Aberration recovery by imaging a weak diffuser

Abstract

We present a computational method for field-varying aberration recovery in optical systems by imaging a weak (index-matched) diffuser. Using multiple images acquired under plane wave illumination at distinct angles, the aberrations of the imaging system can be uniquely determined up to a sign. Our method is based on a statistical model for image formation that relates the spectrum of the speckled intensity image to the local aberrations at different locations in the field-of-view. The diffuser is treated as a wide-sense stationary scattering object, eliminating the need for precise knowledge of its surface shape. We validate our method both numerically and experimentally, showing that this relatively simple algorithmic calibration method can be reliably used to recover system aberrations quantitatively.

Extreme ultraviolet microscope characterization using photomask surface roughness

“…A blank EUV photomask conveniently meets these requirements, due to intrinsic surface roughness 22 , 23 . Similar methods have been demonstrated in optical microscopy, using a diffuser with index-matching oil 24 , 25 , and in electron microscopy, using amorphous carbon (i.e the Zemlin tableau method) 26 – 29 .…”

“…These properties enable the use of a forward model that describes the spatial Fourier spectrum of an intensity measurement, , under plane wave illumination angles indexed by j , and computational DC-suppression. The model, derived in 25 , is: where are independent and identically distributed, is a deterministic Gaussian support function related to the mean surface roughness, and denotes element-wise multiplication. The Rayleigh distribution parameter, , is also related to the surface roughness and can be estimated from data (see “ Methods ”).…”

“…Using a variety of azimuthal angles, , further diversifies the interference patterns in measurements. We model the spatial Fourier spectrum of the photomask as an instance of white noise, , within a Gaussian support, 24 , 25 . Since the atomic-scale features on the photomask are smaller than the imaging resolution, this Gaussian support extends beyond the imaging bandlimit and ensures that the object probes the entire pupil.…”

Large dynamic range autorefraction with a low-cost diffuser wavefront sensor

“…In this report, we develop a diffuser wavefront sensor (DWS) for autorefraction, characterize performance tradeoffs, and compare metrics that are relevant for autorefraction. We show that wavefronts can be measured by the deformation of incoherent caustic intensity patterns, rather than relying on the memory effect of speckle intensity patterns utilized in other works [26][27][28][29]. By constructing and testing a DWS and a SHWS in parallel, we measure refractive error in a model eye and directly compare the performance of the two devices under three different illumination techniques: a laser diode (LD), a laser diode with a laser speckle reducer (LD+LSR), and an incoherent light emitting diode (LED).…”

“…Recently, Berto et al demonstrated the fundamentals for using a diffuser to measure high resolution wavefronts using integrated transverse displacement maps, which were generated from non-rigid image registration of speckle pattern distortion between planar and aberrated wavefronts [26]. Further, Gunjala et al used a statistical approach to reconstruct aberration profiles from multiple images through a weak diffuser at distinct angles of illumination [29].…”