A novel video-based microsphere localization algorithm for low contrast silica particles under white light illumination

Abstract

On the basis of a brief review of four common image recognition algorithms for microspheres made of polystyrene or melamine resin, we present a new microsphere localization method for low-contrast silica beads under white light illumination. We compare both the polystyrene and silica procedures with respect to accuracy and precision by means of an optical tweezers setup providing CMOS video microscopy capability. By that we demonstrate that our new silica algorithm achieves a relative position uncertainty of less than ±1 nm for micron-sized microspheres, significantly exceeding the precision of the other silica approaches studied. Second, we present an advancement of our single microsphere tracking method to scenarios where two polystyrene, melamine resin or silica microspheres are in close-to-contact proximity. While the majority of the analysis algorithms studied generate artefacts due to interference effects under these conditions, we show that our new approach yields accurate and precise results.

Introduction

Particle tracking constitutes a key feature in a broad variety of modern optical experiments in the field of micro- and nanoscience. In particular, many optical tweezers experiments rely on an accurate and precise tracking of microspheres, which usually have diameters of only a few micrometres [1], [2]. These microspheres are used, e.g., as probes for research in material, colloid and polymer science [3], [4], [5], [6], [7], [8], [9], as handles for biomolecules [10], [11], [12], [13], [14], [15], [16], [17] or as model systems for fundamental research at the nanometre and piconewton scale [18], [19], [20]. A microscopic diffraction image of one or more microspheres being the basis, there are essentially three established approaches for determining the planar and three-dimensional position of these particles [1], [21], [22]: pattern recognition by video image analysis, the use of a quadrant photo diode (QPD) and video holographic microscopy. While the QPD and the video holographic approach are commonly employed under laser illumination, video image analysis enables to work under white light conditions as they are provided, e.g., by conventional cold light sources. Recently, fast real time particle tracking of polystyrene PS microspheres with a frame rate of 10 kHz was reported to have been accomplished by fibre illumination imaging [23]. Compared to the intrinsically faster QPD and video holograph approaches, image analysis on the basis of white light high numerical aperture video microscopy bears certain technical advantages as there is no need for the exact alignment of an illumination laser [23]. For the realization of video-based microsphere tracking, CMOS cameras are usually used to acquire streams of high frequency grey-scale images of the light backscattered by the beads. These video streams are analyzed either simultaneously to the acquisition or at the end of the experiment after having been stored to RAM or permanent data storage devices [23], [24].

The pattern recognition algorithms applied for video-based microsphere tracking strongly depend on the characteristics of the video microscopy imaging. These are, in turn, defined by the optical setup (including the employed light source type) and the microsphere material. In current experimental applications, mainly microspheres made of polystyrene (PS), melamine resin (melamine formaldehyde, MF) or silicon dioxide (silica, SiO₂) are used. In this paper, we will focus on analyzing white light video microscopy images of such microspheres with diameters of 2–5 μm that are acquired under the common backscattering imaging scenario. As regards PS microspheres producing high contrast images, several accurate and precise pattern recognition algorithms have been developed and employed for two-dimensional [1], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34] and less frequently for three-dimensional tracking [1], [30], [35], [36], [37]. The achieved relative sub-pixel resolution reaches values of ∼1 nm. Commonly, these pattern recognition algorithms are either based on fitting the intensity profile of a video image to an empirical function [33], [34], fitting certain image characteristics to known geometric patterns [31] or on locating the symmetry centre (centroid) by means of cross-correlation analysis [23], [24], [30]. Regarding MF microspheres, the higher refractive index leads to an even higher imaging contrast. Because of this, the PS microsphere localization algorithms can generally be applied for MF beads (cf. Figs. 1 and A.1 in the Appendix) without modification. Because of this, we will not differentiate between PS and MF algorithms in this paper, but rather treat them together as a unit with the designation PS/MF.

For silica microspheres, however, only less accurate pattern recognition algorithms have been available because the contrast of their images is significantly lower compared to PS/MF beads [31]. Silica bead localization has thus been restricted to detecting basic geometric features (usually one circular edge, see Ref. [31]) or to finding the centroid by cross-correlation analysis (see below). In this paper, we will propose a new pattern recognition approach for grey-scale video images of silica microspheres that provides more accurate and more precise results than the algorithms used so far in the context of video microscopy in optical tweezers experiments. In order to motivate our approach, we will first briefly discuss and evaluate four common PS/MF algorithms for single microspheres with special attention paid to accuracy and precision. On the basis of this, we will present a new algorithm for localizing silica microspheres and compare it to the ones hitherto used. We will demonstrate that its accuracy and precision are significantly improved. Finally, special attention will be paid to the scenario where two PS/MF and two silica particles are in close-to-contact proximity because many established algorithms show particle tracking artefacts under these conditions [33], [38]. Here, we will provide a solution for pairs of PS/MF and silica microspheres that is based on our single microsphere tracking algorithms. This new pair localization algorithm is not subject to such close-to-contact artefacts so that the two particles are tracked correctly with a relative position uncertainty of about ±1 nm. In addition, this new approach may easily be extended to more than two beads.