Autoconfocal microscopy (ACM) is a simple implementation of a transmitted-light confocal microscopy where a nonlinear detector plays the role of a virtual self-aligned pinhole. We report here a significant improvement of ACM based on the use of graded-field (GF) imaging. The technique of GF imaging involves introducing partial beam blocks in the illumination and detection apertures of an imaging system. These partial beam blocks confer phase-gradient sensitivity to the imaging system and allow control over its background level. We present the theory of the GF contrast in the context of ACM, comparing it to GF contrast in a non-scanning widefield microscope, and discuss various performance characteristics of GF-ACM in terms of resolution, sectioning strength, and an “under-detection” light collection geometry. An advantage of ACM is that it can be readily combined with two-photon excited fluorescence (TPEF) microscopy. We present images of rat brain hippocampus using simultaneous GF-ACM and TPEF microscopy. These images are inherently co-registered.
©2007 Optical Society of America
Confocal microscopes applied to biological imaging are usually operated in a fluorescence mode. There are several reasons why confocal microscopes are rarely operated in a non-fluorescence mode. The first is that biological samples predominantly scatter light in the forward direction. To obtain good signal, therefore, a non-fluorescence confocal microsope should be designed to monitor scattered signal in the forward, or transmitted-light, direction. This is very difficult to achieve in practice since it requires that the confocal-detection pinhole be placed on the opposite side of the sample as the illumination. If the illumination focal spot is scanned in the sample, as it is in a standard laser scanning confocal microscope, then the detection pinhole must be perfectly aligned (conjugated) with this focal spot and descanned in synchrony, which poses technical problems. Solutions have been evisaged involving highly elaborate descanning schemes  or, alternatively, sample scanning rather than beam scanning, however neither of these solutions works in the interest of speed and simplicity.
We have previously reported an implementation of transmitted-light scanning confocal microscopy known as autoconfocal microscopy (ACM) [2, 3]. ACM makes use of a nonlinear detector in place of a pinhole. Nonlinear detection can be achieved, for example, by placing a second-harmonic crystal in front of an ordinary (linear) detector. Because the second-harmonic crystal emits light with a quadratic relationship to the incident fundamental light, the output signal is inversely proportional to the size of the focal spot, producing a similar effect as a physical pinhole. The advantage over a real pinhole lies in the size of the crystal - the “virtual” pinhole effect is exhibited everywhere on the surface of the crystal, and is not limited to one specific site. As a result, ACM is automatically self-aligned without any need for complicated descanning optics.
In practice, ACM is most naturally combined with two-photon excited fluorescence (TPEF) microscopy, since it can be operated with the same laser source and makes use of the same detection electronics. ACM and TPEF signals are inherently co-registered, comparable in spatial resolution, and complementary in the sense that ACM is based on scattered light whereas TPEF is based on fluorescence.
We report here a significant improvement to ACM based on the use of a technique called graded-field (GF) contrast . GF is a simple double-Schlieren technique that produces phase-gradient contrast in a transmitted-light configuration. We have previously described GF contrast in the context of a standard white-light brightfield microscope, and shown that it produces images similar in character to Nomarski differential interference contrast (DIC) [5, 6]. Here, we apply GF contrast to an ACM, which is a scanning microscope. The principles of GF remain largely identical. GF confers added phase-gradient contrast to normal ACM images, rendering them 3D in appearance, similar to DIC. We present a detailed description of combined GF-ACM imaging, and discuss various issues affecting ACM contrast. Finally, we present experimental results involving combined simultaneous GF-ACM and TPEF imaging in a rat brain slice.
We note that other techniques have been reported that produce phase relief images on a scanning laser system, such as differential phase contrast (DPC) imaging  or scanning DIC imaging . However, GF-ACM differs from DPC in many ways: only one detector is needed, and a confocal technique affords far superior axial sectioning, a key parameter for imaging in thick tissue. Compared to the scanning laser DIC method, GF is simpler to implement, is polarization independent, and does not require the use of specialized optics.
The schematic of an ACM is shown in Fig. 1 without (left) and with (right) the implementation of GF contrast. A scanning laser beam is focused by illumination optics to a point in the sample. The detection optics image that point onto the virtual pinhole. GF contrast enhancement is obtained by inserting partial beam blocks in the apertures of both the illumination and detection optics such that most of the light traversing the sample is blocked before arriving at the detector.
In the trivial case of a null sample the beam blocks simply lead to a reduction in laser power, producing a uniform image whose gray-level can be adjusted from dark to bright depending on the positions of beam blocks. However, if there is a phase gradient in the sample, the laser light at the at the focal point is deflected to the right or left (from the frame of reference of the figure), and the amount of light that reaches the detector is decreased or increased, respectively. In this manner, the beam blocks define the background level and confer phase-gradient sensitivity to an ACM, leading to a significant improvement in image quality, as will be demonstrated below.
3. Effective pinhole size
In a conventional confocal microscope, the effective pinhole size is simply the physical size of the pinhole as projected through the imaging system into the sample. The sizes of the laser focus and of the pinhole are both involved in determining the sectioning ability of a confocal microscope. The more restrictive of these sizes is dominant in determining sectioning ability.
In contrast, no physical pinhole exists in ACM. The “virtual” pinhole size is determined by the diffraction-limited laser spot size in the sample as seen by the detector . It is therefore determined by the detection numerical aperture (NAdet) and to a first approximation is roughly given by wp ≈ λ/2NAdet. As with a conventional confocal microscope, the overall sectioning ability of an ACM is governed by both the illumination spot size and the “virtual” pinhole size. Because there are two separate lens systems for illumination and detection, there may be two different numerical apertures associated with these (see discussion of this condition in section 6), and the overall sectioning ability is determined by the wider of the two NA’s (i.e. the more restrictive of the spot sizes). For a typical configuration of our specific system, our detection NA is ≈ 0.9 and the wavelength 1.03 μm, so the effective pinhole size is ≈ 0.6 μm.
We note that with a physical pinhole, there is a trade-off between signal strength and pinhole size. To achieve finer sectioning, a smaller pinhole is required, but this usually results in lower signal levels. When using a SHG virtual pinhole, no such trade-off is occasioned. A finer focus resulting from a higher detection numerical aperture results in both a smaller effective pinhole size and higher overall signal, owing to the nonlinear nature of the crystal (we overlook issues related to phase matching in the SHG crystal, which we defer to section 6).
Since the SHG crystal effectively acts as a pinhole, we can effectively regard an ACM system as a transmission confocal microscope with a physical pinhole that is perfectly descanned. We will use this approximation when developing the theory of GF-ACM in section 5.
4. Axial sectioning
An important concept in confocal microscopy is that of depth sectioning, defined as the ability to reject the effect of objects out of the focal plane on the image. For example, in a fluorescence confocal system, the signal from a thin uniform plane of fluorescence decays as 1/z 2, where z is the distance of the plane away from the focus . However, in a transmission confocal system, a uniformly absorbing plane affects the sample equally regardless of its vertical position, a result of the well-known “missing cone” problem . The detected light must pass through the absorbing plane, and so the same net light power is absorbed no matter where in the sample the plane is encountered.
The situation changes, however, when dealing with objects that scatter light rather than absorb it. To illustrate this, we consider the electric field of the light at the detector plane, which we divide into two components: ballistic (B(x⃗3)) and scattered (S(x⃗3)), where x⃗3 is a two-dimensional vector representing the spatial coordinates at the detector. Both B and S components combine at the detector. A detailed description of the resultant ACM signal was presented in reference , and we present a more heuristic description specifically to consider the effects of GF on depth sectioning.
Let us consider a thin uniform plane in the sample, either absorbing or scattering, or both. We can consider any thick sample to be a collection of thin planes if we consider only single-scattering events. Multiply-scattered light cannot be localized in depth, but is largely rejected by the virtual pinhole in any case, since it tends to be poorly focused and spatially incoherent.
Neither the total power nor the lateral distribution of of the ballistic light depends on the depth of the thin plane. On the other hand, the lateral distribution of the scattered light does vary depending on z. We therefore write S as a function of both x⃗3 and z, while B(x⃗3) is independent of z.
The detected signal is proportional to the total SHG crystal output, which is an integral of the input intensity distribution squared:
Light that falls diffusely on the crystal is generally not sufficient to generate significant SHG signal because the nonlinear integrand preferentially selects sharp, well-focused components. The out-of-plane, weakly focused component of the S term can therefore be neglected. What remains is the ballistic light as well as light scattered from near the focal plane. Both of these components are well-focused on the crystal. The integrand |B(x⃗3)+S(x⃗3,z)|4 is thus a sharply peaked function, and the integral of such a function is approximately equal to the product of the peak value with the characteristic area of the peak. The characteristic area of the peak therefore corresponds to the area of our virtual pinhole, and is effectively diffraction-limited as was already argued in section 3. If we define our coordinate system such that the focus is located at x⃗3 = 0, then Eq. (1) simplifies to
which, when distributed, becomes (omitting all constant prefactors)
The pinhole effect is now apparent, since the signal depends only upon the intensity at a single point on the detection plane.
When there is no scattering, or when ACM is operated without GF, then B is generally much larger than S. Sectioning in this case is weak because B is invariant with respect to z. On the other hand, when the partial blocks are introduced for GF imaging (as described in section 2), the ballistic light can be gradually reduced to the point where the S-containing terms in Eq. (3) become increasingly significant. Because progressive terms in Eq. (3) contain higher orders of S, they correspondingly exhibit greater sectioning strength. The degree to which the partial blocks are inserted effectively tunes the relative weights of B and S. There is typically insufficient scattered light to rely solely on S to generate a second-harmonic signal, and some degree of B is usually required to amplify S and produce adequate SHG. B essentially acts then like the local oscillator beam in an Optical Coherence Tomography system. GF imaging is normally accomplished in the regime where S ≈ B.
For illustrative purposes, let us examine the case of a uniform planar sample whose scattering is isotropic, so that the phases of the scattered light are locally randomized. In this case, the field S(0,z) decays as 1/z . Let us also examine the extreme darkfield case where the GF blocks are adjusted such that B is completely excluded, and SHG ∼ S(0,z)4 ∼ 1/z 4. At first glance it might appear that the GF-ACM sectioning strength in this scenario is better than that of a fluorescence confocal microscope, whose sectioning strength scales as 1/z 2. This is not the case. An extra power of 2 in the GF-ACM sectioning strength is occasioned simply by the quadratic nature of SHG detection (i.e. this extra power of 2 would arise just as well if we squared the detector output of a standard fluorescence confocal microscope). A proper comparison between a darkfield GF-ACM and a fluorescence confocal microscope would require us to take the square root of the GF-ACM image to recover a linear dependence of the GF-ACM signal on the imaging contrast source (namely, scattering cross-section). Once this square-root is taken, then the sectioning strength of a darkfield GF-ACM is the same as that of a fluorescence microscope.
5. GF-ACM theory
In Ref. , we analyzed the effect of adding GF contrast to a standard widefield microscope. Here we analyze the effect of adding GF contrast to an ACM. Several key differences underline this new analysis: 1) an ACM provides confocal-like pinhole detection whereas a standard widefield microscope does not; 2) the illumination source in an ACM is spatially coherent (a laser) whereas in a standard widefield microscope it is spatially incoherent (generally a lamp); 3) in an ACM the illumination is scanned whereas in a widefield microscope it is not; 4) in an ACM the detector is a single element instead of an array (e.g. a CCD camera); and 5) an ACM image must be constructed point-by-point rather than in a single shot.
Bearing these differences in mind, we proceed along a similar line of reasoning as was laid out in Ref. . That is, we define the electric field at the illumination aperture and then trace its mutual coherence function through progressive stages of the microscope. For simplicity, we consider only unit magnification and square apertures, which allows us to treat the x and y axes separately (we confine our analysis to the x axis since GF plays no role along the y axis); these conditions do not detract from the generality of our GF analysis. Our goal will be to derive the final optical power incident on the ACM detector, where we will make the approximation that nonlinear ACM detection acts like an ideal pinhole.
The convention we use is as follows. We define four planes in the optics - the aperture of the illumination optics (0), the sample (1), the aperture of the detection optics (2), and the detector (3). Each plane is related to adjacent planes by a Fourier transform. Subscripts on functions denote the function at that given plane. Roman letters represent spatial coordinate variables and constants, while Greek script letters are variables in Fourier coordinates.
The illumination is a spatially coherent narrowband source, and so can be defined as a plane wave
where the Fourier coordinate ξ 0 = kx 0/fa, and k = 2π/λ. The parameter xs is the effective scan angle, which is a tilt in the plane wave at the illumination aperture that will be translated to a position of the laser focus in the sample.
The field amplitude at plane 1 is related to that at plane 0 by the Fourier transform. From Eq. (4), we have
where α 1,2 = ka 1,2/fa, and a 1,2 are the limits of the illumination aperture along the x axis. The prefactors associated with Fourier transforms have been omitted for simplicity.
Evaluating Eq. (5) results in
where x 1s = x 1 - xs. We can further simplify this equation by introducing the variables and αd = α 2 - α 1. The parameter αc is the location of the aperture centroid, and αd is the width of the aperture in Fourier coordinates, obtaining
We cast our theory in terms of the mutual coherence function, defined by 
where the overbar denotes a time average, leading to
Employing our previous strategy, we transform our coordinate system to represent two sample points as a centroid and difference instead of explicitly addressing them individually. That is, we write:
which, when substituted into Eq. (9), lead to
The superscript in indicates that the mutual coherence function here is incident on the sample.
Denoting Jout 1(x 1c,x 1d;xs) as the mutual coherence function emanating from the sample, we use Eqs. (10) and (11) from our previous publication  to relate Jout 1(x 1c,x 1d;xs) to I 3(x 3), the intensity function at the detector plane. These equations are
where the definition for β is identical to that for α, except that it refers to the detection aperture.
The only remaining unaccounted component is the sample itself. As before , we characterize the effect of the sample as a complex transfer function that modulates the incoming field amplitudes:
In keeping with our use of the mutual coherence function and other conventions, we write
and from Eqs. (12 – 16), we obtain
where Tr(x 1c,x 1d) and Ti(x 1c,x 1d) are respectively the real and imaginary components of T(x 1c,x 1d) (respectively even and odd in x 1d), and we have introduced the transfer functions
also respectively even and odd in x 1d. Tr and Ti characterize the sample whereas Ke and Ko characterize the microscope optics. Eq. (18) will serve as the basis for the remainder of our analysis.
To begin, we digress by first considering the case where there is no pinhole in front of the detector. In this case the intensity I 3 is detected as a total power and not as a distribution. That is,
Making use of the identity
This result is identical to our previous incoherent widefield illumination result , except that the roles of the detection and illumination apertures are exactly reversed. That is, the illumination aperture in the scanning case here has the same effect as the detection aperture in our prior incoherent illumination case, and vice-versa. This similarity in results is predictable from the van Cittert-Zernike theorem, which states that the mutual coherence function of a partially coherent system propagates in the same way as the electric field of a purely coherent beam . Moreover, the reversal in the roles of the illumination and detection apertures can be understood in qualitative terms: essentially, a scanning system is equivalent to an inverted widefield system. In widefield imaging, the illumination is a large single incoherent source, whereas in scanned imaging, it is the detector that is large, single and incoherent. In widefield imaging, a CCD array detects intensities at small points in space, which is the same as scanning a single-element detector along the pixel locations in the array. In a scanning laser system, it is the illumination instead that effectively scans the small points of light imaged to the sample plane. The key difference between the two modalities is that in a scanning system, spatial selection of the pixel is done on the illumination side, whereas in a widefield system, it is done at the detector.
Our digression, which began at Eq. (20), does not properly describe an ACM since it does not take into account the virtual pinhole effect obtained by nonlinear detection. As argued above, this effect is essentially the same as that of a perfectly descanned physical pinhole. To a simple approximation, then, we can describe GF-ACM by introducing a delta function δ(x 3 + xs) in Eq. (20) to represent the descanned pinhole. Such a delta function is somewhat unrealistic in that it corresponds to a pinhole size that is infinitesimally small; however, it provides physical insight into the effects of GF on ACM imaging. The final ACM signal is then given by Eq. (17), except that x 3 is replaced with -xs in the definitions of Ke and Ko (Eqs. (19a) and (19b) respectively).
As in the case of widefield detection, Ke and Ko play the roles of imaging transfer functions for the coordinate x 1c, similar to a point spread function. The product of the sinc functions is centered around x 1c = xs, effectively confining the imaging to the point being scanned in the sample. This fixes the contributing x 1c values to those near xs.
Ke and Ko also play the roles of window functions for the coordinate x 1d. For samples that are purely absorbing and exhibit no non-uniform phase-shifting properties, Ti is zero and Ke alone is responsible for imaging the sample to the detector. On the other hand, when the sample contains no phase non-uniformities, then Ti has a contribution and Ko acts like a first-derivative finder, owing to its odd parity in x 1d.
The functions Ke and Ko are diffraction limited by both the illumination and detection aperture widths (αd and βd respectively), both of which govern lateral GF-ACM resolution. 3D plots of Ke and Ko as a function of x 1c and x 1d are illustrated in Fig. 2 for the special case where the illumination and detection apertures have the same width and offset: αc = βc and αd = βd. In this case,
Finally, in the case where both apertures are centered, αc = βc = 0, then Ko goes to zero. No phase-gradient information can be gained when the apertures are not offset. This is the case of standard ACM without GF. However, once the apertures are offset by inserting a partial block in either the illumination or detection aperture (or both), then Ko becomes nonzero and phase-gradient information is revealed.
6. Transmitted light under-detection
Because ACM is a transmission imaging technique, there are two independent sets of optics for the illumination and detection. The two optics need not be identical; indeed, in our setup, they frequently are not. We typically employ a microscope objective on the illumination side and an ordinary condenser lens on the detection side.
In the case where the detection NA is lower than the illumination NA, a situation we call “under-detection”, the light traveling through the sample at high angles cannot be detected. For a null or purely absorbing sample, this high-angle light is simply lost and becomes irrelevant to the image. However, in the case of a scattering sample, some of this light can be deflected into the detection acceptance range. In the case of a locally curved refractive object in the sample, such as a bead, the illumination beam can be focused wholesale, confining the angular spread of the light, and increasing its detectability (see Fig. 3). Thus, certain objects in the sample can actually appear brighter than a completely transmissive background, which at first glance seems unphysical, but is permissible because of transmitted light under-detection.
We have observed this type of brightening when imaging beads, which implies that we are in a condition of under-detection. This bead brightening effect remains evident even when the condenser NA is equal to or even slightly greater than that of the illumination objective NA. An explanation for this phenomenon comes from realizing that the condenser optics is not the only component governing the overall detection NA, and that we must also consider the SHG crystal itself. While our SHG crystal is thin, it may not be thin enough that we can completely neglect the issue of phase matching.
To verify that SHG phase-matching plays a role in limiting detection NA, we plotted the z-profile of the detected signal from a polystyrene bead as a function of bead defocus for symmetric NA’s in the illumination and detection optics, and with and without the use of a SHG crystal (in the case of no SHG crystal, our detector was a simple linear photodiode). These z-profiles are shown in Fig. 4. The brightness of the bead never exceeds the background in this case of linear detection, confirming that no under-detection occurs when there is no SHG crystal.
We further measured the angular acceptance profile of our crystal, type LBO with a thickness of 200 μm, the result of which is shown in Fig. 5. Indeed, we do observe a limited angular acceptance profile. Light incident at high angles is rejected, effectively limiting the NA on the detection side.
We note that treating an incident cone of light as the sum of beams at independent angles relies on the principle of superposition, which is valid only for a linear system, a condition that our nonlinear crystal does not satisfy. Our treatment of the angular acceptance limitation as a simple degradation in effective detection NA is therefore not entirely accurate. How the crystal responds to cones of light of various angular content is not completely specified by the response of the crystal to plane waves of varying obliqueness, as we have measured. Nevertheless, the overall effect of phase-matching in the SHG crytsal is still a decrease in the ability to detect higher angle components, leading to the under-detection clearly apparent in Fig. 4.
This effect has both benefits and drawbacks. The transmitted light under-detection provides a new contrast mechanism; small round objects that can focus the beam become brighter, even in ordinary ACM without any GF enhancement. This essentially provides added sensitivity to the local curvature, or second derivative, of the phase profile. However, this benefit comes at the cost of signal level and resolution, since the detection NA is being limited and outer angles of light are rejected.
7. Imaging results
As noted in the introduction, an advantage of ACM is that it can be readily combined with TPEF microscopy. To demonstrate this, we performed imaging of a tissue sample extracted from a rat brain hippocampus. The illumination source was a Amplitude Systèmes ytterbium glass laser, emitting pulsed light at 1030 nm. An average power of approximately 100 mW incident at the sample was used for the images in this section. The detector for the ACM mode was a Hamamatsu HC-125-02 photomultplier, and for the TPEF detection, an Electron Tubes P25PC-05 trialkali PMT. The pixel acquisition rate was 100 kHz. To obtain TPEF contrast, the brain slice was infused topically with sulforhodamine 101, a dye that specifically labels astrocytes (a type of glial cell) with a rhodamine-like fluorophore. The penetration depth of this labeling was about 60 μm.
First, a comparison of ACM without and with GF is shown in Fig. 6, illustrating the clear contrast enhancement and 3D relief appearance conferred by the addition of GF.
Still images from fixed depths in the rat hippocampus using combinations of GF-ACM and TPEF imaging are presented in Fig. 7. Movies representing a 3D stack of images are provided as online supplemental material to this paper.
The GF-ACM images appear very similar in character to DIC, with a notable advantage in depth penetration. The slice shown in Fig. 7 was taken approximately 40 μm below the tissue surface, and the accompanying video clip shows structure beyond 100 μm in depth.
From the images below, it is clear that GF-ACM and TPEF provide complementary information. TPEF only reveals objects in the sample that are fluorescently labeled, comprising astrocytes here and some capillaries. GF-ACM, on the other hand, is not based on fluorescence and reveals the surrounding tissue structure. In particular, different strata in the hippocampus are readily identifiable. The top left portion of Fig. 7 (top panel) corresponds to the stratum oriens and the bottom right portion to the stratum radiatum, both of which are separated by the stratum pyramidale, comprising a clearly visible band of pyramidal neurons which are not accessible to TPEF because they are not florescently labeled. The overlay of the GF-ACM and TPEF images reveals the spatial distribution of neuron versus astrocyte locations along with the overall structural context of the tissue. We emphasize that the GF-ACM and TPEF images are automatically co-registered. Spatial selection for both modalities is performed by the illumination beam, and since both modalities share the same illumination, the same point in the sample is simultaneously probed by both detectors.
The addition of our GF-ACM module onto our TPEF microscope was straightforward, another result of using the same scanning illumination for both imaging modalities. Though the characters of the images are quite different, a TPEF microscope and an ACM differ only by a detection module that consists of nothing more than simple lenses and a SHG crystal. The further implementation of GF is even more straightforward, requiring only the addition two partial beam blocks in the appropriate apertures.
We have improved upon autoconfocal microscopy with the graded-field technique, which provides phase-gradient contrast similar to DIC. A two-photon microscope can be readily adapted for ACM; in turn, the GF contrast enhancement is a technologically trivial upgrade to ACM. The effect of adding GF to a scanning ACM is formally similar to adding GF to non-scanning widefield microscope, the net effect being the conversion of phase gradients in the sample into intensity variations at the detector. The GF-ACM system is particularly useful for dual-mode imaging in conjunction with TPEF, since it provides structural context inaccessible to fluorescence. GF-ACM and TPEF microscopy are inherently co-registered and complementary, and both provide a high degree of sectioning and depth penetration. Given the simplicity of combining the modalities, it is likely that the GF-ACM and TPEF will be found together in future imaging applications.
This work was funded by the Whitaker Foundation and by the NIH (1R21CA109982).
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