bessel-beam is invariant, depends on the beam diameter and on the degree of the beam collimation at the axicon input. Therefore, in this setup we imaged the source (waist), with a diameter of ∼4 mm, to the axicon input (from plane A to plane B in Fig. 2). This led to a magnification of the source diameter by a factor of ∼4 and also ensured that all wavelengths within the pulsed THz spectrum are collimated and have the same diameter at the axicon input. This last property is crucial when we plan to produce
Fig. 2. (Color online) Setup sketch of the imaging system for scanning the resolution target with a broadband Bessel beam. The region between the axicons is the area where the broadband J 0 Bessel-like beam is produced.
R : n − 1 · α
(1)
Our simulations have shown that the weighted broadband THz J 0 Bessel-like beam produced in this setup has a central peak power diameter of ∼2.6 mm as expected. Figure 3(a) shows the intensity distribution measured when placing the previously described resolution target at a distance of 30 mm from the objective lens. For comparison, Fig. 3(b) shows the intensity distribution measured for the same location of the resolution target from the first axicon. In Figs. 3(c)–3(f) we show the intensity distribution measured where the resolution target is placed at a distance of 40 and 50 mm, respectively. Figure 4 summarizes the total contrast along the z direction for both broadband Gaussian (dashed curve) and broadband Bessel (solid curve). The contrast was calculated from the averaged cross section profile along the direction. This value is defined as contrast
I max − I min ; I max I min
(2)
where I max and I min are the maximum and minimum signals, respectively. From Fig. 4 one can observe, as expected, that a Gaussian beam gets its maximum contrast at the focal plane (40 mm). Moreover, the total contrast shape, as a function of the distance (focal range), resembles the squared sinc function, matching Goodman’s study [17]. On the other hand, the contrast shape of the broadband Bessel beam as a function of
Fig. 3. Intensity distribution of the resolution-target at different distances from the objective-lens\axicon: (a) 30 mm from lens, (b) 30 mm from axicon, (c) 40 mm from lens, (d) 40 mm from axicon, (e) 50 mm from lens, and (f) 50 mm from axicon.
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Fig. 4. Comparison between imaging-contrast of a resolution target using broadband Gaussian (dashed) versus broadband Bessel (solid) beams. Imaging DOF was measured while placing the target in several distances from the objective lens\axicon.
the distance behaves completely different. It shows higher contrast, i.e., enhanced spatial resolution. In addition, we observed that there is a decrease in contrast in the focal plane (Z max ∕2). This can be explained by the fact that although axicons produce J 0 Bessel-like beams having an invariant central peak power along Z max , the side lobes are varied along obtainable distance. This variation expresses itself in the profile of these lobes and the total energy hidden in them as a function of propagation along the z direction. The highest perturbation induced by these side lobes is at the focal plane where all diffracted beams from the axicon lens interfere. These side lobes diffract from the resolution target result in the reduction of the slit’s resolving capability. From these results it is clear that by combining pulsed THz radiation in an imaging system together with J 0 Bessel-like beams, one can significantly reduce the trade-off limitation of axial and lateral resolution. Many studies have shown that THz radiation has the advantage of providing information to many optically opaque materials. By using a pulsed THz imaging system, one can significantly improve the axial resolution, mainly by shorter pulses. On one hand, there is the advantage of a THz imaging system that can give full three-dimensional (3D) information but with limited DOF. On the other hand, the use of nondiffractive beams such as J 0 Bessel-like beam gives us the opportunity to significantly extend this DOF. This combination opens a new window to a variety of research fields. The originality of this manuscript lays in the comparison analysis of the contrast differences between the broadband THz Bessel and broadband Gaussian beams along the full range of DOF; while we refer to the imaging contrast variation along the DOF for the case of Gaussian and Bessel beams. In addition, this manuscript rigorously
makes a comparison between the two types of beams. As a baseline for this comparison we needed to find a suitable condition in which both beams will share the same contrast at the focal plane and the same beam size. This manuscript is also unique in its usage of point receiver on a scanning translated system to perform imaging. In conclusion, we have demonstrated the advantage of combining nondiffraction Bessel beams with a pulsed THz radiation. Figures 3 and 4 stress the improvement in the transverse separation ability when using broadband Bessel beams instead of broadband Gaussian beams. As mentioned above, pulse THz radiation can be used in imaging systems such as TOF to get depth information. Whereas the imaging depth is determined by the pulse time length, i.e., coherence length, preservation of the spatial resolution along the optical axis is affected by the beam shape. A comparison between axicon and biconvex lens suggests that the former can be integrated in THz TOF imaging systems in order to significantly improve the ability to construct a full 3D image. References 1. W. L. Chan, J. Deibel, and D. M. Mittleman, Rep. Prog. Phys. 70, 1325 (2007). 2. J. H. McLeod, J. Opt. Soc. Am. 44, 592 (1954). 3. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987). 4. J. Lloyd, K. Wang, A. Barkan, and D. M. Mittleman, Opt. Commun. 219, 289 (2003). 5. Y. Yu and W. Dou, Opt. Express 17, 888 (2009). 6. S. Winnerl, B. Zimmermann, F. Peter, H. Schneider, and M. Helm, Opt. Express 17, 1571 (2009). 7. M. U. Shaukat, P. Dean, S. P. Khanna, M. Lachab, S. Chakraborty, E. H. Linfield, and A. G. Davies, Opt. Lett. 34, 1030 (2009). 8. Y. Yu, in Progress in Electromagnetics Research Symposium Proceedings (2010), 1471. 9. J. Liu, L. Wang, J. Li, W. Wang, and Z. Hong, Proc. SPIE 7854, 7854Z-1 (2010). 10. Z. Zhang and T. Buma, Proc. SPIE 7938, 793806 (2011). 11. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, Opt. Express 27, 243 (2002). 12. P. Fischer, C. T. A. Brown, J. E. Morris, C. Lopez-Morsical, E. M. Wright, W. Sibbett, and K. Dholakia, Opt. Express 13, 6657 (2005). 13. J. Van Rudd and D. M. Mittleman, J. Opt. Soc. Am. B 19, 319 (2002). 14. I. Pupeza, R. Wilk, and M. Koch, Opt. Express 15, 4335 (2007). 15. Y.-S. Jim, G.-J. Kim, and S.-G. Jeon, J. Korean Phys. Soc. 49, 513 (2006). 16. A. Bitman, Y. Lumer, I. Moshe, and Z. Zalevsky, J. Opt. Soc. Am. B 29, 1436 (2012). 17. J. W. Goodman, Introduction to Fourier Optics (McGrawHill, 1968).
