When the axial gain length of a stimulated Raman microscope is less than about 40% of the emission wavelength significant dipole-like ballistic backscatter will occur. Here we analyze a scanning microscope configured with orthogonal water dipping pump and probe objectives that satisfies this criterion. The pump beam focus may be a Gaussian spot or a droplet Bessel beam which minimizes the secondary Bessel beam lobes and provides multiple simultaneous pump focal spot regions. Radial and linearly polarized pump beams enable backscattered polarized signals along both transverse axes of the probe beam. Low level Mie backscatter is the primary photon noise source which should enable rapid sub-wavelength resolution 3-dimensional imaging of label-free Raman contrast for in-vivo pathology, as well as, imaging physiologic concentrations of Raman labelled metabolites and drugs.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Stimulated Raman Scattering (SRS) microscopy is useful for label-free imaging of molecular vibrational transitions . Recently significant results have been achieved for un-fixed and unstained images of neurosurgical biopsy material [2,3]. In addition, SRS has been demonstrated to be capable of imaging small molecules in cells, such as glucose using alkyne and isotope Raman labels [4,5]. This is important because many small molecules may not be tagged with large fluorescent labels. Both alkyne and isotope labels exploit the Raman signal free region between 2000 and 2600 cm−1. For example, the Alkyne stretch frequency at 2125-cm−1 and the stretch mode of C-D is at 2133 cm−1. Pre-resonance collection of variously modified dye molecules have been shown to enable multiplexed detection of many separate Raman tags .
In-vivo multiple backscatter SRS epi detection microscopy systems have been built and images have been successfully obtained [3,7,8]. In these systems SRS occurs preferentially in the forward scattered direction. Therefore, backscatter imaging requires multiply scattering events to record from the tissue surface. This process reduces the imaging depth into tissue, reduces concentration sensitivity and results in a lower resolution in order to obtain fast imaging rates.
It would be valuable to produce dipole-like ballistic backscatter to enable direct single scattering epi-detection imaging from the in-vivo focal region in a SRS microscope. A single emitter will produce, with equal probability, stimulated emission into the forward and backscattered modes of the stimulated emission beam . For a volume of emitters the forward traveling probe photon wave will increase in intensity as the SRS adds in phase to this wave. However, in the backscatter direction the emission will add out phase due to backscattered axial emission position differences and Gouy phase effects. As the emission gain length increases to above about one half the emission wavelength destructive interference reduces backscattered SRS. Unfortunately, the axial gain length in a high NA microscope is larger than the emission wavelength and produces little ballistic backscatter.
Methods have recently been proposed for stimulated fluorescence and SRS imaging that reduce of the axial diameter of the focal emission region to less than one half of the emission wavelength in order to produce significant ballistic backscatter . In this note we analyze a system with orthogonal pump and probe beams that reduces the probe gain length to less than 40% of the emission wavelength . Here the transverse diameter of the pump focal spot provides a limited excitation volume along the probe optical axis. This configuration is called Orthogonal Stimulated Raman Scattering (O-SRS) microscopy.
Direct dipole backscatter O-SRS enhances the Signal to Noise Ratio (SNR) of images by several orders of magnitude over standard co-confocal pump and probe forward SRS detection systems . This is because the dipole emission photon noise in the backscattered direction is primarily due to tissue MIE scattering rather than the incident pump or probe beam photon noise present in forward scattered confocal imaging. The greatest MIE backscattering (which is from Melanosomes) is about 5 x 10−4 of the incident beam , which should enable detection of several order of magnitude lower emitter concentrations and much more rapid scans than is in forward scattered SRS systems.
The transverse diameter of the central lobe of a Bessel Beam (BB) microscope focus is much narrower than that of a confocal focal spot of similar numerical aperture and therefore is useful to consider for the pump beam delivery [12,13]. However, the multiple secondary BB lobes may corrupt microscope transverse resolution and may be particularly problematic in an O-SRS system. Recent work has demonstrated methods to suppress focused BB secondary lobes in Stimulated Emission Depletion Microscopy and high aspect ratio hole drilling for micromachining [14,15]. These approaches use phase plates of different design for annular and axicon focus geometries. Another approach to removing the second and third BB beam lobes in the pump beam is the use of two interfering annular rings to create a droplet BB . In addition, the axial droplet structure results in the production of multiple focal spots along the pump axis. These spots may be used for multiplexed acquisition of the same or different SRS wavelengths. In this note we will investigate the use of droplet BB for the pump focus in O-SRS.
In Raman applications the polarization of the pump and probe beams should match. However, as shown in Fig. 1a only the x axis of the system is a transverse axis of the both pump and probe beams. Interestingly, as shown by Richards and Wolf, in high NA focal systems the edge rays may create longitudinal polarization along the optical axis at focus for a high numerical aperture (NA) objective . This longitudinal polarization is the basis of the formation of optical needles from radially polarized illumination beam [18–20]. In O-SRS systems radial polarization of the pump beam provides y axis polarization for the probe beam and enables polarization matching along the y axis for both pump and probe beams. Therefore, to enable recording along the x and y axes, the use of both linear and radial polarization for the pump beam are analyzed.
In this note we use vector diffraction theory to examine the issues and potential performance of confocal and droplet BB O-SRS systems using linear and radial pump polarization.
2. System overview
Figure 1a shows an expansion of the focal region of an O-SRS system using droplet BB pump excitation. The multiple confocal probe beams of different wavelengths are shown to be focused alone the droplet BB pump beam, although one wavelength may be used for multiple sampling to enhance signal to noise. The optical axis of the probe system is the z axis, while the optical axis of the pump system is the y axis. The x axis is the only axis where the direction of linear polarization the pump and probe beams may be collinear. The y axis is the direction of polarization of focal longitudinal polarization for a radially polarized pump beam that will have the same polarization as a y axis polarized probe beam.
The maximum NA’s of the pump and probe beam lines are limited by the requirement that the angular coverage of the pump and probe system should to be less than 180 degrees, while maintaining orthogonal beams. It is assumed that water immersion objectives are used, the pump NA is 1.0 and the probe NA is 0.7. The pump NA is chosen to be greater than that of the probe to minimize the axial gain length of the stimulated emission region of the probe beam.
A basic system layout for an O-SRS system is shown in Fig. 1b. The droplet BB pump beamline is labeled as beamline 1 and the confocal probe beamline is called beamline 2. The system is used as a scanning microscope. Uniquely, compared to scanning confocal microscopy, it is required to provide overlapping focal scanning of two orthogonal beams with motion in 3 dimensions during collection of a 2 dimensional image. Rapid galvanometric scanning is not possible along the optical axes of either the pump or probe beams.
Rapid optical axis scanning is enabled by advances in extended depth of field (EDOF) imaging . For O-SRS the best approach may be MEMS deformable mirrors which operate, at up to 20 KHz (Boston Micromachines Corporation (Cambridge MA)) [21,22].
To acquire a planar image stack approximately parallel to the surface the tissue, the system first performs forms a line scan along the x axis. Then to advance to an adjacent line the y axis galvanometer position and the z axis EDOF mirror positions are adjusted in both pump and probe beams to create a 0.4μm change in the line scan position in the image plane. The maximum speed of the EDOF is about 100 μsec. Therefore with a 2μsec pixel dwell time a line scan time for a 500 x 500 pixel image is 499 x 2μsec + 1 x 100 μsec = 1096 μsec. A 500 x 500 pixel image is acquired in 0.55 seconds.
In the figure Beamline 1, includes a dual annular opening mask to create the droplet BB beam. It also includes a polarization module that may create both linear polarization along the x axis and radial polarization to create longitudinal polarization at focus along the y axis. Many methods are currently available to create radial polarization from a linearly polarized laser including a liquid crystal component from ORoptix (Switzerland). Beamline 1 includes an acousto-optic modulator that turns the pump beam on and off during image scanning to enable lock-in or differential stimulated emission detection.
The pump and probe beams may be produced by fiber lasers, or solid state lasers. Pulse widths are ideally about 2 picoseconds. The backscattered stimulated emission probe light is collected in beamline 2 and is focused through multiple pinholes to create simultaneous multiple wavelength backscatter detection. A lock-in detection system may be used as in standard SRS systems, or because of the enhanced SNR a differential measurement approach may be used.
3. Pump beam polarization and focal characteristics
One method of eliminating the secondary rings in BB microscopy is to use interference between two annular rings to form a droplet beam [16,23]. It has been shown that if the secondary ring is about half of the radius of the outer annulus, the secondary and tertiary Bessel rings are mostly eliminated, although the fourth ring is still present . In O-SRS the fourth ring is of less importance than in single beam BB microscopy because of the multiphoton nature of the SRS process and the fact the confocal axial intensity of the probe beam is somewhat reduced at the position of this outer ring position. The field and intensity of the pump beam are best calculated using vector rather than scalar calculations because of the polarization sensitive nature of the stimulated emission process and the orthogonal stimulating probe beam.
The field and intensity distributions of the droplet and confocal pump for linearly polarized light along the x axis are well described in terms of the vector diffraction theory developed by Richards and Wolf . In our calculations we use their Eqs. (2).30 and 2.32 modified for a water dipping objective. As the pump beam is orthogonal to the probe beam only the x axis provides equivalent polarizations for linearly polarized beams. A radial polarized pump beam may produce longitudinal polarization along the y axis at focus. This may be used in conjunction with a y axis polarized probe beam. We use the theory described by the extension of vector theory to radial polarization by Youngworth and Brown (Eqs. (8) and others for radial illumination of a confocal full aperture and annular rings . In the calculations we assume the use of water dipping or confocal pump objectives with a 1.0 NA and a 0.70 NA probe objective. The goal of the system design is to reduce the probe gain length to enhance ballistic backscatter production. Therefore, it is more important to reduce the transverse pump focal diameter, rather than to provide higher probe resolution
In a high NA objective the edge rays of a linearly polarized laser will partially convert at focus into longitudinally polarized light along the optical axis . This conversion is much enhanced with the use of radial polarization [18,19]. In the O-SRS system described here the detection system will be polarization dependent detection to minimize orthogonal polarization noise. Figure 2a and Fig. 2b show the polarization dependent focal intensities for linear and radially polarized pump beams respectively. We assume that the droplet beam has a water dipping objective with an outer annular maximum NA of 0.98 and an annular ring width of 0.08 NA. The inner annulus has a maximum NA of 0.49, also with an annular ring width of 0.08 NA. The pump wavelength is assumed to be 790nm, while the probe is 1040 nm.
Figure 2a shows plots of the focal intensities for x axis linearly polarized input inner and outer annuli and the droplet intensity. The droplet is formed by summing the fields of the outer annulus and inner annulus. The outer annulus BB peak intensity and the peak of the droplet intensity are normalized to 1 to show the reduced transverse resolution along the x and z axes for the droplet beam. The linear polarization is along the x axis, the only axis with shared polarization between the pump and probe beams. The inner annulus (shown in green) of the droplet has significantly reduced resolution compared to the outer annulus (shown in red). The half width of the linearly polarized droplet beam is 360nm, while that of the outer annulus (shown in red) is 300nm. This loss of resolution is made up for by the reduction of the secondary lobe to about 1% of the peak on axis intensity and elimination of the third order lobe. The fourth order lobe is still about 4% of the peak.
The production of y axis longitudinal polarization is well known for high NA focal spots [24,25]. This is shown in the light blue trace in Fig. 2a. The outer annular component of the droplet produces a z axis two lobe structure, shown in the light blue trace in Fig. 2a, with longitudinal polarization along the y axis. This longitudinal beam is about 24% of the maximum x axis droplet focal trace. In intensity measurements, this lobe creates a non- symmetric focal spot [26,27]. The inner low NA lobe produces insignificant longitudinal polarization which is shown as the magenta trace along the horizontal axis. This orthogonal longitudinal polarization is not useful for O-SRS, because of its multi-lobe structure. However, because the polarization axis of the probe beam is along the x axis, minimal y polarization stimulated emission will occur, and thus the probe polarization, and a linear polarization detector filter eliminate interfering signals from the y polarized lobes.
In order to get significant longitudinally pump intensity, polarized along the y axis, and narrow enough to produce a significant backscatter probe signal, a radially polarized pump beam is used. The results of radially polarized intensity calculations are shown in Fig. 2b. The inner annulus (the green trace) is not nearly as efficient in creating y axis polarization as the outer annulus (red trace), because the NA of the inner annulus is significantly reduced. Therefore, in order to get good reduction of the secondary and tertiary lobes of the droplet beam, as shown in the blue trace, twice the field of the inner annulus must be added to the field of the outer annulus by using the appropriate neutral density filtration in the outer annulus. In Fig. 2b, the light blue trace shows the significant radially polarized component at focus from the outer annulus. As in the case of a linearly polarized pump, the appropriate polarization provided by the probe beam and detector y axis filtration, reduce the off axis polarization noise.
The reduction of resolution of the droplet beam, compared to a single annulus makes it useful to consider using both linearly and radially confocal pump beams. Focal spots for these pump beams are plotted in Fig. 3a compared to a droplet pump beam, along with a trace of the 0.70 NA probe axial intensity. The half width of the droplet central lobe is 360 nm, that of the radially polarized confocal beam is 364 nm and the linearly polarized confocal beam is 392 nm. The radially polarized confocal beam’s transverse half width is very close to that of the droplet because most of the rays of the radially polarized focus originate from the outer part of the beam, as has been previously shown [19,20]. The confocal beams have small secondary lobes that are much closer to the primary lobe than the droplet beam’s fourth lobe. The radially polarized confocal beam has a more intense secondary lobe than the linearly polarized confocal beam. It is about 6% of the peak intensity, which is a little larger than the outer droplet lobe. The probe beam axial intensity is relatively flat over the pump beam excitation area, as shown in Fig. 3a. This suggests most of the reduction in probe gain length in O-SRS systems is caused by the sub-wavelength transverse dimensions of the pump beam.
Figure 3b shows the relative axial intensity distributions for droplet pump components, the droplet beam, and linear and radial confocal polarizations. In addition, the overlapping transverse probe focal region is plotted. The droplet structure (shown in blue) enables multiplexed acquisition of probe focal spots of the same or different wavelengths. The probe y axis cross section fits neatly in the sinusoidal structure of the droplet focal beam, causing a 100 nm reduction in the half width of the emission region, compared to a confocal pump.
4. Stimulated Raman Scattering
Stimulated Raman Scattering microscopy, is a form of coherent Raman spectroscopy that uses strong optical fields at a microscope focus to drive the third-order contribution to the polarization of a medium , at the probe frequency, ωpr,, to initiate stimulated emission as described in Eq. (1),
Here r is a point at focus, (ωpr, r) is the complex molecular susceptibility of the medium for the relevant third order process, Epr(r) is the probe electric field and Epu(r) is the pump field. As the polarizability depends on the real part of the square of the pump field, the polarization is independent of the angle between the pump and probe beams .
Traditionally the induced pump local oscillator electric field ELO(r) at point r near focus generates a signal field Es(r). At a far field point R the coherently mixed field is detected by a heterodyne detection process where there are defined phases for both fields. These fields are defined by Eqs. (2) and 3 .
The two phases α and ϕ make important contributions to the far field detected signals in both forward scattering and ballistic backscatter SRS. In a high NA microscope the Gouy phase of a 2 dimensional wavefront in a high NA microscope is a total of π radians, with a phase change of α = π/2 at focus. This is the forward scattering detected local oscillator phase in forward SRS. As shown in Fig. 4, at the axial distance r from focus (r is positive in the propagation direction beyond focus), the position dependent Gouy phase shift is given by -tan−1 (r/rR) [30,31]. The quantity rR, is the one half width of the Rayleigh range of the beam waist, πn(ω0)2 /λpr, were n is the refractive index in the medium and where ω0 is the beam radius at the focus (waist). There is a phase change in the detected emission signal field phase ϕ as defined in forward propagation by the position of the emitters near focus. When small objects are present in the focal plane ϕ = 0 and the detected probe signal gain is ∝ Im[χ(3)(ωpr)]. However, if the emitters are out of focus ϕ becomes non-zero, because the emission is generated by a Gouy phase shifted local oscillator field. In this case Re[χ(3)(ωpr)] may contribute to the detected signal .
The O-SRS system does not produce a classical heterodyne detection system. However, the signal field may interfere in the far field with the variable Mie backscattered background (bsb) field Ebsb(r) created at or near focus. In addition, the back propagating signal emission points within the focal volume may add with a variable phase from pixel to pixel.
The back propagation phase in the detection plane, β(R), from emission points in the focal region is described by Eq. (4),
In the system described here the Gouy phase shift from the emission region is much slower, and hence less significant, than the back propagation phase shift. However, it is included in the calculation of the backscattered signal field. It is assumed that the total phase shift from each emission point φ(R) given Eq. 5 the sum of the backscattered reflection phase and Gouy phase. The signal in the detection plane is computed use of by eq. 5. Then the sum of the backscatter in the detection plane is computed by Eq. (6); where r0 is the edge of the summation range. A discrete summation is used because the number of emitters is relatively low.
The Intensity Is(R) at the detector plane defined by Eq. (7),
Figure 5 shows the product of pump intensity, Ipu, and probe intensity, Ipr, along the x, y and z axes for droplet and confocal pump and probe illumination. For linear polarization x axis input beam polarization is assumed. In the case of focal linear polarization along the y axis of the probe, we assume the use of radial illumination in the pump beam. The plots are all normalized to a maximum intensity of 1. As can be seen the outer lobe of the droplet beam has a 4.2% intensity along the z axis centered around 1.4 microns from the center of focus. The y axis emission regions are larger than along the other two axes and more closely mimic the longer wavelength of the probe beam, and low NA probe beam focal spot. However, the droplet beam half width is significantly smaller than the pump confocal half width along the y axis because of the droplet y axis intensity modulation structure as shown in Fig. 3. The z axis emission defines the gain length for backscatter imaging.
Table 1 lists the half widths of each axis for both confocal and droplet pump systems. The droplet beam provides a smaller focal spot at the expense of less efficient use of the pump beam energy and the presence of a fourth order lobe. The z axis (the gain axis), as shown in Table 1 has a half width of less than about 40% of the wavelength of the probe beam for both the droplet and probe pump beams. The half width of the droplet beam is ~9% less than that of the confocal beam.
In Fig. 6 we assess the normalized forward scattered SRS emission If(R) (plotted in red) relative to backscattered SRS signal Is(R) (plotted in blue) along the z gain axis for both the confocal probe (Fig. 6a&c) and droplet (Fig. 6b&d) systems. We assume one dimensional constant concentration of Raman emitters whose length along the z axis is plotted on the horizontal axis. The goal of the figure is to illustrate the peak backscatter efficacy and the saturation in the backscattered signal regardless of the size of the scatterer. In addition the figure shows the efficiency of scatter as a function of the pump optics and choice of wavelength.
The focal characteristics of the pump and probe beams clamp the minimum emitted signal. The plots in Fig. 6a&b assume a pump wavelength of 790 nm and probe wavelength of 1040, while 6c&d assume a longer wavelength pump/probe pair of 1166 nm/1750 nm. Both wavelength pairs would stimulate a Raman vibrational wavelength of 3043 cm−1 which is on the long end of the C-H vibrational band. We calculate the performance of the longer wavelength pair to illustrate how longer wavelengths perform relative to shorter wavelengths in efficiency of backscatter SRS emission because the longer wavelengths will penetrate deeper into tissues as discussed below. All 4 graphs provide similarly structured plots, but differ in quantitative details. As can be seen in Fig. 6a&b the forward backscattered signals diverge as the scattering gain length increased to about 200 nm for the short wavelength pair. The back signal is a maximum at about 400 nm, while it plateaus near 700nm. The fall in emission occurs as the backscattered emission starts to destructively interfere. The maximum signal at about 400 nm and the plateau level at 800 nm are labelled. The droplet backscatter is about 25% more efficient than the confocal pump system.
Figure 6c and 6d show that using the same NA objectives, the longer wavelength pair provides more efficient backscatter than the shorter wavelengths as can be seen in the labeled peak signals around 650 nm and the plateaus at 1250 nm. Image resolution is not directly plotted here. The enhanced backscatter efficiency is primarily because of the stretching out of the wavelength phase with longer wavelength pump light. The longer wavelengths will provide reduced image resolution but enhanced scattering efficiency for larger emitter structures.
Table 2 further illustrates the backscatter efficiency of the system as a function of Raman scattering wavelength and longer and shorter pump/probe wavelength pairs. Raman regions from 900 cm−1 - 3000 cm−1 are shown. The more the separation in pump and probe wavelengths, the more efficient the backscatter efficiency. Shorter wavelength pump/probe pairs are less efficient than longer wavelength probes for all Raman bands.
Using deep near infrared pairs of 1116nm and 1750nm for imaging a 2899cm−1 Raman transition, results in significant backscatter efficiency improvement, at the expense of reduced resolution as shown in Table 2. This particular pairing may be useful for deep tissue imaging, because tissue scattering and water absorption are reduced . In tissues the MIE backscatter cross section scales approximates as here b ~.8-2.4 depending on the study and tissue, suggesting the backscatter decreases as the incident wavelength moves above 1000nm . This is consistent with Optical Coherence Tomography studies showing enhanced backscatter imaging depth at 1700nm compared to 1300nm . Enhanced depth of penetration in tissue at a wavelength greater than 1.5 μm is also consistent with enhanced depth of 3 photon fluorescence imaging, compared to 2-photon excitation [35,36].
5. Signal to Noise Ratio
In forward scattered SRS, if the laser noise is minimized, the pump or probe photon shot noise (I1/2) of the measured heterodyne signal (pump or probe) is the main noise limit on the detection threshold . In backscattered O-SRS the noise sources are different. Backscatter photon noise and shot noise includes Rayleigh and Mie scatter, some multiple forward scattering, and refractive index layer change in tissues. In this section we will not discuss electrical noise which also lengthens the scan time and raises the detection threshold in SRS systems. We may consider backscattered noise sources as the non–SRS backscatter field Ebsb(r), which is the signal field measured in reflective confocal microscopy.
As shown in Fig. 4, in O-SRS the measured background Ebsb(R) comes from the full focal volume of the probe beam. Thus the small emission region, quantitated in Table 1, is about 2-4% of the potential probe background volume. The backscatter background may be thought of as a low resolution image superimposed on the higher resolution O-SRS image. At wavelengths > 800nm, a major source of direct backscatter is MIE backscatter from small structures such as ribosomes, collagen fibers, as well as, larger structures of more than several hundred nanometers, such as mitochondria, cellular nucleus structure and centriole sub-structure and melanosomes in skin .
In general the higher the scatterer refractive index, and the larger the scattering particle, the more the tissue backscatters. Ellipsoidal melanosomes in retina and skin of radius 0.5-3 μm and real refractive index of 1.6-1.7 will produce relatively high levels of backscatter at about 5x10−4 of the incident photons at focus . For cell nuclear structures with significant water content, and diffuse 100nm chromatin structures, the bulk refractive index may be about 1.4 or below [38,39]. This is similar to the refractive index of ribosomes. The refractive index of full multi-microns sized nuclei with heterogeneous structures at 100-200 nm size may have lower a refractive index at 1.34 creating very poor scattering contrast . Measurements for in-vivo tissue confocal reflectance microscopy of many structures result in scattering efficiency of - about 5x10−6 of the incident intensity.
The backscatter background phase ϕbsb, includes the scatter phase, the Gouy phase, and the double pass positional phase change as show in Eq. (8). Incorporating the phase of the scattering relative to the zero position of the focus defines the backscatter background field, Ebsb (R), in the detector plane is described by Eq. (9). There may be multiple backscatter sites within the focal volume, but what will be recorded is the sum of all the backscatter throughout the focal spot.
When the pump field is on, the stimulated emission in the backscatter field is present and adds coherently to Ebsb(r) as shown in Eq. (10) and Eq. (11) to create the total backscatter field Ebs (R) in the detection plane and the measured intensity Ibs(R):
The limit of SNRO-SRS of the system, defined by signal and background shot noise as defined in Eq. (12);
In order to calculate the SRS signal Is(R) from the measured Ibs(R), the backscattered background Ibsb(R) and phase relationship of Ebsb(R) and Es(R) in the heterodyne term in Eq. (11) must be determined. The backscatter tissue background Ibsb(R) source may be measured with the pump beam off. The backscattered probe beam may be acquired in a line scan or image scan with the pump off. Alternatively the probe may be measured directly when the pump beam is off, during the standard SRS pump-on/pump-off frequency detection lock-in protocol . Alternatively, a new approach called in-line balanced detection may be deployed . In this technique a birefringent crystal is used to create a time delayed orthogonally polarized probe pulse reference probe pulse than may be also used to remove laser noise contributions to the signal .
One method of heterodyne term phase determination is to measure the backscatter intensity at each pixel at two or more intensities of the pump and or probe beams. This may be accomplished multiple ways. If droplet illumination is used for the pump beam, as shown in the y axis pump plots in Fig. 3, adjacent focal regions generate the changes in pump intensity directly. In a confocal pump system a line scan may be performed two or more times at different pump or probe intensities. We assume the system operates under conditions where there is a linear relationship between pump or probe beam intensity changes that result in linear changes in the SRS emission intensity (as will be discussed below). If there is a sub-linear increase in Ibs(R) with an increase in pump or probe power, there is a negative sign in the heterodyne term, while a supra-linear scaling will result from a positive heterodyne term. The magnitude of the non-linearity may be used to estimate the heterodyne phase.
To quantitate the detectivity of the O-SRS system, we calculate the photon noise limited SNRO-SRS for multiple concentrations of Raman emitters, at different depths in the tissue and multiple pixel dwell times. We are interested in two main applications of in-vivo O-SRS. The primary application is the imaging of label-free C-Hn vibrational bonds in lipids, proteins and nucleic acids to provide the equivalent imaging to Hematoxylin and Eosin (H&E) microscope sections for pathological diagnosis [2,41]. Here the concentration of vibrational emission bonds is likely to in the 10-20mMolar range or above. The other application is low concentration imaging of Raman labelled drugs and small molecule metabolites in the emitter concentration range of 20μMolar to 2mMolar. Our goal is to image both high and low concentrations as rapidly as possible with an SNRO-SRS of at least 2-3.
Practically, the focal volume of the O-SRS system is significantly smaller than in standard forward scattering systems. In droplet pump system, the axial focal half width ratio of (emission region)/(probe axial focal length) is (0.35μm /3.10 μm) = 0.11; while the transverse cross sectional area ratio is (0.14μm2/0.45μm2) = 0.31. Therefore only about 2% of the probe photons are used for O-SRS emission. The confocal system focal volume is about 45% larger than the droplet emission volume, while the backscatter efficiency is 25% lower. With a confocal pump beam the axial half width ratio is (0.397μm/3.10μm) = 0.13, transverse cross section ratio is (0.18μm2/0.45μm2) = 0.4.
In the quantitative calculations of the SNRO-SRS we assume the use of a confocal pump system. In a 1mMolar concentration of emitters there will be about 30,000 bonds within the confocal emission volume. The linear polarization of the laser beams means that about 1/3 of randomly oriented emitters will provide signal. Furthermore, only about 20% of the emission will be in the backscattered direction. In order to have the best SNR O-SRS as many of the molecules as possible should be stimulated to emit.
As in multi-photon fluorescent microscopy, the maximum scattering occurs when the system is driven close to saturation . It has recently been shown that saturation in SRS occurs at a focal intensity as low as ~1-2 TW/cm2 [43,44]. However, the focal saturation intensity for a particular bond may vary as it is a function of the Raman cross section, as well as, the vibrational excited state lifetime. Bond vibrational lifetimes may range from less than a picosecond to over hundreds of picoseconds depending on intramolecular and intramolecular molecular energy transfer in addition to the solvent coupling [45–48].
The non-linear pulsed optical damage threshold in corneal stroma for photon wavelengths above 1 μm for 100 fs pulses has been shown to be about 20 TW∕cm2 for laser wavelengths above 1000nm . This is well above focal intensity level for SRS saturation. It should be noted that the longer pulses deliver more heat to the tissue which suggest use of pixel dwell times that are as short as possible.
In order to calculate Is(R) the Raman emission should be in the linear range. Thus the ideal focal intensity should be about 0.1-0.4 TW/cm2. Here we assume about 10-20% of the correctly oriented bonds participate in the emission process [45,46].
We assume that in a confocal pump system, the lasers have 2ps pulse duration and that operate at 40MHz. The probe energy is about 150mW (3.75 nJ/pulse) and the pump energy is chosen to be 100mW (2.5 nJ/pulse). The pump transverse area is about 3.4 times that of the pump. Thus the maximum intensities available, near the sample surface, are ~1 TW/cm2 for the pump and ~0.44 TW/cm2 for the probe. In our analysis we do not increase the laser beam intensities as we scan deeper in the tissue in order to continually maintain the efficiency of the SRS process.
Deeper into the tissue there is significant falloff in SNRO-SRS that depends on multiple factors. The ballistic SRS backscatter signal Is(R) and background signal Ibsb(R) that are collected in the epi direction in the probe beam are described by Eq. (13) and Eq. (14) respectively;50]. The Stimulated Raman Backscatter fraction (SRBF) is 0.20 of the forward scattered signal.
For the plots in Fig. 7 we assume that the Ibsb(r) is 1 x 10−5 of the probe beam, and that it comes from the entire probe focal volume. This is about ten times the in- vivo backscatter value from inside the cell nucleus . We have chosen a high background Mie scattering efficiency signal level since the pixel scattering will vary between within cells and between tissues. The lengths z and y are equal to the perpendicular distance from surface divided by sin (45°). In Fig. 7 are plots of the SNRO-SRS as a function of depth in the tissue for pixel dwell times from 0.2 - 200μsec and Raman emitter concentrations of 20mMol −20μMol. Pixel dwell times and Raman emitter concentrations are shown in the legend of the figure.
In the scan protocol where a backscatter line scan is acquired prior to an emission line scan, the dwell time per pixel may be adjusted to the measured background to maximize the SNRO-SRS in pixels where the background backscatter is high. The estimates in the figure do not assume a variable pixel background or dwell time.
It can be seen that for label-free imaging of emitters with concentrations of 20mMol the SNRO-SRS is quite high with a 0.2 μsec pixel dwell time. If we assume that a SNRO-SRS of 2 is the minimal acceptable detectivity, then the acceptable image depth is close to 350μm. If the appropriate laser powers are available, longer wavelength pump and probe beams would increase this depth. At lower concentrations, useful for Raman labeled drug and metabolite imaging (0.2 mMolar to 0.20 μMolar), the pixel dwell time has to be increased to enhance signal detectivity. At deeper image depths the intensity of the beams may also be increased to compensate for the loss of intensity at depth.
In this note we analyze the use of orthogonal pump and probe beams for in-vivo backscatter ballistic SRS imaging applications. At normal tissue backscatter levels, the system may provide rapid label-free SRS imaging down to about 350μm below the tissue surface. The use of adaptive optics should provide clearer images at depth, but was not analyzed here [51,52].
Two pump beam geometries have been analyzed; a 1.0 NA water dipping objective configured with a confocal Gaussian or droplet BB pump beams; both of which are orthogonal to a 0.7 NA probe beam. For both geometries linear and radial polarization pump beams were investigated. The droplet geometry provides less efficient use of pump radiation, but provides a 25% enhancement in efficiency of backscatter signal generation; 25% enhancement of y axis resolution; and the ability to collect 3 adjacent focal spots simultaneously. These focal spots may be used for multiplexed SRS imaging or imaging of different intensities to de-convolve the SRS signal from the backscatter noise.
It is worth comparing the use of forward scattering SRS and O-SRS systems in-vivo and in-vitro. In-vivo forward scattering SRS systems achieve lower resolution with high speed at a reduced depth of penetration in the tissue. In addition they are likely to be simpler to manufacture than O-SRS systems. Another advantage of forward scattered imaging is the use of shorter wavelength pump beam signal loss detection. In general this allows use of highly sensitive silicon photon detectors. At this stage O-SRS has only be analyzed for the longer wavelength probe beam, where detector technology is not as good. In a collinear forward scattering geometry it is easier to use the highest resolution optics and provide better use of the pump and probe photons.
In-vivo the use of O-SRS ballistic backscatter imaging should provide certain advantages over multi-backscatter forward emission imaging. Firstly, the reduced z axis gain length should provide much better optical sectioning capability in tissues. This is also true for cell culture imaging, as well as, in-vitro applications. In tissue imaging applications O-SRS systems should provide transverse resolution as good as stained sections with the addition of enhanced optical sectioning capability. The use of ballistic backscatter photons should enable deeper tissue imaging. This should be further enhanced with the use of photons of wavelengths longer than 1300 nm. A major advantage of O-SRS, compared to forward scattering systems, is the excellent SNR achieved because of the lack of interference with the forward scattered probe beam. The low background level should enable imaging of very low concentrations of emitters enabling detection metabolites and drugs in tissues. This would be a new in-vivo capability of SRS imaging.
An interesting in-vitro application of O-SRS would be in conjunction with techniques that clarify and expand tissue samples [53,54]. It has recently been shown that certain clarification techniques can successfully be applied to SRS imaging for metabolic imaging and provide a 10 fold increase in forward scatter imaging depth in clarified tissues [55,56]. O-SRS tissue backscatter photon noise in these applications would be significantly reduced, pushing the molecular detectivity close to the single molecule level, while extended tissue sections to greater depths.
In this article it is shown that the ballistic backscatter efficiency increases as the probe wavelength moves further into the near infrared, with some loss of resolution. As with 3-photon microscopy it is desirable to develop high power, high repetition rate sources from 1200nm-1750nm that can drive targeted Raman transitions near saturation. Presently, an inexpensive fiber optic laser source with appropriate bandwidth, pulse width, wavelength, and power is not commercially available. Soliton laser sources have a lot of promise for 3 photon fluorescence and with bandwidth restriction may be appropriate for O-SRS [57,58].
O-SRS systems have the potential to accelerate in-vivo 3 dimensional SRS imaging of Raman labeled and unlabeled tissues in research and medicine.
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