The application of radiation pressure force to trap atoms and neutral particles was pioneered by Arthur Ashkin cite {ashkin70s}. This was followed by a series of fundamental experiments using the radiation pressure force cite{ashkin80}, for example in the displacement and levitation in air and water of micron-sized particles cite{ashkin-levitate}, and together with Steve Chu , for the development of a stable three-dimensional atom cooling and trapping experiment using frequency-detuned counter-propagation laser beams cite {chu-MOT}. In particular, the demonstration of {optical tweezers} cite{ashkin-tweezer}, based largely on the strength of the transverse gradient of a single focused Gaussian optical beam, has made a significant contribution to optical trapping in biology citate{ashkin-tweezera }. systems, optical tweezers were initially used to trap and manipulate viruses and bacteria mentioned{bacteria}. This was followed by an increasing number of experiments using optical tweezers for measurements of DNA/RNA elongation and unfolding (cite{gore, bustamantea, bustamantea, bryant-dna, smith}), intracellular probing, gamete cell manipulation, trapping of vesicles, membranes and colloids cite {langblock, neuman} and DNA sequencing using RNA polymerase cite {greenleaf}. In particular, for the first time, the quantitative biophysical study of the kinetics of cite{bustamante-motor} molecular motors (e.g. myosin cite{myosin} and kinesin cite{kinesin}) at the single molecule level was made possible by the use of optical tweezers. Coupled with conventional position-sensitive detectors (e.g. using quadrant photodetectors cite {langblock, gittes, pralle}), the position and force on a bead bound to a molecular mot… at the center of the paper… .s of a single base pair ladder (e.g. 3.4~AA~on dsDNA) cite{moffitt} and the bacterial DNA translocase FtsK moves at speeds of 5 kilobases per second cite{pease}. Therefore, advanced particle detection could elucidate these finer features with higher sensitivity than conventional particle detection techniques in optical tweezer systems. This paper begins by formalizing an optimal parameter estimation procedure for particle detection based on the analysis of the spatial properties of the scattered field from a particle in an optical tweezer. We show that split sensing is suboptimal and consequently propose an optimal measurement scheme based on homodyne spatial sensing. The effectiveness of particle detection is evaluated using signal-to-noise ratio (SNR) and sensitivity measurements; and the effectiveness of homodyne spatial sensing and split sensing systems is compared.
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