Quantitative Phase and Intensity Microscopy Using Snapshot White Light Wavefront Sensing

Abstract

Phase imaging techniques are an invaluable tool in microscopy for quickly examining thin transparent specimens. Existing methods are limited to either simple and inexpensive methods that produce only qualitative phase information (e.g. phase contrast microscopy, DIC), or significantly more elaborate and expensive quantitative methods. Here we demonstrate a low-cost, easy to implement microscopy setup for quantitative imaging of phase and bright field amplitude using collimated white light illumination.

Modeling classical wavefront sensors

“…Small z (≈10 µm, as in curvature sensing) achieves wavefront resolution at pixel sampling rate of 100 mm −1 , whereas larger z (≈1 mm, as for most slope tracking sensors) achieves approximately 1/5 pixel resolution in this case. Similar results have previously been obtained in experiments for speckle-tracking wavefront sensors [21,22]. As a short conclusion, Eq.…”

“…(3) could be reformulated in terms of optical path differences (OPD), i.e., without wavelength λ. That said, strictly temporally coherent light sources (such as lasers) are not necessary and this formula works under broadband illumination, as been experimentally verified [22]. With d(r) denoting the OPD, we get φ(r) = 2πd(r)/λ, and Eq.…”

“…We implemented the wavefront solver using an optimization scheme that solves for a and φ in an alternating fashion [22], with source code available online [41]. The real-time solver was implemented in CUDA, running efficiently in parallel, requiring approximately 100 ms solving time per frame for a megapixel input image on a Nvidia Titan X (Pascal) GPU.…”

“…Illumination-side coding techniques include differential phase contrast and variants [1][2][3], Fourier ptychography [4], background illumination [5] or background-oriented Schlieren [6], and many others. 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].…”

Phase‐Retrieval Algebraic Solution Based on Window Modulation

“…Phase retrieval is developed to solve this problem, where the hidden phase information is recovered by digitally computing from the coded intensity patterns, based on a specific optical configuration and the corresponding relationship (decoding method) between the unknown phase and the measurable intensity. There are mainly four types of QPI techniques: external-reference interferometry (ERI), such as digital holography [12], phase-shift interferometry [13], and wavefront-divisional digital holography [14] and its variations based on diverse techniques [15,16]; Self-reference interferometry (SRI), such as Zernike phase contrast (ZPC) [17], generalized phase contrast (GPC) [18] differential interference contrast (DIC) [4], diffraction phase microscopy [4], quadriwave lateral shearing interferometry [20] and phase-shifting phase contrast [21]; Transport of intensity equation (TIE) based deterministic near-field phase retrieval [22] and its generalized forms such as speckle contrast phase imaging [23][24][25]; Phase retrieval from multi-intensity measurements based on diffraction principle [26][27][28][29]. In particular, if the object has a small phase range, then based on firstorder Taylor linearization, there obtain some closed-form analytical solutions [30][31][32].…”