Resolution limit of single-pixel speckle imaging using multimode fiber and optical phased array

Abstract

Imaging through a multimode fiber (MMF) is a promising strategy for in vivo endoscopy due to its nature of simultaneously realizing high spatial resolution and minimal invasiveness. In MMF-based speckle imaging systems, a spatial light modulator (SLM) with a large number of pixels is commonly employed to enable independent controls of all the linearly polarized (LP) modes inside the MMF. Here, instead, we show that such an SLM can be replaced by a compact optical phased array (OPA) with a much smaller number of phase shifters without causing any penalty in resolution or sensitivity. Due to the nonlinear process inherent in field-to-intensity conversion, an OPA with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> phase shifters is capable of generating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>∼</mml:mo></mml:mrow><mml:mrow class="MJX-TeXAtom-ORD"><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math> independent illumination patterns. Since the resolution limit imposed by an MMF with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi></mml:math> LP modes per polarization is approximated as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>4</mml:mn></mml:mrow><mml:mi>M</mml:mi></mml:math> , we show that only <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mn>4</mml:mn><mml:mi>M</mml:mi></mml:msqrt></mml:math> phase shifters are essentially required to utilize the full spatial capacity of MMF. We can therefore enjoy the unique benefits of a low-cost, compact, and high-speed OPA that does not require thousands of phase shifters to achieve high-resolution imaging through an MMF.

Topics & Concepts