Comparison of objective lenses for multiphoton microscopy in turbid samples

Avtar Singh; Jesse D. McMullen; Eli A. Doris; Warren R. Zipfel

doi:10.1364/BOE.6.003113

1. Introduction

Over the past 25 years, deep optical sectioning ability has made multiphoton microscopy the method-of-choice for fluorescence-based in vivo imaging [1,2]. Although confocal microscopy has long been able to achieve optical sectioning by using a pinhole to reject out-of-focus fluorescence, it also rejects in-focus fluorescence that is scattered on its path to the detector. Nonlinear microscopies based on multiphoton absorption and harmonic generation achieve optical sectioning in a fundamentally different way. By employing the nonlinear intensity dependence of two-photon or higher order absorption to create a 3D localized observation volume, these methods are free to collect scattered fluorescence, resulting in increased signal at larger focal depths. For these reasons, multiphoton microscopies may image to depths of ~1mm while confocal microscopy is typically limited to a few hundred μm.

While two-photon excited fluorescence is usually confined to the objective lens focus when the laser power is sufficiently low, the loss of ballistic excitation photons by tissue scattering requires that the excitation intensity be increased to maintain constant signal as the focal plane is moved deeper into tissue. At higher laser powers, substantial out-of-focus background fluorescence may be generated, particularly near the sample surface. As the focal depth increases, the signal-to-background ratio (S/B) diminishes and image quality is degraded [3]. Several groups have used high rep-rate regenerative amplifier systems to redistribute energy into fewer, but much higher energy pulses. Using these systems, imaging depths of up to 1 mm in brain tissue have been achieved [4]. Analytical models indicate that shorter pulses produce a higher S/B ratio in scattering samples and that the effect is particularly strong for durations less than 50 fs [3]. However, since photobleaching and photodamage increase dramatically with excitation dose [5, 6], higher energy approaches to increasing the imaging depth have significant drawbacks.

Excitation losses due to tissue scattering are greatly reduced at longer wavelengths. In addition, longer wavelengths allow for the use of redder fluorophores with emissions that are less scattered and absorbed by the sample. As new red dyes and fluorescent proteins become available, as well as ultrafast lasers that operate at wavelengths greater than 1000 nm, this strategy holds the most promise for deeper multiphoton imaging. Imaging depths beyond 1 mm in brain tissue have been demonstrated by moving to two-photon imaging at 1280 nm [7] and three-photon at 1700 nm [8].

While the strategies described above address ways of maintaining sufficient nonlinear excitation deep in tissue, optimizing signal collection is equally important. Two-photon microscopes typically employ whole-field non-descanned detection rather than a confocal pinhole approach since fluorescence photons originating from the focal volume are too precious to reject, regardless of whether they have been scattered. The collection efficiency of the microscope objective and the optical path to the detector is a key factor that determines the signal-to-noise ratio. Epifluorescence collection through the objective lens can be supplemented by a detector below the specimen to collect transmitted fluorescence, but this is not practical when dealing with thick specimens or live animals. While the fraction of ballistic photons detected is primarily determined by the objective numerical aperture (NA) and transmittance, scattered light collection is affected by additional parameters such as field-of-view (FOV) [9, 10]. In highly scattering specimens, light collection depends on both the spatial and angular distribution of photons incident on the objective front aperture (OFA) [11].

Over the past decade microscope manufacturers have produced new dipping objectives optimized for MPM and in vivo imaging, the first being the Olympus XLUMPlanFl 20x/0.95 water immersion objective, which became a preferred MPM objective lens due to its high NA, large field-of-view (low magnification) and improved collection of scattered fluorescence. More recently, Olympus and other vendors have manufactured lenses that are even more promising for deep-tissue multiphoton microscopy. In this study, we compare some of these newer dipping objectives to the older generation and experimentally verify theoretical predictions about multiphoton excitation and epifluorescence collection in turbid samples. Given the relatively high cost of the new optics, our comparisons are useful for assessing the value of currently available multiphoton objectives for use in scattering specimen.

2. Background theory

In a typical multiphoton microscope, scanning mirrors steer a collimated beam from a mode-locked laser to the objective back aperture (OBA) and the objective lens focuses this light down to a small diffraction-limited volume in its focal plane. If illumination enters the OBA parallel to the optic axis, the focus is located along the same axis at a distance wd (the working distance of the objective) from the objective front aperture (OFA) or front lens. When scanning, the beam enters the OBA at an angle (θ_f) and the focal spot is displaced laterally in the focal plane up to a distance r_f, which defines the objective’s field-of-view radius for the given laser-scanning design. For beam delivery angles greater than the corresponding θ_f, illumination is not transmitted through the lens. Ideally, MPM objectives have high transmittance in both the visible and near-IR (with typical excitation wavelengths from Ti:Sapphire oscillators being in the 700-1000 nm range, and newer femtosecond lasers now tuning to 1300 nm or higher).

2.1 Two-photon fluorescence losses due to scattering of excitation

As illumination photons propagate toward the objective focus, they can undergo scattering and absorption processes related to the optical properties and geometry of the sample. Since the precise distribution of refractive index inhomogeneities is generally unknown, tissue scattering is often modeled using a few parameters that summarize the average behavior of the sample [8, 9]. The scattering mean free path $ℓ_{s}$ indicates the average distance traveled before a scattering event and increases with wavelength in accordance with Mie theory; for this reason, near-IR illumination photons undergo roughly half as much scattering as visible light photons. The degree of randomization of photon direction by scattering processes is embodied by the scattering anisotropy factor g = <cos θ>. It is also conventional to define a transport mean free path l_t = l_s /(1 - g) which characterizes the average length over which a photon maintains its direction of propagation. In addition to scattering, photons may be absorbed by either intrinsic molecules or exogenous labels. Typically, intrinsic one-photon absorption cross-sections are fairly small at NIR illumination wavelengths, but non-negligible for fluorescence emission. Although two-photon absorption is usually confined to the focal volume at low illumination levels, imaging in scattering media necessitates higher powers that yield out-of-focus excitation both at the specimen surface, where ballistic intensity is high, and in the space between the surface and perifocal region, where scattered photons can interact with ballistic ones [3]. The amount of background generated depends on the staining inhomogeneity and can be greatly reduced by using specific labels that localize only to structures of interest. Several reviews include comprehensive summaries of scattering and absorption parameters in various types of tissue [12, 13]. Typical values for mouse cortex at a wavelength of 500 nm are l_s = 100 μm and g = 0.9, while skin, for example, can be considerably more turbid with values on the order of l_s = 40 μm and g = 0.75 [13].

When imaging at depths much less than one scattering length of the excitation wavelength, sufficient ballistic photons reach the objective focus that the illumination intensity can be kept relatively low. In these scenarios, out-of-focus two-photon absorption is negligible and excitation is confined to a small ~Gaussian ellipsoid volume with 1/e radii of ω_x,y and ω_z in the lateral and axial directions, respectively [2]. The rate of in-focus fluorescence emission is given by:

\begin{array}{l} F = \frac{1}{2} ϕ_{F} σ_{2 P} \int C (r) < I^{2} (r, t) > d r = \\ C_{a v g} \frac{σ_{2 P}^{*} g_{p}}{R τ} \frac{{(\frac{P λ}{h c})}^{2}}{{(\iint_{a r e a} P S F (x, y, 0, N A, λ) d x d y)}^{2}} (\underset{v o l u m e}{∭} P S F {(x, y, z, N A, λ)}^{2} d x d y d z) \end{array}

In the generalized form for the generation of two photon fluorescence (first equation above), C(r) is the position-dependent fluorophore concentration, σ_2P is the two-photon absorption cross-section, ϕ_F is the fluorescence quantum yield, and <I²(r,t)> the time-averaged instantaneous intensity squared. The integral is over the bounds of the 3D focal volume, which converges due to the quadratic dependence on intensity, and is well-approximated as a 3D Gaussian volume. <I²(r,t)> can be shown to be equal to g_p<I>²/Rτ where <I> is the time-averaged intensity, R the laser repetition rate, τ is the pulse duration and g_P is a dimensionless factor that depends on the pulse shape (typically ~0.6). The second expression above is a working formulation that is more closely related to measurable system parameters. Pλ/hc is the average power passing through the z = 0 plane converted to photons per second, which is normalized by the area of the PSF at z = 0. PSF(x,y,z)² is the volume defined by the squared point spread function (i.e. the two photon PSF) and C_ave is the average concentration of fluorophore. A 3D Gaussian volume estimate of PSF(x,y,z)² is readily calculable based on NA and refractive index using the equations given in [2].

When imaging deeper into scattering specimen, scattered illumination photons may miss the objective focus and fail to be recorded as in-focus fluorescence. In order to maintain signal, the laser intensity must be increased to compensate for lost ballistic photons. An approximation of the fraction of ballistic photons lost as a function of NA and scattering length can be derived by assuming a uniform intensity distribution across the objective front aperture and calculating the ratio (γ) of the irradiance that reaches the focus in the scattering and non-scattering cases:

γ = \frac{2 π \int_{0}^{r_{O F A}} R (θ) I_{0} e^{- \frac{L (θ)}{l_{s} (λ_{e x c})}} d R}{2 π \int_{0}^{r_{O F A}} R (θ) I_{0} d R}

Here, 2πRI₀dR represents the photon flux through an infinitesimal ring located at a radius R on the OFA (Fig. 1(a)). The exponential term in the numerator represents the fraction of these photons that remain ballistic during propagation to the focus. L is the path length for these ballistic photons within the scattering medium and l_s(λ_exc) is the mean free path between scattering events at the excitation wavelength. We can rewrite the above integral in terms of θ using L(θ) = z₀/(cos θ) and R(θ) = z₀ tan θ, where z₀ is the depth of the focus below the specimen surface and θ is the angle between the optical axis and line segment connecting the ring at radius R with the focal point. Solving the ratio of the two integrals integrated from θ = 0 to θ_NA (i.e. arcsin (NA/n)) yields:

γ = \frac{\int_{0}^{θ_{N A}} \tan θ \sec^{2} θ e^{- \frac{z_{0}}{l_{s} (λ_{e x c}) \cos θ}} d θ}{\int_{0}^{θ_{N A}} \tan θ \sec^{2} θ d θ} = \frac{2}{\tan^{2} (θ_{N A})} [(1 + \frac{z_{0}}{l_{s} (λ_{e x c}) \cos (θ_{N A})}) e^{\frac{- Z_{0}}{l_{s} (λ_{e x c}) \cos (θ_{N A})}} - (1 + \frac{z_{0}}{l_{s} (λ_{e x c})}) e^{\frac{- Z_{0}}{l_{s} (λ_{e x c})}}]

For a given z₀ and l_s(λ_exc), γ decreases with increasing NA because peripheral photons travel longer paths to the focus and thus have a higher probability of scattering. This equation quantifies the known reduction of effective NA in an absorbing-scattering sample [4], which increases significantly at higher NAs. Using the above derived parameter γ, we can modify our two-photon fluorescence relation to take the excitation scattering losses into account:

Fig. 1 (a) Diagram of illumination photons propagating from the Objective Front Aperture (OFA) to the objective focus. The flux through a ring of radius R(θ) at the OFA propagates a total distance of wd / cos θ, of which L(θ) = z₀ / cos θ is below the specimen surface, where θ ranges from 0 to θ_NA. (b) Schematic of the fluorescence beam exiting the Objective Back Aperture (OBA), showing a relatively collimated beam when imaging in a clear specimen and a more divergent beam when imaging in turbid samples.

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F = C_{a v g} \frac{σ_{2 P}^{*} g_{p}}{R τ} \frac{{(\frac{γ P λ}{h c})}^{2}}{{(\iint_{a r e a} P S F (x, y, 0, N A, λ) d x d y)}^{2}} (\underset{v o l u m e}{∭} P S F {(x, y, z, N A, λ)}^{2} d x d y d z)

2.2 Two photon fluorescence losses due to emission collection

Epifluorescence collection through the objective lens is also best understood by considering the non-scattering and scattering scenarios separately. In each case, a fraction of the light is captured by the OFA. If the sample is non-scattering, this fraction is equal to the fractional solid angle collected by the objective NA:

Ω_{f} (N A, n) = \frac{1 - \sqrt{1 - {(\frac{N A}{n})}^{2}}}{2}

The transmission of fluorescence photons back through the objective lens depends upon the transmittance of the lens, as well as the optical design (lens elements, positions of apertures and baffles, etc.). The emission beam exiting the OBA is typically picked off by a dichroic mirror and directed to collection optics that guide photons to a photodetector. If the specimen scatters fluorescence from a point emitter located at the objective focus, we have to consider the various photon trajectories to evaluate the fraction of light collected by the objective lens. Trajectories are generally grouped into three classes: ballistic, snake-like and diffuse. The ballistic fraction decays exponentially with focal depth and is negligible when the depth is much greater than l_s(λ_em). Snake-like trajectories undergo a few scattering events but still maintain some memory of their original direction. Meanwhile, diffuse photons have scattered so many times that their directions are essentially randomized. Snake-like trajectories are dominant when the focal depth is small compared to the transport mean length l_t(λ_em), while the range z₀ >> l_t(λ_em) is referred to as the diffuse limit. Although analytical equations for the collected fraction are difficult to obtain, Monte Carlo simulations have been used to estimate the spatial and angular distributions of photons at the specimen surface for various sets of scattering parameters [3, 9]. In the diffuse limit, photons at the specimen surface fall into a distribution that has a lateral FWHM of 1.53 z₀, irrespective of the scattering mean free path, and a Lambertian angular distribution [11]. In order to collect as many photons as possible, objective lenses with a large spatioangular acceptance range are preferred, i.e. lenses with a large field of view and numerical aperture. In addition, the increase in skew rays incident on the OFA is thought to result in a divergent beam exiting the OBA (Fig. 1(b)), and many groups advocate large post-objective lens collection optics so that the emission beam does not suffer vignetting [9]. One goal of this work was to measure the emission beam divergence under realistic scattering conditions to determine how to best optimize the collection pathway.

3. Methods and results

3.1 Objective lenses for multiphoton microscopy

As mentioned earlier, the Olympus XLUMPlanFl 20x/0.95W (now 20x/1.0W) ∞/0 objective is the lens-of-choice for many multiphoton imaging applications. Olympus also released the first lens specifically designed and optimized for multiphoton microscopy: the XLPlan N 25x/1.05 W MP ∞/0-0.23/FN18. This objective combines a high NA with high transmittance through the visible and IR to improve light collection. In addition, it has a correction collar that can be used to minimize spherical aberration. Olympus also offers the XLUMPlanFl 10x/0.60 W, which provides a larger field-of-view. Zeiss and other vendors provide similar high-NA objectives with improved NIR coatings; for example, the Zeiss Plan-Apochromat 20x/1.0 Vis-IR ∞/0 objective is also an excellent choice for multiphoton use. For comparison, we also examined an older high-magnification objective that has been commonly used for multiphoton imaging, the Olympus LUMPlanFl 60x/0.90 W ∞/0. Key properties of these objectives are summarized in Table 1.

Table 1. Objective lens properties of lenses used in this study.

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New optical coatings provide greater transmission in the IR than older lenses. Objective lens transmittance was measured using illumination from a white light source directed through a 150 μm diameter pinhole to create a light source much smaller than the OFA. The objective was mounted in the entrance port of an integrating sphere and output was connected to a spectrometer (Ocean Optics QE 65000) via an optical fiber to record spectra with and without the objective in place (Fig. 2(a)). As expected, the newer objectives have substantially improved transmission through the visible and IR, particularly in comparison to the older Olympus 20x lens (Fig. 2(b)). Our values matched manufacturer data within ~5-10%.

Fig. 2 (a) Experimental apparatus used to measure lens transmittance. A small pinhole was used to create a thin “beam” of white light which was incident on the OFA of an objective lens. Light transmitted through the objective was collected by an integrating sphere and relayed to a spectrometer using an optical fiber. (b) Transmittance curves were generated by taking a ratio of the spectrometer counts at each wavelength when the objective was in place and removed from the apparatus. Newer lenses show substantially better transmission than the earliest version of the Olympus 20x/0.95W we used in these measurements.

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3.2 MPE in turbid media

During in vivo multiphoton imaging, tissue scattering diminishes the number of ballistic excitation photons that reach the objective focus and creates a spread in the fluorescence distribution at the sample surface, reducing the objective’s ability to collect emitted photons. To study these phenomena, we built a two-channel measurement chamber for photon-counting of both the transmitted and epi-detected fluorescence signals (Fig. 3(a)). Mode-locked illumination at 800 nm (Spectra Physics Mai Tai) was intensity controlled using a Pockels cell and coupled through a beam expander to overfill the back aperture of each objective. Focused light was incident on a fluorophore-scatterer sample cell consisting of a layer of 100 μM fluorescein (λ_em = 520 nm) below a layer of immersion medium. The layers were separated by a thin (~40 micron) plastic sheet of fluorinated ethylene propylene which has a refractive index similar to water (FEP, Welch Fluorocarbons, n = 1.338). Scattering properties of the immersion medium were set by controlling the concentration of 1 μm polystyrene microspheres (Polysciences). Scattering parameters were calculated using the online Mie scattering calculator (http://omlc.org/calc/mie_calc.html).

Fig. 3 (a) Experimental setup for two-channel detection of epi-collected and transmitted fluorescence. Laser illumination was focused through a scattering medium into a solution of fluorescein. Emissions were collected in both epifluorescence and transmission channels. A confocal pinhole in the lower path was used to reject any back-scattered light from the bead layer. An iris in the upper channel was adjusted to controllably vignette the beam in order to measure the emission beam divergence. (b) Plot of fluorescence detected in the transmitted light channel as a function of power out of the objective lens without added scatterer. All data (with and without scatterer) fit well to F = aP², where a = ηγ². η is the fraction of emission collected by the lower channel times excitation-related parameters (Eq. (4)) and γ is the fraction of ballistic photons lost (squared for two-photon excitation). For the data in 3b without added scatterer, γ = 1. (c) Calculated two-photon excitation potential within the focal volume as a function of NA for diffraction limited and under-filled back apertures demonstrating the NA-dependence of nonlinear excitation for a diffraction limited focal volume. The intensity PSF was calculated using the method of Richards and Wolf [16] modified to take OBA under-filling into account. The 3D intensity PSF was then squared, integrated and divided by the focal plane beam area (Eq. (6)). Data is normalized to the diffraction-limited (β = 0) case for lowest NA used in the calculation (0.25). β = 3 approaches the expected paraxial limit under which the two-photon excitation is independent of NA. Inset: Predicted relative net epifluorescence collection for the diffraction-limited (black line) and paraxial (blue line) cases, calculated as the fractional solid angle x two-photon excitation potential as a function of NA. (d) Comparison of experimental values for the ballistic fraction of illumination squared (γ²) for two different values of z_s and z_s’ to the theory presented in Eq. (3). Black lines and symbols (X’s) are calculations and measurements, respectively, made with scattering conditions of z_s = 1.6 (dotted line) and z_s’ = 0.16 (g = 0.9, solid line) at 800 nm. Blue lines and symbols are for scattering conditions of z_s = 2.7 (dotted line) and z_s’ = 0.27 (solid line) at 800 nm.

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A measurement using two detection channels as described above provides a means to measure the epifluorescence collection efficiency of an objective lens under various scattering conditions. The ratio of the epi-signal to the transmitted signal is proportional to the fraction of fluorescence passing through the objective lens, since photons detected in the transmitted channel experience no scattering. A confocal pinhole was used in the transmission path to ensure that any fluorescence backscattered by the turbid layer was not collected by the transmission detector. The lower channel serves as a constant collection pathway that provides a measure of the total fluorescence generated at the focus. The fluorescence collected back through the objective lens was reflected by a 50 mm diameter dichroic mirror through a focusing lens onto a photomultiplier tube. The dichroic was 50 mm from the OBA for all objective lenses. A 50 mm adjustable iris was placed before a large area (30 mm photocathode) PMT, and was adjusted to controllably vignette the beam in order to measure the fluorescence beam divergence. The distance from the iris to the OBA was 100 mm. The output of the two PMTs were collected using a two-channel photon counter (SR400, Stanford Research Systems) and laser intensity was controlled to keep the total counts in either channel less than ~8 x 10⁵ s⁻¹ to avoid pulse pileup. A micrometer stage was used to position our sample cell so that the objective focus was always at a depth of 50 μm within the fluorescein layer. By varying the laser power and recording counts in the lower (transmission) channel, P² curves were generated using water and various concentrations of polystyrene microspheres as the immersion media.

In these experiments we characterized the amount of scattering as a dimensionless parameter z_s, defined as the ratio of the imaging depth through the scattering solution (wd – 50 μm denoted as z_o) and l_s, the mean free path. Therefore z_s is the number of scattering mean free paths between the OFA and the focal plane. z_s’ denotes the ratio in which the transport mean free path (l_s /(1 - g)) is used in place of l_s for certain calculations.

We note that there are some differences between our experimental geometry and an actual in vivo two-photon microscopy imaging scenario, in which the focus might be 0.8 mm into the sample with 1.2 mm of water between the OFA and sample surface. In our arrangement, there is no non-scattering, transparent layer of immersion medium directly after the OFA, but rather a continuous layer of non-fluorescent scattering beads. The separation of fluorophore and scattering microspheres into distinct layers was necessary so that the transmission channel could serve as a reference unaffected by the scattering properties of the sample, and in this way separate the measurement of multiphoton excitation from fluorescence detection. During a deep-tissue multiphoton imaging session in a typical sample, one also might expect some surface-level background [3], but our sample geometry precludes this effect since no fluorophores are present within the scattering layer. The setup we employ allows us to understand specifically how scattering affects in-focus fluorescence and to study excitation in turbid samples without the complication of out-of-focus surface fluorescence. Finally, others have reported that fluorescence photons whose trajectories are initially directed away from the OFA (i.e. downward) have some finite probability of being back-scattered into the acceptance range of the objective [9]. Although a minor effect, the lack of scattering particles below the focal plane in our experimental setup means that we do not observe this phenomenon.

To measure the fractional loss of ballistic nonlinear excitation photons, the number of counts detected in the transmission channel was plotted against power delivered through the objective lens and fit to the equation F_trans = ηγ²P² where η is the fraction of emission collected by the lower channel times the excitation related parameters (Eq. (4), and P is the laser power out of the objective lens. η is independent of the sample scattering properties and a constant for each objective lens. η can be obtained from the P² curve collected in the absence of scattering (γ² = 1). The transmission path P² curves also showed that the Olympus 10x/0.6 NA lens generated fluorescence more efficiently than the other lenses (Fig. 3(b)), demonstrating that the dogma that two-photon fluorescence is independent of NA (for example, ref [14]) is not quite true. Assuming a uniform fluorophore concentration, the two-photon excitation potential from the focal volume as a function of numerical aperture is proportional to (see Eq. (1)):

Focal volume 2P excitation potential \propto \frac{\underset{v o l u m e}{∭} P S F {(x, y, z, N A, λ)}^{2} d x d y d z}{{(\iint_{a r e a} P S F (x, y, 0, N A, λ) d x d y)}^{2}}

For a diffraction limited focus at high NA, the PSF is sufficiently complex and the conventional NA⁻¹ and NA⁻² formulas for radial and axial widths fail as approximations. The rate of two-photon excitation is not independent of NA and is less than one would expect based on paraxial approximations. In addition to the empirical measurements presented here, the NA dependence of nonlinear excitation is evident by applying more accurate approximations for intensity PSF dimensions at high NA [2, 15], or by numerical integration of Eq. (6). The relatively large difference we found in the amount of 2P fluorescence generated between NA’s of 0.6 and ~1.0 led us to detailed calculations in order to better understand our measured result. Using the method of Richards and Wolf [16], we calculated the two photon excitation potential (Eq. (6) as a function of numerical aperture at different ratios of aperture diameter to 1/e beam diameter (a parameter we call β). As the paraxial limit is approached (β→∞) the rate of two photon excitation becomes independent of NA as expected (Fig. 3(c)). However, for the diffraction limited case (β = 0), the non-linear excitation potential decreases with higher NA, reflecting our experimental observation that the focus of the 0.6 NA objective lens produced more fluorescence than the other four objectives used which have numerical apertures between 0.9 and 1.05. The inset graph in Fig. 3(c) illustrates the net effect of decreasing 2P excitation as NA increases, coupled the expected NA-dependent increase in fluorescence collection (i.e. the product of the fractional solid angle (Eq. (5)) and the 2P excitation potential (Eq. (6)). In the diffraction-limited case, the net difference in collected two-photon generated epifluorescence as a function of NA is not as large as one might expect based on paraxial optical approximations.

The data shown in Fig. 3(b) provides a means to extract $γ^{2}$ (defined in Eq. (3)) from P² curves measured at various levels of scattering. Since 1 μm beads mostly scatter in the forward direction (g = 0.93, similar to tissue), we expect that γ² would fall somewhere between calculations made using scattering mean free path (ℓ_s) and those made using the reduced or transport mean free path (ℓ_s /(1 - g)), which represents the upper and lower limits expected for two-photon excitation loss due to scattering of the excitation beam. This allows us to estimate the degree to which slightly forward scattered photons can still generate two-photon fluorescence. We found that γ² lies much closer to calculations made using the non-reduced mean free path (ℓ_s, dotted line in Fig. 3(d)), indicating that even small angular deviations in photon path have a significant effect on the nonlinear excitation potential. In actual samples, the reality is probably even closer to the non-reduced case, since a pool of dye gives scattered photons the highest opportunity to generate background fluorescence.

3.3 Epifluorescence collection from turbid media

In a non-scattering sample that is refractive index matched to the particular objective lens (1.33 for water, in our case), an objective lens collects a solid angle fraction (Ω_f) of the total fluorescence emitted at its focus (Eq. (5)). The collection efficiency is further influenced by the transmittance of the lens at the emission wavelength (Fig. 2), and the net collection is the product of fractional solid angle times the lens transmission. Sample turbidity further influences the amount of light collected by the lens, as well as the divergence of the light delivered to the detector due to generation of skew rays from the scattering process. Using our objective lens testing setup, we measured the epi-collection efficiency and the divergence of the fluorescence beam exiting the objective lens as a function of sample scattering for five objective lenses commonly used in multiphoton microscopy. Figure 4(a) shows the ratio of epi-counts to transmitted (non-scattered) counts; Fig. 4(b) normalizes these data for each lens by dividing by its collection efficiency in water. The reported quantity is a direct measure of the epi-collection efficiency of each objective under scattering conditions which is independent from scattering caused excitation losses. These values (uncorrected for differences in transmission) increase with NA more or less as expected based on their solid angle of collection. By fitting the decay of epi-signal as a function of the scattering parameter z_s, we obtained decay lengths that could be correlated with objective lens parameters such as the ratio of the objective back and front aperture diameters (OBA/OFA – Fig. 4(c)) and the field number (Fig. 4(d)). Although efficient epi-collection of scattered signal by objectives has been correlated with increasing field number (FN) of the objective [9], we found only a weak correlation. However, our data shows a much stronger correlation between the OBA/OFA ratio. This ratio can be expressed in terms of basic objective lens parameters (Eq. (7)) to show the relationship between resolution (NA), field of view (Magnification) and working distance, with epi-collection efficiency in turbid samples. Depending on the particular multiphoton imaging scenario and objective lenses available, these parameters can be selected based on the required resolution, imaging depth and field of view in order to achieve optimal performance.

Fig. 4 Epi-collection objective lens characteristics in scattering media. (a) Ratios of counts in the epifluorescence channel to counts in the transmission channel for each lens at z_s = 0 (water), 3 and 5, showing the decrease in epi-collection efficiencies as a function of sample scattering. (b) Normalized ratios (relative to z_s = 0 value for each lens) with data taken over a larger number of z_s values. Error bars are SEM (n = 4). (c and d) Correlation between the scattering dependent epi-collected signal decay with objective lens OBA/OFA ratios (c) and objective field number (d). Signal decay lengths for each objective lens were obtained from fits of the data in (b) to a single exponential decay model: y0 + exp(-(z_s-z_s,0)/ε) to parametrize the scattering loses through each lens. Each lens is colored coded as indicated by the key in (b). (e) Measured epi-collected fluorescence emission beam 1/e² radius 100 mm from the OBA as a function of solution scattering (z_s = 0, 3, and 5) and objective lens. The corresponding angular divergence values are noted at top of each bar. (f and g) Correlation between the measured emission divergence angle and the OBA/OFA ratio (f) and field number (g). (h) Diagram illustrating the effect of the divergence for each lens measured at z_s = 5 (worst case scenario) 200 mm from the OBA (where a detector might typically be placed).

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\frac{O B A}{O F A} = \frac{2 N A f_{o b j}}{2 w d \tan (θ_{N A})} = \frac{f_{r e f t u b e l e n s} n \sqrt{1 - {(\frac{N A}{n})}^{2}}}{M a g \times w d}

Previous measurements with an infinite-plane diffuse light source indicated that there may be a substantial angular spread in the beam exiting the OBA [9] and based on this, many advocate the use of large (50 mm or larger) collection optics positioned close to the OBA. However, this can be difficult in implement within the confines of a microscope body, and further knowledge of the beam divergence in more realistic scenarios (below the diffuse limit) is useful to design optimal MPM systems. To this end, we used a calibrated iris to vignette the beam and calculate the emission beam divergence as a function of z_s. Assuming a Gaussian beam exiting the OBA, we expect the fraction of the emission beam clipped at iris radius r to be given by 1-exp(−2r²/ σ²), to which we fit our data to obtain the 1/e² radius σ. Figure 4(e) shows these measurements for the five objective lenses we tested. In a non-scattering sample, σ measured at 100 mm from the OBA was slightly less than the radius of the OBA, in accordance with our expectation of a parallel emission beam. One exception was the Olympus 60x/0.9 objective which had a slight divergence in our setup even without scattering. The 1/e² radius σ increases with z_s and approaches a limiting value for each objective. The amount of emission beam divergence in the presence of scattering decreased with increasing OBA/OFA (Fig. 4(f)) and increasing field number (Fig. 4(g)), further indicating that large OBA/OFA and field numbers are beneficial for imaging in scattering samples. We note however, that in our experimental measurements based on a real 2P excitation volume located below a scattering layer, we never found divergence on the order of what has been previously reported (> 10 degrees) which was based on observation of white light from full-field uniformly diffusing surface [9] or from Monte Carlo simulations of scattered light passing through a 20x/0.95 Olympus objective lens model [17]. Even at z_s = 5, which would represent a highly scattering sample (equivalent, for example, to imaging ~500 μm deep into mouse brain), the change in divergence was typically less than two degrees. Based on these measurements, we believe need for extremely large optics in the post-objective lens collection path is unwarranted. As the schematic in Fig. 4(h) illustrates, even at high scattering, 25 to 30 mm aperture optics are sufficient. Most high angle skew rays entering the objective are simply lost in the barrel of the lens and never pass through the OBA.

Finally, we examined the combined effects of scattering on illumination and fluorescence collection by measuring the power needed to achieve a given number of counts in solutions with increasing z_s (Fig. 5(a)). At low scattering (z_s <3), the various objective lenses performed approximately the same, while at higher scattering (z_s >4), the Olympus 10x/0.6 lens showed a significant difference in this test, presumably due to its more efficient nonlinear excitation and larger field of view.

Fig. 5 (a) Excitation power needed to achieve 500,000 counts/second in the epifluorescence channel as a function of z_s. (b) Drop-off in integrated bead intensity (n = 3) when imaging fluorescent beads embedded in agarose with added polystyrene microspheres to vary z_s.

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To assess the various objective lenses in an imaging scenario, a low concentration of fluorescent microspheres was embedded in an agarose gel. The objective was focused 50 μm below the agarose surface and data was recorded using water and calibrated concentrations of polystyrene microspheres in the immersion media. The laser intensity was kept constant for each objective and set so that the bead intensity was equal at z_s = 0 for each lens tested. In-focus emitters at 50 μm depth were selected and their average integrated density plotted vs z_s (Fig. 5(b)). In agreement with our previous two-channel measurements, the Olympus 10x suffered the least degradation in pixel intensity while the Olympus 60x fared the worst. The other objectives (20x and 25x Olympus and Zeiss 20x) performed similarly.

4. Conclusion

Working with a new generation of high NA, water immersion dipping objective lenses now commonly used for multiphoton imaging in turbid media, we report that they are vastly superior to the older series of dipping objectives (e.g., 60x/0.9 LUMPlanFl). Within the set of newer objectives we examined, we found that the newest versions, such as the Olympus 25x/1.05 and Zeiss 20x/1.0 lenses also have improved collection characteristics compared to the earlier versions of the same types of objectives, such as the Olympus XLUMPlanFl 20x/0.95 due primarily to improved transmission. We note that the particular lens we tested was one of the first XLUMPlanFl 20x/0.95 objectives made available, and Olympus now produces an upgraded version of their XLUMPlanFl workhorse lens, which has improved transmission characteristics and higher NA (1.0). If the lower resolution of a 0.6 NA lens can be tolerated, the Olympus 10x/0.6 objective further aids in the collection of scattered fluorescence. We also note that the diffraction-limited focus of the lower NA 10x/0.6 lens excites two-photon fluorescence more efficiently than the higher NA objectives used in our measurements, which may be particularly useful when imaging is power-limited. Others have also previously suggested that low-NA lenses may be advantageous for power-efficient two-photon imaging [18]. Related to epi-collection in a scattering medium, we noticed a strong correlation between the decay length of scattered light collection signal and the OBA/OFA ratio. This suggests that, for a given NA, one should seek a low-magnification objective to maximize collection. Furthermore, it helps to avoid using a lens with a working distance much longer than necessary, since this decreases the OBA/OFA ratio. We also find that the divergence of the fluorescence beam exiting the OBA is much less than previously reported. In general, 25 or 30 mm optics are sufficient for the detection pathway, provided they are situated relatively close to the objective. This finding is also conducive to the miniaturization of two-photon microscopes, which is a key consideration for commercial applications or custom multiphoton instruments designed for experiments with unusual spatial constraints.

The objective lens is a primary determinant of the epifluorescence collection efficiency and therefore plays a critical role in image quality (e.g. S/N) and in controlling photodamage and photobleaching. Although the mechanisms are still not completely understood, photodamage during two-photon microscopy within the focal plane has been shown to be highly nonlinear, with multiple reports indicating that damage scales as P^μ where μ is typically greater than 2 [5, 6]. Thermal damage due to one-photon absorption by water has been deemed largely inconsequential at wavelengths available from a typical Ti:S laser (700 – 1000 nm) [19], but as the use of longer wavelength lasers in the 1200 to 1700 nm range becomes more common, heating is once again becoming a concern due to strong water absorption in this wavelength range. For these reasons, efficient detection schemes are critical to minimize bleaching, phototoxicity and excess sample heating by reducing the excitation intensity required to collect a sufficient fluorescence signal for imaging.

Because two-photon excitation is largely confined to a diffraction-limited volume, all fluorescence may be collected as signal and, accordingly, several groups have published designs that decouple the illumination and detection pathways to improve collection. Vučinić et al. suggest constructing a reflective shroud around the refractive lens components and predict that collection efficiency may be improved two to four-fold [20]. Combs et al. take this idea one step further by implementing a parabolic reflector and second detector to achieve three times higher signal-to-noise than a standard 0.75 NA lens [21]. While these methods are promising, they rely on nonstandard components and restrict possible sample geometries. Others have proposed augmenting standard epifluorescence collection by surrounding the objective by a collar of waveguides [22] or light guides [23] and have profoundly increased detection efficiency. In particular, when the latter is used with a 4x 0.28 NA objective, the lens-light guide combination achieves an effective collection NA of 0.55 and 0.80-0.90 in non-scattering and scattering specimens, respectively. These improvements have immediate implications for cell tracking, calcium imaging in neuronal networks, and other applications where large FOV is a priority and micron resolution is sufficient. Seeking to address these same niches for multiphoton microscopy, we have also designed a de novo multiphoton water-immersion objective with an incorporated dichroic beam splitter that achieves a collection NA of 0.98 while maintaining an excitation NA of 0.35 [24]. By placing an emphasis on photon-efficient collection for in vivo multiphoton microscopy, image quality (S/N) can be improved while specimen perturbation is minimized.

Acknowledgments

The authors would like to thank Olympus, Watt Webb and Chris Schaffer for providing some of the objectives used in testing, and Rebecca Williams for useful insights concerning multiphoton excitation and imaging. WRZ acknowledges support from NIH/NIBIB P41 RR04224 and NIH/NCI R01 CA116583

References and links

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*Objective*	*Abbrev.*	NA *θ_NA*	WD *(mm)*	FN *(mm)*	*OBA* *(mm)*	*OFA* *(mm)*	*OBA* *OFA*	*%T(800nm)* *%T(521nm)*
Olympus XLUMPlanFl 10x/0.60 W ∞/0	Oly. 10x	0.60 26.8°	3	28	21.6	3.0	7.1	75.4% 81.9%
Olympus LUMPlanFl 60x/0.90 W ∞/0 IR	Oly. 60x	0.90 42.6°	2	26.5	5.4	3.7	1.5	75.4% 83.4%
Olympus XLUMPlanFl 20x/0.95 W ∞/0	Oly. 20x	0.95 45.6°	2	22	17.1	4.0	4.2	62.5% 72.9%
Zeiss W Plan-Apochromat 20x/1.0 DIC Vis-IR ∞/0	Zeiss 20x	1.00 48.8°	2.4	20	16.5	5.5	3.0	81.3% 84.8%
Olympus XLPlan N 25x/1.05 W MP ∞/0-0.23/FN18	Oly. 25x	1.05 52.1°	2	18	15.1	5.1	2.9	86.1% 86.7%

Comparison of objective lenses for multiphoton microscopy in turbid samples

Abstract

1. Introduction

2. Background theory

2.1 Two-photon fluorescence losses due to scattering of excitation

2.2 Two photon fluorescence losses due to emission collection

3. Methods and results

3.1 Objective lenses for multiphoton microscopy

3.2 MPE in turbid media

3.3 Epifluorescence collection from turbid media

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Tables (1)

Equations (7)

Biomedical Optics Express