We selected two GRIN singlet rod lenses (hereon GRIN rods) suitable for multiphoton fluorescence imaging in ventral regions of the mouse brain. The two selected GRIN rods had NA = 0.5 on both sides, 500 µm diameter, 1.5 and 2.0 pitch, and 6.4 mm and 8.8 mm length, respectively. For both GRIN rods, we modeled an optical assembly composed of the GRIN rod, a thin layer of glass (representing a 100-µm-thick glass coverslip) attached to the back end of the GRIN rod, and an aspheric corrective lens (here on called corrective lens) aligned to the rod and attached to the opposite side of the glass coverslip with respect to the GRIN rod (Figure 1A and B). We designed the aspheric surface of the corrective lens using ray-trace simulations at the wavelength (λexc) of 920 nm, the excitation wavelength commonly used for 2P imaging of the popular genetically encoded calcium indicator GCaMP. The design of the corrective lens was an iterative process in which the parameters that define the corrective lens surface were automatically varied to obtain the highest and most homogeneous spatial resolution possible over the longest possible radial distance from the optical axis (see Supplementary file 1 and Materials and methods for details on simulation parameters). More specifically, we simulated the corrective lens profile such that the Strehl ratio (defined as the peak intensity of the focal spot of an aberrated optical system normalized to the peak intensity of the focal spot of the ideal optical system, Smith, 2008) of the corrected microendoscope remained above the threshold of 0.8 for the longest possible radial distance from the optical axis. The values of Strehl ratio equal to 0.8 corresponded to the lower bound of the diffraction-limited condition set by the Maréchal criterion (Antonini et al., 2020; Smith, 2008). Our simulations showed that the profiles of the two corrective lenses displayed in Figure 1A and B led to an increase in the radius of the diffraction-limited FOV compared to the case in which the corrective lens was not positioned in the back end of the GRIN rods (uncorrected microendoscopes). The profile of the corrective optical element was specific to the type of GRIN rod considered. The simulated increase in the radius of the diffraction-limited FOV was 3.50 times and 3.35 times for the 6.4 mm-long and 8.8 mm-long probe, respectively (Figure 1C and E). Moreover, we investigated the effect of changing wavelength on the Strehl ratio. We found that the Strehl ratio remained >0.8 within at least ±10 nm from λexc = 920 nm (Figure 1—figure supplement 1), which covered the limited bandwidth of our femtosecond laser. All simulations were performed maximizing aberration correction in the simulated focal plane of the microendoscopes (imaging plane in Figure 1A and B). However, we explored the effect of aberration correction outside the simulated focal plane. In corrected microendoscopes, we found that for off-axis rays (radial distance from the optical axis >40 μm) the Strehl ratio was >0.8 (Maréchal criterion) in a larger volume compared to uncorrected microendoscopes (Figure 1—figure supplement 2), demonstrating that the aberration correction method developed in this study extends for short distances beyond the simulated focal plane. For example, at a radial distance of ~90 μm from the optical axis, the axial range in which the Strehl ratio was >0.8 in corrected microendoscopes was 28 μm and 19 μm for the 6.4 mm-long and the 8.8 mm-long microendoscope, respectively. Decentering the optical axis of the corrective lens from the optical axis of the GRIN rod rapidly disrupted the optical properties of the corrected microendoscopes (Figure 1—figure supplement 3). To visualize the expected improvement of the spatial resolution in corrected microendoscopes, we simulated the PSF of uncorrected and corrected microendoscopes at different radial distances from the optical axis. For both the 6.4 mm-long and 8.8 mm-long GRIN rods, we found that the PSF of the uncorrected probe was strongly aberrated and highly irregular at ~90 µm away from the center of the FOV (Figure 1D and F). In contrast, in the corrected microendoscopes the PSF had regular shape and, at >90 µm away from the optical axis, it was similar to the one measured at the center of the FOV (Figure 1D and F, see also Supplementary file 2).

Due to the small size of the simulated corrective lenses (diameter: 500 µm; height: few tens of µm), we first used 3D microprinting based on 2P lithography to fabricate aspherical corrective lens prototypes (Figure 2A and B; Liberale et al., 2010; Gonzalez‐Hernandez et al., 2023). We then replicated the prototypes using a molding procedure (Schaap and Bellouard, 2013; Figure 2C). The molding strategy enabled us to obtain large numbers of aspherical lens replica directly manufactured onto round glass coverslips in a much faster and cheaper way compared to 3D microprinting. Next, we assembled microendoscopes following the scheme in Figure 2D, using a plain coverslip for the uncorrected case, while we used a coverslip with a corrective lens replica for the corrected case (this applies to all the experiments described in the manuscript). In the assembly of the microendoscope, we attached the round coverslip to the annular support structure shown in (Figure 2D, called hereon ring), which had two functions: (i) to facilitate holding the probe during stereotactic surgery implantation; (ii) to provide stability to the microendoscope once implanted on the animal skull. We used either metallic rings (external diameter: 7 mm) or plastic rings (external diameter: 4.5 mm). Plastic rings were specifically designed and 3D printed to be compatible with commercial holders (ProView Implant Kit, Inscopix Inc Mountain View, CA, US) to ease stereotaxic implantation (see Materials and methods). The alignment and assembly of all the microendoscope components was performed with a custom optomechanical set-up similar to that described in Antonini et al., 2020.

We tested the optical performance of the new corrected microendoscopes in 2P laser scanning microscopy (2PLSM) using a pulsed laser tuned at 920 nm. Microendoscopes were coupled to the 2P microscope using a previously described customized mount (Antonini et al., 2020). To visualize the effect of the corrective lens on the axial extension of the excitation volume, we imaged subresolved homogenous fluorescent layers (layer thickness: ~300 nm) using uncorrected and corrected microendoscopes. Figure 3A–D shows the x,z intensity projections of z-stacks acquired through the subresolved fluorescent layers under both conditions (i.e. uncorrected and corrected microendoscopes). Strong off-axis aberrations of the GRIN lens generated a significant loss of fluorescence intensity in the marginal portions of the FOV in uncorrected microendoscopes (for both the 6.4 mm-long, Figure 3A and B, and the 8.8 mm-long, Figure 3C and D). In contrast, fluorescence signal was collected over longer distances from the center of the FOV in corrected microendoscopes (Figure 3A–D). Moreover, for GRIN rods of both lengths the full width at half maximum (FWHM) of the film profile obtained with uncorrected microendoscopes increased with distance from the optical axis and became rapidly larger than 20 µm. In contrast, the film profile obtained with corrected microendoscopes showed more homogenous FWHM values across an extended FOV (Figure 3A–D).

To evaluate the increase in area of the sample that could be imaged with the corrected microendoscopes, we first characterized potential distortion of the FOV introduced by the microendoscopes. Using a calibration ruler, we measured the local magnification factor at different radial distances from the optical axis (Figure 3E and F). We defined the local magnification factor as the ratio between the nominal pixel size (i.e. pixel size that applies to undistorted images collected with the microscope objective alone) and the real pixel size of the image collected with the same objective coupled to the microendoscope (see Materials and methods). Pixel sizes and distances displayed in the following panels and graphs are calibrated for FOV distortion and indicate real dimensions in the samples (see also Materials and methods and Supplementary file 3). We then measured the spatial resolution of microendoscopes by imaging subresolved fluorescent beads (bead diameter: 100 nm) located at different radial distances from the optical axis (Figure 3G–J). We found that the axial dimension of the beads imaged with uncorrected microendoscopes rapidly increased with radial distance, whereas the spatial resolution of corrected microendoscopes remained more homogeneous over longer radial distances and more similar to the one measured on-axis (Figure 3G–J and Supplementary file 4). We set a threshold of 10 µm on the axial resolution to define the radius of the effective FOV (corresponding to the black triangles in Figure 3I and J) in uncorrected and corrected microendoscopes. We observed a relative increase of the effective FOV radius of 2.17 and 1.53 for the 6.4 mm-long and the 8.8 mm-long microendoscope, respectively (Table 1). This corresponded to an enlargement of the effective FOV area of 4.7 times and 2.3 times for the 6.4 mm-long microendoscope and the 8.8 mm-long microendoscope, respectively (Table 1). These findings were in agreement with the results of the ray-trace simulations (Figure 1) and the measurement of the subresolved fluorescence layers (Figure 3A–D).

The optical characterization described above indicated that corrected microendoscopes of both lengths enabled imaging a larger FOV area compared to uncorrected microendoscopes. This result can be explained by the fact that corrected microendoscopes showed higher spatial resolution and increased probability of 2P fluorescence excitation in the marginal portions of the FOV. Corrected microendoscopes should therefore allow highly contrasted imaging of cell bodies and thin cellular processes over an extended FOV compared to uncorrected microendoscopes. Using both uncorrected and corrected microendoscopes, we confirmed these predictions by imaging the same region of a fixed brain slice expressing jGCaMP7f in neurons. We found that aberration correction enabled to clearly resolve neuronal somata and processes in the lateral portions of the FOV, whereas in the absence of the corrective lens the same structures located in the peripheral portion of the FOV appeared dim, strongly aberrated, and hardly detectable (Figure 4, see also Figure 4—figure supplement 1 for an alternative visualization in which the FOVs of corrected microendoscopes are rescaled to match the real pixel size of the FOVs of uncorrected microendoscopes in the center of the image).

Using simulated calcium t-series, we next evaluated the impact of the improved optical performance of long aberration corrected microendoscopes on the ability to extract information about neuronal activity. To this aim, we compared simulated calcium traces imaged with either uncorrected or corrected microendoscopes with the ground truth neuronal activity, that is the neuronal activity used to generate the simulated t-series. To build synthetic calcium data, we first generated neurons with 3D distribution and anatomical properties (i.e. cell size and cell density) similar to those measured in the mouse olfactory cortex (Suzuki and Bekkers, 2010; Suzuki and Bekkers, 2011), the ventral brain region which we will be imaging in vivo (see next section of Results), and the biophysical characteristics of one of the two indicators used in our experiments, jGCaMP8f (Zhang et al., 2023; see also Materials and methods). We then simulated the optical sampling of 3D volume of neurons with the PSF properties of the uncorrected and corrected microendoscopes characterized above (Figure 3). Fluorescence signals integrated over the PSF volume were then projected on a 2D matrix of pixels in time, with a frequency of 30 Hz, to obtain synthetic t-series (duration: 5 min, Figure 5A and D). We finally detected neuronal cell bodies and extracted fluorescence traces from regions of interest (ROIs) of synthetic t-series using established methods (Sità et al., 2022) commonly applied to real data and compared between the case of uncorrected and corrected microendoscopes. We found that the use of corrected probes allowed segmenting more ROIs with high SNR compared to uncorrected microendoscopes, shifting the distribution of SNR across ROIs to higher mean SNR values. This was true for both the microendoscopes based on the 6.4 mm-long GRIN rod (Figure 5B) and the microendoscope based on the 8.8 mm-long GRIN rod (Figure 5E). Moreover, for both microendoscope types, aberration correction increased the maximal radial distance at which ROIs with high (>15) SNR could be observed (Figure 5C and F). These findings demonstrate that correcting for optical aberrations increases the probability of recording ROIs with larger SNR of fluorescent signals.

The higher and more homogeneous axial resolution across the FOV afforded by the corrected probes could be useful not only to increase the SNR of neural calcium signals, but also to better isolate individual neurons, decreasing signal contamination across neighboring cells. To test this hypothesis, we considered correlations in ‘adjacent’ simulated neurons, defined as pairs of neurons for which the distance between their centroids was ≤25 µm (the radius of the soma of excitatory neurons in the olfactory cortex is around 10 µm, Suzuki and Bekkers, 2011). Compared to uncorrected probes, we found that corrected microendoscopes of both lengths led to lower fraction of pairs of adjacent cells whose activity correlated significantly more than expected (Figure 6A and F and Supplementary file 5), confirming reduced cross-contamination among cells. The fraction of pairs of adjacent cells (out of the total number of adjacent pairs) whose activity correlated significantly more than expected increased as a function of the peak SNR threshold for corrected and uncorrected microendoscopes of both lengths (Figure 6A and F). This effect was due to a larger decrease of the total number of pairs of adjacent cells as a function of the peak SNR threshold compared to the decrease in the number of pairs of adjacent cells whose activity was more correlated than expected (Figure 6—figure supplement 1). Moreover, in uncorrected microendoscopes the pairwise correlation of adjacent cells showed a larger linear dependence on the radial distance of the pair from the center of the FOV compared to corrected microendoscopes (Figure 6—figure supplement 2A and C, see also Materials and methods). We interpreted these findings on correlated neuronal activity as due to the enlarged PSF of uncorrected microendoscopes in lateral portion of the FOV (Figure 3G–J), leading to increased signal contamination by sampling across neurons. These results thus suggest that corrected microendoscopes decrease the artefactual correlation of nearby neurons by diminishing the spatial extension of the excitation volume used for sampling neuronal activity (PSF, Figure 3G–J).

Using synthetic data, we could precisely quantify the extent to which correcting aberration in microendoscopes decreased mixing signals across neurons. For each ROI, we computed a general linear model (GLM) of the contributions to fluorescence signals of the activity of all ground truth simulated neurons, called ‘sources’, (Figure 6B, C, G and H). From the GLM coefficients, we extracted a source ‘purity’ index, which reached its highest possible value of 1 when only one source contributed to the calcium fluorescent trace in the considered ROI and had values <1 when different source neurons were mixed in the fluorescent signal of the considered ROI. For uncorrected microendoscopes of both lengths, we found that purity rapidly decreased with the radial distance of the ROI from the center of the FOV. In contrast, for corrected microendoscopes the purity index decreased far more slowly with the radial distance and the slope of the linear fit of the purity distribution as a function of the radial distance was significantly smaller than that of the uncorrected probe (Figure 6C and H). For any value of the peak SNR threshold used to select neurons, the purity index was also larger for corrected than for uncorrected probes (Figure 6—figure supplement 2B and D). Moreover, for each ROI we analyzed the correlation of the extracted traces with the most correlated ground truth neuron (‘first ground truth source’) as a function of the radial distance of the ROI (Figure 6D, E,I and J). For microendoscopes of both lengths, we observed that ROIs from t-series generated with corrected microendoscopes displayed larger correlation with the ground truth signal of an individual neuron over longer distances from the optical axis, compared to uncorrected probes (Figure 6E and J). Figure 6J showed a moderate enlargement of the distance at which the Pearson’s correlation with the first ground truth emitter started to drop. This may appear at first in contrast with the enlargement of the FOV shown in Figure 4B. However, it can be understood considering that in Figure 4B, all illuminated neurons were visible regardless of whether they were imaged with high axial resolution (e.g. <10 µm as defined in Figure 3J) or poor axial resolution. In contrast, in Figure 6J we evaluated the correlation between the calcium trace extracted from a given ROI and the real activity trace of the first simulated ground truth emitter for that specific ROI. The moderate increase in the correlation for the corrected microendoscope compared to the uncorrected microendoscope (Figure 6J) was consistent with the moderate improvement in the axial resolution of the corrected probe compared to the uncorrected probe at intermediate radial distances (60–100 µm from the optical axis, see Figure 3J). Taken together, these results indicated that corrected microendoscopes enabled more precise recording of individual cellular source neurons and enhanced demixing of signals coming from different neurons.

We tested long corrected microendoscopes for in vivo 2P calcium imaging experiments in ventral regions of the mouse brain. To this aim, we implanted mice with corrected microendoscopes based on 8.8 mm-long GRIN lenses over the mouse anterior olfactory cortex, a deep region laying >4 mm down the mouse brain surface (Figure 7A and B). Mice expressed genetically encoded calcium indicators, either jGCaMP7f or jGCaMP8f, in excitatory neurons through adeno-associated virus (AAVs) injection. In awake head-fixed mice, we recorded 2P imaging t-series (λexc=920 nm; frame rate: 30 Hz; t-series duration: 8 min) during repetitive olfactory stimulation with various odorants (Figure 7C–E, see Materials and methods).

In recorded t-series, we first observed that the peak SNR of calcium events recorded in individual cells was constant across the FOV (Figure 8A). We then computed the pairwise correlation of the activity traces of pairs of adjacent neurons (defined as pairs of cells with an intersomatic distance of ≤25 µm) as a function of the radial distance of the pair’s position centroid from the center of the FOV (Figure 8B). We found no dependence of the pairwise correlation on the distance from the center of the FOV. In fact, the slope of the linear fit of pairwise correlation as a function of the radial distance was not significantly different from zero (Figure 8B). These findings were in agreement with the results of the optical characterization (Figure 3) and with those of the simulation of calcium data (Figures 5 and 6). These results suggested that the absence of dependence of the pairwise correlation with radial distance reflected the improved and more homogeneous spatial resolution of corrected microendoscopes, which prevented source mixing and artificially inflated correlations of adjacent neurons in the FOV periphery. Varying the distance between centroids of adjacent neurons did not change the result (Supplementary file 6). Running the analysis separately for mice expressing jGCaMP8f and jGCaMP7f also confirmed the previous findings (Supplementary file 6). Finally, the Pearson’s correlation coefficient between the activity traces of any pair of neurons within the FOV decresed as a function of their reciprocal distance (Figure 8C). This decrease in correlation could reflect a slight change in the laminar position of recorded neurons or suggest a decrease in recurrent connectivity between neurons of the olfactory cortex with distance (Franks et al., 2011; Hagiwara et al., 2012).

Combined with the results of the simulated calcium data, these in vivo findings demonstrate that, by decreasing off-axis aberrations of commercial GRIN lenses, long corrected microendoscopes enable unbiased sampling of neural population activity on a large FOV in ventral regions of the mouse brain in vivo.

To identify the design of the corrective optics to obtain aberration corrected microendoscopes, we performed ray-trace simulations using OpticStudio 15 (Zemax, Kirkland, WA, US) and integrating the optical model of two commercially available GRIN rods (NEM-050-25-10-860-S-1.5p and NEM-050-25-10-860-S-2.0p, GRIN needle endomicroscopes, GRINTECH Gmbh, Jena, Germany). The wavelength selected for simulations was 920 nm, the commonly used excitation wavelength for 2P imaging of green-emitting fluorescent indicators (Chen et al., 2013; Dana et al., 2019). In simulations, we placed the aspheric lens, whose refractive index corresponded to that of the UV-curable glue we used for microendoscope fabrication (NOA63, see also below), on one side and the back end of the GRIN rod on the other side. 100 µm of BK7 glass were interposed between the corrective lens and the GRIN rod. The profile of the aspheric lens was identified by optimizing a merit function, which took into account the Strehl ratio of focal spots simulated at different field radial distances (up to 200 µm for the 6.4 mm-long and up to 170 µm for the 8.8 mm-long GRIN rod) after being relayed by the optical assembly. During the optimization, the working distance was constrained to values compatible with neurophysiological experiments (~180–220 µm) and the refractive indices simulated at the two ends of the optical assembly were 1 (air) and 1.33–1.36 (brain tissue). The following formula described the surface profile of aspheric lenses similarly to Antonini et al., 2020:(1)Z(r)=cr21+1−(1+k)c2r2+∑nαnr2n,

where r is the radial distance from the optical axis; c is equal to 1/R, where R is the radius of curvature; k is the conic constant; α_n are asphericity coefficients. We changed the parameters c, k, α_n (with n=1–4) in Equation 1 to maximize the Strehl ratio (Smith, 2008) over the largest possible area of the FOV. We obtained simulated 2P PSFs (Figure 1) by 3D sampling the squared calculated Strehl ratio (Smith, 2008). To compute the spatial resolution of simulated microendoscopes, we fitted x,y,z intensity profiles of the simulated PSFs with Gaussian curves. The ray-trace simulations demonstrated improved Strehl ratio values with GRIN lenses of slightly longer working distances (Table 2, Custom) compared to the two commercial GRIN rods initially considered (Table 2, Commercial). We thus used the GRIN lenses of custom working distance indicated in Table 2 for all results presented in this manuscript. To evaluate the impact of corrective lenses on the optical performance of GRIN-based microendoscopes, we also simulated uncorrected microendoscopes composed of the same optical elements of corrected probes (glass coverslip and GRIN rod), but in the absence of the corrective lens. Final working distances of simulated uncorrected and corrected microendoscopes based on custom GRIN rods are indicated in Table 3.

The aspheric profiles of the corrective lenses obtained with optical simulations were converted into 3D structure files by a CAD software (SolidWorks, Waltham, MA, US). The aspherical lens prototypes were then fabricated with a commercial 3D microprinter based on 2P polymerization (Photonic Professional GT2+, Nanoscribe, Karlsruhe, Germany) using a proprietary photoresin (IP-S, Nanoscribe, Karlsruhe, Germany) and a ×25 0.8 NA microscope objective in Dip-in Laser Lithography (DiLL) configuration. Once the lens’ volume was fully polymerized in Solid printing mode, the residual unpolymerized material was removed with immersion in propylene glycol methyl ether acetate (PGMEA) for 10 min, followed by ~5 min immersion in isopropyl alcohol. The lens prototypes were finally coated with 200 nm of gold with a sputter coater and inspected with scanning electron microscopy to confirm absence of surface defects.

To enable fast manufacturing of multiple corrected microendoscopes, we generated replicas of the aspherical lenses using a molding procedure (Figure 2C) as in Schaap and Bellouard, 2013. We first fabricated negative molds with PDMS (Sylgard 184 Silicone Elastomer Kit, Dow, Midland, MI, US) casted onto the aspherical lens prototype and solidified at room temperature for 48 hr. We then deposited a small drop of optically transparent UV-curable glue (NOA63, Norland Products, Cranbury, NJ, US) to fill the negative mold. Extreme care was used to avoid bubble formation in this experimental step. We placed a round glass coverslip (coverslip diameter: 3 or 5 mm in diameter; coverslip thickness: 100 µm) on top of the drop of UV-curable glue and pressured it against the PDMS mold (Figure 2C). NOA63 was solidified with UV light exposure for 10 min. After UV curing, the corrective lens was visually inspected at the stereomicroscope. In case of formation of air bubbles, the corrective lens was discarded (yield of the molding procedure: ~90 %, n>30 molded lenses). The coverslip with the attached corrective lens was sealed to a customized metal or plastic support ring of appropriate diameter (Figure 2C). The support ring, the coverslip and the aspherical lens formed the upper part of the corrected microendoscope, to be subsequently coupled to the proper GRIN rod (Table 2, Custom) using a custom-built optomechanical stage and NOA63 (Figure 2C; Antonini et al., 2020). The GRIN rod was positioned perpendicularly to the glass coverslip, on the other side of the coverslip compared to the corrective lens, and aligned to the aspherical lens perimeter (Figure 2C) under the guidance of a wide field microscope equipped with a camera. The yield of the assembly procedure for the probes used in this work was 100% (n=27 endoscopes). For further details on the assembly of corrected microendoscope see Antonini et al., 2020.

We performed optical characterization of corrected and uncorrected microendoscopes using 2 P laser scanning microscopes equipped with femtosecond tunable laser sources (80 MHz repetition rate, Chameleon Ultra II or Chameleon Discovery, Coherent, Inc, Santa Clara, CA, US) tuned at 920 nm excitation wavelength and coupled to an Ultima IV or an Investigator scan head (Bruker Corporation, Billerica, MA, US). We used a ×20 dry objective (EC Epiplan-Neofluar, NA = 0.5, Zeiss, Oberkochen, Germany) and coupled it with the microendoscopes using a custom optomechanical mount similarly to Antonini et al., 2020. The mount was equipped with a micrometric translator to adjust the distance between the objective lens and the upper surface of the corrected microendoscope. We acquired series of z-stacks of different calibration samples (subresolved fluorescent films, subresolved fluorescent beads, calibration rulers, and mouse fixed brain slices) moving the whole mount carrying both the objective and the microendoscope, so that their reciprocal distance remained fixed during the acquisition. For all measurements, the distance between the objective and the upper surface of the coverslip was set to 100 µm for uncorrected microendoscopes and to 150 µm and 180 µm for the 6.4 mm-long and the 8.8 mm-long corrected microendoscopes, respectively. This choice was made taking into account the working distances of simulated corrected probes (Table 3). The front end of the GRIN rod was immersed into a drop of distilled water, or phosphate-buffered saline (PBS) for fixed brain slices, which was placed over the calibration sample. Due to the short working distance of the microendoscopes (Table 3), we put no coverslip over the samples. For each measurement, experimental replicates were obtained using corrected microendoscopes assembled with distinct optical elements (i.e. different GRIN lenses and different corrective lenses). The uncorrected microendoscopes were assembled either using different optical elements compared to the corrected ones, or were obtained from the corrected probes after the mechanical removal of the corrective lens. The analysis of z-stacks acquired through calibration samples was performed using Imagej/Fiji and custom code written in Matlab (R2022b, MathWorks, Natick, MA, US). In the following paragraphs, we defined ‘nominal’ pixel size as the one determined by imaging a calibration ruler (see below) with the microscope objective alone.

Experimental and surgical protocols were performed in accordance with the Guide of Care and Use of Laboratory Animals (NIH) and were approved by the Institutional Animal Care and Use Committee (IACUC protocol number: 24-03-0004) at Brown University and by the Istituto Italiano di Tecnologia Animal Health Regulatory Committee, by the National Council on Animal Care of the Italian Ministry of Health (authorization # 1134/2015-PR, # 689/2018-PR) and carried out according to the National legislation (D.Lgs. 26/2014) and to the legislation of the European Communities Council Directive (European Directive 2010/63/EU). C57BL/6 J mice were crossed to Ai14 mice (Madisen et al., 2010) and male and female heterozygous transgenic offspring of 8–12 weeks of age were used. Mice were maintained with unrestricted access to food and water under a 12 hr light/dark cycle and housed individually after surgery.

Viruses (pGP-AAV-syn-jGCaMP8f-WPRE, Zhang et al., 2023, or AAV1-syn-jGCaMP7f-WPRE, Dana et al., 2019) were purchased from Addgene (Watertown, MA, US) and injected using manually controlled pressure injection with a micropipette pulled and a micropipette puller (Sutter Instruments, Novato, CA, US). Mice were anesthetized with isofluorane with an induction at 3% and then maintained at 1–2% with an oxygen flow rate of ~1 L/min and head-fixed in a stereotactic frame (David Kopf, Tujunga, CA, US). Mice subcutaneously received buprenorphine slow release (0.05–0.1 mg/kg). Eyes were lubricated with an ophthalmic ointment and body temperature was stabilized using a heating pad attached to a temperature controller. Fur was shaved and the incision site was sterilized with isopropyl alcohol and betadine solution prior to beginning surgical procedures. A 1.0 mm round craniotomy was made using a dental drill centered to the following stereotaxic coordinates (mm): ML, 3.9; AP, 0.3. The virus solution diluted 1/3 in PBS was injected at speed 100 nL/min in three different spots (total injected volume: 1 μL) using the following coordinates (mm) to target olfactory cortex (ML/AP/DV): 3.85/0.6/–3.8, 3.95/0.3/–3.9, 4.05/0.0/–4.0, all relative to bregma (Paxinos and Franklin, 2012). After 5 min, the micropipette was slowly retracted from the brain at a speed of 500 μm/min. 30 min after viral injections, a corrected microendoscope was implanted above the olfactory cortex. The probe was implanted, centered to the craniotomy, at a speed of 100 μm/min until reaching the following coordinate: DV, –3.6. Once placed, the plastic ring of the endoscopic probe was fixed to the skull with Metabond adhesive cement (Parkell Inc, Edgewood, NY, US). A custom-made aluminum head bar was then attached to the skull using dental cement (Pi-ku-plast HP 36 Precision Pattern Resin, XPdent, Miami, FL, US). Finally, a protective cap made of Kwik-Sil silicone elastomer (World Precision Instruments, Sarasota, FL, US) was applied over the lens. Mice were allowed to recover from surgery for at least 6 weeks prior to imaging experiments. The criterion for inclusion of animal subjects in the study was based on the quality of the surgical implant, that is absence of blood and presence of >30 detectable cells in the maximally enlarged aberration corrected FOV of the microendoscope. Based on this criterion, six out of eight mice were used for subsequent experiments (average number of cells/FOV ± SD: 40±6, n=6 animals).

Animals were habituated to the experimenter and the head-fixation set-up for 30 min per day for at least two days before performing the imaging experiment. On imaging days, odor stimuli were delivered through a custom built 16-channel olfactometer (Automate Scientific, Berkley, CA, US) equipped with a mass flow controller that maintained air flow at 1 L/min. The olfactometer solenoids were triggered by a Teensy 3.6 (PJRC). Vacuum was applied inside the 2P microscope isolation box to evacuate residual odor. For all experimental sessions, mice were habituated to the 2P microscope head-fixation set-up for 10 min prior to imaging. An odor trial lasted 22 s (5 s of pre-stimulus baseline, 2 ss of stimulation, 15 s of post-stimulus acquisition) with inter-trial intervals of 10 s. Odor stimuli were presented in pseudo-randomized fashion and 8 presentations of each odor were performed in a session. The odor panel consisted of (diluted in mineral oil v/v): acetophenone 1%, amylamine 1%, butyl acetate 1%, ethyl hexanoate 1%, 2-Isobutyl-3-methoxypyrazine 1%, β-Ionone 1%, 2,3-Pentanedione 0.1%, Valeric acid 0.1%. A photoionization detector (miniPID 200B, Aurora Scientific, Canada) was used to confirm reliable odor delivery.

A typical imaging experiment lasted ~1.5 hr per mouse. 2P imaging of the olfactory cortex was performed using an Ultima Investigator laser scanning microscope (Bruker Nano, Inc, Middleton, WI, US) equipped with a 8 KHz resonance galvanometer and dual GaAsP PMTs (Cat. No. H10770, Hamamatsu, Hamamatsu City, Japan). Approximately 90–150 mW of laser power (at 920 nm, from Chameleon Discovery laser source [Coherent Inc, Santa Clara, CA, US]) was used during imaging, with adjustments in power levels to accommodate varying signals for each mouse. After focusing on the corrective lens surface using epifluorescence microscopy, optical viewing was switched to live view through the 2P laser, and a FOV was located by moving the objective ∼100–200 μm upward. Images were acquired with a Nikon ×10 Plan Apochromat Lambda objective (0.45 NA, 4.0 mm WD) using a nominal pixel size of 0.72–0.84 µm/pixel. jGCaMP8f or jGCaMP7f signals were filtered through an ET-GFP (FITC/CY2) filter set. Acquisition speed was 30 Hz for 512 pixels × 512 pixels images.

Analysis of 2P experimental t-series requiring detection of cell identities and trace extraction was performed using CITE-ON (Sità et al., 2022) and custom code written in Python 3.7, as for the synthetic t-series. Raw 2P t-series (duration: 8 minutes) were first motion-corrected using the CITE-ON function motion_corr, applied twice in succession when needed. Bounding boxes were detected using the median intensity projection of the motion-corrected t-series as reference. Activity traces, peak SNR and Pearson’s correlations were computed as described for synthetic calcium data. Pairwise correlation of adjacent neurons was explored considering nearby detected cells for which the distance between the bounding boxes centroids was either ≤25 μm or ≤30 μm (Supplementary file 6).

Statistical analysis was performed using Matlab for optical characterization data and using the Python library of statistical functions scipy.stats (https://docs.scipy.org/doc/scipy/reference/stats.html) for synthetic and experimental calcium imaging data. The number n of repeated measurements and the number m of experimental replicates are indicated in figure legends. Normality of data distributions was tested using either Shapiro-Wilk test for small sample sizes (n<50) or D’Agostino-Pearson test (n≥50). The threshold for statistical significance was set at p=0.05 and indicated as follows: *, p<0.05, **, p<0.01, ***, p<0.001. p values higher than 0.05 were considered not significant (n.s.). Data are presented as mean values ± standard error of the mean (s.e.m.), unless otherwise stated. Linear regressions were performed using the function scipy.stats.linregress. To test the significance of linear fit slope being different from zero, we used the Wald test with t-distribution in case the fit residuals were normally distributed and the permutation test with the function stats.permutation_test if the fit residuals were not normally distributed. The null distribution of linear coefficients used in the permutation test was built performing multiple linear regressions on a subset of possible permutations of data (permutation type: ‘pairings’, 10⁴ permutations for n<500, 10⁵ permutations for n≥500). To test the significance of linear fit slopes being different from each other, we used a permutation test in which the observations were randomly assigned to the two samples (corrected or uncorrected). The null distribution was built calculating the difference between the two slopes for a subset of possible permutation of data (10⁴ permutations for n<500, 10⁵ permutations for n≥500). To test the significance of the difference between two means of non-normally distributed samples, we used a permutation test. In this case, the null distribution was built calculating the difference between the two mean values for a subset of possible permutations of data (permutation type: ‘independent’, 10⁴ permutations for n<500, 10⁵ permutations for n≥500).