Quantitative phase imaging has many applications for label-free studies of the nanoscale structure and dynamics of cells and tissues. It has been demonstrated that optical coherence phase microscopy (OCPM) can provide quantitative phase information with very high sensitivity. The excellent phase stability of OCPM is obtained by use of a reflection from the microscope cover glass as a local reference field. For detailed intracellular studies a large numerical aperture (N.A.) objective is needed in order to obtain the required resolution. Unfortunately, this also means that the depth of field becomes too small to obtain sufficient power from the cover glass when the beam is focused into the sample. To address this issue, we designed a setup with a dual-beam sample arm. One beam with a large diameter (filling the 1.2 N.A. water immersion objective) enabled high-resolution imaging. A second beam with a small diameter (underfilling the same objective) had a larger depth of field and could detect the cover glass used as a local phase reference. The phase stability of the setup was quantified by monitoring the front and back of a cover glass. The standard deviation of the phase difference was 0.021 rad, corresponding to an optical path displacement of 0.9 nm. The lateral and axial dimensions of the confocal point spread function were 0.42 and 0.84 μm, respectively. This makes our dual-beam setup ideal for three-dimensional intracellular phase imaging.
© 2013 Optical Society of America
Due to superior phase stability, spectral domain OCT  has become the preferred implementation for optical coherence phase microscopy (OCPM). OCPM is a technique that uses interference phase information to obtain quantitative phase images of thin samples [2,3] with submicrometer sensitivity to optical path length changes [4,5].
The technique has been used successfully for, among other things, highly sensitive molecular detection , studies of diffusive and directional motions in cells , studying the beating of embryonic cardiomyocytes  and the label-free detection of action potentials in nerve bundles .
For all these applications high phase sensitivity is essential. In order to reach high phase stability, phase noise introduced by the experimental environment must be excluded. This is the reason that common-path setups [5,10] have been preferred over split-path systems [11,12].
There are several motivations for increasing the numerical aperture (N. A.) of OCPM setups. First of all, a higher N.A. allows the resolution of smaller features. Second, because the phase information obtained is an average of all scatterers in the focal volume, small motions of scatterers that in principle can be detected by OCPM are lost because of averaging with other scatterers in the focal volume. Thus confining the focal volume by increasing the N.A. not only improves the local resolution but also increases the sensitivity for small dynamical changes. Finally, the strong confocal sectioning provided by high-N.A. objectives, in principle, allows the construction of the full three-dimensional phase map of a cell.
There is, however, a problem combining high-N.A. objectives and traditional common-path setups: since common-path setups rely on reflections from both the cover glass and the sample, the limited depth of field of high-N.A. objectives makes it impossible to obtain sufficient power from the cover glass for high-quality OCPM imaging. Assuming a Gaussian sample beam, the depth of field is given by the confocal parameter:
This work demonstrates a new referencing setup. Two coaxial beams of different N.A.  were part of a common-path design and combined with a reference arm to enable high-resolution studies with high phase stability.
Our system used a broadband Ti:sapphire source with a bandwidth of (Integral Pro OCT, Femtolasers). A single-mode fiber-based coupler separated light into sample and reference arms (Fig. 1). A neutral density filter tuned the power of the reference arm to 1.5 μW.
In the sample arm two beams were created with orthogonal polarization states. A linear polarizer was placed in the sample arm to ensure a stable linear polarization state. A polarizing beam splitter divided the beam into - and -polarized states that travel the same path, but in opposite directions through a Sagnac interferometer (Fig. 2). In the Sagnac interferometer a Galilean telescope (focal lengths and 100 mm, ACN127-025-B and AC254-100-B, Thorlabs) magnified the width of the -polarized beam and narrowed the width of the -polarized beam. The polarizing beam splitter recombined the two beams, resulting in two beams of different diameters that shared a common path. The broad beam was focused into the sample for spatially specific phase information. The narrow beam with a large depth of field was used to detect the phase at the cover glass as a local reference. The power in the - and -polarized beams was adjusted to 0.24 and 3.8 μW, respectively, by rotating a half-wave plate in front of the polarizing beam splitter.
Two galvanometer-based optical scanners (model 6220H, Cambridge Technology) were imaged onto each other with two air-spaced double doublets (four AC254-060-B, Thorlabs). The second galvo mirror was then imaged to the back aperture of the objective by the scan and tube lens pair, both part of the inverted microscope setup (IX71, Olympus). A 1.2 N.A. water immersion objective (UPlanSApo , Olympus) was used. The spectrometer employed a fast line scan camera (spL4096-140k, Basler) for acquiring A-lines at a rate of 10 kHz.
To quantify the phase stability of the dual-beam setup, we compared the phase measured at the front and back of a cover glass (No. 1.5, Menzel-Gläser). A drop of water was placed on the back of the cover glass to minimize the reflection of -polarized light from that surface. The standard deviation of the phase difference is a measure for phase stability. The theoretical phase stability depends on the signal-to-noise level of the reflections from the front and back of the cover glass. The phase stability is given by13,14]. By recording 10,000 spectra at different signal-to-noise levels, we measured the dependence of on SNR (Fig. 3).
The phase stability is the unique characteristic of OCPM that allows for the detection of extremely small movements of scatterers within the focal volume. The standard deviation on the measured optical path displacement is given by
The lateral resolution was demonstrated by imaging a 1951 USAF resolution target. A beam scan orthogonal to the gold lines acted as a lateral resolution knife edge test. The derivative of the step response function was fitted with a Gaussian function. The full width at half-maximum (FWHM) of the Gaussian fit was for the broad beam. The FWHM of the narrow beam was .
The axial resolution was measured at a large golden square on the same resolution target. A piezo linear amplifier and position servo controller (E-665.CR, PI) moved the objective in the axial direction by a long-travel objective scanner (P-725.2CD PIFOC, PI). The FWHM of the axial response function was 0.84 μm for the broad beam. The axial response function of the narrow beam that serves as a phase reference had an FWHM of 58 μm.
To demonstrate phase imaging with this setup, we imaged a muntjac skin fibroblast cell (FluoCells prepared slide No. 6, Invitrogen). We scanned an area of 83 μm × 83 μm through the middle of the cell. Over this scan area interference spectra were collected.
Postprocessing was done in MATLAB. Data were mapped linearly in -space, filtered using a Hann window and corrected for dispersion. Then interference spectra were Fourier transformed into depth profiles. The depth at which the cover glass was found varied over the scan area, indicating a curved focal plane. For showing en face images a correction was necessary. The front of the cover glass was fitted with a second-order polynomial surface, whereupon all depth profiles were recalculated after applying a linear phase ramp to the interference spectra to flatten the focal plane. To reduce the noise level of phase at the cover glass, we applied a moving average over nine complex vectors (containing both phase and magnitude) along the fast scanning direction.
The phase difference between phase measured in the sample and at the cover glass was two-dimensional unwrapped. The phase unwrapping software (MATLAB, B. Spottiswoode) included the phase quality-guided path-following method and Goldstein’s branch–cut method . Further, we calculated the vertical derivative of the unwrapped phase to make the edges of structures more visible. In fact, this phase gradient is very similar to images obtained by differential interference contrast microscopy. Both techniques enhance the contrast, emphasizing lines and edges in the image. All images show the same selected region of interest that contained pixels (Fig. 4).
To conclude, a novel (to our knowledge) setup was demonstrated allowing for high-N.A. imaging with an optical coherence phase microscope, while maintaining high phase stability. Both the axial and lateral resolution were demonstrated to be superior to that previously demonstrated in the literature [12,16]. This setup allows label-free, depth-sectioned phase contrast imaging at submicrometer resolution with high motion sensitivity. Three-dimensional quantitative phase imaging of a cell would become possible by measuring a stack of phase images.
This work was supported by the National Institutes of Health (project R21 RR023139) and has received funding from the EC’s Seventh Framework Programme (LASERLAB-EUROPE, grant agreement no. 228334). We also acknowledge support from the Nederlandse organizatie voor Wetenschappelijk Onderzoek (NWO) through a Verniewingsimpuls (VICI) and NWO-groot grant.
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