Designing a large field-of-view two-photon microscope using optical invariant analysis.

3 Experimental Results 3.1 Experimental Validation with Fluorescein and Fluorescent Microspheres We tested the performance of our system experimentally by placing fluorescein at the sample plane and measuring the fluorescence signal over the FOV with the Olympus XLFLUOR4X underfilled to either NA 0.22 (i.e., input beam diameter to galvo of 10 mm) or NA 0.11 (i.e., input beam diameter to galvo of 5 mm) [ Figs. 8(b) and 8(c) ]. For reference, we also measured the fluorescence signal using a 20 × objective with the same high-throughput relay system [ Fig. 8(a) ]. The fluorescence signal remained above 0.4 times the maximum over FOV diameters of 1.4, 7, and 9 mm with the Olympus XLUMPLFLN ( 20 × , NA 1.0), Olympus XLFLUOR4X underfilled to NA 0.22, and XLFLUOR4X underfilled to NA 0.11, respectively. Fig. 8 Experimental FOV and resolution measurements. (a) Normalized fluorescence signal measured across the FOV using the high-throughput relay shown in Fig. 6 – 7 and the Olympus XLUMPLFLN (20X, NA 1.0). (b) Same as (a), but for Olympus XLFLUOR4X with rear aperture underfilled to an effective NA of 0.22 (10 mm input beam diameter to microscope). (c) Same as (a)-(b), but for Olympus XLFLUOR4X with rear aperture underfilled to an effective NA of 0.11 (5 mm input beam diameter to microscope). (d) Lateral and axial cross section of PSF measured experimentally by imaging 0.5 - μ m diameter fluorescent beads embedded in agarose. Results are for high-throughput relay and NA 1.0 (Olympus XLUMPLFLN). Beads were imaged both on and off axis as specified underneath cross sections. (e) Same as (d), but with the Olympus XLFLUOR4X and effective NA of 0.22. (f) Same as (d)-(e), but with rear aperture underfilled to an effective NA of 0.11. (g) Estimation of lateral resolution measured as FWHM of PSF shown in (d)-(f). (h) Same as (g), but for axial resolution. (i) Profile of lateral and axial PSF for beads imaged on axis shown in (d)–(f). (j) Same as (i), but for beads imaged off axis in the x-direction. (k) Same as (i), but for beads imaged off axis in the y-direction. The resolution was measured over the FOV by imaging 0.5 - μ m fluorescent microspheres [18859-1, Polysciences, Warrington; Figs. 8(d) – 8(h) ] embedded in a thick agarose gel. The FWHM, lateral profiles, and axial profiles of the PSF are also shown in [ Figs. 8(d) – 8(k) ]. As expected, underfilling the objective enables larger field imaging but worsens the resolution, especially axially in comparison with the Olympus XLUMPLFLN. However, our optimal design (XLFLUOR4X underfilled to NA 0.22) can achieve a SBP of 35MP, which is 3.2 times more than what can be achieved with a conventional TPM system ( Table 1 ). The lateral and axial resolutions of the LF-TPM system over the 7-mm-diameter FOV are < 1.7 and < 28 μ m , respectively. This demonstrates the performance and range of imaging fields achievable with these relay lenses, galvanometer, and objective. Table 1 Imaging capabilities of isolated objectives, conventional TPM, and LF-TPM. Lateral resolution for conventional TPM with pixel averaging is effective resolution, not optical resolution. For LF-TPM, the theoretical and experimental lateral resolution are included.

Objective or system NA

Lateral resolution ( μ m ) FOV diameter ( Ø mm ) Rectangular FOV ( mm × mm ) Pixels for rectangular FOV FOV area ( mm 2 ) SBP (MP) Olympus XLFLUOR4X 0.28 1.08 6.63 4.69 × 4.69 8709 × 8709 21.98 75.85 Olympus XLUMPLFLN 20X 1 0.31 1.10 0.78 × 0.78 5081 × 5081 0.61 25.82 Conventional TPM 1 0.31 0.71 0.50 × 0.50 3280 × 3280 0.25 10.76 Conventional TPM (pixel averaging) 1 1.96 0.71 0.50 × 0.50 512 × 512 0.25 0.26 LF-TPM system 0.22 1.37/1.68 7.00 4.95 × 4.95 5893 × 5893 24.50 34.72 For completeness, we also conducted fluorescein and microsphere imaging with the Olympus MVPLAPO 2XC but measured worse resolution off axis than what was achieved with the Olympus XLFLUOR4X (Appendix D ). In Vivo Applications of LF-TPM: Imaging the Cerebral Vasculature and Microglia Cell Bodies After experimental validation of the system, we performed in vivo imaging of the mouse cerebral vasculature and microglia ( Fig. 9 ). To image the cerebral micro-architecture, we removed an ∼ 9 - mm -diameter portion of the mouse skull. 29 , 30 The full surgical procedure is described in Appendix E . We then imaged the cerebral vasculature in male C57BL6 mice after tail vein injection of fluorescein-dextran and the microglia in mice with GFP knocked-in to the Cx3Cr1 locus ( Cx 3 Cr 1 GFP + / − ). Fig. 9 Cerebral vasculature and microglia imaged over the mouse cortex with LF-TPM. (a) Maximum projection image of cerebral vessels imaged with LF-TPM after tail vein injection of fluorescein-dextran. Dimensions of the box are 8 × 8 mm 2 . (b) 1 × 1 mm 2 FOV imaged 3-mm off axis at orange box shown in (a). (c) 1 × 1 mm 2 FOV imaged 3-mm off axis at blue box in (a). (d) 500 × 500 μ m 2 FOV highlighted by dashed blue box in (c). (e) 1 × 1 mm 2 FOV imaged 3-mm off axis at green box shown in (a). (f) 1 × 1 mm 2 FOV imaged 3-mm off axis at red box shown in (a). (g) 500 × 500 μ m 2 FOV highlighted by dashed red box in (f). (h)–(n) Same as (a)–(g), but for microglia imaged in Cx 3 Cr 1 GFP + / − mice . To maximize the information transmitted by our system, we imaged the mouse cortex under optimal system conditions (i.e., XLFLUOR4X underfilled to NA 0.22, SBP approximately 35MP). Due to the large relatively flat field and axial sectioning of the microscope, the curvature of the mouse brain poses a challenge: the image plane is not perpendicular to the surface of the mouse brain over the FOV. Thus, fluorescence signal measured in a single frame is only over an elliptic region of the brain that depends on how the objective front focal plane intersects with the mouse brain. To image over the entire FOV, the brain was scanned axially by moving the mouse on a motorized stage (MLJ050, Thorlabs). Each image was scanned at a 50-Hz line rate. Most of the images were scanned with 1000 lines for a slice acquisition time of ∼ 20 s . The translation time between axial positions was ∼ 1 s and therefore did not contribute significantly to total acquisition time. To demonstrate the capabilities of the system, we scanned both low-resolution scans of the full FOV [ Figs. 9(a) and 9(h) ; 8 × 8 mm 2 , 1000 × 1000 pixels ] and high-resolution scans of smaller fields 3 mm off axis [ Figs. 9(b) – 9(e) and 9(i) – 9(l) ; 1 × 1 mm 2 , 1000 × 1000 pixels ]. Also included are images with a FOV similar to conventional TPM [ Figs. 9(f) and 9(g) and 9(m) – 9(n) ; 500 × 500 μ m 2 , 500 × 500 pixels ]. For all imaging, the mouse remained in the same lateral ( x , y ) position relative to the objective without tracking motion. We also calculated the FWHM of capillary vessel diameters to determine resolution capabilities of our system for in vivo applications. The system was able to image vessel diameters as small as 3 μ m over the entire FOV, as well as ∼ 22,500 microglia with a cell body diameter of ∼ 5 μ m over the cortex of Cx 3 Cr 1 GFP + / − mice .

Experimental Validation with Fluorescein and Fluorescent Microspheres

We tested the performance of our system experimentally by placing fluorescein at the sample plane and measuring the fluorescence signal over the FOV with the Olympus XLFLUOR4X underfilled to either NA 0.22 (i.e., input beam diameter to galvo of 10 mm) or NA 0.11 (i.e., input beam diameter to galvo of 5 mm) [ Figs. 8(b) and 8(c) ]. For reference, we also measured the fluorescence signal using a 20 × objective with the same high-throughput relay system [ Fig. 8(a) ]. The fluorescence signal remained above 0.4 times the maximum over FOV diameters of 1.4, 7, and 9 mm with the Olympus XLUMPLFLN ( 20 × , NA 1.0), Olympus XLFLUOR4X underfilled to NA 0.22, and XLFLUOR4X underfilled to NA 0.11, respectively. Fig. 8 Experimental FOV and resolution measurements. (a) Normalized fluorescence signal measured across the FOV using the high-throughput relay shown in Fig. 6 – 7 and the Olympus XLUMPLFLN (20X, NA 1.0). (b) Same as (a), but for Olympus XLFLUOR4X with rear aperture underfilled to an effective NA of 0.22 (10 mm input beam diameter to microscope). (c) Same as (a)-(b), but for Olympus XLFLUOR4X with rear aperture underfilled to an effective NA of 0.11 (5 mm input beam diameter to microscope). (d) Lateral and axial cross section of PSF measured experimentally by imaging 0.5 - μ m diameter fluorescent beads embedded in agarose. Results are for high-throughput relay and NA 1.0 (Olympus XLUMPLFLN). Beads were imaged both on and off axis as specified underneath cross sections. (e) Same as (d), but with the Olympus XLFLUOR4X and effective NA of 0.22. (f) Same as (d)-(e), but with rear aperture underfilled to an effective NA of 0.11. (g) Estimation of lateral resolution measured as FWHM of PSF shown in (d)-(f). (h) Same as (g), but for axial resolution. (i) Profile of lateral and axial PSF for beads imaged on axis shown in (d)–(f). (j) Same as (i), but for beads imaged off axis in the x-direction. (k) Same as (i), but for beads imaged off axis in the y-direction. The resolution was measured over the FOV by imaging 0.5 - μ m fluorescent microspheres [18859-1, Polysciences, Warrington; Figs. 8(d) – 8(h) ] embedded in a thick agarose gel. The FWHM, lateral profiles, and axial profiles of the PSF are also shown in [ Figs. 8(d) – 8(k) ]. As expected, underfilling the objective enables larger field imaging but worsens the resolution, especially axially in comparison with the Olympus XLUMPLFLN. However, our optimal design (XLFLUOR4X underfilled to NA 0.22) can achieve a SBP of 35MP, which is 3.2 times more than what can be achieved with a conventional TPM system ( Table 1 ). The lateral and axial resolutions of the LF-TPM system over the 7-mm-diameter FOV are < 1.7 and < 28 μ m , respectively. This demonstrates the performance and range of imaging fields achievable with these relay lenses, galvanometer, and objective. Table 1 Imaging capabilities of isolated objectives, conventional TPM, and LF-TPM. Lateral resolution for conventional TPM with pixel averaging is effective resolution, not optical resolution. For LF-TPM, the theoretical and experimental lateral resolution are included.

Objective or system NA

Lateral resolution ( μ m ) FOV diameter ( Ø mm ) Rectangular FOV ( mm × mm ) Pixels for rectangular FOV FOV area ( mm 2 ) SBP (MP) Olympus XLFLUOR4X 0.28 1.08 6.63 4.69 × 4.69 8709 × 8709 21.98 75.85 Olympus XLUMPLFLN 20X 1 0.31 1.10 0.78 × 0.78 5081 × 5081 0.61 25.82 Conventional TPM 1 0.31 0.71 0.50 × 0.50 3280 × 3280 0.25 10.76 Conventional TPM (pixel averaging) 1 1.96 0.71 0.50 × 0.50 512 × 512 0.25 0.26 LF-TPM system 0.22 1.37/1.68 7.00 4.95 × 4.95 5893 × 5893 24.50 34.72 For completeness, we also conducted fluorescein and microsphere imaging with the Olympus MVPLAPO 2XC but measured worse resolution off axis than what was achieved with the Olympus XLFLUOR4X (Appendix D ).