OPTICS LETTERS / Vol. 38, No. 22 / November 15, 2013

Angular-domain scattering interferometry Dustin W. Shipp,1 Ruobing Qian,2 and Andrew J. Berger1,2,* 1 2

The Institute of Optics, University of Rochester, 275 Hutchison Rd, Rochester, New York 14627, USA

Department of Biomedical Engineering, University of Rochester, 275 Hutchison Rd, Rochester, New York 14627, USA *Corresponding author: [email protected] Received August 19, 2013; revised October 10, 2013; accepted October 10, 2013; posted October 10, 2013 (Doc. ID 195953); published November 12, 2013 We present an angular-scattering optical method that is capable of measuring the mean size of scatterers in static ensembles within a field of view less than 20 μm in diameter. Using interferometry, the method overcomes the inability of intensity-based models to tolerate the large speckle grains associated with such small illumination areas. By first estimating each scatterer’s location, the method can model between-scatterer interference as well as traditional single-particle Mie scattering. Direct angular-domain measurements provide finer angular resolution than digitally transformed image-plane recordings. This increases sensitivity to size-dependent scattering features, enabling more robust size estimates. The sensitivity of these angular-scattering measurements to various sizes of polystyrene beads is demonstrated. Interferometry also allows recovery of the full complex scattered field, including a size-dependent phase profile in the angular-scattering pattern. © 2013 Optical Society of America OCIS codes: (290.2558) Forward scattering; (290.5850) Scattering, particles; (350.5030) Phase. http://dx.doi.org/10.1364/OL.38.004750

The angular distribution of elastically scattered light can provide structural details about biological specimens, such as cells and tissues, with precision finer than the resolution of microscope images. Different types of sample volumes can be studied. In many publications, quasi-collimated light strikes an area at least 100 μm in diameter, and the average sizes of whole cells [1], nuclei [2], mitochondria [3], or other organelles [4] in that region are calculated from the scattered intensity pattern. In such cases, the region characterized by the measurement is the size of many cells. Alternatively, angular scattering can characterize regions at the submicrometer level. For example, a microscope with an angular-domain optical processor can report size-sensitive information at a pixel pitch of less than 0.4 μm [5]. The complementary technique of wavelength-resolved elastic scattering can also estimate scatterer sizes from such small volumes [6]. Digital holography techniques have also recently provided measurements of forward-directed angular scattering from cells [7–9]. Although the optical systems in these quantitative phase imaging (QPI) techniques directly record the electric field Ex; y in the sample plane with subcellular resolution, one can indirectly calculate the ensemble scattering as a function of angle, Eθ; ϕ, by numerical propagation of Ex; y to the far field, via a 2D Fourier transform. In this Letter, we describe angular-domain scattering interferometry (ADSI) as a useful method for characterizing scattering regions on the scale of a single biological cell, i.e., 5–20 μm in lateral dimension. In this approach Eθ; ϕ is recorded directly, rather than computed from Ex; y. Directly recording Eθ; ϕ spreads the angular information from each scatterer over the full range of detection pixels, maximizing the retrievable information. In contrast, derivations from Ex; y images confine such information to many fewer pixels, introducing potential binning errors in the subsequent digital Fourier transform and redistributing shot noise from unscattered light. The increased angular sensitivity (obtained at the expense of spatial resolution) allows for more precise size extractions through comparison to models such as Mie 0146-9592/13/224750-04$15.00/0

theory. The additional information provided by interferometry enables speckle-reduction techniques that are not possible with intensity-only measurements. As we show below, ADSI permits the isolation of Mie-scattering signatures and the accurate estimation of scatterer sizes in the presence of speckle, where intensity-only analysis fails. The ADSI system, like most intensity-based angularscattering instruments, makes its measurements in the Fourier plane, conjugate to the back focal plane of the microscope objective. In this plane, the speckle grain size is the same as the smallest resolvable angular feature. This can be calculated as δθs  0.61λ∕D, where D is the diameter of the illuminated region of the sample [10]. When measuring scattering from many cells or from tissue, this illuminated region can be several hundred micrometers in diameter and the speckle features are too small to affect analysis of the scattering pattern. When single cells are studied, however, the illuminated region is intrinsically smaller, which makes the speckle features larger. The consequences of a cell-sized illumination region are illustrated in Fig. 1, which shows angular-scattering patterns recorded from a murine cancer cell and from a static assembly of 1 μm diameter polystyrene beads (a common model for organelle-sized scatterers). These scattergrams suggest that scattering signals from biological cells and static beads are affected similarly by speckle. In each case, a 14 μm diameter region in the

Fig. 1. Noninterferometric scattering intensity from (a) a single squamous murine cancer cell and (b) eight 1 μm beads. In both figures, the smooth scattering distribution predicted by Mie theory is obscured by speckle. The speckle grain size agrees with the predicted value of about 2°. © 2013 Optical Society of America

November 15, 2013 / Vol. 38, No. 22 / OPTICS LETTERS

sample plane was illuminated by the beam waist of a gently focused, 785 nm diode laser (bandwidth

Angular-domain scattering interferometry.

We present an angular-scattering optical method that is capable of measuring the mean size of scatterers in static ensembles within a field of view le...
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