Caustic networks with customized intensity statistics

Abstract

Controlling random light is a key enabling technology that pioneered statistical imaging methods like speckle microscopy. Such low-intensity illumination is especially useful for bio-medical applications where photobleaching is crucial. Since the Rayleigh intensity statistics of speckles do not always meet the requirements of applications, considerable effort has been dedicated to tailoring their intensity statistics. A special random light distribution that naturally comes with radically different intensity structures to speckles are caustic networks. Their intensity statistics support low intensities while allowing sample illumination with rare rouge-wave-like intensity spikes. However, the control over such light structures is often very limited, resulting in patterns with inadequate ratios of bright and dark areas. Here, we show how to generate light fields with desired intensity statistics based on caustic networks. We develop an algorithm to calculate initial phase fronts for light fields so that they smoothly evolve into caustic networks with the desired intensity statistics during propagation. In an experimental demonstration, we exemplarily realize various networks with a constant, linearly decreasing and mono-exponential probability density function.

HiLo microscopy with caustic illumination

“…Most importantly, we show that caustic HiLo provides enhanced robustness against tissue scattering compared to speckle HiLo. Inspired by techniques for customizing caustic intensity statistics [ 11 ] and super-resolution microscopy with “delta” speckles [ 18 ], a promising future direction involves developing custom diffusers to tailor caustic patterns for specific imaging applications.…”

“…Caustics [ 9 ], or randomly focusing patterns characterized by wave-like intensity structures, offer a promising alternative due to their distinct intensity statistical properties, which differ from the Rayleigh statistics of fully developed speckle patterns [ 10 ]. This distinction is advantageous for both illumination efficiency and minimizing photobleaching risks [ 11 ]. Also, owing to the focusing mechanism, caustics not only provide much more versatility in controlling pattern density compared to speckles, but also make the use of incoherent light sources feasible.…”