effective duty cycle of galvanometer-based scanners: impact on oct imaging

Effective duty cycle of galvanometer-based scanners: Impact on OCT imaging

Virgil-Florin Duma,∗1,2 Patrice Tankam3, Jinxin Huang4, Jungeun Won5, and Jannick P. Rolland3,5

1 3OM Optomechatronics Group, Aurel Vlaicu University of Arad, 77 Revolutiei Ave., 310130 Arad, Romania

2 Doctoral School, Polytechnics University of Timisoara, 1 Mihai Viteazu Ave., Timisoara 300222, Romania

3 The Institute of Optics, University of Rochester, 275 Hutchison Rd., Rochester, NY 14627-0186, USA

4 Department of Physics and Astronomy, University of Rochester, 275 Hutchison Rd., Rochester, NY 14627-0186, USA

5 Department of Biomedical Engineering, University of Rochester, 275 Hutchinson Road, Rochester, NY 14627-0186, USA

ABSTRACT

We study experimentally the scanning functions of galvanometer-based scanners (GSs) in order to optimize them for biomedical imaging in general, and for Optical Coherence Tomography (OCT) in particular. The main scanning parameters of the scanning process are taken into account: theoretical duty cycle (of the input signal of the GS), scan frequency (fs), and scan amplitude (θm). Triangular to sawtooth scanning regimes are thus considered. We demonstrate that when increasing the scan frequency and amplitude, the scanning function (i.e., the angular position of the galvomirror) is not able to follow anymore the input signal. Furthermore, as the theoretical duty cycle is increased, the result is unexpected: the effective duty cycle actually decreases – for high fs and θm. A saturation of the device therefore occurs. The practical limits of this phenomenon are discussed. GS users are thus provided with a multi-parameter analysis that allows them for optimizing their scanning regimes and to avoid pushing the devices to their limit – when that actually results in decreasing the quality of the images obtained, by example in OCT. Gabor Domain Optical Coherence Microscopy (GD-OCM) images are made to show effects of this phenomenon.

Keywords: Galvanometer scanners, biomedical imaging, Optical Coherence Tomography, GD-OCM, duty cycle, scanning functions, sawtooth signals, triangular signals, modeling.

1. INTRODUCTION Galvanometer-based scanners (GSs) are one of the most utilized types of laser scanners nowadays [1,2]. They provide a good scanning speed, high precisions and repetability, as well as resonable compactness [3-5]. We have reviewed the main types of optical and laser scanners in [6-8], with a focus on their capability of achieving the expectations of high-end applications such as biomedical imaging – with a focus on Optical Coherence Tomography (OCT) [9-11], but also on Confocal Microscopy (CM), their combinations or related techniques [12].

Thus, polygon mirror scanners provide superior scan speeds but have mechanical issues, the facet is eccentric with regard to the pivot (therefore the scanning function is more complicated), and are more expensive than the GSs [13-17]. Bi-dimensional (2D) refractive scanners with Risley prims are interesting and promising due to their compactness and to the superior scan speeds they provide, but they produce complicated scan patterns [18,19], that have to be followed by appropriate algorithms to reconstruct images [20]. The raster scans of the 2D GSs are in this respect much easier to follow. Acousto- or electro-optical scanners have superior positioning capabilities, as they do not have the issues produced by mechanical inertia – which characterize all the above solutions; however, they are utilized only in niche applications so far, at least in biomedical imaging. The same aspect is actually valid for polygon mirrors and Risley prisms scanners, as GSs remain the most utilized scanning device in biomedical imaging.

∗[email protected]; phone: +40-751-511451; site: http://3om-group-optomechatronics.ro/

Design and Quality for Biomedical Technologies VIII, edited by Ramesh Raghavachari, Rongguang LiangProc. of SPIE Vol. 9315, 93150J · © 2015 SPIE · CCC code: 1605-7422/15/$18

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The technological advancements have provided GSs with an almost standard construction in terms of oscillatory elements, pivots, heat sinkers, mirrors, sensor systems, and testing [3-5, 21-23] – with efforts being made by specialized companies in meeting the requirements of certain domains of application, industrial or biomedical. The aspects related to optimal scanning functions and their related control structures are issues that still have to be improved, as discussed in our previous works, as well [24-29]. In this paper we shall point out some of the main conclusions of our previous researches in this respect, as well as our current investigations on the optimal use of GSs in OCT.

2. MECHANICAL INERTIA AND SCANNING FUNCTIONS OF GALVOSCANNERS One of the main issues of GSs is their mechanical inertia. In comparison with polygon mirrors (which rotate continuously), the oscillatory element (moving magnet and galvomirror – Fig. 1(a)) of the GS has to stop and turn. The scan frequency speed of the device is therefore much lower than for the rotating polygons [7], while the scan is bi-directional. The latter may also be a disadvantage, as in biomedical imaging, by example, uni-directional scan is often more convenient.

The mechanical inertia of the oscillatory element of the GS means that the stop from a given angular scan velocity cannot be made instantaneously; nor can the velocity be increased instantaneously after the stop. The decelerating and the accelerating portions produce a non-linearity of the scanning function of the device (Fig. 1(b)), which is its output signal, given by the current angular position of the galvomirror. These non-linearities may be neglected at low scan frequencies and amplitudes, when one may say that the output signal of the GS is capable to follow almost exactly its input signal (roughly, as shown in [26], up to 50 Hz). However, as the scan frequency (fs) is increased, the stop-and-turn portions of the scanning functions grow more and more non-linear, especially at the high scan amplitudes (θm) which one may want to use in order to have as large as possible fields-of-view (FOV).

This phenomenon has been documented in detail in [26], for three of the most utilized input signals of the GSs: (1) sawtooth, (2) triangular, and (3) sinusoidal. We have thus studied the effect of the scanning regimes and parameters (fs and θm) on the duty cycle η of the device, defined as the time efficiency of the scanning process: ratio of the active time ta (for which the scan is performed with constant velocity) and the time period (T) of the oscillation of the galvomirror.

Figure 1. (a) Schematic illustrating the operating principle of a galvanometer-based scanner (GS). Notations: H, total

scan amplitude; θm, angular scan amplitude; xa, amplitude of the linear scan; θa, scan amplitude corresponding to linear scan; θ(t), scan angle (angular scanning function); x(t), current position of the output beam (linear scanning function); L, distance from the galvomirror axis to the lens; J, axial mass inertia moment of the mobile element (including the galvomirror); k, elastic coefficient; c, damping coefficient. (b) input (triangular) signal and output (linear plus non-linear) signal of the device.

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One has to point out that in most applications (including in biomedical imaging, in general and in OCT, in particular) a constant scan velocity is most convenient, in order to have non-distorted images and thus to avoid post-processing of images as a condition for real time in vivo imaging.

Sinusoidal scan should be, in this respect, avoided, as discussed in [26], despite the advantage of a much smoother mechanical regime of this type of scan – for which the GS can, in consequence, reach much higher (usually double) maximum scan frequencies. An issue remains with resonant scanners, usually built as Micro-Electro-Mechanical Systems (MEMS). These are often utilized in endoscopic probes, a hot topic for biomedical imaging. Most of the MEMS are driven with sinusoidal signals (and few with triangular [30]), so the post-acquisition processing of OCT images comes as a must. The same situation is met when MEMS are utilized in the construction of handheld scanning probes, to obtain probes that are as light as possible [31]. One of our groups has approached this problem by utilizing a 1D GS driven with triangular signals in a simple and light handheld probe, thus avoiding the post-acquisition processing in the OCT system [32-34].

Indeed, from the three input signals of GSs, the experimental studies concluded that triangular scan is the best, as it produces the most distortion-free OCT images [26]. Sinusoidal scanning is the worst from this point of view, while sawtooth scanning have the flyback portions that are increasingly longer at higher fs. Distortions also exist for triangular scanning but they include only several A-scans in OCT, at the margins of the FOV.

The experiments in our group have used in [26], beside direct galvoscanning measurements (of the current position of the galvomirror), imaging with Fourier Domain OCT (Fig. 1, [35]). Several rules-of-thumb were extracted from the study in order to allow for galvoscanners users to make the best of these devices (i.e., to select the parameters of the scanning regimes in OCT). Another group utilized these results in sawtooth scanning applied in Doppler OCT for scanning the retina [36], and discarded the distorted portions to backstitch individual scans in order to obtain a larger image. The increases of the flyback portions caused by the high fs were used, as they have been previously documented.

3. EFFECTIVE DUTY CYCLE OF GALVOSCANNERS Our groups continued this research in [37] by studying the effective duty cycle of the GS (i.e., of its output signal), with regard to the three main scan parameters: theoretical/ideal/imposed duty cycle ηt (i.e., of the input signal of the GS), scan frequency (fs), and scan amplitude (θm). Thus, even the triangular scan can be considered a sawtooth one with ηt equals 50% - if uni-directional scan is considered. In our study, values of ηt from 50 to 90% were considered.

The effective duty cycle η was determined with regard ηt for scan frequencies fs between 50 and 600 Hz and for sets of scan amplitudes θm from 0.2 V to 3.2 V for 50 < fs < 200 Hz; for 200 < fs < 600 Hz the limit scan amplitude is lower in order to provide stability of the oscillations (e.g., 0.8 V for fs equals 500 Hz) - as studied in [26]. In all these experiments, 1V in θm stands for about 7.6 degree optical.

From the series of measurements – as shown by example in Fig. 2, for ηt equals 50% (first column) and ηt equals 90% (second column) – the functions η(ηt) for each fs and θm were obtained. From the conclusions, the most important ones are:

(i) The ƞ(ƞt) functions start identical, regardless of θm for low fs. The graphs of the functions spread more and more for higher fs. The maximum spread is around 200 Hz; at even higher fs they get closer again because all the values of ƞ are dropping, for the now smaller interval of possible θm.

(ii) When the scanning device is pushed to the limit in terms of ƞt, the effect may be opposite to the expectation when one employs high fs and θm. Thus, for fs around 200 Hz, a bending of the ƞ(ƞt) graphs is produced at the higher values of θm. As ƞt increases beyond 75%, ƞ actually starts to decrease, so that a maximum in ƞ is reached around ƞt equals 75%. This phenomenon is more significant at intermediate values of fs as at higher values (e.g., towards 500 Hz), all the values of ƞ drop. Although the phenomenon is still present, it becomes less significant. Thus, for fs> 300 Hz, while increasing ƞt, ƞ remains approximate constant; a saturation of the scanning regime has been reached. However, the same practical conclusion remains valid for GS users: one must not push the device to the limit, as an increase of ƞt over 75% does not provide the results expected, while it only has a negative impact on the device from a mechanical point of view.



(a2) (b2)

Figure 2. Triangular (first column) and sawtooth (second column) scanning functions of the GS: ideal ((a1) and (b1)) –

for low frequencies and with non-linear portions ((a2) and (b2)) – for high frequencies (i.e., 500 Hz).

A mathematical model of the effective duty cycle was obtained for three cases [37]:

(a) For triangular input signals the output signals remain triangular, but with an increasing non-linearity (as fs and θm) for the stop-and-turn portions – Fig. 2(a1), (a2).

(b) For sawtooth input signals there are two relevant cases:

(b1) For low fs and θm, the output function is just beginning to curve due to inertia as fs increases. The peaks of the θ(t) output/scanning function have the same positions as those of the input function. (b2) For higher θm, the two peaks that the graph of θ(t) has per period T migrate, with an increasing non-linearity of the respective portions. This shift of the output signal of the GS has also been documented in the media files provided in [26]. At a certain scan frequency fs, for each ƞt this phenomenon leads to a complete shift of the sawtooth profile to the triangular one. The final profile is triangular with different non-linear portions, as determined experimentally in Fig. 2(b2) by example – for θm equals 0.8 V at fs equals 500 Hz.

4. IMPACT OF THE EFFECTIVE DUTY CYCLE ON OCT IMAGING To study the impact of the above phenomena in OCT, imaging experiments using Gabor Domain-Optical Coherence Microscopy (GD-OCM) were made.

We utilized a custom-designed GD-OCM setup, which provides a high depth and lateral resolution, of 2 µm across a FOV of 2 x 2 mm2, and imaging depth of 1.6 mm [38, 39]. The source is a super luminescent diode (SLD) with the center wavelength of 840 nm and a FWHM of 100 nm (BroadLighter D-840-HP-I, Superlum®, Ireland). A custom spectrometer with a high-speed CMOS line camera (spl4096-70km, Basler Inc.) was implemented to acquire the spectral information [40]. The system allows for a real-time visualization of the sample after the acquisition, using

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multiple Graphic Processing Units (GPU) recently implemented in the system [41]. The probe is equipped with a dual axis XY galvoscanner (Cambridge Technology).

A sample with a regular grid structure was imaged. For high fs and θm, the non-linear portions of the scanning function shown in Fig. 2 produce artifacts in the image of a regular structure image – distortions, as shown in Figs. 3 and 4, in which results are shown for both scanning regimes: triangular and sawtooth.

The mathematical models developed for both scanning regimes can be validated by using the time intervals that can be measured from these images for each scan parameter.

The different parts of the sample imaged were then stitched together in order to obtain the entire image of the sample [37]. Artifact-free collated image can be thus obtained, even at high scan frequencies fs (i.e., up to 600 Hz).

Figure 3. OCT imaging of a regular structure with two scanning regimes: (a) triangular, (b) sawtooth with a theoretical

duty cycle ƞt equals 75%, and (c) sawtooth with ƞt equals 90% - all of them considered for the same scan amplitude (θm equals 1.6 V, where 1 V stands for about 7.6 degree optically) and three different scan frequencies (fs): 50 Hz (a1, b1, c1), 300 Hz (a2, b2, c2), and 500 Hz (a3, b3, c3).

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Figure 4. OCT imaging of the same samples with regular structures, with the sawtooth scanning regime with ƞt equals 75% and for the same scan amplitude (θm equals 1.6 V) and three different scan frequencies (fs): 100 Hz (a), 300 Hz (b), and 500 Hz (c).

5. DISCUSSIONS AND CONCLUSIONSThese studies demonstrated that triangular or even sawtooth scanning, but with certain, optimized parameters is best to obtain artifact-free images with a maximum possible effective duty cycle [26, 37]. However, these researches only addressed the case of the most common input signals of GSs: sinusoidal, sawtooth, and triangular. Besides them, there are other custom-made input signals that may be used. In literature such aspects have been discussed, and it was stated that a triangular signal with specially made non-linear sinusoidal portions is the one capable to produce the highest duty cycle [5].

We have performed an in-depth analysis of the different linear plus non-linear scanning functions [25]: linear plus polynomials of different orders and linear plus different sinusoidal-type functions for the stop-and-turn portions. We demonstrated theoretically that, contrary to what has been considered in literature [5], not linear plus sinusoidal, but linear plus parabolic input signals produce the highest possible effective duty cycle of the device [25].

Another direction of research in our groups comprises of the command functions of the GSs that are capable to produce the above input signals, as well as the advanced control structures of the device [28, 29]. The latter are necessary as one may minimize the response time or the precision of the GSs. An additional PID-L1 controller and a Model-based Predictive Control (MPC) structure were proposed to drive the GSs. We presented a brief overview of our main directions of research regarding GSs, especially for biomedical imaging. Besides the aspects related to optimizing the duty cycle of GSs, scanning and command functions, as well as control structures are essential in order to make the best of the existing scanners technology.

Future work in our groups on these topics in our group include other scanning systems with combinations of polygons and GSs by example [42-44], application of 1D and 2D GSs in handheld scanning probes for OCT [32, 33], for in vivo medical imaging [45], but also for real time imaging in industrial applications [46].

ACKNOWLEDGMENTS

This work was supported by a Partnership grant of the Romanian Authority for Scientific Research, CNDI–UEFISCDI project number PN-II-PT-PCCA-2011-3.2-1682 (http://3om-group-optomechatronics.ro/), the II-VI Foundation, and an NSF STTR grant awarded to LighTopTech Corp. Part of this work was pursued in 2009-2011, with support from the US Department of State through a Fulbright Senior Research Grant 474/2009 (PI Prof. V.-F. Duma) and the New York Science and Technology Association for Research (NYSTAR) Award 054048-002 (PI Prof. J.P. Rolland); they are also gratefully acknowledged.

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effective duty cycle of galvanometer-based scanners: impact on oct imaging

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