1. Introduction

Speckle is produced by mutual interference of light source, which widely exists in optical systems [1]. It could be useful or harmful according to specific applications. In speckle interferometry, like laser speckle contrast imaging, speckle patterns are needed to instantaneously visualize tissue blood perfusion [2, 3]. However, speckle would deteriorate the imaging quality in imaging system illuminated with coherent light sources and need to be suppressed in these applications. The typical methods for suppressing speckle include temporal averaging with a moving diffuser, polarization diversity, wavelength and angle diversity, temporal and spatial coherence reduction [4, 5]. In fiber based light sources, speckle can be reduced by increasing the mode number and decoherence among different modes [6, 7]. Essentially, the above-mentioned methods for suppressing speckle are to realize partially coherent or fully incoherent light, which is also attractive for applications such as ghost imaging and free space communication [8-10].

Speckle-free imaging based on different light sources have experienced extensive investigations in recent years. Random laser (RL), which is a stimulated lasing emission in disordered medium has been demonstrated to be well suited for speckle-free imaging, benefitting from its low spatial coherence and high spectral density [11]. Other technical routes such as using semiconductor-based chaotic microcavity laser [12], Anderson localized random Raman lasing [13], have also been investigated for speckle-free imaging. Fiber-optics based amplified spontaneous emission (ASE) sources [7] and random fiber laser (RFL) [14] are even more preferable for full-field speckle-free imaging, since fiber waveguide structure can keep the emission in one direction and combine high power per mode with low spatial and temporal coherence [15, 16]. Additionally, wide tunability of spatial coherence is also investigated to meet the requirements for individual applications [17, 18].

Especially, optical coherence tomography (OCT) also suffers from speckle induced imaging quality deterioration and many researches have been put forward to break through this limitation [19-22]. For OCT technique, the depth resolution relies on the bandwidth of the light source [23], which means broadband light source for speckle-free imaging is demanded. Supercontinuum (SC) light sources, generated by collective nonlinear effects in nonlinear fibers [24], are widely used in OCT application for their super broad spectral bandwidth. However, conventional SC light sources are also not suitable for speckle-free imaging due to their high spatial coherence.

In this paper, decoherence of SC light seeded by RFL is analyzed to realize speckle-free imaging. The characteristics and laws of evolutionary decoherence process in the extra-large mode area step-index multimode fiber (MMF) are revealed and compared between SC light source (with extremely low temporal coherence) and RFL (with moderate temporal coherence). It is found that spectral bandwidth (temporal coherence), number of spatial transverse modes (the core diameter of the optical fiber and the value of numerical aperture (NA)) and decoherence among different modes (the intermodal delays between all supported modes exceed the source coherence length with accumulated dispersion when light propagating in the MMF) all contribute greatly to the reduction of speckle contrast. The combination of SC light source and large core step-index MMF can improve efficiency of decoherence process remarkably. Therefore, speckle-free imaging can be effectively realized by using broadband light source with certain length of MMF. Although using MMF to reduce light spatial coherence is a conventional technique, the evolutionary decoherence process is provided for the convenience of developing SC light source in application of speckle-free imaging. This work not only enriches the research of speckle-free imaging based on fiber-optics, but also provides ways to optimize partially coherent light generation for applications such as ghost imaging.

2. Experimental setup

The experimental setup is shown schematically in Fig. 1. The SC is generated through a half-opened structure composed of a high reflective fiber Bragg grating (FBG, central wavelength of 1461 nm) and a spool of TrueWave fiber (TW fiber, ~16 km, the zero-dispersion wavelength is 1440 nm with a dispersion slope of 0.045 ps/nm²/km, OFS). A Raman pump with central wavelength of 1365 nm is launched into the fiber through a 1365/1461/1550 nm wavelength division multiplexer (WDM1). Conventional random fiber laser can be firstly generated with the selective feedback of the FBG and random distributed Rayleigh scattering along the TW fiber [25, 26]. Since the wavelength of the random lasing lies in the anomalous region of the TW fiber, the generated RFL can be transformed into SC with the increase of random lasing’s power [27, 28]. WDM2 is connected at the end of TW fiber, which is used to split out the unabsorbed 1365 nm pump light, making sure only the generated SC can pass through for imaging. An isolator (ISO) is connected after the WDM2 to eliminate reflections and ensure all the feedback is due only to the randomly distributed Rayleigh scattering during the random lasing process. In this way, SC (at the 1550 nm port of the WDM2) and RFL (at the 1461 nm port of the WDM1) can be generated simultaneously in this structure for further comparison. Besides, the SC seeded by RFL is also preferable for its simplicity and reliability, which is also important for practical applications.

 

Fig. 1 Schematic diagram of experimental setup. WDM, wavelength division multiplexer. FBG, Fiber Bragg grating. TW fiber, TrueWave fiber. ISO, isolator. VOA, variable optical attenuator. MMF, multimode fiber. GG, ground glass.

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An extra-large mode area step-index MMF (core and cladding diameter are 105 and 125 μm respectively, NA is 0.22, YOFC) is spliced after the variable optical attenuator (VOA) to reduce the spatial coherence of the generated SC, since in single mode fiber (SMF) the spatial coherence is still too high for speckle-free imaging. Speckle pattern is measured by an infrared camera (Xenics, Bobcat-640-GigE) after the light is collimated by a lens (focal length of 6.2 mm) and passing through a ground glass (GG) diffuser. Furthermore, a conventional Kohler illumination system (detailed in Ref. [14]) is applied to characterize the imaging quality of the proposed light source.

3. Experimental results and discussions

Characteristics of the generated SC is firstly analyzed. Figure 2(a) corresponds to spectra of the SC with increased pump power measured at the output port of the ISO. It is shown that when pump power is 0.719 W, random lasing with central wavelength of 1461 nm and 3 dB bandwidth of ~0.5 nm is obtained (central wavelength selected and bandwidth determined by the 1461 nm FBG). With the pump power further increasing, the random lasing starts to act as pump source to excite SC with collective nonlinear effects such as modulation instability, stimulated Raman scattering and four wave mixing. Under pump power of 1.972 W, the 3 dB bandwidth of the SC spectrum is ~70 nm, while the 10 dB bandwidth is ~110 nm, which shows the spectrum reaches good flatness under this pump power. It is well known that the temporal coherence is inversely proportional to the spectral bandwidth, defined by $\Delta c={\lambda }^2/\Delta \lambda$ (where $\Delta c$ is coherent length, $\lambda$ and$\Delta \lambda$ are wavelength and spectral bandwidth). Therefore, the RFL-seeded SC has much lower temporal coherence than the RFL itself, and even other conventional lasers or ASE. It is worth to mention that in this paper the SC is considered only under pump power of 1.972 W. Apart from the generated SC, RFL under pump power of 0.719 W is also considered for comparison.

 

Fig. 2 (a) Spectral variation with the increase of pump power. (b) The output power of the generated SC as a function of input pump power.

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The output power of the generated SC is measured at the 1550 nm port of the WDM2, as shown in Fig. 2(b). Under pump power of 1.972 W, the output power is ~140 mW, which is a relatively high output power as those conventional SC pumped by continuous wave. This characteristic would benefit imaging applications such as full-field imaging and OCT system.

To give an evolutionary process of the mode coupling and propagating in the MMF, the length of the MMF, L_MMF, is ~4 m length originally and shortened by 30 cm every time. It is worth to mention that the coupling condition of the light launching into the MMF is well fixed, since the MMF is fusion spliced with the output port of the VOA. The output field profile at each value of L_MMF is measured, and five representative results of L_MMF = 0, 28, 153, 282 and 408 cm are provided in Fig. 3. It is obvious that for SMF output (i.e., MMF length of 0 cm), both the SC and RFL keep typical Gaussian profile with single transverse mode, as shown in Figs. 3(a) and 3(f). As long as this single transverse mode is injected into the MMF, high order transverse modes can be excited and modal interference induced speckle patterns occur clearly, as shown in Figs. 3(b) and 3(g). With increase of L_MMF, the power profile undergoes a quasi-periodic distribution, e.g., the average power concentrates in the outer ring belt in Fig. 3(c), while it concentrates back into the central region of the profile in Fig. 3(d), and it becomes the ring belt distribution again as in Fig. 3(e). This could be caused by self-imaging effect when light propagating through MMF [29]. For both light source cases, the modal interference induced speckle patterns become more and more even in power distribution with L_MMF increasing. This means that the accumulated dispersion leads to notable decoherence, since the intermodal delays between all supported modes exceed the source coherence length [30]. Figures 3(a)-3(e) and Figs. 3(f)-3(j) also reflect that the decoherence process is much more effective for the broad-band SC light than for the narrow-band RFL light.

 

Fig. 3 Mode field profiles of the outputs from SC (a-e) and RFL (f-j) after propagating through 0 cm (a, f), 28 cm (b, g), 153 cm (c, h), 282 cm (d, i) and 408 cm (e, j) MMF.

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There are several methods to evaluate the spatial coherence of a light source, such as classical double-slit Yong’s setup, Mach-Zehnder interferometer. Among them, the speckle contrast measurement not only gives a rough evaluation of the light source’s spatial coherence, but also directly reveals the connection between light source’s coherence and its capability for speckle-free imaging [11]. Figure 4 gives the representative speckle patterns corresponding to the five values of L_MMF, which is measured after the output light passing through the GG diffuser [7]. It can be seen that, with the increase of L_MMF, speckle formation for both the SC and RFL are well prevented and the power distribution becomes more even. For each individual value of L_MMF, the speckle pattern of RFL is clearly more visible than that of the SC. When L_MMF = 408 cm, output pattern of the SC becomes considerably even, without significant concentration of light dots, while speckles are still clearly visible for the RFL.

 

Fig. 4 (a). Speckles formed after light passing through a ground glass diffuser for SC (a-e) and RFL (f-j) propagating through 0 cm (a, f), 28 cm (b, g), 153 cm (c, h), 282 cm (d, i) and 408 cm (e, j) MMF.

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Using the measured speckle patterns, quantitative analysis of the speckle contrast $C={\sigma }_I/〈I〉$ (where ${\sigma }_I$is the standard deviation of the intensity and $〈I〉$ is the average intensity) as a function of L_MMF is shown in Fig. 5. When L_MMF = 0 (single-transverse-mode regime), C is 0.495 ± 0.0169 and 0.678 ± 0.0433 for the SC and RFL respectively, which means the single-transverse-mode light source with lower temporal coherence (i.e., the SC) has lower speckle contrast. Although the 3 dB bandwidth of the SC is 140 times wider than that of the RFL, the speckle contrast only differs by 27%. Therefore, only through the increase of the spectral bandwidth (decrease the temporal coherence) is far less enough to realize speckle free imaging. Therefore, further reducing the spatial coherence is urgently needed. When light is injected into the MMF, the spatial coherence decreases with excitation of high-order transverse modes, and C reduces significantly for both the SC and RFL [31]. The decoherence process of SC is much more effective than that of RFL. For the first 50 cm, C of the SC light source decreases dramatically, i.e., ~68% reduction. With L_MMF increasing, C generally presents a declining trend, meanwhile it also shows non-monotonic decrease and fluctuates slightly as a function of L_MMF. This is related with the quasi-periodical distribution of the mode field profile caused by self-imaging effect when light propagating through MMF (as shown in Fig. 3), which means the redistribution also affects the spatial coherence. Value of C for the RFL varies similarly, but with a much higher value. For L_MMF≈4 m, C of the SC/RFL light source decreases to 0.052 ± 0.0021/0.115 ± 0.0065. Thus, the 4 m long MMF is almost enough for the decoherence of SC to realize speckle-free imaging, since the threshold of human perception of speckle is ~0.04 [32]. The value of C can be further optimized by increasing the length of MMF, and arbitrary partially-coherent light can also be realized by tailoring the length of MMF.

 

Fig. 5 Speckle contrast of the SC and RFL as a function of the length of MMF.

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From Fig. 5, it can be deduced that spectral bandwidth (temporal coherence), the number of the excited spatial mode (core diameter of the fiber, the NA of the fiber and propagating length) and decoherence among different modes (accumulated dispersion) all greatly contribute to the reduction of speckle contrast. For light sources with different bandwidth, no matter in a SMF or in a fixed-length MMF, light with broader bandwidth would generate lower speckle contrast. For light source with certain bandwidth, the excitation of high order transverse modes and their decoherence during propagation would produce lower speckle contrast. The most efficient way for suppressing the speckle formation should be broaden the bandwidth of light, increase the core diameter and the length of MMF simultaneously.

To realize a sufficiently low value of C for speckle-free imaging, MMF with ~30 m is considered. Figures 6 gives the mode field profiles (Figs. 6(a) and 6(d)), speckle patterns (Figs. 6(b) and 6(e)) and images of a USAF resolution chart (Figs. 6(c) and 6(f)) for the SC (Figs. 6(a)-6(c)) and RFL (Figs. 6(d)-6(f)) respectively. It is observed that output pattern of the SC becomes a standard Gaussian shape, and output pattern of the RFL shows very weak speckles. The spatial contrast is calculated to be 0.0319 ± 0.0052 and 0.0393 ± 0.0022 for the SC and the RFL, respectively. Both the two cases fulfill the requirement of speckle-free imaging considering human perception is ~0.04. The same imaging setup based on a conventional Kohler illumination system as has been discussed in the previous work is applied here to characterize the imaging quality for the two light sources [14]. It is worth to mention in this imaging setup, the GG is also used as diffuser which is placed before the USAF chart. In this way, all the bars and numbers of the USAF chart are clearly visible with uniform illumination of either the SC or the RFL, as shown in Figs. 6(c) and 6(f). Additionally, the time domain characteristics of the SC for the decoherence process in speckle-free imaging are of great interest for real-time imaging applications, since the RFL pump has strongly suppressed amplitude fluctuations and no evidence of resonant frequency.

 

Fig. 6 (a). Mode field profiles (a, d). Speckles formed after passing through a ground glass diffuser (b, e) and images of the USAF resolution chart (c, f) for SC and RFL after propagating through 30 m MMF.

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4. Conclusion

In this paper, the evolutionary decoherence processes of SC light source and RFL in extra-large mode area step-index MMF are analyzed. It is shown that spectral bandwidth, the number of transverse modes and the decoherence among the excited transverse modes all greatly contribute to realizing low speckle contrast for speckle-free imaging. Combination of SC and extra-large mode area step-index MMF can greatly enhance the efficiency of speckle reduction, thanks to low spatial coherence of the SC and multi-transverse modes supported by the MMF. This work would enrich the research of speckle-free imaging to serve the applications that demand broadband light source and benefit the researches where partially coherent light source is needed.