Fourier Transform Imaging Spectroscopy (FTIS) has recently emerged as a widely used tool for spectral imaging of biological fluorescent samples. Here we report on a novel double-pass FTIS system capable of obtaining an excitation as well as an emission spectrum of a fluorescent sample with only a single sweep of the interferometer. This result is achieved by a modification of an existing FTIS system, which now places the excitation source before the interferometer so as to spectrally modulate the excitation as well as the detection. An analysis of the acquired signal allows for the reconstruction of the excitation as well as the emission spectrum of each fluorophore, assuming an independence of the two spectra for each fluorophore. Due to the patterned excitation generated by the Sagnac interferometer, a substantial degree of optical sectioning is achieved at excitation wavelengths. Further analysis of the acquired data also enables the generation of optically sectioned emission images. A theoretical analysis and experimental data based on fluorescent beads are presented.
©2004 Optical Society of America
In the last decade, imaging spectroscopy has proved an extremely useful tool in fluorescence microscopy of biological samples , enhancing the quantification of Förster Resonance Energy Transfer (FRET), the spectral discrimination of a large number of fluorophores  and the reconstruction of spectral shifts caused by the microenvironment of the sample.
Fourier transform spectroscopy provides the means for obtaining spectral images ,. In this approach, a series of images is acquired in which each detected image point is formed by the interference of two alternative optical paths with a variable optical path-length difference (OPD) between the sample and image planes. The OPD is altered throughout the acquisition of a series of images. One realization of the method is exemplified by a commercially available instrument (SpectraCube by Applied Spectral Imaging, Haifa, Israel) and depicted in Fig. 1.
Fourier transform spectroscopy has also been used to stimulate the visual system as well as for fluorescence excitation  and emission  spectroscopic imaging. A combined excitation and emission mode has been proposed that uses two separate Pentaferometers operated at different rotational speeds .
For generating combined excitation/emission spectroscopic imaging, the system shown in Fig. 1 was modified by moving the beam-splitter cube into the infinity beam-path between interferometer and camera (Fig. 2). As an effect of this modification, not only the emission light but also the excitation light passes through the interferometer, giving rise to a spectrum of excitation light transmitted to a point in the sample being dependent on the OPD. With this setup it is not possible to independently influence the OPD of respective excitation and emission; i.e. the OPDs are instead forced to be identical. However, under the assumption that excitation and emission spectra of fluorophore species are independent (implying that a change in excitation wavelength influences the strength, but not the shape of the emission spectrum), it is possible to reconstruct the respective spectra as described below.
2.1. Excitation and emission spectrum from a single OPD sweep
In conventional, emission–Fourier transform spectroscopy, it is known that the detected intensity Idet depends on the emitted spectral intensity Iem(kem) as follows:
The wavenumber kem=2π/λem, with λem being the emission wavelength, was chosen to simplify the equations. Without loss of generality, the fluorophore concentration, brightness and the optical efficiency of detecting light from a point in the sample are contained in the term Iem(kem). The εem(kem,OPD) simply describes the effect of the interferometer on the detected intensity, which can ideally be approximated as
where mem is the degree of modulation (which is, for example, reduced by an unbalanced beam-splitter). By Fourier transformation (FT) of the detected signal Idet (OPD) along the OPD coordinate (centered at OPD=0) FT[Idet (OPD)] and computation of the real-part (or the absolute magnitude), the emitted intensity spectrum Iem(kem) is recovered. As an example, the Fourier transform of the signal originating from a spectrum uniform over a certain frequency range and zero elsewhere is shown in Fig. 3(c). The peak at zero frequency can be attributed to the effect of the constant offset in Eq. (2) and the peak at negative frequency stems from the conjugate exponential when decomposing the cosine function into its complex exponentials.
In the double-pass system, the excitation light is also influenced by interference. The spectral distribution of excitation light Iex(kex,OPD) at a point in the sample is given as:
with εex similar to the definition in Eq. (2), but the degree of modulation (mex) is now also dependent on defocus (see below). For the sake of simplicity the multiplicative influence of the optical system on the excitation spectrum was absorbed into the spectral distribution of the light-source ILs(kex).
In general the spectrally dependent emitted intensity Iem(kex,OPD) at a sample of local fluorophore concentration ρ is a function of the excitation wavenumber kex:
For the reconstruction of the spectra Sex,em(kex,kem,OPD) from the acquired interferogram, it is advantageous to assume that the shape of the emitted spectral distribution of each fluorescent species is independent of its excitation wavelength. The emitted light is thus proportional to a spectral integral (0 to infinity) over the excitation spectrum multiplied by the spectral distribution of the excitation light:
Sex(kex,OPD) and Sem(kem,OPD) are the independent excitation and emission spectrum, respectively.
Under the condition of independent excitation/emission spectra, the acquired signal in each pixel can be described as a product of two terms (both being OPD and spectrally dependent). Eq. (5) was inserted into Eq. (1), then Eq. (3) replaces Iex(kex,OPD):
Since the last equation above is a product of two independent integrals, the Fourier transformation of the detected signal Idet (OPD) along the OPD coordinate will be the convolution of the two Fourier transformations of the individual integrals. The Fourier transformation of these integrals, however, contains information about the excitation and emission spectra, respectively. This can be seen by writing the cos(kem OPD)=[exp(ikem OPD)+exp(-ikemOPD)]/2 in Eq. (2) and performing the integrals:
The constants a and b are the integral of the respective emission and excitation spectrum and δ(k) is Dirac’s delta distribution. In Eq. (7) global proportionality factors have been omitted for clarity reasons.
An example of uniform excitation and uniform emission at spectrally separate bands is depicted in Fig. 4. Due to the convolution in the Fourier transform of the detected signal, the original excitation and emission peaks (B,C) are still visible, but flanked by a difference (A) and a sum spectrum (D). The difference spectrum (A) stems from the correlation of the excitation with the emission spectrum and the sum spectra (D) are a convolution of the excitation with the emission spectrum.
It is interesting to note that the strength of the emission spectrum contribution (B) in the observed signal depends on the integral over the excitation spectrum and the strength of the excitation spectrum distribution (C) depends on the integral over the emission spectrum.
2.2. Multiple fluorophores in a single pixel
The assumption of the shape of the emission spectrum not depending on the excitation wavelength as required for Eq. (5) would not be valid in the case of multiple fluorophores contributing to the same detected signal on the CCD. However, the idea is still valid as long as the assumption of independent excitation and emission spectra holds for each of the contributing fluorophores. This is due to the fact that the detected signal is to a very good approximation a simple sum of individual signals, reflecting the concentration of each individual fluorescent species in the sample. Only a Fourier transformation, which is linear in its arguments, is used in the processing; thus the processed result is a simple sum of the spectra as would be obtained from individual fluorophore species. As a result, it is impossible to directly measure two-dimensional excitation and emission spectra. However, by assuming a fixed number of fluorophores, a two-dimensional spectrum can be estimated from its projections (which were measured).
2.3. Suppression of out-of-focus light
The Sagnac interferometer (Fig. 1) has the interesting property that the OPD depends on the incident angle of entering light. Thus the OPD for illumination is dependent on at least one coordinate in the sample plane, leading to a spatially modulated excitation. The lateral fringesize of this pattern varies with the excitation wavelength, which in combination with a broadband excitation leads to a decrease in modulation at larger OPDs. From the measurement of this decrease in modulation with longer OPDs, the excitation spectral characteristics of the sample are then recovered.
However, if a fluorophore is out-of-focus, an overall decrease of the modulation depth (mex) can be expected due to defocus blurring for each excitation wavelength. Assuming a sinusoidal patterning for each wavelength, this can be modeled as a slightly wavelength-dependent decrease of the modulation depth mex(z) over defocus (z). It should be noted that for spatially (transversal) coherent illumination self-imaging effects (Talbot planes ) can occur, leading to a more complex behavior of mex(z). However, in our experiment with spatially incoherent illumination, an almost monotonous decay mex(z) can be assumed for each excitation wavelength.
After spectral reconstruction (see above), a decrease in mex of the excitation distribution leads to a reduced strength of the excitation peak (e.g. peak C in Fig. 4(b)), leaving the emission-peak unaffected. On the emission side, the emitted light is defocused, but the CCD camera will still show identical contrast between emission fringes, since the interferometer operates on the light-distribution (and its coherence) as given on its input-plane, which is the in-focus plane in the sample. Its spatial relationship to the camera is independent of the fluorophore-position and remains unaltered during axial scanning.
This reduction of the excitation signal with defocus leads to an inherent degree of optical sectioning as can be seen by inspecting the reconstructed images at the excitation frequencies. Furthermore the cross-peaks (sum- and difference-frequency spectrum, e.g. A and D in Fig.4(b) are also reduced in strength with defocus, because they stem from a convolution/correlation of excitation with the emission spectrum of which the excitation spectrum decreases linearly with the reduction in mex.
2.4. Sectioned emission spectra
The acquired as well as the reconstructed data can be described as linear superpositions of signals generated (excited and emitted) from different focal planes. The sum- and difference-frequency peaks are the convolution and correlation, respectively, of excitation with emission spectra, which are reduced for signal stemming from out-of-focus regions. With knowledge of the sectioned excitation information, it is possible to independently calculate a sectioned emission spectral image from each of the sum- and difference-frequency peaks. This can be achieved, for example, by dividing these peaks by the excitation peak (or its flipped counterpart) in OPD-space (all peaks inversely Fourier transformed individually).
To understand why these cross-peaks really allow an independent sectioned measurement of emission light, it is useful to picture the situation of an in-focus and an out-of-focus fluorophore that have emission signals of different spectral signatures but with identical excitation spectra. The emission-only peak would be a mixture of in- and out-of-focus information. The excitation peak would only contain the in-focus excitation signal, which is, however, identical for both species. Thus from these peaks, there is no method for restricting the emission-information to the in-focus fluorophores only. However, the cross-peaks contain only information from the in-focus fluorophores. The signals from different focal planes add only after the spectral convolution for each individual fluorophore has been performed. Thus, using the cross-peaks and the excitation-peak it is possible to compute an independent sectioned emission image. This can be done in various ways, since the problem is basically a matter of deconvolution. One possible way would be to transform the individually extracted peaks (one cross-peak and one excitation-peak) back to real (OPD-) space and divide them to obtain the sectioned emission information after another Fourier transformation. Other deconvolution strategies might be advantageous. For example, it is possible that sectioned excitation and emission images could also be computed by using only the two cross (sum and difference frequency) peaks.
The experimental setup was similar to the one shown in Fig. 2. It should be noted that the two tube lenses (TL) between the interferometer and the objective could be avoided. However, since most microscopes have the tube lens build into their exit ports, this arrangement with an extra tube lens to achieve a parallel light pass was chosen. Some microscopes have appropriate exit ports such that the two tube lenses can be avoided.
The dichroic beam-splitter was a 505 DRLP (Omega Optical, Brattleboro, VT, USA) and the filters were a 470 bandpass (35 nm width, 470DF35, Omega Optical) for excitation and a long pass (510EFLP) for emission. In the setup of Fig. 2, it is essential to minimize the excitation light reaching the CCD camera. This is difficult, since about 50% of the excitation light is directed towards the camera after having passed the interferometer once, thus generating an undesirable interference signal, observed as fringes that, after Fourier transformation, do not correspond to the frequency of the excitation light. Even though the beam splitter and the emission filter block most of this light, it was nevertheless necessary to illuminate the beam splitter-cube at a slightly oblique angle in the experiments reported here. This resulted in two mostly separate regions in the image. One region containing the fringes stemming from unblocked excitation light as well as another region almost devoid of these fringes but with a bright sample signal. Further improvement may be possible by the introduction of appropriate apertures limiting the illumination angles or the use of polarizers (see discussion).
To demonstrate the capabilities of the double-pass Fourier transform imaging spectroscopy method, tests were performed. In the first experiment two species of polystyrene beads (diameter 175 nm, Molecular Probes, Eugene, Or, USA) were mixed and deposited onto a cover slip. Spectral images of the same region were acquired using a standard wide field epi-illumination microscope (with a setup similar to Fig. 1) and the modified double-pass setup (Fig. 2). The obtained Spectra (insets) of a green and a yellow bead are compared in Fig. 5 for the case of ordinary wide field illumination (Fig. 5(a)) and illumination through the interferometer (Fig. 5(b)). The additional excitation spectral information is given in Fig. 5(b).
In Fig. 6 the optical sectioning capability was experimentally tested using a fluorescent plane sample (Langmuir blodget monomolecular fluorescent polydiacetylene film, ). The in-plane integrated signal at various spectral peak positions is plotted in dependence of the axial (z-) position of the sample (PIFOC, Physik Instrumente, Karlsruhe/Palmbach, Germany). Only the excitation-peak and the two cross-peaks (Cross 1=sum frequency peak, Cross 2=difference frequency-peak, see also Fig. 4) showed optical sectioning in accordance with the theory. The measured full-with-at-half-maximum (FWHM) of the excitation peak was 880 nm (Gaussian fit, without subtraction of a background). This z-resolution value is expected to be dependent on the fringe spacing, and therefore the detune-angle β(Fig. 2) and eventually the coherence properties of the source (and excitation filters).
The assumption of independence of the excitation and emission spectrum of a given fluorophore is not strictly valid for many compounds. Due to the inhomogeneous line-broadening, one fluorophore species has to be pictured as having subspecies with slightly shifted spectra. When exciting at the very red edge of the excitation spectrum, a shift in emission spectrum is sometimes observed. This effect is not included in our model. However, since the spectrum can be decomposed into different sub-spectra, a useful spectral representation can still be individually obtained for excitation and for emission. Due to the linearity of the approach, the reconstructed results represents a sum of the spectra of all the subspecies.
A problem of the setup shown in Fig. 2 is that a small fraction of the excitation light can still find its way to the camera, depending on the quality of the filters and dichroic mirror. In fluorescence instruments it is often crucial to minimize background signals, since the fluorescence emission is often very faint. That is, the intensity of the excitation light is several orders of magnitude greater than the emission light. The arrangement of Fig. 2 has the disadvantage of returning approximately 50% of the intense excitation light towards the camera, which has then to be blocked efficiently by the emission filter. The success of epi-fluorescence microscopy is mostly due to the avoidance of this back reflected excitation light.
A possibility to greatly reduce the amount of excitation light on the camera by the use of polarizers and/or polarizing beam splitters is sketched in Fig. 7. The polarization direction of the polarizer near the camera should be perpendicular to the direction of the polarizer next to the light source. After having passed three reflections and returning towards the camera, the polarization will still be oriented the same way and will thus be reflected by the polarizing beam-splitter back to the light source. An additional polarizer in front of the camera together with the emission filter should efficiently block the remaining light. A disadvantage of introducing polarizers/polarizing beam splitters into the detection beam path is that approximately 50% of the fluorescence emission light is blocked, assuming it is depolarized. This effect could eventually be circumvented by the introduction of an image-splitter cube with polarization optics between the microscope (objective) and the interferometer. The polarization of one of the two images, would be such as to be blocked by the polarizer in front of the camera. It can be recovered by introducing an appropriately oriented half wave plate (λ/2) in this part of the split beam.
An additional option to reduce the background of excitation light on the camera exploits the fact that reflected excitation light traces a different light path than the emission light (see Fig. 8). It is especially useful to position the illumination source such that light enters the interferometer under an oblique angle from outside the paper plane (not shown in Fig. 8), since in this case no overlap of reflection with the emission can arise, independent of the rotational position of the interferometer. In the current setup, this effect was exploited by positioning a field-stop in the illumination light at a conjugate image position and adjustment of the angles to best separate the positions of reflected excitation light from emission light. It could be further enhanced by introducing additional baffles at other positions in the beam path.
The concept of Double-Pass Fourier Transform Imaging Spectroscopy described here has many potential applications. Currently imaging spectroscopy is used in spectral karyotyping  to identify chromosomes and possible alterations (e.g. translocations). The capability to acquire the excitation spectrum with this double-pass setup can be used to improve the reliability of spectral karyotyping. In addition is should be possible to simultaneously distinguish between a greater number of different dyes.
A further application is the use of this technology in the measurement of FRET. As indicated, a 2D (excitation-/emission-) spectrum can be estimated from its projections, which are measured by the described method and successive data-processing. Imaging of the excitation and emission spectrum should be very advantageous for resolving FRET related images.
Although Double-Pass Fourier Transform Imaging Spectroscopy has been demonstrated here in an application for fluorescence microscopy, the concept is not limited to this case. Other possible applications could be reflection type microscopy or remote sensing. In these cases it is very important to separate the illumination side from the detection side. In cases where reflected or scattered light instead of fluorescence is measured, it is not possible to use a filter cube with excitation and emission filters. Instead, for the separation of illumination (termed “excitation” in the above) light from emitted (including reflected/scattered) light one could use the aperture or polarization approaches (in combination with an appropriate λ/4 plate). For remote sensing or other applications, the microscope could be replaced by appropriate optics to perform the imaging.
We thank Applied Spectral Imaging and its German representative Michael Koehler for providing the equipment, Yuval Garini for his help in setting up and calibrating the instrument and A. Egner and S.W. Hell for providing filters. S. Höppner and M. Beutler are thanked for revising the manuscript. R.H. was supported through the E.U. grands QLG2-CT-2001-02278 and QLK3-CT-2002-01997. The Max Planck Society is acknowledged for support.
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