Self-interference fluorescence microscopy with three-phase detection for depth-resolved confocal epi-fluorescence imaging

Boy Braaf; Johannes F. de Boer

doi:10.1364/OE.25.006475

1. Introduction

Fluorescence microscopy is a widely used technique in biology and biomedicine for high-resolution visualization of molecules, cells and cell organelles through the detection of fluorophores [1]. The labeling of specific proteins or cellular structures with exogenous fluorescent probes is ideal for localization and identification purposes, and can be used to analyze dynamic cellular processes such as protein expression [2]. The addition of confocal detection techniques to fluorescence microscopy enables high-contrast depth sectioning for the reconstruction of three-dimensional fluorescence image volumes of thick samples [3]. This makes confocal fluorescence microscopy interesting for the non-invasive study of in vivo tissues [4–7]. In medicine the implementation of conventional confocal fluorescence microscopy methods can be difficult since in vivo tissues are prone to movement and provide limited capabilities for the controlled translation that is necessary for confocal depth-sectioning [8, 9]. In addition many tissues of clinical interest are deeply embedded in the human body, e.g. in hollow organs such as the bronchus, and can only be reached via optical fiber-based endoscopy probes [10, 11]. It is therefore necessary to develop a new class of confocal fluorescence microscopy techniques that can adapt to these demands.

Several three-dimensional confocal fluorescence imaging techniques have been developed recently that do not require mechanical depth-scanning including chromatic confocal fluorescence microscopy [12], differential confocal fluorescence microscopy [13], 4Pi fluorescence self-interference microscopy techniques [14–17], and self-interference fluorescence microscopy (SIFM) [18]. The instantaneous depth-sectioning ability of these techniques results in the fast three-dimensional confocal fluorescence imaging that is necessary for the imaging of in vivo tissues. The SIFM technology is especially attractive for clinical implementation since this technique uses epi-fluorescence detection as well as single-mode optical fibers (SMFs) which allows for implementation in miniature catheters and is potentially compatible with other minimally invasive optical imaging techniques such as optical coherence tomography (OCT) [19, 20].

The SIFM technique is based on wavefront splitting interferometry and divides a fluorescence wavefront into two parts that travel along different paths and interfere after recombination [18]. In SIFM the fluorescent light is collected by an epi-fluorescence imaging system with a phase plate, i.e. an annular zone plate, in the back focal plane. The phase plate consists of a glass plate with a hole in its center that causes an optical path length difference (OPD) between the center and edge wavefront parts. Consequently a self-interference signal is observed after coupling the whole wavefront into an SMF. Axial displacement of a sample away from the imaging focus induces a defocus curvature in the emitted wavefront. The defocus curvature changes the OPD and introduces a phase shift on the self-interference signal with respect to the in focus case. The axial position of a fluorescent source can then be determined by spectral phase analysis of the detected SIFM self-interference signal. To date, in SIFM and other fluorescence interferometry methods spectrometers are often used for the spectrally resolved detection of the self-interference signal. These techniques are therefore less sensitive than other (two-dimensional) in vivo fluorescence techniques that use photomultiplier tubes or avalanche photodiodes for detection [21].

In this paper a novel method is presented for SIFM using sensitive interferometric three-phase detection with photon counter detectors. A tabletop epi-fluorescence SIFM setup was developed together with a 3 × 3 fiber-coupler based Mach-Zehnder interferometer (MZI) for the interferometric detection. The MZI imposed a spectral modulation onto a SIFM self-interference signal in order to create three phase-shifted output signals that alternately oscillated in intensity as a function the SIFM spectral phase. As such the MZI signal output encoded directly for the amplitude and phase parameters of the SIFM signal and could be used for the axial localization of fluorescent samples. The novel SIFM method is analytically derived and validated in experiments with controlled axial translation of fluorescent microsphere layers and by comparison with OCT depth measurements. The potential for high-resolution depth-resolved SIFM fluorescence imaging in tissue is shown with fluorescence angiography on a dye-filled capillary blood vessel phantom and for autofluorescence imaging on an ex vivo fly eye.

2. Theory and experimental system description

In this section first the implementation of the SIFM technique in a microscope setup is described and its theory is derived analytically (section 2.1). This forms the foundation for the interferometric three-phase MZI detection of the SIFM signal that is described thereafter (section 2.2). Subsequently these theoretical results are used for signal analysis (section 2.3) and calibration of the setup (section 2.4). Finally, a signal-to-noise ratio (SNR) and phase noise analysis is presented to describe the performance of the setup (section 2.5).

2.1 SIFM microscope and theory

The SIFM method was implemented on an inverted microscope platform (Olympus IX71, Japan) similar to De Groot et al. [18] and is displayed in Fig. 1. In short, samples were excited for fluorescence generation by a 635 nm fiber-coupled laser source (S1FC635, Thorlabs, NJ). The excitation light was first filtered with a bandpass filter (BPF; FF01-640/14, Semrock, NY) to reject any fluorescence light generated in the optical fibers. The filtered excitation light was coupled into the microscope optical path via a dichroic mirror (DM; Di02-R635, Semrock). Subsequently two 4f-telescopes were used to lead the excitation light over two galvanometer scanning mirrors for horizontal (HS) and vertical (VS) raster scanning. A third 4f-telescope was used to image the scanning mirrors into the back focal plane of a microscope objective (MO) before the excitation light was focused on the sample. The emitted fluorescence light from the sample was collected in epi-detection mode, descanned by the return pass over the galvanometer scanning mirrors, and passed in transmission through the DM. A long pass filter (LPF; LP02-671RU, Semrock) was used after the DM to filter out reflected excitation light. The SIFM phase plate (PP) was placed after the LPF in the virtual back focal plane of the microscope objective. After passing through the phase plate the fluorescence light was coupled into an SMF (HI780, Corning, NC) and sent to the detection optics. The phase plate consisted of a No. 1 microscope cover slide with a 4.4 mm diameter circular hole for which the SIFM self-interference signal was close to its maximum modulation depth. The SMF had a 1/e fiber mode field diameter of 3.2 µm. The microscope objectives used in this study had 4 × and 10 × magnifications (UPLSAPO 4X & 10X, Olympus). The objectives were underfilled by a Gaussian excitation beam with a waist radius of 1.94 mm, which resulted in effective numerical apertures of 0.043 (f_{MO 4 ×} = 45 mm) and 0.11 (f_{MO 10 ×} = 18 mm) for the 4 × and 10 × objectives respectively. The limiting optical aperture for the fluorescence emission collection path was lens L₁ with a clear aperture diameter of 9 mm.

Fig. 1 SIFM microscope setup. The microscope uses epi-fluorescence detection mode in which a dichroic mirror (DM) separates the excitation and emission optical paths. Telescopes are used to image the SIFM phase plate (PP) and two galvanometer scanners (HS&VS) onto the back focal plane of the microscope objective. The blue dashed frame denotes the Olympus IX71 inverted microscope platform. Component abbreviations: MO: microscope objective, VS: vertical galvanometer scanner, HS: horizontal galvanometer scanner, DM: dichroic mirror, BPF: band pass filter, LPF: long pass filter, PP: phase plate, SMF: single-mode fiber, Lx: lenses. Lens focal lengths: L₁: 25 mm, L₂: 200 mm, L₃: 50 mm, L₄: 2 × 60 mm, L₅: 60 mm, L₆: 180 mm. Inset: The propagation of the wavefront through the phase plate for the in (upper diagram) and out (lower diagram) of focus case, respectively. The wavefront curvature changes the OPD (black arrows) between the edge and center wavefront parts and induces a phase shift onto the SIFM self-interference signal.

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The inset of Fig. 1 visualizes in red solid lines the propagation of the fluorescence wavefront through the phase plate and its coupling into the SMF. When the sample is in focus (upper diagram) the wavefront is flat and the phase plate causes an OPD as denoted by the black arrow by delaying the edge part with respect to the center. When the sample is positioned out of focus (lower diagram) the wavefront is curved and the inherent path length difference between the edge and center wavefront parts now changes the OPD with respect to the in focus case. Subsequently the wavefront is focused by lens L₁ into the SMF and sent to the detection optics. The SIFM signal is theoretically derived from the individual coupling of the center and edge wavefront parts into the SMF and their subsequent interference.

In the paraxial approximation the wavefront curvature R(δ) at the phase plate is given as:

R (δ) = - \frac{m^{2} f_{M O}^{2}}{δ}

with δ the axial displacement of the fluorescent source from the objective focus, f_MO the microscope objective focal length and m the magnification between the objective back focal plane and its conjugate plane on the phase plate [18]. The path length delay Δ(r,δ) for any location on the wavefront with respect to its center (chief) ray is now given as:

Δ (r, δ) = \frac{r^{2}}{2 R (δ)}

with r as the radial distance from the wavefront center [18]. Assuming a uniform fluorescence emission by the sample its electric field E_s(k,r,δ) at the phase plate aperture can now be given as a function of wavenumber k and path length delay Δ(r,δ):

E_{s} (k, r, δ) = E_{0} (k) \cdot e^{- i k Δ (r, δ)} = E_{0} (k) \cdot e^{- \frac{i k r^{2}}{2 R (δ)}}

where E₀(k) is the field amplitude. The coupling of an electric field into a SMF can be described by a weighting with the SMF fiber mode field E_mf(k,r) which back propagated into the L₁ aperture plane (the lens plane) is given as [22]:

E_{m f} (k, r) = (\frac{k w}{\sqrt{2 π} f_{L 1}}) \cdot e^{- {(\frac{r k w}{2 f_{L 1}})}^{2}}

with w as the SMF 1/e fiber mode field radius and f_L₁ as the focal length of lens L₁. In addition the edge part of the fluorescence wavefront is extended in its propagation by the phase plate as defined by P(k):

P (k) = e^{i k d}

where d represents the path length added by the phase plate. The electric field that couples over into the SMF is now given by the overlap integral of E_s(k,r,δ) and E_mf(k,r) [22] for the radial section of a specific wavefront part in the phase plate plane. In this calculation the back propagation of the collimated bundle of E_mf(k,r) from the L₁ aperture plane to the phase plate plane is neglected since it is assumed to be a simple translation of the wavefront over a short propagation length relative to its beam diameter. The electric field E_center(k,δ) for the center wavefront part is then given by the integration over the phase plate hole as:

E_{c e n t e r} (k, δ) = 2 π \cdot \int_{0}^{a} E_{s} (k, r, δ) E_{m f} (k, r) r d r

with a as the phase plate hole radius. Similarly the electric field E_edge(k,δ) for the edge wavefront part is given by integration over the phase plate edge as:

E_{e d g e} (k, δ) = 2 π \cdot \int_{a}^{b} E_{s} (k, r, δ) E_{m f} (k, r) P (k) r d r

where b is the clear aperture radius of lens L₁.

The SIFM signal intensity I_SIFM(k,δ) as collected by the SMF is subsequently obtained from the interference between E_center(k,δ) and E_edge(k,δ) as:

\begin{array}{l} I_{S I F M} (k, δ) = E_{c e n t e r} (k, δ) \cdot E_{c e n t e r}^{*} (k, δ) + E_{e d g e} (k, δ) \cdot E_{e d g e}^{*} (k, δ) + 2 Re {E_{c e n t e r} (k, δ) \cdot E_{e d g e}^{*} (k, δ)} \\ = I_{c e n t e r} (k, δ) + I_{e d g e} (k, δ) + I_{i n t e r f e r e n c e} (k, δ) \end{array}

in which * denotes the complex conjugate and Re{} describes the real part. In Eq. (8) I_center(k,δ) and I_edge(k,δ) represent the spectral intensities of the center and edge wavefront parts respectively, while I_interference(k,δ) describes the modulated intensity of their interference. The center wavefront part intensity I_center(k,δ) is obtained from E_center(k,δ)·E*_center(k,δ) as:

I_{c e n t e r} (k, δ) = I_{0} (k) \cdot C (k, δ) \cdot (1 + e^{- \frac{k^{2} w^{2} a^{2}}{2 f_{L 1}^{2}}} - 2 \cdot e^{- \frac{k^{2} w^{2} a^{2}}{4 f_{L 1}^{2}}} \cdot Cos (\frac{k a^{2}}{2 R (δ)}))

where I₀(k) is the field strength I₀(k) = E₀(k)·E₀*(k) and C(k,δ) describes the coupling efficiency of the wavefront into the SMF as:

C (k, δ) = \frac{8 π f_{L1}^{2} R {(δ)}^{2} w^{2}}{4 f_{L1}^{4} + k^{2} R {(δ)}^{2} w^{4}} .

The edge wavefront part intensity I_edge(k,δ) is determined from E_edge(k,δ)·E*_edge(k,δ) as:

I_{e d g e} (k, δ) = I_{0} (k) \cdot C (k, δ) \cdot (e^{- \frac{k^{2} w^{2} a^{2}}{2 f_{L 1}^{2}}} + e^{- \frac{k^{2} w^{2} b^{2}}{2 f_{L 1}^{2}}} - 2 \cdot e^{- \frac{k^{2} w^{2} (a^{2} + b^{2})}{4 f_{L 1}^{2}}} \cdot Cos (\frac{k a^{2} - k b^{2}}{2 R (δ)})),

while the interference intensity I_interference(k,δ) is obtained from 2Re{E_center(k,δ)·E*_edge(k,δ)} as:

\begin{array}{l} I_{i n t e r f e r e n c e} (k, δ) = 2 I_{0} (k) \cdot C (k, δ) \cdot (- e^{- \frac{k^{2} w^{2} a^{2}}{2 f_{L 1}^{2}}} \cdot Cos (d k) + e^{- \frac{k^{2} w^{2} a^{2}}{4 f_{L1}^{2}}} \cdot Cos (d k - \frac{k a^{2}}{2 R (δ)}) \\ + e^{- \frac{k^{2} w^{2} (a^{2} + b^{2})}{4 f_{L1}^{2}}} \cdot Cos (d k - \frac{k (a^{2} - b^{2})}{2 R (δ)}) - e^{- \frac{k^{2} w^{2} b^{2}}{4 f_{L1}^{2}}} \cdot Cos (d k - \frac{k b^{2}}{2 R (δ)})) . \end{array}

Equation (8) can be rewritten according to standard two-beam interference theory as:

I_{S I F M} (k, δ) = I_{c e n t e r} (k, δ) + I_{e d g e} (k, δ) + 2 \sqrt{I_{c e n t e r} (k, δ) \cdot I_{e d g e} (k, δ)} \cdot Cos (Ψ (k, δ))

in which the interference term I_interference(k,δ) is rewritten in terms of I_center(k,δ), I_edge(k,δ) and the cosine phase ψ(k,δ). ψ(k,δ) describes the spectral phase dependence of the SIFM signal on the axial position of a fluorescent sample for which the exact expression is given as:

Ψ (k, δ) = Arccos (I_{i n t e r f e r e n c e} (k, δ) / (2 \sqrt{I_{c e n t e r} (k, δ) \cdot I_{e d g e} (k, δ)})) .

Equation (14) can also be modeled in accordance with De Groot et al. [18] by a single spectral frequency term kd that results from the phase plate optical delay and the SIFM phase ϕ(δ) that holds the sample axial position information:

Ψ (k, δ) = k d + ϕ (δ) .

A linear approximation of the SIFM phase ϕ(δ) can then be obtained by calculating the difference in Δ(r,δ) between the edge and center wavefront parts as:

\begin{array}{l} ϕ (δ) \approx k_{0} \cdot (\frac{\int_{a}^{b} Δ (r, δ) E_{m f} (k_{0}) r d r}{\int_{a}^{b} E_{m f} (k_{0}) r d r} - \frac{\int_{0}^{a} Δ (r, δ) E_{m f} (k_{0}) r d r}{\int_{0}^{a} E_{m f} (k_{0}) r d r}) \\ \approx (\frac{k_{0}}{2 R (δ)}) (\frac{a^{2}}{1 - e^{- \frac{k_{0}^{2} w^{2} a^{2}}{4 f_{L1}^{2}}}} - \frac{(a - b) (a + b)}{1 - e^{\frac{k_{0}^{2} w^{2} (b^{2} - a^{2})}{4 f_{L1}^{2}}}}) \end{array}

where k₀ represents the center wavenumber.

In Fig. 2 the SIFM method is simulated for a sample that is axially moved while laterally positioned on the optical axis of the 4 × microscope objective (Rayleigh range: 129 μm). The uniformly emitted fluorescence from this sample was simulated with a Gaussian fluorescence spectrum centered at 750 nm and an FWHM bandwidth of 45 nm. In Fig. 2(a) SIFM intensity spectra are shown according to Eq. (8) for a sample that is in focus (in blue) and after 100 µm axial displacement out of the focus (in red). It can be clearly seen from the shift in the spectrum peaks that the out of focus spectrum was shifted in phase with respect to the in focus spectrum. In addition the out of focus spectrum suffered an overall intensity loss due to the reduced (confocal) coupling into the SMF as described by Eq. (10). In Fig. 2(b) the change in the SIFM phase ϕ(δ) is shown as a function of sample depth. In blue ϕ(δ) is given for the exact model of Eqs. (14)-(15) and shows a largely linear relation over the central 500 µm depth range. The linear approximation for ϕ(δ) according to Eq. (16) is given in red and shows a good agreement with the linear part of the exact model. Outside of the linear depth range the exact model shows a flattening of ϕ(δ) which can be explained by a reduced coupling of the edge wavefront into the SMF. This is illustrated in Fig. 2(c) with the spectrally integrated intensities of I_center(k,δ) and I_edge(k,δ) as a function of sample depth that were normalized to the peak integrated intensity of I_edge(k,δ). It can be seen that both intensities are maximum at the focus and decay in a Gaussian manner with depth. In the focus the coupling of the edge wavefront part is significantly better than the center part but also experiences a stronger signal decay with depth. Around a 300 µm depth displacement from the focus the edge intensity approaches zero which leads to the flattening of ϕ(δ). This behavior of ϕ(δ) with depth is in agreement with the experimental observation by De Groot et al. in [18] and shows the improved description of the SIFM signal with the exact model presented in this paper compared to the earlier linear approximation.

Fig. 2 Simulation of the SIFM method. (A) SIFM intensity spectra according to Eq. (8) for an in focus sample (blue) and a 100 µm axially displaced out of focus sample (red) measured with a 4 × microscope objective. (B) The SIFM phase ϕ(δ) as a function of depth as simulated by the exact model of Eqs. (14)-(15) in blue and for the linear approximation of Eq. (16) in red. (C) The normalized spectrally integrated intensities of I_center(k,δ) in blue and I_edge(k,δ) in red that show the signal decay with depth for both wavefront parts.

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2.2 Fiber-based MZI for SIFM detection

In SIFM the intensity and the axial location of a fluorescent sample are encoded by the amplitude and phase of the spectral SIFM signal. In order to determine these spectral properties in a wavelength-independent manner with photon counter detectors an optical detection circuit was developed based on a fiber-based MZI. The working principle of the MZI is the generation of a reference spectrum with a spectral modulation that demodulates an input SIFM signal to a DC intensity signal that can be measured by a single photodetector. The MZI used a 3 × 3 fiber coupler to generate three reference spectra at the same modulation frequency as the SIFM signal with a 120° phase-separation. This created three phase-shifted demodulated SIFM signals that oscillated as a function of the SIFM signal phase. The MZI signal outputs therefore encode directly for the intensity and phase parameters of the SIFM signal and can be used for the axial localization of fluorophores. The MZI detection requires the use of only three photon counter detectors and is therefore more efficient in the number of used detectors compared to CCD-based spectrometer SIFM detection, while simultaneously it provides higher fluorescence detection sensitivity. This technique is partially based on the work of Shtengel et al. [16] where a similar method was used for 4Pi interferometric photo activated localization microscopy.

The schematic figure of the MZI setup is shown in Fig. 3. A 2 × 2 SMF coupler equally split the input SIFM light from the microscope over two interferometer arms. In each arm the light was transmitted through air to set a specific optical path length difference p between the arms before coupling into a 3 × 3 SMF coupler (Diamond FO, Switzerland). A glass plate (G) and a polarization controller (PC) were included to match the chromatic dispersion and the polarization state between the arms respectively. In the 3 × 3 coupler the light from both arms was recombined and equally divided over three fiber-coupled single photon avalanche diodes (SPADs; SPCM-AQ4C, Excelitas Technologies, Canada). The photon counting signal output of the SPADs was digitized in real-time using a multifunction data acquisition board (NI PCIe-6353, National Instruments, TX) and custom-made software in LabVIEW (National Instruments, TX).

Fig. 3 Fiber-based Mach-Zehnder Interferometer (MZI) for SIFM detection with SPADs. The MZI generated three reference signals with a 120° phase-separation to create three DC output signals that alternately oscillated as a function of the SIFM signal spectral phase. SPAD photon counting digitized these output signals. Component abbreviations: G: glass plate, PC: polarization controller, p: optical path length difference, SPAD: single photon avalanche diode.

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The intensity of the MZI output signals can be described as a multiplication of the SIFM signal I_SIFM(k,δ) and the modulated reference spectra that are generated by the MZI. The modulation frequency of the MZI spectra is set by the OPD p and the phases of the three output signals are separated by 120° (2π/3 rad) angles due to the conservation of energy in the 3 × 3 fiber coupler [23]. The intensity output of the MZI is then given as a function of k as:

I_{SPADx} (k, δ) = (1/3) \cdot {1 + Cos (k p - (x - 1) \cdot 2π/3)} \cdot I_{S I F M} (k, δ)

where x encodes for the numbering of the SPAD detectors from 1 to 3. If I_SIFM(k,δ) is substituted for its expression of Eq. (13) with ψ(k,δ) as given by Eq. (15), Eq. (17) can be rewritten as:

\begin{array}{l} I_{SPADx} (k, δ) = (1/3) \cdot {1 + Cos (k p - (x - 1) \cdot 2π/3)} \\ \cdot {I_{c e n t e r} (k, δ) + I_{e d g e} (k, δ) + 2 \sqrt{I_{c e n t e r} (k, δ) \cdot I_{e d g e} (k, δ)} \cdot Cos (k d + ϕ (δ))} . \end{array}

In Eq. (18) the SIFM modulation term

2 \sqrt{I_{c e n t e r} (k, δ) \cdot I_{e d g e} (k, δ)} \cdot Cos (k d + ϕ (δ))

is mixed with the MZI modulation term

Cos (k p - (x - 1) \cdot 2π/3)

and the difference frequency will be demodulated to

\sqrt{I_{c e n t e r} (k, δ) \cdot I_{e d g e} (k, δ)} \cdot Cos (k (d - p) + ϕ (δ) + (x - 1) \cdot 2π/3)

following the trigonometric product-to-sum identity [24]. If the MZI OPD p is now set equal to the phase plate OPD d the demodulated term becomes k-independent for its cosine modulation. The SPAD detection of the MZI intensity signals is wavelength independent and the detected intensity is therefore given by the integration of Eq. (18) over k. In this process the spectrally modulated terms (i.e. the sum frequencies) are cancelled out and the detected SPAD intensity signals are given by the unmodulated terms as:

\begin{array}{l} Ι_{SPADx} (δ) = \int I_{SPADx} (k, δ) d k = (1/3) \cdot {I_{c e n t e r} (k_{0}, δ) + I_{e d g e} (k_{0}, δ) \\ + \sqrt{I_{c e n t e r} (k_{0}, δ) \cdot I_{e d g e} (k_{0}, δ)} \cdot Cos (ϕ (δ) + (x - 1) \cdot 2π/3)} \cdot I_{0} \end{array}

where I₀ is the integral of the field strength normalized to k₀ as:

I_{0} = \int I_{0} (k) d k / I_{0} (k_{0})

. Eq. (19) shows that also the integrated SPAD intensities are described by three cosine signals that depend directly on ϕ(δ) and are phase separated by 2π/3 rad phase angles.

In Fig. 4 an example is shown of simulated signals to illustrate the working principle of the MZI. In Fig. 4(a) an unmodulated Gaussian fluorescence spectrum is sent into the MZI to show the reference spectra that are generated as modeled by Eq. (17). Due to their phase offsets the reference spectra alternately overlap with the input spectrum along k. In Fig. 4(b) a simulated SIFM signal for a fluorescent source displaced 150 µm out of focus (ϕ(δ) = -π/2 rad) was sent into the MZI. In this case the spectra at the SPADs have different amplitudes, which is caused by the difference in phase between the SIFM signal and the MZI reference spectra. The resulting dependence of the k-integrated SPAD intensities of Eq. (19) on the depth of a fluorescent sample is shown in Fig. 4(c). It can be seen that the integrated SPAD intensity signals oscillate around the axial point-spread function (PSF; in orange) that describes the overall coupling efficiency of the SIFM microscope. In order to emphasize that for every depth position a unique combination of the SPAD intensities exists the integrated SPAD intensity curves were divided by the axial PSF and plot against the simulated SIFM phase ϕ(δ) for its linear range in Fig. 4(d). This graph shows that for every value of ϕ(δ) a unique combination of SPAD intensities exists, which makes it possible to determine the former from the latter. A movie (Visualization 1) is provided in the caption of Fig. 4 that shows how the SPAD signals change with depth and dynamically visualizes the relation between the spectral intensity along k of Fig. 4(b), the integrated intensity of Fig. 4(c) and the SPAD modulations of Fig. 4(d).

Fig. 4 Simulated MZI signals. (A) An unmodulated Gaussian input spectrum (left) and the corresponding three MZI reference spectra as a function of k (right). (B) An input SIFM signal from an out of focus fluorescent sample with ϕ(δ) = -π/2 rad (left) and the corresponding output at the three SPADs (right). (C) The k-integrated SPAD intensity signals as a function of sample depth. (D) The integrated SPAD intensity signals divided by the axial PSF as a function of ϕ(δ) to show the unique combination of the SPAD intensities for every ϕ(δ). Plots (A) - (C) are normalized for the peak of their spectra. Visualization 1 provides a movie that dynamically shows the change in the SPAD signals with depth δ.

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2.3 Three-phase analysis of the MZI signals

In section 2.2 it was shown that the SPADs detect three phase-shifted signals that encode for the SIFM signal. In this section the analysis method is given to extract the SIFM intensity and phase from this three-phase signal system. This method is analogous to the analysis of electrical three-phase circuits which in general use a transformation of the three-phase coordinate system into a two-phase reference frame [25]. For this purpose the phase shifted cosine terms of I_SPAD2(δ) and I_SPAD3(δ) are rewritten using the trigonometric angle sum identity as cos(ϕ(δ) ± 2π/3) = cos(ϕ(δ))·cos( ± 2π/3) - sin(ϕ(δ))·sin( ± 2π/3) [24]. Subsequently Eq. (19) is modelled in matrix form as:

I = M \cdot R

in which the SPAD intensity signals are described by the vector I:

I = [\begin{matrix} Ι_{SPAD 1} (δ) \\ Ι_{SPAD2} (δ) \\ Ι_{SPAD 3} (δ) \end{matrix}]

and the shared terms for all three SPAD signals are given by the vector R:

R = [\begin{matrix} R_{1} \\ R_{2} \\ R_{3} \end{matrix}] = [\begin{matrix} I_{c e n t e r} (k_{0}, δ) + I_{e d g e} (k_{0}, δ) \\ \sqrt{I_{c e n t e r} (k_{0}, δ) I_{e d g e} (k_{0}, δ)} \cos (ϕ (δ)) \\ - \sqrt{I_{c e n t e r} (k_{0}, δ) I_{e d g e} (k_{0}, δ)} \sin (ϕ (δ)) \end{matrix}] \cdot (1/3) \cdot I_{0} .

The elements of R are the 2-phase representation of the 3-phase system of I with an offset term (R₁) and two phase terms (R₂ and R₃) that form the horizontal and vertical components of the phasor that defines the SIFM phase ϕ(δ). M is the transformation matrix that converts R into I and defines the phase shifts for I_SPAD2(δ) and I_SPAD3(δ) with respect to I_SPAD1(δ):

M = [\begin{matrix} 1 & 1 & 0 \\ 1 & \cos (2π/3) & \sin (2π/3) \\ 1 & \cos (-2π/3) & \sin (-2π/3) \end{matrix}] .

The vector R can be determined from I by multiplication with the inverse of M:

R = M_{}^{- 1} \cdot I

where the inverse of M is given by:

M^{- 1} = [\begin{matrix} 1/3 & 1/3 & 1/3 \\ 2/3 & -1/3 & -1/3 \\ 0 & 1/ \sqrt{3} & -1/ \sqrt{3} \end{matrix}] .

Equations (24) and (25) show that the elements of the vector R are simple linear combinations of the SPAD intensity signals. R₁ is given by the average of the three SPADs, R₂ is the proportional difference between I_SPAD1(δ) and the sum of I_SPAD2(δ) and I_SPAD3(δ), and R₃ is the difference between I_SPAD2(δ) and I_SPAD3(δ). These operations are known as the Clarke (or αβγ) transform that is employed to transform the signals of electrical three-phase circuits to a two-dimensional stationary reference frame [26].

In practice optical losses and optical path length deviations from the theoretical optimum compromise the ideal operation of the MZI. These experimental factors lead to changes in the offsets, amplitudes and phase offsets on the SPAD signals and require a refined signal analysis. The three-phase SPAD model is therefore redefined as:

\begin{array}{l} Ι_{SPADx} (δ) = (1/3) \cdot {o_{x} \cdot (I_{c e n t e r} (k_{0}, δ) + I_{e d g e} (k_{0}, δ)) \\ + a_{x} \cdot \sqrt{I_{c e n t e r} (k_{0}, δ) \cdot I_{e d g e} (k_{0}, δ)} \cdot Cos (ϕ (δ) + (x - 1) \cdot 2π/3 + φ_{x})} \cdot I_{0} \end{array}

where the error factors o_x, a_x and φ_x describe the offset, amplitude and phase offset deviations respectively for each SPAD signal compared to Eq. (19). This model is comparable to an unbalanced electrical three-phase circuit [27, 28] and requires the error factors to be known for a correct solution of the phase and amplitude parameters. The measurement of exact values for the error factors is however impractical, since it requires the calibration of the optical losses and path length errors for each MZI path section. The analysis can however be simplified by redefining Eq. (26) as a relative matrix form of Eq. (20) for which I_SPAD2(δ) and I_SPAD3(δ) are expressed relative to I_SPAD1(δ). This refined analysis uses the same measured I vector of Eq. (21) with a redefined R vector:

R = [\begin{matrix} R_{1} \\ R_{2} \\ R_{3} \end{matrix}] = [\begin{matrix} o_{1} \cdot (I_{c e n t e r} (k_{0}, δ) + I_{e d g e} (k_{0}, δ)) \\ a_{1} \cdot \sqrt{I_{c e n t e r} (k_{0}, δ) I_{e d g e} (k_{0}, δ)} \cos (ϕ (δ) + φ_{1}) \\ - a_{1} \cdot \sqrt{I_{c e n t e r} (k_{0}, δ) I_{e d g e} (k_{0}, δ)} \sin (ϕ (δ) + φ_{1}) \end{matrix}] \cdot (1/3) \cdot I_{0}

that includes now the error factors of I_SPAD1(δ), and a redefined matrix M:

M = [\begin{matrix} 1 & 1 & 0 \\ (\frac{o_{2}}{o_{1}}) & (\frac{a_{2}}{a_{1}}) \cdot \cos (2π/3 + φ_{2} - φ_{1}) & (\frac{a_{2}}{a_{1}}) \cdot \sin (2π/3 + φ_{2} - φ_{1}) \\ (\frac{o_{3}}{o_{1}}) & (\frac{a_{3}}{a_{1}}) \cdot \cos (-2π/3 + φ_{3} - φ_{1}) & (\frac{a_{3}}{a_{1}}) \cdot \sin (-2π/3 + φ_{3} - φ_{1}) \end{matrix}] .

The redefined matrix M uses relative error factors to include the offset, amplitude and phase offset differences for I_SPAD2(δ) and I_SPAD3(δ) with respect to I_SPAD1(δ). In Eq. (28) the terms (o₂/o₁) and (o₃/o₁) are the relative offset error factors, (a₂/a₁) and (a₃/a₁) are the relative amplitude error factors, and (φ₂-φ₁) and (φ₃-φ₁) are the relative phase offset error factors. In accordance with Eq. (24) in the refined model the vector R is also determined from I by multiplication with the inverse of M.

The SIFM fluorescence intensity is determined from R as the sum of the unmodulated intensity terms:

I_{f l u} (δ) = 3 R_{1} = o_{1} \cdot (I_{c e n t e r} (k_{0}, δ) + I_{e d g e} (k_{0}, δ)) \cdot I_{0}

in which the offset factor o₁ acts as a scalar. The SIFM phase ϕ(δ) is obtained from R in the [-π, π] range including the phase offset φ₁ using the four-quadrant inverse tangent:

Φ (δ) = atan2 (- R_{3}, R_{2}) = ϕ (δ) + φ_{1} .

The depth position of a fluorescent sample is determined from Φ(δ) via Eq. (16) or via a predefined calibration data set (see section 2.4).

The redefined analysis incorporates effects due to optical losses and path length deviations directly into the signal model. It is therefore not necessary to explicitly calculate corrected versions for the I_SPADx(δ) signals in order to obtain R, which makes the analysis efficient. In addition it only needs to be calibrated for six relative error factors instead of nine absolute error factors, which is significantly simpler. As a consequence the obtained I_flu(δ) and Φ(δ) parameters express relative rather than absolute values for a measured sample. This is acceptable for the majority of the biomedical applications since the fluorescence intensity and fluorophore depth position are normally analyzed relatively within a sample.

2.4 Calibration

In order to obtain the SIFM parameters from experimental data it is necessary to determine the (elements of) matrix M that describes the relative differences between the SPAD signals. In general M can be obtained from a measurement in which ϕ(δ) is known, i.e. the axial position of a fluorescent sample in the objective focus is known, and can be changed in a controlled manner. Such a calibration data set can be easily obtained by axially scanning a thin fluorescent sample through the objective focus using a translation stage similar as shown by Shtengel et al. [16]. Subsequently the calibration data set can be analyzed for the SPAD signal offsets, amplitudes and relative phase angles by fitting the model of Eq. (26) and allows therefore for a reconstruction of M. Alternatively the calibration data set can be used to create a lookup table that directly maps the SPAD signals to depth position.

A method that autocalibrates on a measurement would be more convenient since it eliminates the need for a separate calibration measurement. To this end M can be obtained by numerical optimization using the SPAD modulation depth D(δ) described by R as a feedback parameter:

D (δ) = \frac{\sqrt{R_{2}^{2} + R_{3}^{2}}}{R_{1}} = \frac{a_{1} \cdot \sqrt{I_{c e n t e r} (k_{0}, δ) I_{e d g e} (k_{0}, δ)}}{o_{1} \cdot (I_{c e n t e r} (k_{0}, δ) + I_{e d g e} (k_{0}, δ))} .

D(δ) is independent of the sample’s fluorescence field strength and was found to vary minimally within in the linear depth range of ϕ(δ). The variation of D(δ) should therefore be minimal among the different fluorophores in a data set. However in the case M is wrongly estimated the elements of R become mixed and D(δ) will vary significantly with ϕ(δ). Using a data set with multiple fluorophores at different axial positions it is then possible to estimate the elements of M by numerically minimizing the variance of D(δ).

2.5 SNR and phase noise analysis

Photon counting devices generate a digital signal pulse upon detection of a photon without the electronic amplifiers and analog-to-digital converters that are used in conventional (analog) detectors [29]. The noise measured by these detectors is therefore shot noise limited and can be described by Poisson noise statistics. In this section this shot noise limited model is used to derive the SNR of the SIFM intensity I_flu(δ) and the phase noise on the SIFM phase Φ(δ). In this analysis all the detected photons are assumed to originate from the fluorescent sample and dark counts in the SPADs are neglected.

In photon counting the SPAD intensity is detected as a number of photons: $I_{SPAD} = K_{SPAD} \cdot T$ with K_SPAD as the photon count rate and T as the measurement integration time [29]. The corresponding SPAD signal ${\bar{I}}_{SPAD}$ is defined as the time-averaged value for I_SPAD while the SPAD noise n_SPAD is given by the standard deviation of the observed I_SPAD variation. In the shot noise limited case n_SPAD is given as $n_{SPAD} = \sqrt{{\bar{I}}_{SPAD}}$ and the SPAD SNR is defined as: $S N R_{SPAD} = {\bar{I}}_{SPAD} / n_{SPAD} = \sqrt{K_{SPAD} \cdot T}$ . The signals S_Ry for the elements of R are then given by a linear combination of the three SPAD channels weighted by M⁻¹ according to Eq. (24) as:

S_{R y} = M_{y 1} \cdot {\bar{I}}_{SPAD1} + M_{y 2} \cdot {\bar{I}}_{SPAD2} + M_{y 3} \cdot {\bar{I}}_{SPAD3}

where M_yx are the elements of M⁻¹ denoted by their row (y) and column (x) indices. Correspondingly the noise n_Ry for the elements of R is given as the standard deviation for a weighted sum of independent random variables [30]:

n_{R y} = \sqrt{M_{y 1}^{2} \cdot {\bar{I}}_{SPAD1} + M_{y 2}^{2} \cdot {\bar{I}}_{SPAD2} + M_{y 3}^{2} \cdot {\bar{I}}_{SPAD3}} .

The SNR for the elements of R is then defined as:

S N R_{R y} = \frac{S_{R y}}{n_{R y}}

and since I_flu(δ) is directly derived from R₁ its SNR is given as:

S N R_{I_{flu} (δ)} = S N R_{R 1} = \frac{S_{R 1}}{n_{R 1}} .

The phase angle Φ(δ) is given by the phasor defined by R, denoted as Q from here on, with R₂ and R₃ as its horizontal and vertical components respectively. In the shot noise limited case phase angle noise is often derived from the phasor SNR under the condition of an equal noise amplitude for the horizontal and vertical components [31]. In SIFM this condition is not necessarily guaranteed since n_R₂ and n_R₃ depend on different linear combinations of the SPAD signals. In this study the phase angle noise is therefore derived more generally from the noise component perpendicular to the phasor. The perpendicular noise component of Q is derived as the standard deviation for correlated random variables [30] and is given as:

n_{Q ⊥} = \sqrt{{(\sin (Φ (δ)) \cdot n_{R 2})}^{2} + {(\cos (Φ (δ)) \cdot n_{R 3})}^{2} - ρ (n_{R 2}, n_{R 3}) \cdot n_{R 2} \cdot n_{R 3} \cdot \sin (2 Φ (δ))}

with ρ(n_R₂,n_R₃) as the correlation coefficient for n_R₂ and n_R₃. The correlation ρ(n_R₂,n_R₃) is obtained from the covariance between R₂ and R₃, which can be expressed as a summation of the pair-wise covariances of the I_SPAD_x signals weighted by their M⁻¹ elements [30]:

ρ (R_{2}, R_{3}) = \frac{C o v (R_{2}, R_{3})}{n_{R 2} \cdot n_{R 3}} = \frac{\sum_{n = 1}^{3} \sum_{m = 1}^{3} M_{2 n} \cdot M_{3 m} \cdot C o v (I_{SPADn}, I_{SPADm})}{n_{R 2} \cdot n_{R 3}} .

Assuming the length of Q is much larger than

n_{Q ⊥}

the phase angle noise can be given as the ratio of

n_{Q ⊥}

and the phasor length

S_{Q} = \sqrt{S_{R 2}^{2} + S_{R 3}^{2}}

[32]. The standard deviation of the phase angle noise on Φ(δ) is then given as:

σ_{Φ (δ)} = \frac{n_{Q ⊥}}{S_{Q}} .

In case n_R₂ and n_R₃ are uncorrelated and equal in amplitude Eq. (38) reduces to:

σ_{Φ (δ)} = 2^{- 1 / 2} \cdot S N R_{Q}^{- 1}

with

S N R_{Q} = S_{Q} / n_{Q ∥}

and

n_{Q ∥} = \sqrt{n_{R 2}^{2} + n_{R 3}^{2}}

as was reported by De Groot et al. [18] for a spectrometer based SIFM setup.

3. Results: experimental validation and imaging

In this section first the technical performance of SIFM with the MZI detection is evaluated for its axial positioning response (section 3.1) and its intensity SNR and phase noise (section 3.2). Subsequently its depth-resolved imaging capability is validated (section 3.3), and its opportunities for depth-resolved tissue fluorescence imaging are explored (section 3.4).

3.1 Axial position response and linear imaging depth range

The response of the SIFM setup on the axial position of a fluorescent sample was investigated with a thin layer of fluorescent microspheres (Fluospheres Infrared (715/755), Invitrogen, CA) that were spread sparsely on a glass coverslip and immobilized by drying in air. This sample was moved axially through the microscope focus using a motorized translation stage (Nano-Drive, Mad City Labs Inc., WI) while imaging the same lateral location. For each axial position 20 repeated measurements were obtained for photon counting with an integration time of 2 ms. In Fig. 5 the SPAD intensity signals, the SIFM intensity I_flu(δ) and the SIFM phase Φ(δ) are shown as a function of the axial sample position for both the 4 × and 10 × objectives. The data points in these plots show the mean ± the standard deviation. The excitation powers for the 4 × and 10 × objectives were respectively 17 µW and 2.4 µW. The setup was calibrated using the numerical optimization procedure described in section 2.4 for which the relative error factors are given in the figure caption.

Fig. 5 SIFM signal response as a function of axial position with the 4 × (A)-(C) and the 10 × (D)-(F) microscope objectives. (A)&(D) I_SPAD(δ) signals for SPAD₁ (blue), SPAD₂ (red) and SPAD₃ (green). (B)&(E) SIFM fluorescence intensity I_flu(δ). (C)&(F) SIFM phase Φ(δ) with the exact model phase of Eq. (15) in green and the linear phase model of Eq. (16) in red. The calibration allowed determination of the correct I_flu(δ) and Φ(δ) curves in the presence of small setup alignment errors. The calibration indicated relative error factors for the measurements with the 4 × objective as (o₂/o₁) = 0.88, (o₃/o₁) = 0.88, (a₂/a₁) = 0.85, (a₃/a₁) = 0.93, (φ₂-φ₁) = 0.31 rad, (φ₃-φ₁) = 0.55 rad; and for the 10 × objective as (o₂/o₁) = 1.01, (o₃/o₁) = 0.85, (a₂/a₁) = 0.67, (a₃/a₁) = 0.83, (φ₂-φ₁) = −0.20 rad, (φ₃-φ₁) = −0.11 rad.

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In Fig. 5(a) typical SPAD intensity signals are given for the 4 × objective expressed as count rates in mega-counts per second (MC/s). These curves clearly show the shift in axial position of the SPAD signal peaks similarly as was shown for the simulation results in Fig. 4(c). The SPAD modulation amplitudes were however lower compared to the theory, which is attributed to small optical misalignments, residual chromatic dispersion in the MZI and the insufficient filtering of reflected excitation light. This effect was also visible in the calibrated relative error factors which indicated relative amplitude losses of (a₂/a₁) = 0.85 and (a₃/a₁) = 0.93. Nevertheless under these conditions the correct I_flu(δ) and Φ(δ) could be obtained. In Fig. 5(b) the I_flu(δ) shows the Gaussian-like confocal collection efficiency as a function of axial position which is similar as reported in previous fluorescence microscopy studies [33]. In Fig. 5(c) the Φ(δ) is plotted in black together with the exact model phase of Eq. (15) in green and the linear phase approximation of Eq. (16) in red. It can be seen that the experimental Φ(δ) is in good agreement over the whole depth range with the exact model phase. In addition the central part of the experimental data around the focus center is in good correspondence with the linear phase approximation. The linear range of Φ(δ) for the 4 × objective was estimated to span from −250 µm to 250 µm for which the linear phase approximation showed an excellent fit (R² = 0.99). This 500 µm depth range is equivalent to 3.9 Rayleigh ranges (z_r = 129 µm). These results are in good agreement with the SIFM findings of De Groot et al. [18] who used the same objective.

In Fig. 5(d) an example is shown for SPAD intensity signals obtained with the 10 × objective in which an alignment error on the MZI caused a significant phase offset on all three the SPAD signals. The calibration indicated a SPAD₁ phase offset of φ₁ = −1.6 rad and relative phase offsets for SPAD₂ and SPAD₃ of (φ₂-φ₁) = −0.20 rad, (φ₃-φ₁) = −0.11 rad. Also under these circumstances the correct I_flu(δ) and Φ(δ) could be obtained. In Fig. 5(e) the 10 × objective I_flu(δ) shows the expected Gaussian-like confocal axial point spread function. In Fig. 5(f) Φ(δ) is plotted (in black) and shows a good agreement with the exact model phase (in green) and the linear phase approximation (in red) for its central part. The linear range of Φ(δ) for the 10 × objective was estimated to span from −40 µm to 40 µm (R² = 0.99). This 80 µm depth range is equivalent to 3.9 Rayleigh ranges (z_r = 20.7 µm).

These results confirm that the theoretical modeling of sections 2.1 – 2.3 correctly describe the signal output of the SIFM setup and can be used for calibration. In addition linear ranges for Φ(δ) were identified that can be used for depth-resolved fluorescence imaging.

3.2 Intensity SNR and phase noise performance

In section 2.5 the intensity SNR of I_flu(δ) and phase noise performance of Φ(δ) were derived to be dependent on the number of detected photons. In order to investigate this relation the fluorescent microsphere sample was positioned in the center of the focus of the 10 × objective and photon counting measurements were taken for 10 seconds with an integration time of 10 µs. These measurements were processed for I_flu(δ) and Φ(δ) at different integration times up to 10 ms by adding multiple subsequently obtained photon count measurements. An excitation power of 2 µW was used which resulted in a I_flu(δ) count rate of 3.3 MC/s. The results are shown in Fig. 6 for which the data points give the mean ± the standard deviation over 10 different data sets.

Fig. 6 (A) The intensity SNR of I_flu(δ) and (B) the phase noise performance of Φ(δ) as a function of integration time. In both plots the experimental data is shown in black dots, the theoretical shot noise limited performance is shown as the green line, and the theoretical optimal setup as the blue line. In (B) the red line shows the simplified phase noise model of Eq. (39).

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In Fig. 6(a) the SNR of I_flu(δ) is plotted in black dots as a function of integration time. The SNR values were determined from the measured photon counts according to Eq. (35) where the signal S_R1 was calculated as the mean and the noise n_R1 as the standard deviation over the R₁ values in a data set. The plot shows the expected square root dependence of $S N R Iflu (δ)$ with the integration time. In green the theoretical shot noise limit is shown which was calculated according to Eqs. (32)-(35) using the ${\bar{I}}_{SPADx}$ values. It can be seen that the experimental data is in good agreement with the theory which indicates that the SIFM setup performs at the shot noise limit for I_flu(δ) detection. In blue a curve is shown that represents the case of a theoretical optimally functioning setup for which M⁻¹ is defined by Eq. (25) with M₁₁ = M₁₂ = M₁₃ = 1/3. $S N R Iflu (δ)$ can be correspondingly defined in this case as: $S N R I_{flu} (δ) = \sqrt{{\bar{I}}_{SPAD 1} + {\bar{I}}_{SPAD2} + {\bar{I}}_{SPAD 3}}$ . It can be seen that the experimental data has a lower SNR by 10% with respect to the optimal case. It can therefore be concluded that the SIFM setup operates close to optimal conditions for I_flu(δ) detection.

In Fig. 6(b) the phase noise σ_Φ(_δ₎ is given as a function of integration time on a log-log scale. The phase noise values were obtained from the standard deviation of the Φ(δ) values for every integration time over all data sets. In green the shot noise limited phase noise according to Eq. (38) is given which is in good agreement with the experimental data especially for integration times above 1 ms. In red the simple phase noise model of Eq. (39) is given which shows a minimal difference with respect to the shot noise limited model. It can therefore be concluded that the simple phase noise model is a reasonable alternative for the more complicated shot noise limited model, and thus that the phase noise mainly depends on the SNR of the phasor Q. In blue the phase noise curve is given for the theoretical optimal setup, which was calculated with Eqs. (36)–(38) assuming uncorrelated SPAD signals and an M⁻¹ according to Eq. (25). It can be seen that the experimental phase noise is on average 25% higher than the optimal case. This is attributed to the reduced SPAD modulation amplitudes as was indicated in section 3.1, which led to smaller values for S_Q and consequently to an increase of the phase noise as can be seen from Eq. (38). In general the longer the integration time is taken, the higher the SNR of the phasor Q becomes. This results in a decrease of the phase noise σ_Φ(_δ₎ and therefore in an improvement of the SIFM depth localization accuracy.

Based on these results an integration time of 2 ms was chosen in subsequent experiments to achieve shot noise limited I_flu(δ) performance and low σ_Φ(_δ₎. At this integration time the average σ_Φ(_δ₎ was found to be 0.12 rad, which corresponds to SIFM depth localization accuracies of 11.4 µm and 1.81 µm for the 4 × and 10 × microscope objectives respectively. These localization accuracies relate to approximately 44 depth locations within the depth range (3.9 × Rayleigh range) assuming a constant SNR for phasor Q over the depth range.

3.3 Imaging validation

In order to validate the SIFM imaging performance a sample of known dimensions was constructed including capillaries filled with fluorescent dye. As schematically shown in Fig. 7(a) double layers of double-sided tape with a thickness of 180 µm [34] were gradually stacked into a staircase structure on a microscope slide. On three successive steps rectangular capillaries (Rect. Bore Capillaries 5002, CM Scientific, United Kingdom) were placed with inner diameters of 20 µm in thickness and 200 µm in width. These capillaries (denoted as c₁, c₂ and c₃) were filled with Indocyanine Green (ICG) dye through capillary action by dripping the dye on one capillary end. The ICG (IR125, Radiant Dyes Laser & Accessories, Germany) was dissolved in ethanol at a 180 µg/ml concentration.

Fig. 7 SIFM imaging validation. (A) Schematic drawing of the sample consisting of a microscope slide, layers of double-sided tape and rectangular capillaries (c₁, c₂ and c₃). (B) OCT cross-section image of the sample showing the capillaries as rectangles on top of the double-sided tape layers. The OCT image size is 0.93 mm × 2.0 mm (height × width) and the scale-bar indicates 100 µm. (C) SIFM intensity I_flu(δ). (D) SIFM phase Φ(δ). (E) SIFM depth δ. The imaged sample area for SIFM was 1.7 mm × 1.7 mm and the scale-bars in (C)-(E) indicate 200 µm.

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The depth distances within the sample were determined with OCT. OCT is an interferometric imaging modality that provides non-invasive three dimensional structural imaging of semi-transparent samples with micrometer resolutions [19]. An experimental swept-source OCT instrument at 1310 nm as described by Li et al. [35] was used with a handheld scanner that provided 15.6 µm axial and 20 µm lateral resolutions in air. In Fig. 7(b) a 1000 times averaged cross-sectional OCT image is shown of the capillary sample of 2 mm in width and 0.93 mm in depth. The gray-scale of the image encodes for the sample reflectivity while the depth dimension represents the optical path length through the sample. The stacked tape layers are clearly visible with changing reflectivity for the different glue and plastic components. The three capillaries can be seen as the rectangular objects placed on top of the tape as denoted by the white arrows. The extra optical path length added by the capillaries consequently shifted the perceived depth position of the tape layers below them compared to neighboring locations. The depth distances were measured to be t₁ = 184 ± 4 µm between capillaries c₁ and c₂ and t₂ = 185 ± 3 µm between capillaries c₂ and c₃ respectively.

SIFM imaging was performed over a 1.7 × 1.7 mm sample surface area with the 4 × objective and an excitation power of 24 µW. A single data set contained 250 × 360 pixels (height × width) for which the total measurement time was 3 minutes. In Fig. 7(c) the SIFM I_flu(δ) shows equivalent information as normally obtained for conventional fluorescence microscopy. The three capillaries are seen as the bright horizontal image sections against a non-fluorescent dark background. It is clear from this image that capillary c₂ was well placed in the focus since it displays the highest intensity. It is however less clear what the depth is of the other two capillaries with respect to c₂ since they show similarly decreased fluorescence intensity. In Fig. 7(d) the SIFM phase Φ(δ) is shown from which it is immediately clear that the three capillaries are located at different depths. In Fig. 7(e) Φ(δ) is converted into depth δ and shows that capillaries c₁ and c₃ are respectively more superficially and deeper located than capillary c₂. In order to minimize the noise in the SIFM depth image an intensity threshold was used that masked pixels with an I_flu(δ) below 0.2 MC/s to black. From five different sample locations SIFM data sets were obtained and the depth distances t₁ and t₂ were measured. Average distances of t₁ = 186 ± 19 µm and t₂ = 194 ± 11 µm were found, which are in good agreement with the OCT findings and the known thickness of the double tape layer. These results show that SIFM is capable of correctly measuring the depth position of multiple fluorescent objects within a sample.

3.4 Towards depth-resolved fluorescence imaging in tissue

In tissues fluorophores are distributed throughout a three-dimensional scattering environment and can be present at multiple depths simultaneously. In order to test the suitability of SIFM for imaging in tissue a phantom with controlled scattering properties and fluorescent dye concentration was developed. This phantom was used for the simulation of fluorescence angiography in which a fluorescent dye is injected into an in vivo vascular network for clinical vascular photography. The phantom was created with liquid absorbing fibers from a diaper (Depend Bed, Kimberly-Clark, TX) that were immersed in ICG dye (ethanol dissolved at 200 µg/ml) for several seconds. Afterwards the fibers were placed onto a microscope coverslip and surplus ICG dye was removed by gently tapping the fibers with a tissue. Subsequently the fibers were immersed into silicon elastomer (Sylgard 184, Dow Corning, MI) mixed with TiO₂ particles at a 0.5% volume concentration to obtain a matrix with a tissue-equivalent attenuation coefficient of 10 mm⁻¹ [36]. Finally the sample was covered with a second coverslip and double-sided tape was used as a spacer to create a 270 µm sample thickness. As such the dye soaked fibers represented blood vessels filled with ICG, while the TiO₂ silicon elastomer mixture mimicked a tissue environment. The diameter of the fibers ranged from 10 to 70 µm, which is comparable to capillary-sized blood vessels in tissue. SIFM was performed with the 4 × and 10 × microscope objectives which respectively imaged surface areas of 1.7 mm × 1.7 mm and 0.68 mm × 0.68 mm with excitation powers of 27 µW and 5 µW. In the case of the 4 × microscope objective this experiment closely mimicked a measurement in a human eye for a ~1.4 mm beam diameter on the cornea with a similar numerical aperture (NA_{4 ×} = 0.043 vs. NA_eye = 0.042). In addition the 500 µm depth range of the 4 × objective is compatible with fluorescence detection over the full retinal thickness.

In Fig. 8(a) the I_flu(δ) is shown for multiple clustered fibers with the 4 × objective. The fibers shows a large variation in intensity throughout the sample since this is dependent on the dye-holding capacity of individual fibers and on their axial location in the focus. In Fig. 8(b) the SIFM depth δ shows that the fibers are spread out over a 300 µm depth range which matches the preset sample thickness. As indicated with dashed colored boxes in Fig. 8(a) two areas were selected for detailed SIFM imaging with the 10 × objective. Figure 8(c) shows that for the tighter focus of the 10 × objective the I_flu(δ) decreases strongly the further away the fibers are located from the focus. In addition it can be appreciated from Fig. 8(d) that the fibers are stacked in depth from the left (superficial) to the right (deeper) in the image. In Fig. 8(e) several sparsely placed but overlapping fibers are shown. The SIFM depth image in Fig. 8(f) shows that for individual pairs of overlapping fibers in general the depth of the most superficial fiber is detected. This result suggests that SIFM can reliably detect the depth position of a sample in the presence of background fluorescence. The results of Fig. 8 show that SIFM can be performed in a scattering sample comparable to in vivo tissue and that SIFM is potentially useful for three-dimensional in vivo fluorescence angiography in the human eye.

Fig. 8 SIFM imaging on a capillary blood vessel phantom with ICG-soaked diaper fibers. (A)&(B) were obtained with the 4 × microscope objective, while for (C)-(F) a 10 × microscope objective was used. (A), (C) and (E) show the SIFM Intensity I_flu(δ). (B), (D) and (F) show the SIFM depth δ. The scale-bars indicate 200 µm in (A)&(B) and 80 µm in (C)-(F). The locations of (C)-(D) and (E)-(F) are indicated in (A) by respectively red and blue dashed frames.

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In addition to dyes in biomedical applications often tissue autofluorescence is used for imaging contrast. In order to demonstrate the autofluorescence imaging capability of SIFM the head of a crane fly was imaged. In flies autofluorescence can be measured from the pigmentation that is present in e.g. the compound eyes [37] and the exoskeleton [38, 39]. A diseased fly was placed on its back on a microscope coverslip and SIFM was performed using the 4 × and 10 × objectives with an excitation power of 1.35 mW. In Fig. 9(a) a white light photo shows the body of the fly with a length of 8 mm and a (wing span) width of 19 mm. In Fig. 9(b) a zoomed white light photo shows the fly’s head with the compound eyes and the two forward pointing small antennae that were visualized by the SIFM imaging.

Fig. 9 SIFM imaging on a crane fly. (A) White light photo of the fly over a 14.7 mm × 19.0 mm field-of-view. Scale-bar indicates 2 mm. (B) Zoomed white light photo over 2.6 mm × 2.6 mm that shows the fly’s head including the compound eyes and the small antennae. Scale-bar indicates 200 µm. (C)&(D) SIFM I_flu(δ) and depth δ measured with the 4 × objective over a 1.7 mm × 1.7 mm field-of-view of the fly’s head. Scale-bar indicates 200 µm. (E)&(F) SIFM I_flu(δ) and depth δ obtained with the 10 × objective over a 0.27 mm × 0.27 mm field-of-view of the left eye. Scale-bar indicates 30 µm. The inset image in (F) magnifies 4 facets for improved visualization of the depth difference between the facets and within the interfacet grooves.

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In Fig. 9(c) the SIFM I_flu(δ) image is shown taken with the 4 × objective over a 1.7 mm × 1.7 mm area. The compound eyes are uniformly fluorescent over their entire hemispheres while the antennae show more dim inhomogeneous fluorescence. In Fig. 9(d) the SIFM depth image reveals the hemispherical shape of the compound eyes. Both eyes show an equivalent depth variation along their surface of nearly 100 µm although both eyes were positioned at different depth positions within the microscope focus. In Fig. 9(e) the SIFM I_flu(δ) is shown of the left eye as obtained with the 10 × objective. The imaged area was 0.27 mm × 0.27 mm and 10 data sets were averaged for noise suppression. The improved magnification with the 10 × objective shows the individual (polygonal) facets of the compound eye including the (less fluorescent) interfacet grooves. Figure 9(f) shows the SIFM depth image from which the gradual shift in the depth position of the facets along the eye’s surface can be appreciated. In addition it can be seen that the interfacet grooves are deeper located as the facets itself for which an example is highlighted by the inset image. These results demonstrate that SIFM is suited for the imaging of autofluorescence and is potentially interesting for the surface profiling of fluorescent biological samples.

4. Discussion

SIFM provides three-dimensional fluorescence imaging without mechanical depth scanning of the microscope objective or sample. This increases the imaging speed compared to conventional confocal fluorescence imaging methods since it is not necessary to image multiple depth planes. The associated distortions between depth planes due to sample motion [40] are therefore absent in SIFM. In addition depth-resolved fluorescence detection allows for the distinction between fluorescence intensity and axial location, and will therefore be better able to quantify the strength of a fluorescent source in the case of a fluorescent background [41].

The novel SIFM detection using photon counters is expected to outperform spectrometer-based implementations with one to two orders of magnitude in sensitivity [21]. This is illustrated in this study in section 3.1 where 17 µW of excitation power provided similar results as the 650 µW used with the spectrometer-based setup of De Groot et al. [18] for a similar microscope and fluorescent microsphere sample. Further studies on the theoretical and experimental performance of both SIFM implementations are however necessary to fully confirm this observation. The improved detection sensitivity with photon counters will allow for the detection of weaker fluorescent signals, the further improvement of the imaging scan speed, or the use of lower excitations powers to reduce sample photobleaching.

The advantages of SIFM come with only a minor increase in hardware complexity. The SIFM excitation light delivery as described in this study is equivalent to other fiber-based confocal microscopes [10], while in the fluorescence emission collection path only the SIFM phase plate was added. The novel fiber-based SIFM detection MZI was found to be stable in its alignment and performance over the course of multiple minutes when placed in an enclosure on an optical table. In future clinical implementations outside the laboratory environment it might however be necessary to extent the MZI with a calibration light source on the unused input port (see Fig. 3) to follow and correct for interferometer fluctuations similar as used in 3 × 3 coupler-based fiber optic interferometric sensors [42].

In the current study only low numerical aperture objectives were used that are suitable for tissue imaging over a significant depth range. It is however expected that the SIFM method can be extended to imaging with high numerical aperture objectives for microscopy on the cellular or single particle scale. In this case Eq. (1) has to be derived for the non-paraxial situation. The use of SIFM imaging for high numerical aperture applications could be of interest to achieve axial super-resolution.

The analysis of tissue fluorescence can be complex due to the contributions of multiple fluorophores from different tissue layers. Depth-resolved fluorescence imaging with SIFM has the potential to better distinguish between these different fluorophore contributions, especially when multiple excitation wavelengths and emission filter configurations would be used. In ophthalmology depth-resolved imaging of the autofluorescence from the retina has the potential for the early detection of anomalies such as age related macular degeneration [43, 44]. In oncology it was further shown that fluorescence depth localization could help in the detection of premalignant lesions or early cancer [45, 46]. It is therefore expected that SIFM will contribute to an improved fluorescence analysis for disease diagnosis in future ophthalmoscopy and endoscopy instruments.

5. Conclusions

In conclusion, we have demonstrated a novel method for depth-resolved epi-fluorescence imaging based on self-interference fluorescence microscopy using photon-counter detectors. The axial position of fluorophores could be determined within image depth ranges with a linear SIFM phase response of 80 µm and 500 µm for 10 × and 4 × microscope objectives respectively. The SIFM fluorophore depth-localization was in good agreement with OCT depth measurements on dye-filled capillaries. The potential of SIFM for depth-resolved fluorescence imaging in tissue was shown successfully on a fluorescence angiography phantom and on an ex vivo fly eye. These results indicate the potential of SIFM for the in vivo three-dimensional measurement of fluorescence angiography and autofluorescence. SIFM might therefore be an interesting technique to include in future endoscopy and ophthalmoscopy instruments for improved fluorescence analysis in pathologies.

Funding

This research was supported by the Dutch Technology Foundation STW (Grant #13935) which is part of the Netherlands Organization for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs, a ZonMW VICI grant (Grant #918.10.628) from the Netherlands Organization for Scientific Research (NWO), the International Foundation Alzheimer Research (ISAO grant #14518), the European Union's Horizon 2020 research and innovation program under grant agreement number 654148 LaserLaB Europe, and Heidelberg Engineering.

Acknowledgments

The authors like to thank M. de Groot for useful ideas and discussions, J. J. Weda for his expert advice on sample preparation methods and F. Feroldi for assistance with the OCT imaging.

References and links

1. J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2(12), 910–919 (2005). [CrossRef] [PubMed]

2. B. N. Giepmans, S. R. Adams, M. H. Ellisman, and R. Y. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312(5771), 217–224 (2006). [CrossRef] [PubMed]

3. J. G. White, W. B. Amos, and M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105(1), 41–48 (1987). [CrossRef] [PubMed]

4. V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol. 13(1), 195–208 (2003). [PubMed]

5. V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8(1), 1–33 (2006). [CrossRef] [PubMed]

6. R. K. Jain, L. L. Munn, and D. Fukumura, “Dissecting tumour pathophysiology using intravital microscopy,” Nat. Rev. Cancer 2(4), 266–276 (2002). [CrossRef] [PubMed]

7. L. E. Meyer, N. Otberg, W. Sterry, and J. Lademann, “In vivo confocal scanning laser microscopy: comparison of the reflectance and fluorescence mode by imaging human skin,” J. Biomed. Opt. 11(4), 044012 (2006). [CrossRef] [PubMed]

8. M. Rajadhyaksha, S. González, J. M. Zavislan, R. R. Anderson, and R. H. Webb, “In vivo confocal scanning laser microscopy of human skin II: advances in instrumentation and comparison with histology,” J. Invest. Dermatol. 113(3), 293–303 (1999). [CrossRef] [PubMed]

9. F. Helmchen, M. S. Fee, D. W. Tank, and W. Denk, “A miniature head-mounted two-photon microscope. high-resolution brain imaging in freely moving animals,” Neuron 31(6), 903–912 (2001). [CrossRef] [PubMed]

10. B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005). [CrossRef] [PubMed]

11. L. Thiberville, S. Moreno-Swirc, T. Vercauteren, E. Peltier, C. Cavé, and G. Bourg Heckly, “In vivo imaging of the bronchial wall microstructure using fibered confocal fluorescence microscopy,” Am. J. Respir. Crit. Care Med. 175(1), 22–31 (2007). [CrossRef] [PubMed]

12. Q. Xu, K. Shi, S. Yin, and Z. Liu, “Chromatic two-photon excitation fluorescence imaging,” J. Microsc. 235(1), 79–83 (2009). [CrossRef] [PubMed]

13. D. R. Lee, Y. D. Kim, D. G. Gweon, and H. Yoo, “Dual-detection confocal fluorescence microscopy: fluorescence axial imaging without axial scanning,” Opt. Express 21(15), 17839–17848 (2013). [CrossRef] [PubMed]

14. A. Bilenca, A. Ozcan, B. Bouma, and G. Tearney, “Fluorescence coherence tomography,” Opt. Express 14(16), 7134–7143 (2006). [CrossRef] [PubMed]

15. M. Dogan, A. Yalcin, S. Jain, M. B. Goldberg, A. K. Swan, M. S. Unlu, and B. B. Goldberg, “Spectral self-interference fluorescence microscopy for subcellular imaging,” IEEE J. Sel. Top. Quantum Electron. 14(1), 217–225 (2008). [CrossRef]

16. G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009). [CrossRef] [PubMed]

17. S. W. Hell, E. H. K. Stelzer, S. Lindek, and C. Cremer, “Confocal microscopy with an increased detection aperture: type-B 4Pi confocal microscopy,” Opt. Lett. 19(3), 222–224 (1994). [CrossRef] [PubMed]

18. M. de Groot, C. L. Evans, and J. F. de Boer, “Self-interference fluorescence microscopy: three dimensional fluorescence imaging without depth scanning,” Opt. Express 20(14), 15253–15262 (2012). [CrossRef] [PubMed]

19. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

20. S. Yuan, C. A. Roney, J. Wierwille, C. W. Chen, B. Xu, G. Griffiths, J. Jiang, H. Ma, A. Cable, R. M. Summers, and Y. Chen, “Co-registered optical coherence tomography and fluorescence molecular imaging for simultaneous morphological and molecular imaging,” Phys. Med. Biol. 55(1), 191–206 (2010). [CrossRef] [PubMed]

21. J. Art, “Photon detectors for confocal microscopy,” in Handbook of Biological Confocal Microscopy (Springer), pp. 251–264.

22. P. J. Winzer and W. R. Leeb, “Fiber coupling efficiency for random light and its applications to lidar,” Opt. Lett. 23(13), 986–988 (1998). [CrossRef] [PubMed]

23. M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers,” Opt. Lett. 28(22), 2162–2164 (2003). [CrossRef] [PubMed]

24. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), pp. xlv, 1171 p.

25. H. Akagi, E. H. Watanabe, and M. Aredes, Instantaneous power theory and applications to power conditioning (John Wiley & Sons), Vol. 31.

26. W. C. Duesterhoeft, M. W. Schulz, and E. Clarke, “Determination of instantaneous currents and voltages by means of alpha, beta, and zero components,” Trans. Am. Inst. Electr. Eng. 70(2), 1248–1255 (1951). [CrossRef]

27. H.-S. Song, H.-G. Park, and K. Nam, “An instantaneous phase angle detection algorithm under unbalanced line voltage condition,” in Power Electronics Specialists Conference,1999. PESC 99. 30th Annual IEEE, 533–537.

28. S. Kanna, D. H. Dini, Y. Xia, R. Hui, and D. P. Mandic, “Distributed widely linear frequency estimation in unbalanced three phase power systems,” arXiv preprint arXiv:1410.0617 (2014).

29. Hamamatsu Photonics, Photomultiplier Tubes - Basics and Applications, 3rd ed. (Hamamatsu Photonics K.K. Electron Tube Division).

30. W. C. Navidi, “2. Probability,” in Statistics for Engineers and Scientists, 3rd ed. (McGraw-Hill), pp. 48 −165.

31. B. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005). [CrossRef] [PubMed]

32. W. Loh, S. Yegnanarayanan, R. J. Ram, and P. W. Juodawlkis, “Unified theory of oscillator phase noise I: white noise,” IEEE Trans. Microw. Theory Tech. 61(6), 2371–2381 (2013). [CrossRef]

33. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007). [CrossRef] [PubMed]

34. P. Lam, K. J. Wynne, and G. E. Wnek, “Surface-tension-confined microfluidics,” Langmuir 18(3), 948–951 (2002). [CrossRef]

35. J. Li, F. Feroldi, J. de Lange, J. M. Daniels, K. Grünberg, and J. F. de Boer, “Polarization sensitive optical frequency domain imaging system for endobronchial imaging,” Opt. Express 23(3), 3390–3402 (2015). [CrossRef] [PubMed]

36. D. M. de Bruin, R. H. Bremmer, V. M. Kodach, R. de Kinkelder, J. van Marle, T. G. van Leeuwen, and D. J. Faber, “Optical phantoms of varying geometry based on thin building blocks with controlled optical properties,” J. Biomed. Opt. 15(2), 025001 (2010). [CrossRef] [PubMed]

37. D. Stavenga, “Insect retinal pigments: spectral characteristics and physiological functions,” Prog. Retin. Eye Res. 15(1), 231–259 (1995). [CrossRef]

38. S. Zill, S. F. Frazier, D. Neff, L. Quimby, M. Carney, R. DiCaprio, J. Thuma, and M. Norton, “Three-dimensional graphic reconstruction of the insect exoskeleton through confocal imaging of endogenous fluorescence,” Microsc. Res. Tech. 48(6), 367–384 (2000). [CrossRef] [PubMed]

39. M. Smolla, M. Ruchty, M. Nagel, and C. J. Kleineidam, “Clearing pigmented insect cuticle to investigate small insects’ organs in situ using confocal laser-scanning microscopy (CLSM),” Arthropod Struct. Dev. 43(2), 175–181 (2014). [CrossRef] [PubMed]

40. C. Vinegoni, S. Lee, A. D. Aguirre, and R. Weissleder, “New techniques for motion-artifact-free in vivo cardiac microscopy,” Front. Physiol. 6, 147 (2015). [CrossRef] [PubMed]

41. R. Birngruber, U. Schmidt-Erfurth, S. Teschner, and J. Noack, “Confocal laser scanning fluorescence topography: a new method for three-dimensional functional imaging of vascular structures,” Graefes Arch. Clin. Exp. Ophthalmol. 238(7), 559–565 (2000). [CrossRef] [PubMed]

42. D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “Symmetric 3 x 3 coupler-based demodulator for fiber optic interferometric sensors,” in OE Fiber-DL tentative, 328–335.

43. M. G. Gräfe, A. Hoffmann, and C. Spielmann, “Ultrafast fluorescence spectroscopy for axial resolution of flurorophore distributions,” Appl. Phys. B 117(3), 833–840 (2014). [CrossRef]

44. F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, and J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Vis. Sci. 36(3), 718–729 (1995). [PubMed]

45. R. A. Schwarz, W. Gao, D. Daye, M. D. Williams, R. Richards-Kortum, and A. M. Gillenwater, “Autofluorescence and diffuse reflectance spectroscopy of oral epithelial tissue using a depth-sensitive fiber-optic probe,” Appl. Opt. 47(6), 825–834 (2008). [CrossRef] [PubMed]

46. G. A. Wagnières, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68(5), 603–632 (1998). [CrossRef] [PubMed]

Self-interference fluorescence microscopy with three-phase detection for depth-resolved confocal epi-fluorescence imaging

Abstract

1. Introduction

2. Theory and experimental system description

2.1 SIFM microscope and theory

2.2 Fiber-based MZI for SIFM detection

2.3 Three-phase analysis of the MZI signals

2.4 Calibration

2.5 SNR and phase noise analysis

3. Results: experimental validation and imaging

3.1 Axial position response and linear imaging depth range

3.2 Intensity SNR and phase noise performance

3.3 Imaging validation

3.4 Towards depth-resolved fluorescence imaging in tissue

4. Discussion

5. Conclusions

Funding

Acknowledgments

References and links

Supplementary Material (1)

Cited By

Figures (9)

Equations (39)

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