Fluorescence Interferometry Principles and Applications in Biology

Abstract

The use of fluorescence radiation is of fundamental importance for tackling measurement problems in the life sciences, with recent demonstrations of probing biological systems at the nanoscale. Usually, fluorescent light–based tools and techniques use the intensity of light waves, which is easily measured by detectors. However, the phase of a fluorescence wave contains subtle, but no less important, information about the wave; yet, it has been largely unexplored. Here, we introduce the concept of fluorescence interferometry to allow the measurement of phase information of fluorescent light waves. In principle, fluorescence interferometry can be considered a unique form of optical low-coherence interferometry that uses fluorophores as a light source of low temporal coherence. Fluorescence interferometry opens up new avenues for developing new fluorescent light–based imaging, sensing, ranging, and profiling methods that to some extent resemble interferometric techniques based on white light sources. We propose two experimental realizations of fluorescence interferometry that detect the interference pattern cast by the fluorescence fields. This article discusses their measurement capabilities and limitations and compares them with those offered by optical low-coherence interferometric schemes. We also describe applications of fluorescence interferometry to imaging, ranging, and profiling tasks and present experimental evidences of wide-field cross-sectional imaging with high resolution and large range of depth, as well as quantitative profiling with nanometer-level precision. Finally, we point out future research directions in fluorescence interferometry, such as fluorescence tomography of whole organisms and the extension to molecular interferometry by means of quantum dots and bioluminescence.

Introduction

Fluorescence imaging is a rapidly evolving field, with a broad spectrum of applications in biology and medicine. In general, the wide variety of existing fluorescence imaging techniques can be classified into four groups, namely, nanoscopy, microscopy, mesoscopy, and macroscopy, according to their achievable optical resolution and depth of penetration (Fig. 1). Typically, these methods aim to discriminate fluorescence photons emerging from one given point within the imaged specimen against most other fluorescent light. To accomplish this task, we used various fluorescence-discrimination mechanisms, such as on–off photo-switching of fluorophores,^1–5 stimulated emission depletion of fluorescence,^5–7 spatial filtering of out-of-focus florescence photons by confocal detection schemes,⁸ nonlinear excitation (e.g., two-photon absorption),^9,10 evanescent near-field diffraction,¹¹ and off-axis collection of fluorescent light.^12,13 Other techniques such as fluorescence molecular tomography¹⁴ and bioluminescence imaging¹⁵ use diffusion models of photon propagation in turbid media to solve the inverse imaging problem. Common to most existing and proposed fluorescence imaging methods is their reliance on detection of the fluorescence intensity (rather than the fluorescent field) to provide optical sectioning of the sample. The reason for this characteristic is simple: Photodetectors can extract only the magnitude of the incident optical field. As we discuss below, however, the phase of the fluorescent wave also encodes information, which would be useful for a broad spectrum of application in the life sciences.

FIGURE 1.

Dependence of various fluorescence imaging techniques on spatial resolution and depth of penetration. FRET, fluorescence resonance energy transfer; NSOM, near-field scanning optical microscopy; PALM, photoactivated localization microscopy; STORM, stochastic reconstruction microscopy; STED, stimulated emission depletion; I⁵M, image interference and incoherent interference illumination microscopy; OPT, optical projection tomography; SPIM, selective plane illumination microscopy; FMT, fluorescence molecular tomography; BLI/BLT, bioluminescence imaging/tomography.

In this article, we address this issue and introduce the concept of fluorescence interferometry, which allows one to convert phase variations of fluorescent light into amplitude variations. This amplitude-to-phase conversion offers new forms of fluorescence imaging based on the phase of fluorescent light waves and yields new paradigms of fluorescence tomography and fluorescence nanometer-level profiling. We demonstrate that the treatment of fluorescence fields as low-temporal-coherence optical fields and their manipulation with self-reference interferometry is useful for imaging, sensing, and profiling applications. Interestingly, manipulation of low-temporal-coherence optical fields is largely used in imaging through tissue and cells and has profoundly affected biomedical optical imaging. For instance, optical coherence tomography^16–20 uses coherence gating to simultaneously provide micron-scale optical sectioning while maintaining a large depth of field. Another example is quantitative phase microscopy,^21–26 which enables measurements with nanometer-scale sensitivity. Finally, the phenomenon of fluorescence interference has been investigated in fundamental studies of molecules in front of reflecting surfaces,^27,28 applied to the assessment of nanometer displacements of a fluorescent molecule above a reflector by measuring variations of the emission intensity^29,30 and spectral phase shifts,^31,32 used in 4Pi and I⁵M microscopy^33–36 for achieving optical resolution beyond the diffraction limit, and used in spectroscopy^37,38 as well.

We first describe the principles of fluorescence interferometry and their potential use for providing new measurement capabilities, such as wide-field and cross-sectional imaging with high resolution and quantitative profiling of surfaces with nanometer-level precision. Next, we present experimental realizations of fluorescence interferometry in both the time and the Fourier domains, and we use them to demonstrate fluorescence tomography across a wide field (millimeter scale) with optical sectioning at the micron scale over a large range (hundreds of microns), as well as accurate profiling of surfaces at the nanometer scale. Finally, we give a summary and outlook.

Fluorescence Interferometry: Principles of Operation

Consider a fluorescent marker placed between two opposing lenses such that the emitted fluorescence is collected from both sides of the probe and then directed to a beam splitter by using mirrors (Fig. 2). As a result, the clockwise and counterclockwise fluorescence fields are combined. An interference pattern (or fringe) is detected only when the coherence condition is fulfilled, that is, when the optical path length difference of the clockwise and counterclockwise fluorescence fields is equal to or less than the coherence length (L_C) of the fluorophore, which is typically on the order of a few microns. For a fluorescent probe located far from the zero-differential optical path length point (z₀) of the two opposing lenses interferometer (positions 1 and 3), no interference pattern is detected, and therefore the received signal is only a constant that is proportional to the emission intensity of the fluorophore. As the fluorescent tag comes close to z₀ (position 2) to within L_C, a clear fringe pattern is produced. The maximum intensity of the interference signal is generated when the marker is located at z₀, for which the optical path lengths traveled by the clockwise and counterclockwise fluorescence fields are matched. This result has two important implications for depth-resolved imaging and nanoprofiling. First, thin fluorescent markers (i.e., those having width smaller than one-half of the fluorophore’s center emission wavelength) that are located at different axial positions separated by greater than one-half of L_C along the same axial line (or depth) can be distinguished because an interference pattern is detected only for the probe residing at z₀ ± L_C/2. That is, it is the path length resolving power of fluorescence interferometry that enables the new ability of resolving depth information at the micron scale about specimens that are selectively labeled with fluorescent markers. Second, differential phase shift analysis of the measured interference patterns will yield the powerful ability to localize individual fluorescent probes with nanometer-level accuracy, as reported in detail by, for example, Choma et al.²⁴ and Joo et al.²⁵ and briefly described afterward in the text.

FIGURE 2.

Operational principles of fluorescence interferometry. Fluorescence waves emitted from an excited fluorophore located between two matched, opposing lenses are directed using mirrors to a beam splitter, where they combine. An interference pattern is detected when the fluorophore is close to point 2, that is, near the zero-differential path length point (z₀) of the interferometer. For locations far from z₀ (points 1 and 3), only the constant fluorescence intensity is recorded.

The next section deals with two potential experimental designs of fluorescence interferometry—the first using time-resolved interferometry and the other, spectral interferometry—and describes in detail their capabilities and limitations.

Fluorescence Interferometry: Experimental Realizations

In general, the implementation of fluorescence interferometry requires the use of a self-reference interferometer (e.g., using two opposing lenses or a reflecting surface, as discussed below) together with proper design of the excitation optics and the time- or Fourier domain detector. The experimental realization of time-domain fluorescence interferometry consists of three main components (Fig. 3A): (1) excitation optics, (2) a configuration of two opposing lenses, and (3) a detection unit. The excitation optics must be properly designed to achieve the desired measurement capabilities; for instance, depth-resolved en face imaging needs a wide-field excitation (Fig. 3B), whereas depth-resolved point-scanning imaging requires a confocal excitation scheme (Fig. 3C). The self-reference interferometer comprises two opposing matched lenses, which collect fluorescent light from both sides of the specimen, and two mirrors to direct the light to a beam splitter, which combines the fluorescence fields. Lenses with low numerical aperture (NA) are selected when large depth of field and moderate transversal resolution are desired (Fig. 3B), whereas moderately high NAs can be used for improving optical sectioning capabilities of confocal microscopy (Fig. 3C). In this context, we point out that 4Pi and I⁵M microscopy^33–36 use fluorescence interferometry together with high-NA objective lenses. Unlike our techniques, these methods aim to break the diffraction limit of light and do not use the power of path length–based measurements for imaging, sensing, or profiling applications. The detection unit includes appropriate imaging and focusing optics as well as a suitable photodetector, such as a two-dimensional charge-coupled device (CCD) camera for wide-field imaging or a point detector for confocal imaging. A key requirement of time domain–based interferometry is the need to translate the sample along the optical axis and to demodulate the recorded signals to obtain information from deep within the sample. As explained in the previous section, only fluorescent markers for which the coherence condition is satisfied produce a fringe pattern. The amplitude profile of this interference pattern therefore determines the axial point-spread function (PSF) or the coherence gate shape of the system and thus establishes the optical sectioning capabilities of fluorescence interferometry (Fig. 3B and C).

FIGURE 3.

Time-domain fluorescence interferometry. (A) Experimental realization, (B) detected signal for wide-field excitation, and (C) detected signal for point excitation.

An alternative setup for fluorescence interferometry uses concepts of spectral interferometry³⁸ to realize the so-called Fourier domain interferometry. The main parts of such fluorescence interferometric system include (1) the excitation optics, (2) a self-reference interferometer, and (3) a spectrometer (Fig. 4A). The illumination optics may have a point focus or a line focus. The latter excitation method allows one to excite one plane within the sample and as a result parallelizes the collection of information (Fig. 4B), whereas the former illuminates only one axial line inside the specimen. On the other hand, for moderate excitation power levels, it enables the simultaneous use of confocal detection to further improve the rejection of scattered fluorescent light from undesired points within the sample. As for the time-domain fluorescence interferometry design, the interferometer consists of two opposing matched lenses that collect fluorescent light from both sides of the sample and two mirrors that direct the light to a beam splitter at which the fluorescence fields are combined. Once more, lenses with low NA are preferred for achieving large depth of field and moderate transversal resolution, whereas higher NAs may be used when it is desirable to preserve an adequate transversal resolution at the expense of a smaller depth of field. Unlike the time-domain scheme, the Fourier domain configuration acquires the entire fluorescence profile along a specific depth without axially translating the sample. Moreover, when operating in the shot–noise or intensity–noise detection-limited regime, Fourier domain fluorescence interferometry should theoretically provide an increased signal-to-noise ratio (SNR) compared with that obtained using the time domain scheme because of the decor-relation of noise detected in the Fourier domain.³⁸ Using the Wiener–Khintchine theorem,³⁹ one can show that the location of each fluorophore along a particular axial line is encoded by an interferometric frequency modulation of the emission spectrum, where the frequency is proportional to the fluorophore’s distance from z₀. The axial position of the excited fluorophores may then be retrieved by calculating the modulus of the inverse Fourier transform of the spectral interferogram intensity. When an excitation line focus is used, a cross-sectional fluorescence image is obtained when all points along the line are processed identically (Fig. 4C). Importantly, the “no moving parts” feature of Fourier domain interferometry opens up the possibility for phase-sensitive measurements with fluorescent light. Explicitly, it allows one to record minute phase shifts in the spectral fringe pattern of individual fluorophores and hence to localize them with high accuracy; the localization precision is determined by the detected SNR and roughly increases inversely with its square root.^24,25 Phase-sensitive measurements with fluorescence on planar reflectors have been performed with nanometer-level sensitivity.^30,31 Advantages of planar reflectors include simple alignment and high sensitivity due to the common-path characteristic of the interference process, though with limited transversal resolution. This drawback stems from the need to collect mostly low-angle back-reflected fluorescence to suppress washout of the detected fringe pattern. To circumvent the transversal resolution problem, either an interferometer with two opposing high-NA objective lenses (i.e., a 4Pi microscope configuration) or concave reflectors could be used. However, these modifications would result in more complicated alignment procedures.

FIGURE 4.

Fourier domain fluorescence interferometry. (A) Experimental realization, (B) line-focus excitation, and (C) self-interference fluorescence from the sample is imaged along the transversal dimension and spectrally resolved in the spectral dimension of the two-dimensional detection array. The axial (depth) ranging profile of the fluorophore distribution along each transversal sample location is obtained by inverse discrete Fourier transforming (DFT⁻¹) each horizontal CCD line. (Reproduced from Ref. 42, figure 1, with permission of the Optical Society of America.)

The temporal resolution in fluorescence interferometry has a significant effect on artifacts that can occur as a result of sample or excitation beam motion. Whereas in time-domain interferometry the motion at a given time will affect only the particular sampling volume that is being acquired, the effect of motion in Fourier domain interferometry is likely to be more severe and complex because the signal is integrated over time and is obtained by the Fourier transform integration. In general, the magnitude of motion artifacts in Fourier domain interferometry will be governed by the total axial or transverse displacement during one axial line signal acquisition time. Finally, for a given sample motion, as the temporal resolution improves, the axial and transverse displacements are decreased, and so are the motion artifacts in both time- and Fourier domain interferometry.

Intriguingly, a comparison between fluorescence interferometry and optical low-coherence interferometry (LCI)^{16–22,24,25} reveals that the former can be considered a hypothetical optical low-coherence interferometric system in which the examined sample also acts as a spatially incoherent source with low temporal coherence. Because the source for fluorescence interferometry is spatially incoherent, coherent cross-talk that degrades measurement quality in LCI is suppressed in fluorescence interferometry. However, unlike LCI, fluorescence interferometry suffers from limited light collection efficiency that is dictated by the NA of the lenses because its reference signal results from self-interference and not from a separate strong reference signal as in LCI. Therefore, the heterodyne gain commonly used by LCI to place the detection system in the shot–noise limited regime cannot be used by fluorescence interferometry, which consequently requires the use of low-noise, high-sensitivity CCD cameras and relatively bright fluorescent emitters. Moreover, the absence of heterodyne gain results in an SNR curve that monotonically increases with fluorescence power, in fundamental contrast to SNR curves of LCI, which have a global maximum at a particular reference power level.

Finally, the detection sensitivity of fluorescence interferometry is determined by the specific radiating fluorophore distribution along the excitation beam. As a result, for fluorescence interferometry systems operating in the shot–noise or intensity–noise detection-limited regime, a high-intensity fluorophore at any point inside the sample increases the noise floor, making it difficult to detect weaker fluorophores located along the same axial line. To circumvent these limitations, fluorescence coherence tomography (FCT) could be potentially combined with fluorescence lifetime imaging techniques.⁴⁰ As in spectral interferometry, the phase ambiguity that occurs for fluorophores located at positive and negative distances from the zero-differential optical path length point of the interferometer can be readily resolved by recording the complex spectral density,⁴¹ thereby doubling the maximal ranging depth.

Fluorescence Interferometry: Applications

The application of fluorescence interferometry for tackling measurement problems particularly in biological or biological-like settings yields new abilities for imaging, sensing, profiling, and ranging. Two such capabilities are (1) wide-field optical sectioning with high resolution and large depth range, which result in a new form of cross-sectional fluorescence imaging and ranging method, dubbed spectral domain fluorescence coherence tomography (SD-FCT),^42–47 and (2) measurement with nanometer-level precision along the optical axis, which allows one to profile structures at the nanoscale.

To characterize the optical sectioning ability of fluorescence interferometry, we implemented a Fourier domain–based experimental setup (Fig. 4A) and measured the axial PSF by using one thin fluorescent layer. Sharp axial PSFs with full widths at half-maximum of approximately 3 μm were obtained at shot–noise limited SNR levels of 15–30 dB.^42–47 The full width at half-maximum of the axial PSF is an adequate measure for the axial resolution of FCT, which can be determined accurately by Fourier transforming the detected spectral profile of the fluorophore emission. A first-order approximation to the FCT axial resolution level is given by Cλ₀²/Δλ, where C is a constant, and λ₀ and Δλ are the peak wavelength and bandwidth of the fluorescence emission spectrum, respectively. C is determined by the exact shape of the emission spectrum; for example, a Gaussian profile yields a constant of C = 2 ln2/π. Under the Gaussian spectral shape assumption, common fluorescent markers, such as cyan fluorescent protein (CFP) and 4′,6′-diamidino-2-phenylindole (DAPI), would provide theoretical axial resolution levels of 1.8 and 0.9 μm, respectively. However, non-Gaussian spectral emission profiles will result in the presence of sidelobes in the axial PSF that generate spurious structures in the FCT images and mask weak fluorophores located near a strong fluorophore.

Importantly, we detected the lower levels of SNR when the fluorescent layer was positioned farther away from the zero-differential optical path length point of the interferometer (z₀). This behavior stems from averaging of the spectral fringes because of the spectrometer’s finite resolution, which becomes stronger as the oscillation period of the spectral fringe increases, that is, for increased distances between the fluorescent layer and z₀. Also, the detection sensitivity may be degraded for a continuous distribution of fluorophores that extends along the axial dimension over a range greater than one-half of the fluorophore’s center emission wavelength because spectral fringes produced by fluorophores distributed along the axial dimension are linearly combined. Therefore, fluorescence interferometry for imaging and ranging applications is appropriate mostly when one is using selective fluorescence labeling rather than nonspecific labeling. The term selective fluorescence labeling refers here to discrete fluorophore distributions for which the extent of each discrete mode is less than one-half of the fluorophore’s center emission wavelength and the separation between adjacent discrete modes is greater than one-half of the fluorophore’s coherence length. Interestingly, this characteristic of fluorescence interferometry is similar to that of LCI; the latter is sensitive to well-defined specularly reflecting interfaces (produced by discontinuities in the scattering potential) that are separated by more than one-half of the coherence length of the light source.

One key advantage of SD-FCT is its ability to acquire cross-sectional images across a wide field and over a large depth without scanning. To demonstrate this capability of SD-FCT, we imaged a dual-layered fluorescent sample (Fig. 5A) and recorded the cross-sectional fluorescence distribution (Fig. 5B) and the corresponding tomogram of the two-layered fluorescent sample (Fig. 5C). To reduce noise floor fluctuations, we performed these measurements by averaging five consecutive images, each acquired in 0.1 s. Two fluorescence layers can be clearly observed over a wide transverse field (>1 mm). The mean distance between the layers was measured to be 120.1 μm. In contrast to conventional lens-based light imaging systems, the axial resolution in SD-FCT is decoupled from the lateral resolution; whereas the latter is determined by the optics, the axial resolution depends solely on the fluorescence emission bandwidth. Using low-NA objectives in SD-FCT to obtain a large depth of field limits the lateral resolution to the range of 5–30 μm, making SD-FCT suitable for imaging of large transversal area samples, such as Drosophila melanogaster embryos. Alternatively, higher-NA lenses and spatial filtering or nonlinear excitation may be used to confine the axial extent of the excitation/detection volume at the expense of imaging depth.

FIGURE 5.

SD-FCT cross-sectional imaging of fluorescent samples. (A) Dual-layer fluorescent phantom, (B) fluorescence emission distribution along the axial (z) and transversal (y) coordinates of the phantom, and (C) SD-FCT tomogram of the two-layered fluorescent sample. (Reproduced from Ref. 42, figure 6, with permission of the Optical Society of America.)

To achieve measurement capability with nanometer-level sensitivity by using fluorescent light, one needs to evaluate the differential phase information from the interferograms of the self-interference fluorescence signals (inset of Fig. 6A). That is, the relative variation between the phase shifts of spatially, temporally, or optically resolved fringe patterns provides a powerful ability to quantitatively probe dynamics and structures at the nanoscale, where in general the sensitivity of the measurement in the shot–noise limited detection regime is proportional to $1/\sqrt{SNR}$ or $1/\sqrt{N}$, with N representing the number of recorded photons as derived in detail by Choma et al.²⁴ For instance, a milliradian differential phase sensitivity would require the detection of 10⁶ photons. Similarly, spectral self-interference fluorescence microscopy extracts phase information to localize fluorophores on reflecting surfaces with nanometer-level precision.^31,32 Likewise, 4Pi spectral self-interference fluorescence microscopy, which is similar to SD-FCT but uses high-NA objective lenses to increase lateral resolution at the expense of depth of field,⁴⁸ also operates with nanoscale precision.

FIGURE 6.

SD-FCT nanometer-level profiling of transparent surfaces. (A) Axial displacement sensitivity of SD-FCT and (B) SD-FCT profile of a nanoetched surface.

To measure the displacement sensitivity of SD-FCT, we performed the following procedure with one thin fluorescent layer: First, we recorded K samples of the SD-FCT signal and fast Fourier transformed them after resampling. Resampling is necessary to obtain a signal that is evenly spaced in wave number rather than in wavelength, the latter being the domain in which the SD-FCT signal is detected by the spectrometer. Next, the phase of the pixel at the peak of the resulting K/2 pixel complex–valued axial profile was recorded as a function of time, and phase (∠I peak(t)) was converted to displacement (δz) by use of the fact that δz(t) μ ∠I peak(t) ∠I peak(t = t₀). This peak-intensity pixel corresponds to the position of the fluorescent layer to within the axial resolution of FCT; once more, this resolution is determined by the fluorescence emission bandwidth (Δω) and is proportional to 1/Δω. The histogram of the displacement variable (δz) reveals a nanometer-level stability, which was defined as the standard deviation of the displacement signal over time (Fig. 6A). To demonstrate the ability of SD-FCT to measure with nanometer-level accuracy, we used a calibrated sample consisting of a step pattern etched on one surface of a coverslip, where fluorescent beads were dried on the second surface (bottom panel of Fig. 6B). The step profile was obtained by computing the differential spatial phase of excited fluorophores along one axial cross-section of the sample by using a similar procedure to that described above, where z|(x,y) μ ∠I peak(x,y) − ∠I peak(x = x₀, y=y₀). Here z|(x,y) represents the axial displacement at a given transversal coordinate (x, y). The surface profile was obtained by averaging 15 consecutive profiles, each acquired in 0.1 s (Fig. 6B). This measurement predicts a step profile with a thickness (depth) of approximately 55 nm, which is comparable to the 47-nm thickness measured independently by spectral domain phase microscopy.^24,25 In principle, scanning the excitation line across the sample would enable recording several axial cross-sections and as a result open up a new possibility for quantitative phase-contrast imaging, which is similar to that reported for LCI.²⁵

Summary and Outlook

Most fluorescence microscopy methods use the intensity of fluorescent waves averaged over time, which is easily measured by detectors. The phase of the fluorescence wave is, by contrast, typically ignored. However, it also contains a significant source of information about the wave and can be used to yield new forms of mesoscopy and nanoscopy modalities. In this report, we presented two new methods to probe this phase information at the frequencies of fluorescent light by using interferometry, and we demonstrated cross-sectional imaging (or FCT) and nanometer-level profiling. Fourier-based parallel FCT (or SD-FCT) can be useful for one-shot, scanning-free, wide-field, and cross-sectional imaging of structures in biological specimens that are selectively labeled with fluorescent markers, such as the embryonic nervous system of Drosophila melanogaster.⁴⁹ Also, our recent report on image formation in fluorescence coherence–gated imaging through scattering media⁴³ indicates that coherence gating in fluorescence imaging may provide an improved approach for depth-resolved imaging of fluorescently labeled samples. With FCT, high axial resolution (a few microns) can be achieved with low NAs (NA < 0.09) while maintaining a large depth of field (a few hundreds of microns) in a relatively low scattering medium (six mean free paths), whereas moderate NAs can be used to enhance depth selectivity in highly scattering biological samples.

Several future research directions are possible in fluorescence interferometry. First, the effect of multiple scattering of fluorescent light on the imaging performance of FCT is still unexplored, and both experimental and Monte Carlo studies^50–52 are required. Second, a detailed analysis of the effect of temporal resolution on motion artifacts in FCT should be performed. Third, the potential use of FCT for whole-organism three-dimensional imaging using quantum dot labeling and bioluminescence is attractive and must be investigated. Finally, finding ways to use the phase shifts of the interference patterns cast by the fluorescence waves is necessary to develop new forms of far-field optical nanoscopy and phase-contrast microscopy strategies.