Förster resonance energy transfer (FRET) is an important method in studying biochemistry reactions. But quantifying FRET rapidly is difficult to do because of crosstalk between free donor, free acceptor and FRET fluorescent signals when only excitation or emission property of a FRET sample is measured. If FRET is studied with excitation-emission matrix (EEM) measurements, because the fluorescence intensity maxima of donor, acceptor, and FRET emissions occupy different regions within the EEM, FRET fluorescence can be easily separated out by linear unmixing. In this paper, we report a novel high-speed Fourier Fluorescence Excitation Emission spectrometer, which simultaneously measures three projections of EEM from a FRET sample, which are excitation, emission and excitation-emission cross-correlation spectra. We demonstrate that these three EEM projections can be measured and unmixed in approximately 1 ms to provide rapid quantitative FRET in the presence of free donors and acceptors. The system can be utilized to enable real-time biochemistry reaction studies.
©2010 Optical Society of America
Förster resonance energy transfer (FRET) is an energy transfer phenomenon that happens when two fluorophores are closely separated (10 nm or less) . FRET causes the excited-state energy from a donor fluorophore to transfer to a nearby acceptor through nonradiative dipole - dipole coupling. The transfer results in quenching in donor excitation and acceptor emission enhancement. The degree of energy transfer, or the FRET efficiency, is influenced by the distance between the pair as well as the spectral properties of the donor and the acceptor. The power of FRET is that once the FRET efficiency is quantitatively measured, the exact distance between donor and acceptor can be calculated with Å-level precision . FRET has long been used as an optical ruler for macromolecular structures and as an indicator for biochemistry reactions [3–8]. Furthermore, when FRET is measured at high speeds (milliseconds), it can be used to study structure changes and reaction in real time [9–15].
FRET usually is measured via its spectral signature, including donor emission quenching and acceptor emission enhancement. However, FRET cannot be readily quantified by just measuring the emission of the acceptor. One has to correct for the emission spectral bleed-through, which is a result of the overlap between donor and acceptor emission spectra, and the excitation spectral bleed-through, caused by the overlap between the donor and acceptor excitation spectra, which leads to direct acceptor excitation. Conventional FRET measurements employ “three-cube FRET” fluorescence microscopy [16–19], which detects and separates fluorescent emission intensities by changing various fluorescence emission filters. The method can correct the emission spectral bleed-through but not excitation spectral bleed-through because FRET intensity and direct excited acceptor intensity are not distinguishable in the emission spectra [20, 21].
Alternative approaches for combating these artifacts have been proposed to truly quantify FRET. To correct direct acceptor excitation, the acceptor needs to be intentionally bleached so that FRET signals with or without acceptors can be compared [22–25]. However, because it is impossible to quantify the efficiency of acceptor bleaching and the unwanted bleaching effect on donors, the acceptor bleaching method is not ideal for quantifying FRET efficiency. Furthermore, the acceptor bleaching method provide no means to quantifying FRET efficiency in the present of free donors and free acceptors, which occurs before a kinetic reaction reaches equilibrium or when donor and acceptor concentrations are mismatched [5,26, 27]. Fluorescence lifetime measurements  can independently determine FRET efficiency without being affected concentrations. However, lifetime systems require high cost equipments and longer acquisition times, which make them not ideal for clinical applications and real-time studies.
Alternatively, to fully characterize FRET in the presence of free donor and acceptor by only spectral measurements, fluorescent emission as a function of both the excitation and the emission wavelength (excitation and emission matrices, EEM) needs to be measured. In an EEM, FRET originated acceptor emission can be easily separated from direct acceptor excitation-emission by their different excitation wavelengths. EEM contributions from free donor, free acceptor and donor-acceptor pairs can be separated via a simple linear unmixing algorithm. Thus, FRET efficiency, FRET pair concentration and free donor/acceptor concentrations can be obtained simultaneously. The EEM approach furthermore eliminates excitation bleaching and emission spectral bleed-through.
If EEM measurements can be performed within milliseconds, FRET could be used to monitor macromolecule conformational changes and inter-molecular reactions in real time. However, conventional EEM methods are very slow because they require scanning through all excitation wavelengths one by one, while detecting fluorescent emission spectra in parallel [29–33]. Approaches used to rapidly scan excitation wavelengths include fast variable excitation filters [34, 35] and tunable excitation sources, or dye lasers with fast-switching dye cells [30, 32]. These methods can acquire an EEM within from tens of seconds  to less than 200 ms . However, fast-switching methods have a relatively low excitation spectral resolution of 5 ~10 nm. In a FRET sample, excitation peaks of donors and acceptors often are separated by only 20-30 nm. Fast-switching methods do not provide enough excitation points to perform accurate spectral linear unmixing on FRET results. Another approach that has been used to obtain rapid EEM measurements on a single point is parallel fluorescence excitation detection, using a double Fourier Transform Spectrometer (FTS) where the excitation light is modulated by a first scanning interferometer and the photoluminescent emission is detected using a second scanning interferometer [36, 37]. We have previously implemented a double Fourier transform spectrometer that is capable of obtaining a full EEM  with an 81-cm−1 (equivalent to 2 nm at 500 nm, or 3.4 nm at 650 nm) spectral resolution in 40 seconds. The FTS method provides good resolutions in both the excitation and the emission dimension, which allows subtle spectral changes caused by FRET to be analyzed with high accuracy.
To improve the acquisition speed and achieve dynamic FRET measurements, we reduced the double FTS to a double-pass FTS that can measure excitation and emission spectra, as well as the diagonal projection of the intensity EEM simultaneously . The use of a double-pass FTS to measure excitation and emission spectra has been reported previously , but not investigated for FRET. Although the approach does not provide full EEMs, excitation, emission and diagonal projections of an EEM are sufficient for separating FRET from free donor and free acceptor backgrounds.
In the present study, we designed a fluorescence FTS that has a much higher acquisition speed and a better spectral resolution than previously reported . We demonstrate that this FTS is capable of measuring excitation, emission and cross-correlation (diagonal projection of the EEM) spectra within 1 ms. We developed a linear-unmixing algorithm to analyzing these spectral projection in FRET stoichiometric experiments, and determined the concentrations of free donors, free acceptors, FRET pairs simultaneously.
Figure 1 depicts a schematic of the high-speed Fluorescence Excitation Emission instrument. Collimated light from a xenon arc lamp (Oriel 75W) was transmitted through DM1 (DM550, Semorck) and DM2 (DM740, Semorck) and sent into the scanning interferometer. The scanning interferometer utilized an all-reflective optical delay line . In the delay line, scans were created by continuous rotary motion of a galvanometer driven tilting mirror M1 (Modal 6880, CTI). The delay line scans 200 μm delay at 600Hz, providing the capability to measure FRET spectral properties in 1 ms with 1 nm resolution.
Spectrally-encoded pump light [36, 37] from the output port of the interferometer was focused onto the sample by an objective lens(10 × , 0.45NA, Nikon). Fluorescent emission was collected through the objective and sent back into the same interferometer. The double-passed FTS geometry configuration guaranteed synchronization between the excitation and emission delay scans. The modulated emission light was detected by the photomultiplier PMT2 (R928, Hamamatsu).
In order to monitor and delay scan nonlinearities, two monitoring channels were used . A small portion of the light was reflected by a beam-pickup and projected into a second photomultiplier PMT1 (HC125-01, Hamamtsu). The interference fringes detected by PMT1 were also used to determine the time at which the differential delay of the interferometer was zero. To monitor the movement of the delay line, a 780 nm IR laser was coupled into the interferometer via DM2. The interference signal from the IR laser was detected by an amplified Si photo detector (PDA55, Thorlabs). All channels were sampled simultaneously by a DAQ card (PCI6115, NI) at a 1M sampling rate.
The optical delay scan was performed by a tilting based delay line proposed for FTS previously . We used a galvanometer mirror M1 to scan the tilting angle at 600Hz. When the tilting mirror tilts at an angle of φ from its zero-position θ, the optical path delay (OPD) can be determined , as shown below:
3. Spectral reconstruction
Fourier analysis was used to reconstruct the excitation, emission, and excitation-emission cross-correlation spectra .
When the optical delay of the double-pass interferometer scans, the intensity of the illumination light after the interferometer is modulated by interference. If we use a single wavelength excitation source at wavenumber σ1 with a total power P0, the power of modulated illumination beam on the sample PIllum is a function of optical path delay OPD of the interferometer:
The emission intensity of fluorophore responds at the same modulation frequency as the excitation modulation frequency. In the case of pure fluorophores, whose EEM is the product of excitation and emission spectra, the fluorescent emission collected from the sample is
After transmitting back through the same interferometer, the emission signal detected on PMT2 is:
When the illumination light is a broadband source S0(σ1), the emission power detected on PMT2 becomes
Fourier transformation of Eq. (5) yields the emission intensity on PMT2 as a function of wavenumber σ:
The four terms in right side of Eq. (6) sequentially represent the integrated fluorescence intensity, the excitation spectrum (0 degree projection of the EEM), the emission spectrum (90 degree projection of the EEM), and the cross-correlation of the excitation and emission spectra (45 degree diagonal projection of the EEM). With the double-pass Fourier interferometer, we can therefore obtain three spectral fingerprints: excitation, emission and cross-correlation spectra in a single scan.
If there are two kinds of fluorophores in the sample, for example donors and acceptors that do not exhibit the FRET effect, Eq. (6) will be a linear combination of spectral properties of the two fluorophores. Signals from the fluorophores can be easily separated by spectral unmixing of the excitation and emission spectra. If the sample exhibits FRET in the presence of free donors/acceptors, the FRET signal can be treated as a third fluorophore component, whose excitation spectrum is identical to the donor excitation spectrum and whose emission spectrum is identical to the acceptor emission spectrum. Whereas the excitation or emission spectra of FRET signals are not unique, the 45 degree EEM projection, i.e. the cross-correlation of excitation and emission spectra is different from both donor emission signals and acceptor direct excitation signals. Thus, being able to measure 3 EEM projections together allows us to fully quantify a FRET system even when there are free donors or acceptors.
When all are calibrated, amplitudes from any donor-acceptor mixture can be obtained by linear unmixing. can then be used to quantitatively analyze FRET in the mixture.
4. FRET quantitative analysis
When a mixture contains a total donor concentration of CD, and a total acceptor concentration of CA, which forms a donor-acceptor pair concentration of CDA, spectral amplitudes of each EEM projection are given by :16, 18]:
The G factor and the FRET efficiency can be measured by titration experiments. Equation (8) contains 7 linear equations for only 3 variables, concentrations of free donors/acceptors and D/A pair. Equation (8) is an over-determined problem, which means there are more linear equations than unknown variables. When the values of all equations are measured by experiments, an over-determined model makes the solution of the concentrations more precise and less sensitive to measurement uncertainties. Our system measures concentrations at a very high speed. The noise in the system is inevitably higher because of the measurement uses less integration time. Solving the concentrations through an over-determined model helps improving quantification precision.
To calibrate and test the system, we performed FRET experiments using Alexa Fluor 514 and Alexa Fluor 568. FRET pairs were formed by immunoreactions between Alexa Fluor 514 labled goat anti-rabbit IgG (donor) and Alexa Fluor 568 labled rabbit anti-mouse IgG (acceptor) diluted in 1 × Phosphate-buffered saline). Samples were first measured in their pure form and then in different mixture ratios at equilibrium (10 min after mixing in room temperature). Raw data sets were taken at a M1 rotary rate of 300Hz. Spectral projections were measured at 600 sets per second. Excitation, emission and their diagonal projections of EEM were reconstructed by Fourier transform. The spectral resolutions were 1 nm at 500 nm for excitation and 2 nm at 650 nm for emission, respectively.
Figure 2 plots EEM projections of pure Alexa 514 at 50μg/ml, pure Alexa 568 at 10μg/ml and their mixture at equilibrium. All projections were normalized by their total peak areas and used as basis functions in the linear unmixing algorithm. For the 0 degree projections (excitation spectrum), the excitation of the mixture is dominated by the donor and the excitation peak of the mixture was close to the donor excitation peak [Fig. 2(a)]. With the 90 degree projection (emission spectrum), the emission from the acceptor was increased [Fig. 2(b)], indicating FRET effect from the immunoreactions. Figure 2(c) plots diagonal projections (excitation-emission cross-correlation), where intensity peaks of three samples occupy different positions. Diagonal projections have high noise because they are the weakest interference signals amongst the three kinds of projections. Diagonal projections are generated by cross-correlation between the first and second passes in the interferometer, thus they suffered most from wave-front distortions in optics. However, the diagonal projection of the mixture contains the FRET excitation-emission cross-correlation, which is an independent spectral component and not a linear sum of pure donor and acceptor signals. As shown in Fig. 2(c), the diagonal projection of the mixture has the same peak width as the donor or the acceptor, but is at a different position. Despite the higher noise, diagonal projections are easy to separate because of their completely different spectral peak locations.
After calibrating the spectra of the pure samples, two sets of titration experiments were performed. The first experiment was an acceptor titration experiment, in which the donor concentration was kept constant at 10 μM/ml while the acceptor concentration was gradually increased. The donor titration experiment was carried out in the opposite way: the donor concentration was increased whereas the acceptor concentration was held constant at 20 μM/ml. These titration experiments served dual purposes: the first purpose was to calibrate the G factor and the FRET efficiency, and the second, was to study FRET results when there are free donors or acceptors. Agreements from two different titration experiments provide further data demonstrating that the system and the quantitative analysis method we used are valid.
Figure 3 plots results from the acceptor titration experiment. Amplitudes of excitation, emission and excitation-emission cross-correlation projections of EEM are plotted in Fig. 3(a), 3(b) and 3(c) representatively. Since FRET signals have the same excitation property with the donor, in the excitation amplitude plot [Fig. 3(a)], there was no independent data from FRET signals, and the excitation amplitudes from donor were the sum of donor excitation and FRET. Similarly, in the emission amplitude plot [Fig. 3(b)], because FRET signals have the same emission property with the direct acceptor excitation-emission channel, the acceptor emission amplitudes contained FRET and direct acceptor signals together, and there is no independent FRET emission data. The excitation-emission cross-correlation of FRET signals was very different with either the donor or the acceptor [Fig. 2(c)], thus, linearly unmixing excitation-emission cross-correlation spectra of mixture samples gave amplitudes for all three fluorescent channels: donor emission, direct acceptor excitation, and FRET [Fig. 3(c)].
The acceptor titration experiment started with a low acceptor concentration, which generated a low donor-acceptor concentration whereas most donors were free. By the end of the acceptor titration, we observed quenching in both the donor emission [Fig. 3(b)] and donor cross-correlation [Fig. 3(c)]. Meanwhile cross-correlation signals from FRET saturated . These phenomena indicate that the acceptor concentration exceeded the donor concentration in the end, and that the mixture had free acceptor instead of free donor when the acceptor concentration was higher than 20 µg/ml. Figure 3 plots fitted dose response curves of all spectral amplitudes, , and , indicating the degrees of donor/acceptor molecule reaction. These spectral amplitudes were fitted with saturated dose response curves.
The acceptor emission amplitude contained both FRET signal, which saturated at high acceptor concentration, and the direct excitation of acceptor, which was linear with the acceptor concentration. Therefore the acceptor emission amplitude curve was fitted with the sum of a linear model and a saturated dose response model.
The donor total excitation is the sum of the donor emission and the FRET signal, thus we should have ~ + . When the acceptor concentration increased, the donor emission was quenched by FRET, and the FRET signal was enhanced. In Fig. 3(a), the donor excitation was fitted with the sum of a positive saturation model (FRET signals) and a negative saturated dose response model (donor quenching). As the result, the spectral amplitude of donor excitation was not a monotonic function to the acceptor concentration. By comparing fitting co-efficiencies in Fig. 3(a) and 3(c), we found , which matches our prediction.
Acceptor excitation and acceptor excitation-emission cross-correlation are linear to the acceptor concentration. They were fitted with linear models.
By comparing the decrease in donor cross-section and the increase in FRET cross section before adding the acceptors and after adding the excess acceptors, we have
By comparing the donor cross-correlation (or donor emission ) before adding the acceptor and after adding overdosed acceptor, we have
From the acceptor titration experiment, the FRET efficiency between two fluorophore-labeled secondary antibodies was determined to be 0.50 ± 0.03 (by ) and 0.50 ± 0.02 (by ). The FRET efficiency obtained with our Fourier system match the result measured with a standard grading based spectrometer (Jobin Yvon Fluoromax-3).
The cross-correlation amplitudes plot [Fig. 3(c)] was sufficient for measuring the G factor and the FRET efficiency. Because the double-passed interferometer measured emission and excitation spectra together with the cross-correlation, emission [Fig. 3(b)] and excitation spectra [Fig. 3(a)] provided a second way to quantify FRET efficiency, by which we obtained results matching well with those from the cross-correlation data.
In the donor titration experiment (Fig. 4 ), the concentration of donor molecule was increased until donor emission saturated the PMT. Due to the approximate 50: 1 weight reaction ratio between the donor and acceptor protein, the donor titration experiment was in the linear region of the dose-response curve. Since the immunoreactions were generally strong, we assumed that every donor molecule was combined with an acceptor and CDA was linear to CD.
According to Eq. (8) slopes of and must satisfyEq. (12) and (13) should be 1.80 ± 0.25 at g = 1.8 ± 0.2 and ρFRET = 0.50 ± 0.03, according to the acceptor titration experiment. In the donor titration result, the slope ratios were 1.64 ± 0.017, which agreed with the acceptor titration results within the margin of error.
In this paper, we have demonstrated a dual-passed high-speed Fourier Fluorescence Excitation Emission spectrometer with a 50 cm−1 spectral resolution for both excitation (from 550 to 700 nm) and emission (from 450 to 540 nm) using a high-speed optical delay line. The instrument simultaneously measures emission, excitation, and cross-correlation spectra in 1.5 ms. Through two independent titration experiments, we proved that the double-pass Fourier spectrometer can provide fast and reliable measurements of FRET signals in the present of free donor or acceptor. We also developed a quantitative analysis algorithm that incorporates linear unmixing of 3 EEM projections to separate true FRET signals from donor and acceptor direct excitation-emission signals. The speed of this system makes it ideal for monitoring macromolecular reactions in real-time via FRET, such as protein folding. The system’s speed can be further improved by using a broadband laser, such as a commercially available supercontinuum laser, instead of an incoherent lamp, so that optical delay scanners with much higher scan rates can be employed [43, 44], and the system can be linked with a high-speed laser-scanning confocal microscope to map donor, acceptor, pair concentrations and FRET efficiency simultaneously.
References and links
1. T. Förster, “Zwischenmolekulare energiewanderung und fluoreszenz,” Ann. Phys. 437(1-2), 55–75 (1948). [CrossRef]
2. J. R. Lakowicz, Principles of fluorescence spectroscopy (Kluwer Academic/Plenum Publishers, 1999).
8. K. Truong and M. Ikura, “The use of FRET imaging microscopy to detect protein-protein interactions and protein conformational changes in vivo,” Curr. Opin. Struct. Biol. 11(5), 573–578 (2001). [CrossRef]
14. M. Margittai, J. Widengren, E. Schweinberger, G. F. Schröder, S. Felekyan, E. Haustein, M. König, D. Fasshauer, H. Grubmüller, R. Jahn, and C. A. M. Seidel, “Single-molecule fluorescence resonance energy transfer reveals a dynamic equilibrium between closed and open conformations of syntaxin 1,” Proc. Natl. Acad. Sci. U.S.A. 100(26), 15516–15521 (2003). [CrossRef] [PubMed]
17. M. G. Erickson, B. A. Alseikhan, B. Z. Peterson, and D. T. Yue, “Preassociation of Calmodulin with Voltage-Gated Ca2+ Channels Revealed by FRET in Single Living Cells,” Neuron 31(6), 973–985 (2001). [CrossRef] [PubMed]
18. G. W. Gordon, G. Berry, X. H. Liang, B. Levine, and B. Herman, “Quantitative Fluorescence Resonance Energy Transfer Measurements Using Fluorescence Microscopy,” Biophys. J. 74(5), 2702–2713 (1998). [CrossRef] [PubMed]
19. R. D. Mitra, C. M. Silva, and D. C. Youvan, “Fluorescence resonance energy transfer between blue-emitting and red-shifted excitation derivatives of the green fluorescent protein,” Gene 173(11 Spec No), 13–17 (1996). [CrossRef] [PubMed]
21. Y. Chen, J. P. Mauldin, R. N. Day, and A. Periasamy, “Characterization of spectral FRET imaging microscopy for monitoring nuclear protein interactions,” J. Microsc. 228(2), 139–152 (2007). [CrossRef] [PubMed]
22. E. B. Van Munster, G. J. Kremers, M. J. Adjobo-Hermans, and T. W. Gadella Jr., “Fluorescence resonance energy transfer (FRET) measurement by gradual acceptor photobleaching,” J. Microsc. 218(3), 253–262 (2005). [CrossRef] [PubMed]
24. V. M. Mekler, A. Z. Averbakh, A. B. Sudarikov, and O. V. Kharitonova, “Fluorescence energy transfer-sensitized photobleaching of a fluorescent label as a tool to study donor-acceptor distance distributions and dynamics in protein assemblies: studies of a complex of biotinylated IgM with streptavidin and aggregates of concanavalin A,” J. Photochem. Photobiol. B 40(3), 278–287 (1997). [CrossRef]
25. G. Valentin, C. Verheggen, T. Piolot, H. Neel, M. Coppey-Moisan, and E. Bertrand, “Photoconversion of YFP into a CFP-like species during acceptor photobleaching FRET experiments,” Nat. Methods 2(11), 801 (2005). [CrossRef] [PubMed]
27. J. Wlodarczyk, A. Woehler, F. Kobe, E. Ponimaskin, A. Zeug, and E. Neher, “Analysis of FRET signals in the presence of free donors and acceptors,” Biophys. J. 94(3), 986–1000 (2008). [CrossRef]
28. S. Padilla-Parra, N. Audugé, M. Coppey-Moisan, and M. Tramier, “Quantitative FRET analysis by fast acquisition time domain FLIM at high spatial resolution in living cells,” Biophys. J. 95(6), 2976–2988 (2008). [CrossRef] [PubMed]
29. A. R. Muroski, K. S. Booksh, and M. L. Myrick, “Single-Measurement Excitation/Emission Matrix Spectrofluorometer for Determination of Hydrocarbons in Ocean Water. 1. Instrumentation and Background Correction,” Anal. Chem. 68(20), 3534–3538 (1996). [CrossRef]
30. R. A. Zângaro, L. Silveira, R. Manoharan, G. Zonios, I. Itzkan, R. R. Dasari, J. Van Dam, and M. S. Feld, “Rapid multiexcitation fluorescence spectroscopy system for in vivo tissue diagnosis,” Appl. Opt. 35(25), 5211–5219 (1996). [CrossRef] [PubMed]
31. A. F. Zuluaga, U. Utzinger, A. Durkin, H. Fuchs, A. Gillenwater, R. Jacob, B. Kemp, J. Fan, and R. Richards-Kortum, “Fluorescence Excitation Emission Matrices of Human Tissue: A System for in Vivo Measurement and Method of Data Analysis,” Appl. Spectrosc. 53(3), 302–311 (1999). [CrossRef]
32. M. G. Müller, A. Wax, I. Georgakoudi, R. R. Dasari, and M. S. Feld, “A reflectance spectrofluorimeter for real-time spectral diagnosis of disease,” Rev. Sci. Instrum. 73(11), 3933–3937 (2002). [CrossRef]
33. A. Muñoz-Losa, C. Curutchet, B. P. Krueger, L. R. Hartsell, and B. Mennucci, “Fretting about FRET: failure of the ideal dipole approximation,” Biophys. J. 96(12), 4779–4788 (2009). [CrossRef] [PubMed]
34. M. Gouzman, N. Lifshitz, S. Luryi, O. Semyonov, D. Gavrilov, and V. Kuzminskiy, “Excitation-Emission Fluorimeter Based on Linear Interference Filters,” Appl. Opt. 43(15), 3066–3072 (2004). [CrossRef] [PubMed]
35. C. D. Tran and R. J. Furlan, “Spectrofluorometer based on acousto-optic tunable filters for rapid scanning and multicomponent sample analyses,” Anal. Chem. 65(13), 1675–1681 (1993). [CrossRef] [PubMed]
36. J. G. Hirschberg, G. Vereb, C. K. Meyer, A. K. Kirsch, E. Kohen, and T. M. Jovin, “Interferometric measurement of fluorescence excitation spectra,” Appl. Opt. 37(10), 1953–1957 (1998). [CrossRef]
38. L. Peng, J. A. Gardecki, B. E. Bouma, and G. J. Tearney, “Fourier fluorescence spectrometer for excitation emission matrix measurement,” Opt. Express 16(14), 10493–10500 (2008). [CrossRef] [PubMed]
39. A. D. Hoppe, S. L. Shorte, J. A. Swanson, and R. Heintzmann, “Three-dimensional FRET reconstruction microscopy for analysis of dynamic molecular interactions in live cells,” Biophys. J. 95(1), 400–418 (2008). [CrossRef] [PubMed]
40. J. G. Hirschberg and E. Kohen, “Pentaferometer: a solid Sagnac interferometer,” Appl. Opt. 38(1), 136–138 (1999). [CrossRef]
41. P. R. Griffiths, B. L. Hirsche, and C. J. Manning, “Ultra-rapid-scanning Fourier transform infrared spectrometry,” Vib. Spectrosc. 19(1), 165–176 (1999). [CrossRef]
42. V. Saptari, Fourier-Transform Spectroscopy Instrumentation Engineering, Tutorial texts in optical engineering (SPIE Press, 3 November 2003), Vol. TT61, p. 118.
44. G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett. 22(23), 1811–1813 (1997). [CrossRef]