Abstract
We present an image formation model for deterministic phase retrieval in propagation-based wavefront sensing, unifying analysis for classical wavefront sensors such as Shack-Hartmann (slopes tracking) and curvature sensors (based on Transport-of-Intensity Equation). We show how this model generalizes commonly seen formulas, including Transport-of-Intensity Equation, from small distances and beyond. Using this model, we analyze theoretically achievable lateral wavefront resolution in propagation-based deterministic wavefront sensing. Finally, via a prototype masked wavefront sensor, we show simultaneous bright field and phase imaging numerically recovered in real-time from a single-shot measurement.
Highlights
Wavefronts cannot be directly measured by image sensors
Our model extends the degrees of freedom for classical Transport-of-Intensity Equation (TIE) systems to allow for a custom modulation mask (reflected as a customizable reference image I0(r), for which in TIE is usually uniform), making it possible for single-shot measurement
The original image sensor was replaced by our wavefront sensor
Summary
Wavefronts (or, phase) cannot be directly measured by image sensors. To encode wavefronts into image measurements, one may opt for either illumination-side or sensor-side coding, as the duality reflects. Sensor-side coding, on the other hand, employs a point light source (so-called guide star) or annular illumination [7], in company with custom optics or moving elements to encode wavefronts onto image sensor, including Shack-Hartmann [8] or Hartmann masks [9], pyramid sensors [10], lateral shearing interferometry gratings [11,12], curvature sensors [13,14,15], and speckle-tracking sensors [16,17,18,19,20,21,22]
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