1. Introduction

Two-fiber or multiple-fiber probes are fairly common for Raman scattering and fluorescence measurements [1–3]. Large-core, multimode fibers are often chosen to collect the fullest possible range of signals emitted from samples under study. Moreover, many modified probes have been proposed to improve the efficiency of light collection, as is well summarized in [1] and [3]. Due to its unique advantages including compact size, low cost of probe design, implementation and signal interrogation; ability to access tiny volumes or hard-to-reach areas, immunity from electromagnetic interference; and its flexibility of operation, this type of probe is still preferred for many emerging applications, such as current hot research areas in photobiology [4, 5, 9].

Particularly, two-fiber probe architecture is often preferred to perform fluorescence or Raman spectra measurements associated with different samples. Three categories of samples are typically found: a liquid sample [3, 6, 11], a membrane layer (which may operate with a liquid immersion medium) [7, 8] or a specific solid form of sample such as a tissue [9]. Clearly, it is important to improve the sensor system performance by taking into account the properties of different samples. In this paper, we choose a specific dry membrane layer cast on a glass substrate as a representative of membrane samples for our investigation of probe system performance enhancement.

Light collection efficiency and signal quality improvement are two major concerns related to this probe. While reducing the cladding size of the fiber will greatly enhance the light collection efficiency, the thin cladding can not trap all of the illuminating light in the core region. Part of the light will leak out of the core and penetrate into the neighboring fiber if it is the same fiber type. For example, for the CF01493-11 multimode fiber from 3M® with 15 μm thickness of cladding compared with 300 μm core size, a crosstalk was observed in our experiments which generated a much stronger noise level than the intensity of the collectable fluorescent light. For fiber with a thicker cladding, a dead zone between the illuminating and collecting fibers will tremendously reduce the collectable amount of fluorescent light. This dead zone is valuable when the fiber probe is dipped into a turbid immersion medium with a high absorption even in a tiny volume. We have recently addressed the issue for the case of a liquid immersion medium [11].

When it comes to improving signal quality, it is not enough to consider only the light collection capability of the fiber probe. The quality of the beam formed by the collected light rays has a remarkable influence on the signal-to-noise ratio of the spectrometer connected with the fiber probe. The major factor contributing to this effect is light gathering power, or étendue G. It is expressed as [12, 13]:

where A is the source area and Ω is the solid angle subtended at the source by the entrance aperture of the optical system. Étendue remains a constant throughout all the internal optical components of the spectrometer. Usually, the maximum solid angle Ω will be limited by the internal aperture such as the size of the reflection mirror [2] or the diffraction grating [12, 13]. The entrance slit size is typically the limiting factor in maintaining a good spatial resolution for the source area A. An additional optical imaging system is often placed immediately before the entrance slit to improve incident beam quality. However, this arrangement only provides a trade-off between the spot size and the incident angles at the entrance slit [12, 13] and such systems are usually expensive and cumbersome. The radiant flux, defined as

where t is the transmittance and I is the source radiance (or fluorescent intensity output of the probe in our later discussion), suggests that the only way to further increase the amount of radiant flux is to use a higher radiance source. This implies that a beam with a small incident angle and high energy concentrated on a tiny spot is desired by spectrometers.

As we indicate later on, the two concerns, however, are associated with each other. Although numerous papers have studied the light collection efficiency of fiber probes and spectrometer performance enhancement, most of them focus on modification of the individual probes or spectrometer components. In fact, once a probe with a specific sample is connected to a spectrometer, a sample-probe-spectrometer system is formed. Fully using the spectrometer capability requires a smooth signal transition in both sample-probe and probe-spectrometer interfaces. Such a smooth transition will provide the spectrometer with an enhanced signal and suppressed noise level. However, to reach this goal, comprehensive consideration must be given in a cost-effective way to the factors affected by the properties of the probe, sample, spectrometer, probe-sample interface and probe-spectrometer interface. To date, not enough effort has been devoted to this issue.

The remaining sections of this paper follow the system point of view presented above to investigate a two-fiber probe connected with a spectrometer for the measurement of fluorescent light emitted from a layer of membrane. The detailed experimental and theoretical studies are reported to prove that by modifying the fiber probe based on the comprehensive consideration of the above factors, the system performance can be significantly improved. The potential applications of this approach to other sample types are also highlighted.

2. Experimental investigation of two-fiber probe

Figure 1 illustrates the principle of the proposed two-fiber probe. A CF01493-11 multimode fiber from 3M® with removed buffer is used as an illuminating fiber. It has a core / cladding / buffer size of 300 / 330 / 650 μm and a numerical aperture of 0.37. Another fiber of the same type, but with the buffer layer intact, serves as the receiving fiber. It can be moved along the z axis by a precision translation stage. The different positions of the receiving fiber are indicated as planes P₀-P′₀, P_i-P′_i and P_n-P′_n, respectively. The other end of the receiving fiber is directly connected to a USB2000 Spectrometer from Ocean Optics®. The maximum acceptance angle of the spectrometer is matched to the 0.22 numerical aperture of multimode fiber [2]. The fiber acts as the entrance aperture. The sample membrane [14] cast on a glass substrate is positioned at an angle of δ = 37° to plane P₀-P′₀ at a separation of d to reduce the unnecessary excitation light reflected from the membrane surface. This substrate is also movable along the z axis by another precision translation stage. The different positions of the substrate are shown as d₀ in Fig. 1(a) and d_n in Fig. 1(b) with d_n > d₀ and d₀ → 0 (very close to the probe tip), respectively. Light from the Argon laser with 488 nm and 514 nm wavelengths is launched into the illuminating fiber to excite the membrane. Its intensity is adjusted to a lower level to avoid the saturation effect and thus maintain the relationship I_F ∝ I_E, where I_E and I_F represent the intensity of excitation and fluorescence emission, respectively. The membrane has an emission wavelength of 642 nm (central wavelength). For each separation of d, the observed fluorescence peak intensity from the spectrometer is recorded through the OOIBase32 software by adjusting the separation L.

 

Fig. 1. Configuration of a two-fiber probe. The maximum launch and reception angles of the illuminating and receiving fibers, determined by the NA of the fiber, are indicated by the dotted lines. The thicker red lines represent the emitted light rays from higher excitation / emission intensity areas. (a) The probe-membrane sample separation d₀ is small (d₀→0), so a smaller overlap area is created. (b) The probe-membrane sample separation d_n is wider (d_n>d₀), so a larger overlap area is formed.

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Figure 2 shows the experimental results for different membrane positions at d = 0.3 mm, 0.85 mm, 2.0 mm, 3.25 mm and 3.5 mm, respectively. Now we introduce a parameter describing the maximum relative collection efficiency associated with each individual probe-membrane separation d, which is defined as ^dη _max:

 

Fig. 2. Fluorescence intensity observed from the spectrometer vs. the fiber end face separation L of the receiving fiber at different membrane positions d. The dashed red line indicates the position where the acceptance angle of the spectrometer is fully used at L = 2 mm. The red arrow to the left marks the areas where the spectrometer will receive the light rays with angles exceeding the maximum acceptance angle of the entrance slit. The unit of intensity is based on the estimated sensitivity of the USB2000 Spectrometer at 86 photons / count.

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where ^dI _F-max (L≠0)is the maximum fluorescent intensity received by the spectrometer for - max each specific separation d, and ^dI_F(L = 0) is the fluorescent intensity received by the spectrometer when the receiving fiber is at position P₀-P′₀, which is the reference point for the calculation of ^dη _max, respectively. Surprisingly, even though for the fiber at planes P_i-P′_i and P_n-P′_n, portions of the light acceptance angles are blocked by the illuminating fiber, the value of ^dη _max is not at position P₀-P′₀ (L = 0), yet this position is taken as the standard basis for this type of probe configuration throughout the academic research and commercial products. Instead, this value is found at a position where L ≠ 0. More clearly, the value of ^dη _max is determined by the combined effects of L and d. For example, at d = 0.3 mm, 2 mm and 3.25 mm, the maximum fluorescence emissions are observed at L = 3.5 mm, 2.5 mm and 1.5 mm, which correspond respectively to over 10, 7 and 4 times more than the cladding size of this fiber. Figure 3 further reveals how membrane separation d associates with the receiving fiber separation L to achieve relative maximum fluorescence emission ^dI _F-max. We notice that in Fig. 2 the curves for d = 0.3 mm and 0.85 mm have an opposite trend of peak position shift compared with other curves. This phenomenon is mainly due to the flatter intensity distribution at a lower intensity level when d is very small. For the curve of d = 0.3 mm, such an intensity distribution is more sensitive to measurement error and leads to peak position ambiguity. This interpretation also applies to the errors of data sets within d < 1 mm in Fig. 3. The reverse situation observed for the data sets within the range of 1.5 mm < d < 2.5 mm in Fig. 3 is mainly caused by the difficulty of positioning the receiving fiber flush with the illuminating fiber accurately at plane P₀-P′₀, which is the reference point for each measurement. However, it is still safe to conclude from the trend in Fig. 2 that for a wider separation d, the maximum fluorescence emission is shifted towards a shorter L. On the other hand, Fig. 4 shows that for a shorter separation d, a higher ^dη _max is expected. More detailed analysis will be given in the next several sections.

3. Theoretical investigation of the observed phenomena

To explain these experimental results, for two different membrane sample positions d₀ and d_n shown, Fig. 1(a) and (b) highlight the same sets of light rays BA, B′A′, ED, E′D′ and B″A″ with their incident angles of α, β < sin^-1 NA to the receiving fiber at planes P₀-P′₀, P_i-P′_i and P_n-P′_n, respectively. We assume that the laser excites all of the modes in the illuminating fiber so that the entire light illuminating cone is filled. Laser speckles are observed in the near and far fields. Based on Fresnel diffraction theory, the average intensity of this speckle spot is a Gaussian-shaped profile [15]:

and

 

Fig. 3. The optimum separation of receiving fiber L _opt for maximum relative collection efficiency ^dη _max vs. separation of probe-membrane d. The pink arrow highlights the L and d for optimum system performance.

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Fig. 4. Value of ^dη _max vs. position of membrane d. The pink arrow highlights the L and d for optimum system performance where the maximum absolute fluorescent intensity I _F-max takes place. This position combination yields ^dη _max =17%.

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where λ is the wavelength of the laser, a is the core radius of the illuminating fiber, ζ₀ is the mean speckle radius of the source at plane z = 0, r is the radial coordinate in the cylindrical coordinate system and I ₀ is a constant. Parameter q(z) represents the extent of the average intensity distribution at z where this intensity falls to e ^-2 times the maximum value at r = 0.

The obvious conclusion from Eqs. (4) and (5) is that for a plane perpendicular to the z axis at any z > 0, the intensity has its maximum in z axis and decreases gradually when r increases. Noticeably low intensity is observed near the edge of the light acceptance cone. For the tilted membrane, the Gaussian-shaped profile is stretched to distribute in an elliptical cross-section which needs more complex analysis; this analysis is ongoing in our lab. However, as indicated in Eq. (4), most energy from the illuminating fiber locates at z axis and vicinity. The larger change in probe-membrane separation occurs only in the position far away from z axis where a very low level of excitation / emission is expected. Therefore it is valid to assume that the theory that posits symmetrical distribution on a plane perpendicular to the z axis can still apply to this tilted area.

As indicated in Fig. 1(a), for the membrane at the position d₀ close to the fiber probe tip, the receiving fiber at plane P₀-P′₀ has an overlap area with the illuminating fiber. This corresponding area is blocked for the receiving fiber at plane P_n-P′_n. However, as shown in Eq. (4), this overlap area has a low intensity of excitation and emission. The emitted light from this area will be incident on the receiving fiber core at very large angles (close to sin^-1 0.37 = 22°) and form a group of rays corresponding to the higher-order modes. At the output end of the receiving fiber, these rays create a poor quality beam with low energy distributed on the outer edge of a large spot. This beam will become the source of stray light reaching the spectrometer or will just be blocked when the slit size is small enough. In contrast, a comparison of the areas of BB′ and EE′ seeable from the receiving fiber at planes P₀-P′₀ and P_n-P′_n, respectively, shows that the receiving fiber at plane P_n-P′_n receives fluorescent light rays with small incident angles from an area closer to the z axis which is represented by a thick solid red line BA. For the receiving fiber at plane P₀-P′₀, these fluorescent rays are blocked by its cladding. Similarly, some other rays possessing slightly larger incident angles but higher intensity levels as indicated by the line B″A″ can also be collected by the receiving fiber at P_n-P′_n. The 3.5 mm separation L leads to β_max = 7°, which is less than the maximum acceptance angles of the selected multimode fiber and the spectrometer, determined by sin^-1 0.37 = 22° and sin^-1 0.22 = 13°, respectively. All of these rays have small incident angles and form a congruence of several rays corresponding to a group of low-order modes in the electromagnetic model [16]. This group of modes lie on or near the center position of the fiber core at the output end. As a result, a beam with a smaller incident angle and spot size but a higher energy density is generated. For a spectrometer, this beam is desirable to simultaneously enhance the spatial resolution and maximize the light through the system. Such a beam cannot be obtained by any other combination of expensive optical components inserted between the receiving fiber output end and the entrance slit of the spectrometer [12]. When the receiving fiber moves to position P_i-P′_i, from an analysis similar to the above, we conclude that the received rays excite the modes towards a lower-order group to generate a beam with an improved quality and power level compared to what can be achieved with the receiving fiber positioned at P₀-P′₀. On the other hand, it must be stressed that this improvement highly depends on the separation L. For a very short L, it is obvious that rays with higher incident angles of β_max > 7° will be included in this mode group whose beam quality will not be as good as when the receiving fiber is at position P_n-P′_n. For example, in Fig. 2, all the curves on the rising side in the range of L < 2 mm include the contributions from the light rays with incident angles of β_max > 13°, which exceeds the maximum acceptance angle of the spectrometer. This will introduce unfavorable effects to the system performance as described before.

When the membrane is moved to position d_n (d_n > d₀) as shown in Fig. 1(b), the receiving fiber at plane P₀-P′₀ has a significantly larger overlap area with the illuminating fiber. At both planes P₀-P′₀ and P_n-P′_n the receiving fiber will “see” the light rays with the smaller incident angles of α and β. However, in contrast to the case of the fiber at plane P_n-P′_n, if the separation d_n is not wide enough, Fig. 1(b) indicates that rays from membrane position B and vicinity will hit the receiving fiber at plane P₀-P′₀ with larger incident angles. They will still form undesired higher-modes in the output spot. Hence the same conclusion still holds that at plane P_n-P′_n, a better spot quality with higher energy level concentrated on its center and vicinity is expected. This is proved by the rising front ends of 3 curves (d = 0.3 mm, 0.8 mm and 2 mm) in Fig. 2 even when L > 2 mm and β_max < 13°.

Given a further increase in the separation d_n, and in accordance with Eq. (4), the illuminating light intensity distribution tends to be flat in a larger area when z increases, leading to a reduced excitation / emission intensity level for both overlap areas BB′ and EE′ as well as a smaller intensity difference between them. For both positions P₀-P′₀ and P_n-P′_n, the intensity of emitted rays from B and vicinity start to drop. Moreover, because of the larger illuminated area, more emitted rays exceed the maximum acceptance angle of the receiving fiber and no longer hit the fiber core. Therefore the total output intensity begin to drop as indicated by the falling ends of all curves in Fig. 2.

On the other hand, when L increases to a very large scale, the light rays at the small angles of α and / or β will be blocked for the receiving fiber at plane P_n-P′_n but can still be seen by the receiving fiber at plane P₀-P′₀. This time, the fluorescent light collected by the receiving fiber at P_n-P′_n will decrease gradually to a level lower than that received at plane P₀-P′₀. This phenomena is indicated in Fig. 2 that the right side of each curve has a position where the intensity is the same as that at L = 0 and continues to drop when L increases further.

The same theory also applies to Fig. 4, indicating that ^dη _max is greatly enhanced when the membrane is placed at a very short separation from the probe. Up to ^dη _max = 63% at d = 0.7 mm and L = 3.5 mm is obtained for this probe configuration. However, this is not the membrane position yielding the maximum absolute fluorescent intensity I _F-max. As highlighted in Fig. 3, Fig. 4 and Fig. 5 (which is described further in section 5), the value of I _F-max is reached under conditions of L = 2 mm and d = 2.75 mm when ^dη _max = 17% is achieved.

4. Minimizing mode coupling and bend loss

In a real system, coupling of energy from one mode to another arises within the multimode receiving fiber because of structural imperfections, fiber diameter, refractive index variations and microbends. However, it is valid to assume that for the 1.5 m length of receiving fiber used in this probe, mode coupling occurs between lower-order modes only [17]. This restriction assures that only lower-order modes will operate in the fiber. On the other hand, proper selection of fibers will help to minimize mode coupling and bend loss. Recent technical progress in fiber core and cladding materials has tremendously improved fiber performance. Excellent bend performance is evidenced by the multimode fiber products series of Thorlabs® where organic material is adopted to create fiber claddings [18]. Theoretical and experimental demonstrations show that high and low NA fibers could possess curvature losses lower than the minimum set by the current standard [19]. Extruding a compressible jacket over the receiving fiber would be an alternative method of minimizing microbending losses [20].

5. Simultaneous enhancement of fluorescence signal level and spatial resolution: further discussion

From Eq. (1) and (2) and reference [8], it is clear that the optimum capability of the spectrometer can best be achieved by fully filling the acceptance angle of the slit. By mixing higher and lower modes together, we can target an optimized spot onto the entrance slit so that it matches the size of the slit and fills the entire acceptance angle as well. This will maximize fluorescence collection and simultaneously maintain the required spatial resolution. It seems to be in contradiction if a separate slit smaller than the receiving fiber core is used. However, it is still possible to maximize the signal level in this case by properly adjusting both L and d. When the fiber core is used as a slit, the optimum separation L of our probe is fixed for any membrane sample positions once the size of the core/cladding and / or buffer (if included in the probe tip) of the receiving fiber has been determined. The separation L for the full acceptance angle of 13° is 2 mm. The optimum separation d depends on the intensity distribution in the overlap area which is in turn affected by the sizes of illuminating and receiving fiber and the light launching conditions. From the analysis in section 3, we conclude that the absolute maximum fluorescence intensity among all combinations of L and d will take place somewhere where L ≠ 0. Fluorescence intensity will reach its highest level when the acceptance angle of the slit is fully filled. Experimentally, we found that our probe has the optimized membrane sample separation at d = 2.75 mm as shown in Fig. 5(a). Figure 5(b) clearly shows that with the highlighted combination of L and d, the fluorescence intensity of this probe reaches its highest value. For the range L < 2 mm indicated by the red arrow to the right in Fig. 5(b), the maximum emission level starts to drop. The reason is that emitted rays with higher intensity from z axis and vicinity are blocked by the cladding now when the receiving fiber is closer to the plane P₀-P′₀. To access this better illuminated area, a larger probe-target separation d is required. However, at this new position, intensity level in this area drops as well. The result is that for L < 2 mm, the receiving fiber will not be able to collect the fluorescent light rays as effectively as it could at L = 2 mm.

 

Fig. 5. Experimental results showing that at L = 2 mm and d =2.75 mm, maximum fluorescence signal meeting the required resolution is achieved. (a) Fluorescence intensity distribution vs. L at d = 2.75 mm. The data point highlighted by the pink arrow indicates the optimized combination of L and d which assures the optimum performance of the spectrometer. A description of the dashed red line, and left and right red arrows is found in the caption to Fig. 2. (b) The maximum relative emission level ^dI _F-max vs. d. The highlighted data point indicates the optimized L and d assuring the highest collectable fluorescence signal of this probe.

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6. Conclusions

In conclusion, a two-fiber probe connected with a spectrometer for the measurement of fluorescence emitted from a membrane on a glass substrate is investigated to optimize the performance of the sample-probe-spectrometer system. This goal is achieved by changing both the illuminating-receiving fiber end face separation and the probe-membrane separation to reorganize the distribution of higher- and lower-order modes in the receiving fiber. When a fiber core is used as the entrance slit, higher and lower modes may be mixed together through the separation adjustment to completely fill the acceptance angle of the spectrometer and simultaneously maximize the fluorescent signal level. For a separate entrance slit smaller than the fiber core, concentrating the energy on the lower-order modes lying on the fiber output spot center and vicinity using the same approach can also improve system performance.

Although the investigation deals with a specific dry membrane sample-probe-spectrometer system, it has the potential to be extended to other spectroscopic systems. For example, by considering the sample properties such as refractive index, turbidity, absorption, scattering and attenuation at the wavelength of excitation / emission, the proposed approach may be adapted to optimize the performance of the liquid sample-probe-spectrometer or the tissue-probe-spectrometer system.